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1. 000000000000 a pannun i 10 Width of indentation 100 1000 Figure III 3 Program output for Au Ni d 6 9 nm A 1 8 nm 232 Texas Tech University H S Tanvir Ahmed December 2010 Characteristic dimension h nm Oe oo NA in A S 0000000000000 OOOO 000000000000 Volume GB area Volume LP area Width of indentation Figure IIL 4 Program output for Au Ni d 13 1 nm 2 5 nm 233 Texas Tech University H S Tanvir Ahmed December 2010 Characteristic dimension h nm 00000000000000 0000 OH HHOOOOO0000H Volume GB area Volume LP area E Be eee a E E E EEEE 10 100 1000 Width of indentation Figure II 5 Program output for Au Ni d 11 4 nm 1 2 nm 234 Texas Tech University H S Tanvir Ahmed December 2010 Characteristic dimenion h nm 12 10 a 8 eo 00000000000000 00000 eo 0000000000000060 6 Volume GB area Volume LP area 4 be 2 F 8 Zug aa man a 8 E 8 S eee 0 1 1 1 1 1 j it 1 1 1 1 1 p44 1 1 1 1 1 10 100 1000 Width of indentation Figure IIL 6 Program output for Au Ni d 16 7 nm 2 6 nm 233 Texas Tech University H S Tanvir Ahmed December 2010 II C Depth of Indentation as a Function of Tip
2. ss 228 II B Program Output for Au Ni Samples 230 II C Depth of Indentation as a Function of Tip Radius nm 236 HEC 1 Berkovich HIP SR AS E E ea te oes 236 IMAGE Conical Pen rnc co TEN BN E a NG A dr SG Ng teen ag E 2371 TC CUDE Comer Tp x 4a aes eave ce ote dee ee Oe 238 Vill Texas Tech University H S Tanvir Ahmed December 2010 ABSTRACT Dynamic indentation techniques like micro and nanoscratch compared to static nanoindentation offer more robust extraction of mechanical properties of thin films with higher level of control during experimentations The velocity of the scratch indenter can be changed for probing the material properties at a wide range of strain rate Considering the potential of this technique detailed knowledge about the applicability of scratch method to different material systems is essential to create strategies for controlling appropriate physical feature for better mechanical properties at nanoscale Micro scratch testing of free standing micro to nano porous and dense metal foils shows a different rate sensitivity exponent at higher strain rate suggesting a different mode of deformation Continuous and interrupted tensile testing have been done on foils to provide a base line for comparison of strain rate sensitivity as well as possible stiffening effect under progressive load Tensile testing of nanocrystalline metal alloys has been conducted to do the comparison with prior micro scratch results
3. 8 29 E 4 Hz Fr E 4 Hz AD Channel 2 P r35_Si base_200 900Hz_Apr 04682 016 Line 1 dv 7 58 a u dAm 635 03 pm Am pm 30 4 50 60 70 80 20 100 110 Length 93 1 a u Height 393 794 kHz 7 Figure IL 39 Frequency shift plot of Silicon base 216 Texas Tech University H S Tanvir Ahmed December 2010 II G Frequency shift curves of directional sapphire Channel 1 Pr35_Sapphire 00 2_200 900Hz_Apr 05221 023 Line 1 filter 3 square dV 2 51 au d Fr 7 97 E 4 Hz Fr E 4 Hz AD Vi au Channel 2 Pr35_Sapphire 00 2_200 900Hz_Apr 05221 023 Line 1 dV 2 51 au dAm 1 49 nm Am pm Am 15 20 25 30 35 40 45 Length 33 3 au Height 325 458 kHz zZ Figure IL 40 Frequency shift plot of Sapphire 00 2 217 Texas Tech University H S Tanvir Ahmed December 2010 ILH Frequency shift curves of Ta V samples Channel 1 Pr35_Ta V 1_200 900Hz_Apr 04056 022 Line 1 filter 3 square dv 3 33 a u d Fr 1 55 E5 Hz _ F2 E4 Hz AD Channel 2 Pr35_Ta V 1_200 900Hz_Apr 04056 022 Line 1 dv 3 33 a u dAm 1 55 nm Am pm 3500 3000 Am 2500 2000 35 4 4 50 55 60 65 70 75 80 85 90 Length 59 9 a u Height 399 044 kHz Figure IL 41 Frequency shift plot of Ta V A 8 07 nm Sample 1 218 Texas Tech University H S Tanvir Ahmed Dec
4. DES g L pas 200 a Oo L ra XXe Aya L Ress 100 4 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 200 400 600 800 1000 1200 1400 Actual elastic modulus E GPa Figure 4 10 Variation of reduced elastic modulus with respect to actual elastic modulus as a function of Poisson ratio Table 4 2 Frequency shift data of calibration materials with corresponding elastic modulus Sample Poisson Actual modulus Reduced modulus Slope ratiov E GPa EF GPa Polycarbonate 0 37 3 0 3 47 0 65 0 03 Sapphire 0 3 495 381 25 7 05 0 49 Silicon 100 0 27 130 13 126 99 4 04 0 11 Fused Silica 0 17 72 70 24 2 18 0 08 Fused Quartz 0 17 72 70 24 2 23 0 22 Ta 110 0 34 192 3 186 95 4 98 0 5 V 110 0 37 124 7 130 35 4 05 0 41 Ag 111 0 37 120 51 126 39 4 53 0 34 Ni 111 0 31 305 269 28 5 41 0 38 Hydroxyapatite 0 27 100 93 02 2 6920 3 129 Texas Tech University H S Tanvir Ahmed December 2010 Table 4 3 Calculation of sample modulus from calibration curve Sample Layer Poisson Slope a Calculation from calibration curve ane TAUNK Reduced modulus Actual modulus Lan E GPa E GPa Au Ni 0 8 0 365 4 4 0 43 172 67 171 93 Au Ni 4 5 0 365 3 68 0 39 122 18 116 59 Au Ni 1 8 0 365 4 03 0 42 145 67 141 75 Au Ni 25 0 365 4 16 0 44 154 91 151 92 Au Ni 1 2 0 365 4 07 0 43 148 48 1
5. 4 Texas Tech University H S Tanvir Ahmed December 2010 widths of the filaments assuming that the filaments have a bamboo type structure wherein grains are adjacent to one another to form the structure The average grain size irrespective of the pore sizes of the samples is measured to be 2 47 0 19 um Table 1 1 summarizes the measurements of the foils of each nominal pore size Table 1 1 Measurements on the foils according to their nominal pore sizes Pore size Average Ave filament Average Ave grain size um thickness um size um Porosity um 0 22 571 6 08 2 50 0 258 0 008 2 77 0 62 0 45 60 3 8 12 5 62 0 341 0 017 2 33 0 41 0 80 79 2 3 81 41 54 0 482 0 019 2 27 0 43 3 00 792 5 87 3 60 0 502 0 045 2 50 0 52 Both in plane and cross sectional SEM images reveal that the pores transit through the thickness as well through the cross section which denotes the pore structure to be three dimensional For a porous material it is necessary to use corrected cross sectional area instead of the geometrical cross sectional area in the measurement of stress and elasticity The corrected cross sectional area A is given by A A p 1 3 where A is the geometric cross sectional area p is the porosity and n 1 for 2 D pore morphology wherein the pores run through the thickness only 1 5 for 3 D pore morphology 1 A representative plan view and cross section SEM i
6. bone 10 y 2 9855x 19 T o g no Nn c B I 1 1 1 kn 1 1 1 1 pi ni 1 1 1 1 1 ji oo 1 0E 02 1 0E 01 1 0E 00 1 0E 01 Strain rate 1 sec Figure 3 14 Strain rate sensitivity of the Hydroxyapatite coating 4991012 Ti 97 Texas Tech University H S Tanvir Ahmed December 2010 Table 3 1 Hardness values calculated for the Hydroxyapatite film 4991012 Ti as per strain rates Nominal Actual Nominal Actual Width Strain rate Hardness Scratch Scratch Load N Load N w H velocity Velocity uN UN nm 1 sec GPa nm sec nm sec 556 815 665 8 39 36 7 53 0 46 3 23 0 4 ay YAN NU 542 21 723 08424 41 6 92 0 24 2 65 0 18 569 082 710 03 54 75 2 83 0 23 2 92 0 48 2000 2000 1000 613 6 668 34 1 31 2 99 0 006 3 5 0 01 603 266 681 11 26 27 2 94 0 11 3 32 0 26 506 623 26 39 2 01 0 085 3 34 0 28 1000 1250 1000 546 760 7 42 6 1 65 0 09 2 42 0 26 448 697 92 18 09 1 79 0 05 2 35 0 12 632 17 654 59 49 0 96 0 086 3 84 0 68 a 6 gt 1000 652 28 704 43 31 45 0 89 0 04 3 36 0 3 381 580 57424 95 0 19 0 008 2 89 0 25 109 vee 1900 408 639 71 42 67 0 170 012 2 57 0 38 488 616 39 88 10 092 0 0057 3 31 0 39 50 56 82 1000 458 686 86 31 63 0 083 40 0038 2 49 0 23 405 584 57 26 22 0 097 0 0043 3 03 0 26 707 829 71 30 92 0 012 0 0004 2 62 0 19 10 10 10 1000
7. 186 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_V_200 900Hz_Apr 05056 010 Line 1 filter 3 square Fr 7E 4 Hz dY 5 18 a u d Fr 9 18 E 4 Hz AD Channel 2 Pr35_V_200 900Hz_Apr 05058 010 Line 1 Am pm dV 518 a u dAm 1 48 nm 45 50 55 60 Length 53 8 a u Height 303 712 kHz Figure IL 10 Frequency shift plot of V 110 187 Texas Tech University H S Tanvir Ahmed December 2010 II B Frequency shift curves of Au Ni samples Channel 1 Pr35_Sample 1_200 900Hz_Apr 03510 004 Line 1 filter 3 square Fr E 4 Hz dv 6 37 au d Fr 1 88 E 5 Hz AD Channel 2 Pr35_Sample 1_200 900Hz_Apr 03510 004 Line 1 Am pm dw 6 37 au dAm 1 41 nm Length 81 6 au Height 375 490 kHz Figure IL 11 Frequency shift plot of Au Ni A 1 7 nm Sample 1 188 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 2_200 900Hz_Apr 03335 01 6 Line 1 filter 3 square dv 5 56 au d Fr 1 22 E 5 Hz Fr E5 Hz 184 AD Vi au Channel 2 Pr35_Sample 2_200 900Hz_Apr 03335 016 Line 1 dY 5 56 au dam 1 46 nm Am pm 10 o 10 20 30 4 50 60 70 60 90 Length 109 1 a u Height 1752 520 kHz Figure II 12 Frequency shift plot of Au Ni d 16 0 nm A 0 8 nm Sample 2 189 Texas Tech University H S Tanvir Ahmed December 2010 Chan
8. 38 269x 25 074 R 0 9959 5 H 0 1 1 1 1 1 1 1 2 0 0 1 0 2 0 3 0 4 0 5 0 6 Porosity Figure 1 23 Variation of elastic modulus with porosity for silver membranes as measured using tensile test initial onset of yielding and interrupted test at ultimate strength From Figure 1 23 it is clearly evident that the porous membranes progressively stiffen when subjected to increasing plastic deformation The intercept value found using a linear fit for the stiffened modulus suggests a small increment from 25 07 GPa at the initial yield condition to 27 93 GPa at the maximum stiffened condition i e at ultimate stress This suggests that higher porosity membranes stiffen more under progressive loading compared to lower porosity membranes Both monotonic loading and interrupted loading predicts similar elastic modulus values at fully dense condition The linear extrapolation of the curve for maximum modulus 39 Texas Tech University H S Tanvir Ahmed December 2010 value in Figure 1 23 also suggests the critical porosity Pc porosity at which strength goes to zero to be 0 79 which is in very well agreement with modeling data found from tensile testing 1 3 3 Tensile test of electrodeposited nanocrystalline Ni The tensile test specimens on nanocrystalline Nickel are obtained as pulsed electrodeposited thin films 63 on stainless steel surface Copper is used as a buffer layer on the stainless steel to provide the ease of remov
9. 4 2 Background Many investigations on methods of non destructive elastic modulus measurement methods for thin films are reported now a days Arnold et al 119 and Reinstadtler et al 120 studied the torsional resonance mode TRmode of Atomic Force Acoustic Microscopy AFAM method to measure elastic constants of anisotropic materials In this method a piezoelectric device is excited using an AC voltage to induce vibrations in the AFM cantilever while the tip is in contact with the sample surface Indentation elastic modulus is extracted from the tip surface interaction assuming Hertzian contact mechanics DeVecchio et al 121 used a similar technique wherein the deflection of the AFM cantilever was used to determine the localized modulus Etienne et al 122 studied the elastic modulus of thin films as a function of concentration depth Vibrating reed measurements proposed by Whiting et al 123 has similarities with the AFM technique The major difference is in the vibrating reed method the sample along with the substrate is exposed to piezoelectric vibrations whereas in AFM technique the probe cantilever is vibrated Oscillating bubble method 124 is another technique or measuring surface elasticity however is only limited to the measurements of liquids 108 Texas Tech University H S Tanvir Ahmed December 2010 Perhaps the most popular technique for measuring modulus is depth sensing Nanoindentation as represented
10. Nano scratch testing on nanocrystalline nanolaminates and artificial ceramic bone coatings of hydroxyapatite are tested to reveal strength and strain rate sensitivity In addition a new technique known as the tapping mode measurement is investigated to determine the elastic plastic transition and measure the elastic modulus of metallic nanolaminates and hydroxyapatite thin films for comparison to static nanoindentation IK 1 1 2 1 3 1 3 2 3 3 4 1 4 2 4 3 Texas Tech University H S Tanvir Ahmed December 2010 LIST OF TABLES Measurements on the foils according to their nominal pore sizes eeeeeeeeeeeeeee 5 Strain rate sensitivity exponents for different regimes of all specimens 70 Hardness values calculated for the Hydroxyapatite film 4991012 Ti as per RUE NT ER LES ecn a an aa Pan A ang a E aE RAE ee a niaga Na Ato 98 Scratch parameters at 100 um sec for the sample shown in Figure 3 15 99 Hardness values calculated as per strain rates for the Au Ni sample 101 Elastic modulus of calibration materials 125 Frequency shift data of calibration materials with corresponding elastic IMOCWUUG nie es ag DAN E T N TEENI 129 Calculation of sample modulus from calibration curve s es 130 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 1 20 1 21 Texas Tech Universit
11. P 4 Predicted by equation E 5 0 15 3 L lt L a x v 5 N 01 N L s L NS 4 oos ie 0 1 X 1 10 100 1000 Grain size d nm Figure 1 33 Strain rate sensitivity as a function of grain size for nanocrystalline Au Cu samples 1 4 Summary 1 Tensile testing of porous silver membranes and fully dense foils are done at various strain rates The measured elastic modulus for the porous membranes appear to be indicative of the G modulus and follows a trend line as the porosity goes from 80 to fully dense condition The change of yield strength with porosity has been modeled with the theory of Li and Aubertin 45 and is found to have good correlation with the experimental data A 2 47 um average grain size of the membranes is measured from SEM images of the porous membranes and is somewhat invariant with porosity Strain rate sensitivity found from the rate dependent tensile testing has been plotted as a function of the grain size and is in well accordance with the analytical 50 Texas Tech University H S Tanvir Ahmed December 2010 model provided by Gu et al 26 Alternately it is proposed 1 that strain rate sensitivity exponent can be modeled if the filament size and porosity are substituted in the analytical equations Models for these expressions in equations 1 29 and 1 30 are plotted in Figure 1 16 and Figure 1 17 against the experimental data and are found
12. Strain rate sensitivity of hydroxyapatite coatings Poster presented at AVS 56th International Symposium and Exhibition San Jose California November 9 13 2009 111 H S T Ahmed A F Jankowski Strain rate sensitivity of nanocrystalline nanolaminate Poster presented at the AVS 55th International Symposium and Exhibition Boston Massachusetts October 21 23 2008 112 A F Jankowski H S T Ahmed Plasticity of nanocrystalline nanolaminates strain rate sensitivity 15th International Symposium on Plasticity ed Akhtar S Khan Proceedings Plasticity 09 NEAT Press 2009 403 405 113 A F Jankowski Interface Effects on the Mechanical Properties of Nanocrystalline Nanolaminates Mechanical Behavior at Small Scales Experiments and Modeling eds J Lou B Boyce E Lilleodden L Lu Materials Research Society Symposia Proceedings 1224 2010 114 A F Jankowski Measurement of lattice strain in Au Ni multilayers and correlation with biaxial modulus effects Journal of Applied Physics 71 1992 1782 1789 147 Texas Tech University H S Tanvir Ahmed December 2010 115 M A Wall A F Jankowski Atomic imaging of Au Ni multilayers Thin Solid Films 181 1989 313 321 116 A F Jankowski Modelling the supermodulus effect in metallic multilayers J Phys F Met Phys Vol 18 1988 413 427 117 A F Jankowski T Tsakalakos The effect of strain on the elastic constants
13. TENSILE TESTING OF NANOMATERIALS 1 1 Introduction Porous materials have a combination of mechanical properties that make them attractive for many engineering applications They are lightweight have a capacity to undergo large deformation without generation of localized damaging peak stresses and possess high surface area per unit volume 1 Porous metal membranes may be considered as ideal candidates 2 for lightweight structural sandwich panels energy absorption devices and heat sinks The use of porous metal coatings is ever increasing in renewable energy system applications 3 as solar cells and hydrogen fuel cells Recent researches on nanoporous materials are suggestive of their future uses as electrochemical 4 or chemical 5 actuation tunable conductors 6 7 and magnets 8 9 In particular the scale of porosity in metal coatings is particularly important to their catalytic performance 10 Potentially just as important is the mechanical stability of the porous coating in these devices Thus understanding the mechanical behavior of these foams in a wide range of strain rates is important for such potential applications where the rate of deformation may originate as rapid thermal stress strain cycles Use of compression testing and nanoindentation to reveal mechanical properties of porous materials is been reported by many researchers 2 11 12 13 14 15 16 17 18 In this study a series of rate dependent tensile tes
14. for a particular pore size is constant for the entire range of the strain rate This observation is taken into consideration that the average elastic modulus for a particular pore size sample does not depend on the rate of loading and should remain constant Figure 1 6 shows the average elastic modulus as a function of porosity for different pore size samples Using linear fit the porosity at which the elasticity would go to zero 1 e the elastic modulus at critical porosity Pe is calculated to be 65 5 and the elastic modulus for fully dense Ag i e at porosity P 0 is estimated to be 25 07 GPa 30 25 S E 38 269 P 25 074 R 0 9959 Elastic modulus GPa a 0 0 1 0 2 0 3 0 4 0 5 0 6 Porosity Figure 1 6 Average elasticity plot for different porosity samples 10 Texas Tech University H S Tanvir Ahmed December 2010 Elastic constant of fully dense Ag in pure tension is reported to be c11 124 0 GPa 34 Other elastic constants are reported as c12 93 4 GPa c 2 c11 c12 15 3 GPa and c44 46 1 GPa 34 These values are in well agreement with the reported values for silver at room temperature by Neighbours and Alers 35 and by Overton and Gaffney 36 i e c11 123 99 GPa c12 93 67 GPa c 15 16 GPa and c44 46 12 GPa Similar values are obtained by Hiki and Granato 37 Chang and Himmel 38 and Wolfenden and Harmouche 39 The stiffness constants for cubic structure of Ag ar
15. 150 e r 300 nm ry a r 500 nm e s 100 e s A eo 4 ats 50 4 2 x L M e 7 i F F Fos i oer E 0 200 400 600 800 1000 Width nm Figure IIL 9 Change in depth of indentation as a function of the tip radius of a Cube Corner tip with 90 angle 238
16. Kilmametov R Z Valiev H Gao X Li A K Mukherjee J F Bingert Y T Zhu High pressure torsion induced grain growth in electrodeposited nanocrystalline Ni Applied Physics Letters 88 2006 021909 021911 25 K S Kumar S Suresh M F Chisholm J A Horton P Wang Deformation of electrodeposited nanocrystalline nickel Acta Materialia 51 2003 387 405 26 C D Gu J S Lian Q Jiang W T Zheng Experimental and modelling investigations on strain rate sensitivity of an electrodeposited 20 nm grain sized N Journal of Physics D Applied Physics 40 2007 7440 7446 27 A F Jankowski C K Saw J P Hayes The thermal stability of nanocrystalline Au Cu alloys Thin Solid Films 515 2006 1152 1156 137 Texas Tech University H S Tanvir Ahmed December 2010 28 A F Jankowski Modeling nanocrystalline grain growth during the pulsed electrodeposition of gold copper Electrochemical Society Transactions 1 2006 1 9 29 A F Jankowski C K Saw J F Harper R F Vallier J L Ferreira J P Hayes Nanocrystalline growth and grain size effects in Au Cu electrodeposits Thin Solid Films 494 2006 268 273 30 J D Hige C M Yu S A Letts Metal coatings for laser fusion targets by electroplating Journal of Vacuum Science and Technology 18 1981 1209 12013 31 Y M Wang A F Jankowski A V Hamza Strength and thermal stability of nanocrystalline gold alloys Scripta
17. LB 2 Scratch Hardness Amal ysis ssiiisnmentnannainenmenimeanesiuss 162 I C Elastic Modulus Measurement seen cee Ae Bene 166 LCT Producing approach Curves sasasi anaa ang E E nee nee 166 LD PPro Tan 0 a E E A AE tole Ag ora 169 REFERENCE FOR APPENDIX I sssssnennnnnnnnnsnnnnnnsnnsencese 177 APPENDIX IT APPROACH CURVES FOR ELASTIC MODULUS MEASUREMENTS ccssssssssssssssessoeees 178 ILA Frequency shift curves for Calibration samples 0 0 0 0 ceseeseeseeeeseeeneeeeeeees 178 I B Frequency shift curves of Au Ni samples 188 I C Frequency shift curves of Au Nb samples 205 I D Frequency shift curves of Cu NiFe samples 209 ILE Frequency shift curves of Hydroxyapatite coatings 211 ILF Frequency shift curves of Silicon wafers 215 I G Frequency shift curves of directional sapphire 217 I H Frequency shift curves of Ta V samples 0 0 00 ee eesessceceseeeseeeeeeeseeeeneeeeeens 218 APPENDIX IIT PROGRAM AND OUTPUT FOR BOUNDARY INTERFACE AREA CALCULATION OF NANOLAMINATES ss sstcecentecescacavisedeatecandeitiscidcs bausbiviatacnieatie esa a en ena nengen Sainan sarnana 226 THA MATLAB program secs ciaiiesdiacs ees ceansendiaea eungtcnvenec sacs cacy tan ei destine nine nest 226 ILA Grain Boundary Intercept Area Calculation nen 226 IL A 2 Layer Pair Intercept Area Calculation
18. i e not in 154 Texas Tech University H S Tanvir Ahmed December 2010 contact with the sample This will move the sample area under the probe Correct optical microscope offset OM offset needs to be set before this can work perfectly This is generally calibrated from the factory but can be done in house in case of need see the Optical microscope manual Also please refer to the section 3 2 24 on page 44 of the NA 2 manual I B 1 d Once the sample is located under the probe make sure to turn the microscope light and the camera off Keeping them on will use valuable memory and retard the speed of the data acquisition system I B 1L e Approach the sample with z movement with velocities from very fast to normal drop down list on the Move tab with care Bring the probe to about half a millimeter above the surface and then click on Find surface This will automatically find the sample without damaging the tip Once the surface is found a new window will pop up with the information Surface Found Press OK to close that box Please refer to the image on page 14 of the NA 2 manual LB 1 f Go the Scan tab Before producing a scratch or even an elasticity curve it is highly recommended to scan the area A high resolution scan is not necessary as it will unnecessarily wear the tip and can take a lot of time So change the speed and step size of the scan from the Scan tab and then select the area
19. surface defects which need to be avoided during the experiment To reduce the possible effect of thermal drift due to air currents the NanoAnalyzer machine is operated with an environmental cover A number of constant load scratches are made with the tip on the test surface using different nominal load values Ng of 1OOUN to 2 mN The actual normal load N is measured for each scratch using a load cell The length A of the scratches can be made arbitrary In this study h is limited to 5 microns for all the scratches After the scratches are produced the surface is scanned 94 Texas Tech University H S Tanvir Ahmed December 2010 for scratch width in the direction perpendicular to the scratches Only the widths that correspond to both grain boundary and layer pair interface contribution see Figures 3 8 and 3 9 of that particular sample are taken into account for calculation The scratches are measured at seven different sections and an average width is computed to provide a statistical standard Velocity dependent scratches are conducted to induce strain rate effects on hardness and then the scratch hardness H of the test material for that particular strain rate is computed using equation 3 13 Figure 3 12 shows scratches with 1 mN indenter force and at 50 nm sec scratch velocity on Hydroxyapatite ceramic coating on silicon substrate 109 with Ti as buffer layer Figure 3 12 Scratches on Hydroxyapatite 4991012 Ti at 50 n
20. w 06 ui 0 4 0 2 0 1 1 1 1 1 1 1 1 0 0 2 0 4 0 6 0 8 1 1 2 p ps Figure 1 9 Relative elastic modulus as a function of relative density Li and Aubertin 45 proposed a general equation for the prediction of uni axial strength based on actual porosity P and critical porosity Pc as follows ele Feet Ga 1 15 where Op is the strength at a particular porosity P 0 is the strength of the fully dense solid corresponding to P 0 x and x2 are material parameters and _ are the MacCauley brackets z 0 5 z Iz This equation can be used for both tension and compression Hence the MacCauley brackets are used to take care of the sign of 16 Texas Tech University H S Tanvir Ahmed December 2010 the stress Under tensile conditions the author 45 reported a reduction of equation 1 14 which is given by zP O o 1 sin 1 16 E 7 kii A similar approach is taken to generate functions for trendlines for the elastic modulus with one inflection point near the critical porosity and another inflection point near the fully dense modulus value eos tee Les E 1 17 2 P 2 P z isa EE 1 18 P where E E P and P hold same notions as described earlier Approximating a b and c to be 0 25 2 2 and 0 83 respectively equation 1 17 and 1 18 are plotted in Figure 1 10 along with other trendlines for prediction of elastic modulus The approximations of a b and
21. 0 03 0 035 0 04 Engineering Strain e Figure 1 7 Engineering stress strain plot of fully dense silver at different strain rates 12 Texas Tech University H S Tanvir Ahmed December 2010 45 40 35 30 F Elastic modulus E GPa 25 20 F 15 1 1 tt fri 1 1 i trir 1 1 x er et 1 1 tot rit 1 1 tf ritti 1 00E 05 1 00E 04 1 00E 03 1 00E 02 1 00E 01 1 00E 00 Strain rate Figure 1 8 Elastic modulus of fully dense silver measured at different strain rates The elastic modulus of fully dense silver from the plot of Figure 1 6 is estimated towards a value in between the G and E value by the linear trend line as porosity goes to zero For comparison similar rate dependent tensile tests are done on fully dense silver 99 95 pure specimens and the measured elastic moduli are plotted on Figure 1 7 and Figure 1 8 The average elastic modulus of dense silver is calculated to be 36 35 1 54 GPa from these experiments However lack of surface finish of the specimens may undermine the value by a bit The author believes the major discrepancy to be resulting from the surface irregularities and micro cracks present in the sample as evidenced from the cross section image on Figure 1 3 Some level of stress concentration factors are also introduced during the making of the 13 Texas Tech University H S Tanvir Ahmed December 2010 specimens using the die These affect the yield strength and
22. 17 80 a u dAm 730 38 pm Am pm 30 4 50 60 70 80 20 100 110 120 130 5 160 Length 131 2 a u Height 659 306 kHz gt 7 Figure IL 25 Frequency shift plot of Au Ni A 1 3 nm Sample 16 202 Af Am Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 17_200 900Hz_Apr 04018 024 Line 1 filter 3 square Fr E 4 Hz dV 7 85 a u d Fr 1 26 E 5 Hz Channel 2 Pr35_Sample 17_200 900Hz_Apr 04018 024 Line 1 dV 7 85 a u dAm 1 23 nm Am pm 3500 3000 2500 2000 Length 51 6 a u Height 293 718 kHz Figure II 26 Frequency shift plot of Au Ni A 2 9 nm Sample 17 203 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample B1118_200 900Hz_Apr 03837 029 Line 1 filter 3 square Fr E 4 Hz 304 a 254 eS lt D 204 154 104 d 20 11 au d Fr 1 08 E 5 Hz Vi au Channel 2 Pr35_Sample B1118_200 900Hz_Apr 03837 029 Line 1 5000 4500 4900 3500 4 g 3000 2500 2000 1500 1000 500 Length 109 1 a u Height 383 683 kHz Am pm 20 30 4 so 60 70 dv 20 11 au dAm 797 84 pm 80 90 100 110 120 Figure IL 27 Frequency shift plot of Sample B1119 204 Texas Tech University H S Tanvir Ahmed December 2010 II C Frequency shift curves of Au Nb samples Channel 1 Pr35_Au Nb 606 _200 900Hz_Apr 05431 036 L
23. 22b 0 36Gb F L _0 59508Gb L b L where G is the shear modulus of rigidity and b is the Burger s vector The constant 1 653 at the end of expression arose following the assumptions of edge dislocation and a Poisson ratio of 0 33 Activation volume V equals Lb for dislocation based deformation 26 Relationship between activation volume and strain rate sensitivity is originally proposed by Cahn and Nabarro 60 and is given by V3kT m V o 1 23 where k is Boltzman constant 8 62x10 eV K T is temperature K and is the flow stress The constant of V3 originates from assuming Von Mises criterion for yielding and hence converting the original expression of shear mode of deformation to tensile mode of deformation Using equation 1 22 and 1 23 the final relationship between m and V is given as below 1 1 5 3 0 5 m GETZ if 1653 1 24 0 36G V V The general relationship can be given as 26 Texas Tech University H S Tanvir Ahmed December 2010 m c nf a 1 25 V V where c and c2 are constants depending on shear modulus G Burger s vector b and temperature T For experiments at the same room temperature c and c2 will only depend upon G and b It is not possible to have dislocations extending beyond the grain boundary limit Hence the upper limit of the length of dislocation line L should depend on the grain size hy Conceptually L h approaches unity for very small hy and
24. Double click on that cell of the table and input necessary values for example the start and end positions of the scratch and the load value You may draw as many vertical lines as necessary up to certain maximum and edit them from the table Please refer to the image on page 18 of the NA 2 manual 156 Texas Tech University H S Tanvir Ahmed December 2010 LB 1 j Once the table is finished the machine is ready to produce scratches at the tabulated locations with the tabulated properties Now go to the UMT panel and select Data tab from the semi automatic panel Click on unbias all 1111 and then bias all 0000 This will bias the force sensor and make the Fx and Fz values zero Then click on the Blackbox tab and click on Browse give it a filename for the experiment that is going to be conducted and click save You may choose to record every 10 data point or 20 data point depending on your need and that can be defined on the field record every N data or average of N data Click on Run button from the menu bar of the UMT This will start recording data points from the force sensor I B 1 k Now go to the NA software and check that the FB mode is set to Close This is the force feedback system which needs to be closed for scratches of velocities up to 1000nm sec For making higher speed scratches the feedback mode needs to be open 142 I B 1 1 Click on Run bu
25. Figure 4 6 Probe in contact with a surface having a stiffness of ks Thus the frequency of oscillation of the system described by equation 4 9b is given by 27 f Kh 4 10a m Qrfy te 4 10b Replacing m by substituting equation 4 8b into equation 4 10b yields GAP EE orn 4 11 Solving for f yields a z3 4 12 119 Texas Tech University H S Tanvir Ahmed December 2010 The change of frequency or frequency shift from natural oscillation fo to that after in contact with the surface f is given by Af f f 4 13 Substituting equation 4 12 into equation 4 13 yields w heti 4 14 Using Taylor s expansion with first two terms only on equation 4 14 gives Af ff 4 15 Now the stiffness of the surface k can be modeled as P k 4 16 S 4 16 From equation 4 6b we find that the load P equals 4 P VRE 4 17 Substituting equation 4 17 into equation 4 16 P 4 k 2VRE Vz 4 18 z Putting the expression of ks from equation 4 18 into equation 4 15 yields an expression of the frequency shift 120 Texas Tech University H S Tanvir Ahmed December 2010 Are LR pe 4 19 c Taking squares on both sides of equation 4 19 gives Af az 4 20a a fy 4 20b Z where Of is the slope of the square of frequency shift versus probe displacement plot and is given by E 4 21 Equation 4 21 is a simplified formula derived using only
26. Height 409 060 kHz Figure IL 33 Frequency shift plot of sample Cu NiFe 303 A 6 7 nm 210 Texas Tech University H S Tanvir Ahmed December 2010 ILE Frequency shift curves of Hydroxyapatite coatings Channel 1 Pr35_Hydroxy Coating 4991105 R Si_200 900Hz_Apr 05589 030 Line 1 filter 3 square dY 8 14 a u d Fr 8 59 E 4 Hz Fr E4 Hz as AD Vv au Channel 2 Pr35_Hydroxy Coating 4991105 R Si_200 900Hz_Apr 05589 030 Line 1 dV 8 14 au dAm 449 25 pm Am pm 5000 4500 4 3500 3000 2000 1500 1000 500 4 o4 60 70 60 30 100 110 120 130 140 150 160 Length 106 6 a u Height 428 976 kHz 7 Figure IL 34 Frequency shift plot of sample 4991105 R Si 211 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Hydroxy Coating 4991105 Ti Si_200 900Hz_Apr 05647 031 Line 1 filter 3 square dv 6 19 a u d Fr 2 77 E4 Hz as AFF TES H2 4 AD Channel 2 Pr35_Hydroxy Coating 4991105 Ti Si_200 900Hz_Apr 05647 031 Line 1 dV 6 19 a u dAm 237 38 pm 60 70 80 20 100 110 120 130 140 150 160 Length 108 4 au Height 377 567 kHz Figure IL 35 Frequency shift plot of sample 4991105 Ti Si 212 AD Am Channel 1 Pr35_Hydroxy Coating R Si_200 900Hz_Apr 05490 005 Line 1 filter 3 square Fr E 4 Hz Channel 2 Pr35_Hydroxy Coati
27. Materialia 57 2007 301 304 32 GE Silver Membranes GE Osmonics Labstore 5951 Clearwater Dr Minnetonka MN 55343 http www osmolabstore com OsmoLabPage dll BuildPage amp 1 amp 1 amp 326 33 Surepure Chemetals 5 W Nottingham Drive Florham Park New Jersey 34 H B Huntington The Elastic Constants of Crystals Chapter in Solid State Physics 1958 35 J R Neighbours G A Alers Elastic constants of silver and gold Physical Review 111 1958 707 712 36 W C Overton Jr J Gaffney Temperature variation of elastic constants of cubic elements I Copper Physical Review 98 1955 969 977 37 Y Hiki A V Granato Anharmonicity in noble metals Higher order elastic constants Physical Review 144 1966 411 419 138 Texas Tech University H S Tanvir Ahmed December 2010 38 Y A Chang L Himmel Temperature dependence of the elastic constants of Cu Ag and Au above room temperature Journal of Applied Physics 37 1966 3567 3572 39 A Wolfenden M R Harmouche Elastic constants of silver as a function of temperature Journal of Materials Science 28 1993 1015 1018 40 J F Nye Physical Properties of Crystals 1960 Oxford 41 J Kovacik The tensile behaviour of porous metals made by GASAR process Acta Materialia 46 1998 5413 5422 42 O Yeheskel M Shokhat M Ratzker M P Dariel Elastic constants of porous silver compacts after acid assisted conso
28. N J 90 t Elastic modulus 40 80 F Tag 70 m A Polos 60 i gt i j S Z r iy i i 125 5 50 A e we 4 1 S 5 1 of i ts DE 4 9 o L 3 ad 8 ee H H 4 t A it a he fr a 120 5 w Le ee oe a F A Mit li lt oi gt k E it pe fe fe de Pe fa som 30 eo ee Ca 2 13 E tf eo be ott pro it i C i Pole d ji si l ps io 8 10 en cee ee a a er ce eae ee t t t j LIR pe Er fe Pi Pies te gede Po Ee i 15 Cee heer es eee eee cee bof tab Ld bag ty eh f j bat kad kad fad fad fad id il on a ua ia l 0 200 400 600 800 1000 1200 1400 Time sec Figure 1 21 Change in elastic modulus of dense silver with progression of load at a strain rate of 10 per second 37 Texas Tech University H S Tanvir Ahmed December 2010 70 60 7 50 f T A a 40 5 5 g 30 a amp O 1 00E 02 sec Ww 1 00E 03 sec 20 F m 1 00E 04 sec 10 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 50 100 150 200 250 300 350 400 Strength MPa Figure 1 22 Elastic modulus from interrupted test of dense silver as a function of applied engineering stress over different strain rates 38 Texas Tech University H S Tanvir Ahmed December 2010 25 Continuous tensile test L y 35 365x 27 926 R 0 9953 E Maximum value from interrupted test 20 T A 2 5 o 3 3 3 E 2 3 10 ui y
29. Tanvir Ahmed December 2010 potential for work hardening of the face centered cubic material samples which Gu et al did not take into consideration during explaining his results For the scratch and tensile tests of porous silver membranes this author believes that the test method is not the underlying reason for the observed change in the strain rate sensitivity Rather the change of deformation mechanism from alloy and dislocation based strengthening region I in Figure 2 1 to higher dislocation based strengthening region II in Figure 2 1 is the fundamental cause of the observed higher rate sensitivity exponent as obtained by the micro scratch experiments in these cases Similar behavior is observed by many researchers for other materials at high strain rates 20 72 74 79 The region of phonon drag region II in Figure 2 1 is observed at even higher strain rates and generally occurs at strain rates higher than 10 sec To access this phonon drag regime higher strain rate experiments are necessary as may be obtainable by other techniques for example nano scratch testing 2 3 2 Micro scratch experiment of nanocrystalline Ni Electro deposited nanocrystalline Ni foils are mounted in cross section using epoxy Prior to the scratch test the preparation of the samples involved grinding and polishing at different smoothness levels to remove surface roughness and other possible artifacts from the vacuum casting process Rate dep
30. The scratch hardness can be computed in two methods calibration method and direct method In calibration method several different scratches at the same loading rate typically at a median velocity of the entire scratch speed range is conducted on surfaces with know hardness values for example fused silica 9 5 0 5 GPa A particular width of scratches is targeted for this purpose In this instance let us take an example for the case of the nanolaminate modeled in Figure 3 8 From Figure 3 8 both the grain boundary and layer pair interfaces will contribute to interfaces that 90 Texas Tech University H S Tanvir Ahmed December 2010 affect the hardness of the sample if the scratch width is at least 40 nm So similarly wide scratches are to be produced on the known surface for comparison This scratch hardness data on the calibration surface would provide the basis of comparison at all velocity scratches on the unknown material According to sclerometry technique 105 hardness value H of a surface is calculated as H k 3 5 WwW where k is a coefficient of the tip shape F is the constant indenter load and w is the resulting scratch width For the material under study the comparative hardness equation can be written as 106 2 moe i where the subscripts S and R denote sample and reference materials respectively If similar width scratches are conducted on both the reference material and the sample the tip shape coe
31. applications of nanocrystalline nanolaminates include optical band pass filters for x rays and neutrons 88 89 90 91 giant magneto resistance 92 93 for high density recording media in low temperature stability analysis 94 95 96 for bonding through high energetic reactivity and ultra high wear resistant coatings 97 98 99 100 In spite of their advantages the strengthening behavior for 77 Texas Tech University H S Tanvir Ahmed December 2010 nanocrystalline nanolaminates has not been fully explained whether it is due to grain size or the layer pair spacing In addition experimental observation of the potential softening behavior in the Hall Petch effect at grain size less than 10 nm is not sufficiently documented in the literature With scratch testing on the surfaces of the ncnl the hardness of the material can be calculated as shown by many researchers 83 101 102 103 which can then be correlated with the strength of the material 81 82 The hardness and strength of a hydroxyapatite ceramic coating and metallic nanocrystalline nanolaminates is now measured using a NanoAnalyzer capable of micro and nano scale scratches By varying the time of scratches i e the scratch velocity the material surfaces are subjected to different strain rates The results are used to determine the strain rate sensitivity of these metal metal composites The implications of grain size and laminate spacing on the strength i e har
32. artifacts or prior deformation Also for best results the surface needs to be purely flat since the underlying assumption of tapping mode elastic measurement is Hertzian contact mechanics 1 e the probe meets the surface only at a point However it may not always be the case and that is why repeated experiments at same condition will give a better confidence level Once a defect free area of the sample is scanned the standard operating procedure is as follows I C l a The first step is to allocate the amount of frequency shift and the position of the approach curve measurement For this the scanned area needs to be sent to the measurement panel the test mode needs to be changed from scratch to approach curves from the drop down list in the lower part of the measurement tab and the amount of frequency shift needs to be put on the dialogue box Please refer to the image on page 18 of the NA 2 manual It is recommended to produce at least 3 approach curves for the same frequency 166 Texas Tech University H S Tanvir Ahmed December 2010 shift The range of frequency shift is varied generally from 200 1200 Hz For softer materials lower range is sufficient while for harder stiffer materials a larger range is needed The aim is to produce approach curves typically looks like a flattened S curve which would have a linear elastic regime of loading as well as some plastic loading see Figure I 1 Afo Linear Elas
33. asymptotically approaches very small values or zero for very large h 59 Based on these physical boundary conditions it can be reasonably assumed that for a single grain larger than the theoretical limit of the grain size where the line length for a single dislocation is basically the physical dimension of the grain L n A h 1 26a 8 Lach 1 26b where c is a constant with the unit of nm n is an exponent that is less than unity The actual value of this power factor depends on the mechanism of deformation 26 Assuming Hall Petch relationship for large grain size i e comparing the second term of equation 1 22b with that of equation 1 19 it is reasonable to assume 1 L c h 1 27 8 27 Texas Tech University H S Tanvir Ahmed December 2010 Hence the value of the power factor n in equation 1 26b is assumed to be 1 2 Thus assuming Hall Petch the functional relationship between grain size h and strain rate sensitivity m can be derived from equation 1 25 and 1 27 1 L 1 5 L 0 5 O vm 2p 0 5 C m cb of Si c 1 28b m c in c r 65 1 280 where c3 c4 and cs are constants Equation 1 280 is used to curve fit represented by the dashed line on Figure 1 15 the h value of m for silver taking c3 c4 and cs to be 0 044 15 3 and 1 65 respectively and assuming that for grain sizes above several microns typical m values are equal to 0 01 0 02 This corrobor
34. b top view of the schematics of indentation with a pyramidal Berkovich tip on a nanocrystalline nanolaminate the columnar grain size d is the diameter of the circular equivalent of the hexagonal grain and 4 is the layer pair size For modeling the grain boundary interface it is necessary to compute the number of the grains that are being intercepted by the indentation because the grain boundary effect is a direct function of the number of the grains Densely packed hexagonal grains of columnar type are incrementally placed against each other to find out the maximum number of coincident boundaries Figure 3 2 The number of 79 Texas Tech University H S Tanvir Ahmed December 2010 common interfaces is being recorded as the number of cells increases This data is fitted as an excel plot with x axis being number of cells and y axis being number of common boundaries as shown on Figure 3 3 Different order polynomials are used to fit the data to provide a suitable equation for predicting the number of grain boundary interfaces In the case of a lower order polynomial the lower limit of the number of grains at which there exists a practical intercept area is high For example a fourth order polynomial can predict the number of interfaces within 10 of the actual number of interfaces only at a minimum of 13 grains A sixth order polynomial on the other hand can predict the values with significant accuracy at a minimum of 3 grains H
35. by the Oliver Pharr method 125 In this technique the indentation elastic modulus is calculated from the unloading part of the load penetration depth curve Often loading is done using a three sided Berkovich tip and the area function is achieved using indentations on calibration materials with known hardness and modulus The major underlying assumption of this technique is to treat the sample material as homogeneous and isotropic which in reality is seldom the case Behaviors like material pile up and sink in from deformation are not well understood Moreover the directionality of the extracted modulus is not well defined since the elastic response of the material comes from three directions of the indentation displacement using the Berkovich tip and from the deformed structure which lost its original configuration because of the indentation Linear fitting of the initial unloading curve 125 using a power law function is a challenge since fitting of different percentage of the unloading curve may produce different results Very little indentation depth can be obtained on ceramic materials which have limited ductility prior to fracture 4 3 Experimental Technique UMT NanoAnalyzer tool manufactured by CETR is equipped with a ceramic cantilever which has a diamond Berkovich tip mounted on it As the freely oscillating tip is brought closer to the material to be examined the amplitude of vibration decreases while the frequency of vibratio
36. c are generated from the interest of making the trendlines go through the experimental data set as closely as possible Using different critical porosity values P may result in a better fit However in this case the intention is to compare different equations with the same base parameters As it can be seen from Figure 1 6 and Figure 1 10 both equation 1 13 and equation 1 18 are good approximations for elastic modulus at different measured porosity 17 Texas Tech University H S Tanvir Ahmed December 2010 40 p Porous Silver 35 A Dense Silver Equation 1 12 4 Equation 1 13 30 Se O Equation 1 17 Wait Equation 1 18 T O Ah 8 25 NG D N a 6 5 3 20 E 2 8 15 ui 10 5 L 0 E 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Porosity Figure 1 10 Trend lines for prediction of elastic modulus of Ag at different porosity In addition to the role of porosity on elastic modulus the dependency of mechanical yield strength on structural features of the porous membranes is investigated here A Hall Petch formulation 46 47 48 49 50 51 52 is indicative of dislocation based plasticity and relates the dependency of strength to the square root of structural size O 0 ko 1 19 A h where ois the yield strength oo is the intrinsic strength kc is the strengthening coefficient and h is the measure of dimensional size Since
37. curve is complicated by the fact that the force is continually increased as the probe moves into the sample on the surface 111 Texas Tech University H S Tanvir Ahmed December 2010 instead of keeping it at a constant value Being able to record the frequency shift value at a constant load thereby at a constant z height and use of an acoustic sensor to record the sound when the material plastically deforms would be helpful in this regard Nevertheless use of an acoustic sensor can be highly demanding in terms of the surrounding environmental condition Determining the linear regime of the frequency shift plot in regime 3 of Figure 4 1 can be very demanding analytically as 1s especially so for highly compliant and highly stiff materials For the case of highly compliant materials the plot in Figure 4 1 will be almost continuous without the presence of a distinct linear regime The reason is the elastic portion is so short that the plastic regime ensues at almost no extra load and without a horizontal damping section Hence the plot from regime 1 to 4 looks like a polynomial curve without clear cut segments Therefore this tapping mode technique gives good results for materials having elastic modulus greater than approximately 50 GPa On the other hand the problem associated with highly stiff materials is that the linear regime is so steep and has such high slopes that very few data points are readily achievable This is not a
38. inherent flaws such as defects stress concentrations surface roughness etc present in the test specimen which can then undermine the genuine strain rate sensitivity Measurements at even higher strain rates can be done with SHPB However in SHPB there is a shock front and in shock loading there is possibility of phase change during the experiment because of sudden spike in the temperature wiping out the necessary thermal equilibrium condition though not likely for Ag A method to investigate the 75 Texas Tech University H S Tanvir Ahmed December 2010 strain rate sensitivity of materials at higher strain rates is micro scratch testing Experimental data on rate sensitivity of various porosity silver membranes are obtained using scratch testing at different velocities Shockless continuous loading makes it possible to explore the rate sensitivity without the effect from phase changing Use of actual area as opposed to projected area of scratch front does not improve the rate sensitivity value by much An increase of rate sensitivity value occurs at a typical value of about 10 per second strain rate This higher rate sensitivity exponent occurs mostly from the higher interaction between dislocations and grain boundaries Experimental results show that shockless micro scratch experiments can well simulate the mechanical behavior at higher strain rates making it a suitable method compared to SHPB where a shock front exists during high
39. linear fashion with increasing porosity though it seems that at higher porosity values the strength may decrease more rapidly In accordance with equation 1 15 the effect of porosity on strength of porous materials has been studied by Aubertin and Li 55 and has been shown that the plastic deformation in porous materials occur in more than one way tension shear bending etc The non linear relationship of multi axial inelastic 20 Texas Tech University H S Tanvir Ahmed December 2010 deformation leading to the strength of the porous material as a function of porosity 1s proposed 45 as shown in equation 1 15 As stated earlier this equation reduces to equation 1 16 under uniaxial tensile condition Figure 1 12 shows the trend lines based on equation 1 15 and Figure 1 13 shows the trend lines based on equation 1 16 as a function of porosity for different strain rates In these figures the experimental value from fully dense silver is not plotted as these values are not appropriate for comparison most likely because of different grain size In Figure 1 12 x and x are fit as 6 and 2 respectively critical porosity P 80 The critical porosity and the intercept strength values at P 0 are determined using curve fitting with the experimental data In linear fit the critical porosity value comes to be about 81 Figure 1 11 Hence these two Pc values are in good agreement with each other However the intercept values of yiel
40. number_of_grain_c lt 43 0 area_c_const 2e 8 number_of_grain_c 6 3e 6 number_of_grain_c 5 0 0002 number_of_grain_c 4 oe 0 0056 number_of_grain_c 3 0 0861 number_of_grain_c 2 0 7155 number_of_grain_c 0 6003 number_of_grain_c 226 Texas Tech University H S Tanvir Ahmed December 2010 ol else area_c_const 0 2056 log number of grain _ c 1 7013 number_of_grain_c de ol ol end number_of_grain_s vol_sphere vol_grain ol if number_of_grain_s lt 43 0 area_s_const 2e 8 number_of_grain_s 6 3e 6 number_of_grain_s 5 0 0002 number_of_grain_s 4 0 0056 number_of_grain_s 3 0 0861 number_of_grain_s 2 0 7155 number_of_grain_s 0 6003 number_of_grain_s ole ol ole ol else area_s_const 0 2056 log number_of_grain_s 1 7013 number_of_grain_s do oo ol end are a i 2 sqrt 3 hg 6 layer_size 100 3 0 number_of_grain_c 3 0 number_of_grain_s j area_c_constt area_s_const j 2 0e 12 number_of_grain_c 6 1 0e 9 number_of_grain_e d 5 0e 7 number_of_grain_c 4 1 0e 4 number_of_grain_c 3 0 01 number_of_grain_c 2 2 2725 number_of_grain_c 4 3681 Hines 2 0e 12 number_of_grain_s 6 1 0e Srtnumber Of Grains Ses 5 0e 7 number_of_grain_s 4 1 0e 4 number_of_grain_s 3 0 01 number_of_grain_s 2 2 2725 number_of_grain_s 4 3681 3 2074 number_of_grain_c 1 5873 3 0504 number_of_grain_s j su
41. of noble metals J Phys F Met Phys Vol 15 1985 1279 1292 118 A F Jankowski J Go J P Hayes Thermal Stability and Mechanical Behavior of Ultra fine bcc Ta and V Coatings Surface and Coatings Technology 202 2007 957 961 119 W Arnold S Hirsekorn M Kopycinska M ller M Reinst dtler and U Rabe Quantitative measurement of elastic constants of anisotropic materials by atomic force acoustic microscopy International Committee for Non Destructive Testing ICNDT 16th World Conference on Nondestructive Testing 2004 pp TS5 9 3 120 M Reinstadtler T Kasai U Rabe B Bhushan and W Arnold Imaging and measurement of elasticity and friction using the TRmode Journal of Physics D Applied Physics 38 2005 R269 R282 121 D DeVecchio and B Bhushan Localized surface elasticity measurements using an atomic force microscope Rev Sci Instrum 68 1997 4498 4505 122 S Etienne Z Ayadi M Nivoit J Montagnon Elastic modulus determination of a thin layer Materials Science and Engineering A 370 2004 181 185 123 R Whiting and M A Angadi Young s modulus of thin films using a simplified vibrating reed method Meas Sci Technol 1 1990 662 664 148 Texas Tech University H S Tanvir Ahmed December 2010 124 K D Wantke H Fruhner J Fang and K Lunkenheimer Measurements of the surface elasticity in medium frequency range using the oscillating bubble met
42. of by reducing the Gain control A high gain image will look sharper and crisper whereas a low gain image will look dull However a high gain image means more noise So the gain control is a compromise between noise and resolution that has to be optimized during the actual scanning Tip contamination can also lead to poor images So it is necessary to clean the tip using an alcohol rinse from time to time only when the probe is far from the sample surface and the machine is not being in use 144 I B 1 p During scanning of the scratched area it is possible that the probe may loose contact with the sample surface which will become evident as the Z nm indicator will go up without staying at the middle operating zone of the entire range Or at this point the so far scanned image will become dark without showing the topography any more The former case may happen mainly due to thermal drift high surface inclination as well as due to contact with some surface features caused by pile ups of sample material debris along the path of long scratches That is artifacts can arise if the probe has to scan an area with a significant difference in Z i e the height levels This problem can be taken care of by waiting for few minutes or by putting more force on the cantilever of the probe accomplished with decreasing the set point on the feedback panel However care must be taken not to decrease the set point too much This can break th
43. rate Figure 2 1 Schematic of different regions of rate sensitivity The first segment denoted as I is referred to the region where low strain rates and high temperatures are active and has almost a constant rate independent flow stress The major underlying rate controlling mechanism in this region in stated to be athermal flow where presence of precipitates puts forward long range friction stress Thermal vibrations in the lattice are insufficient in providing energy to overcome this long range barrier Even though crystal structure of the material has some influences on this athermal friction stress the major positive contributions come from the presence of alloy content in the material Materials with higher alloy content will show lower strain rate sensitivity 20 72 The second segment II is the region where higher strain rates are active at lower temperatures 72 and a linear dependence of flow stress on the logarithmic strain rate in observed The transition from region I to region II is reported to be around 107 strain rate for annealed mild steel at room temperature 72 At this section of the rate sensitivity short range barriers such as dislocations and their interactions become relatively more important compared to the long range barriers 1 e alloy 56 Texas Tech University H S Tanvir Ahmed December 2010 content The flow stress is thermally activated which means the lattice vibrations can assist by supplying
44. statistical average Figure 2 3 shows an optical microscope image of a sample containing all the scratches at different velocities Figure 2 2 Micro scratch test rig 59 Texas Tech University H S Tanvir Ahmed December 2010 Figure 2 3 Scratches at different velocities on a single membrane mounted on plan view Data XY Chart E n 7 2 50000 R i 2 50000 s 7 50000 12 50000 Le 4 a Ea lt gt 17 50000 0 0 30 0 60 0 90 0 120 0 150 0 Micrometer Figure 2 4 A sample scan on one of the scratches using the profiler using a 0 7 um tip 60 Texas Tech University H S Tanvir Ahmed December 2010 The width of the micro scratch profiles are scanned using a Veeco Dektak 150 surface profiler mounted on an air suspended table The scan of the scratch width is done using a spheroconical tip of radius 0 7 um that has a 45 deg angle of inclination with a stylus tracking force of 8 mg 78 4 UN Figure 2 4 shows a typical output from the profiler which shows the scan of the width of a scratch and also shows the background surface profile Since the material is porous scan on an apparently flat surface provides lots of ups and downs Thus defining a horizontal background from which the scratch width would be measured becomes difficult Defining the marker positions to evaluate the width is a challenge for the porous materials be
45. technique limitation but rather a machine resolution limitation and the real time performance of the data acquisition In almost all cases the amplitude curve plays a significant role in determining the linear part provided that the amplitude to tip radius ratio is of the order or 5 or less Typically an amplitude value of 5 nm works very well for a wide range of materials using a diamond Berkovich indenter of about 100 nm radius Note must be taken that this value is not the set amplitude value which is generally of the order of 100 nm Rather this is the value to which the probe is tuned to before measuring approach 112 Texas Tech University H S Tanvir Ahmed December 2010 curves Sharper tips as achieved through the use of cube corner indenters should better ensure conditions of point contact with flat surfaces Since the material starts to deform plastically as the probe is pressed further into the surface the associated deformation imparts a damping action on the vibration of the probe which results in a linear horizontal decrease in the frequency on the frequency shift plot and the amplitude becomes close to zero On the other hand it can be said that plastic deformation in the material starts when amplitude becomes zero This phenomenon is observed for a wide range of materials and can be used to determine the upper part of the linear regime of the frequency shift However in analysis before positioning the right marke
46. that the probe increased in temperature during scratch test and hence thermal drift will occur The phenomenon of thermal drift is observable during scanning an area If the probe is drifting a vertical scratch will appear inclined Thus it is recommended to use Probe Correction from the Probe tab before scanning which would take care of the thermal drift automatically Please refer to the image on page 20 of the NA 2 manual Once the image is imported from the Measure tab to Scan tab using Go to Scan button moving to the Probe tab will not erase the to be scanned area from the Scan tab The difference between Auto Setup and Probe Correction is that Auto Setup is mainly intended to find the resonance of the probe It can take care of the thermal drift too but will retract the tip from the sample surface if used while in contact with the surface The Probe Correction on the other hand only takes care of the thermal drift issue and does not retract the probe from the sample During high resolution scanning after the low resolution quick scan the noise of scanning may go up which would be evident on the Frequency feedback plot 159 Texas Tech University H S Tanvir Ahmed December 2010 Ideally the Frequency the error signal should be close to zero during scanning but may go up to several hundred Hz in practice during the high resolution scan This noise can be taken care
47. the Burger s vectors are given by 65 Dperfect T TS 0 175nm 1 32 a 1 Dpartial B Dperfect 0 1012nm 1 32b 1 Dmixture 5 perfect Dpartial 0 1381nm 1 32c Thus assuming perfect partial and mixture type of dislocations the activation volume becomes 13 677b 70 72b and 27 83b respectively Figure 1 29 shows the strain rate sensitivity of nanocrystalline copper 19 and nanocrystalline nickel 26 as a function of grain size A general trend of increasing 42 Texas Tech University H S Tanvir Ahmed December 2010 rate sensitivity is observed with a decrease in grain size This behavior is predicted by using the formulation proposed by Gu et al 26 in the following form m c In c Vd c J 1 33 where c1 C2 and c3 are constants depending on the shear modulus of rigidity G and burger s vector b This equation is based on the assumption of valid Hall Petch strengthening mechanism A more detailed study on this derivation is documented in the earlier section 1 3 1 Tensile test of Ag foils The behavior of strain rate sensitivity as a function of grain size is predicted using equation 1 33 and is plotted on Figure 1 29 Here c1 c2 and c3 are taken to be 0 018 3 0 and 1 65 respectively 66 The value of strain rate sensitivity of the current study is also plotted in the same figure and is in well accordance with both the previous experimental data found in literature 26 and prediction
48. the grain size of the porous sample sets does not vary beyond the statistical standard deviation a Hall 18 Texas Tech University H S Tanvir Ahmed December 2010 Petch evaluation of yield strength depending on structural dimensional feature for example grain size is not possible Even though a similar statistical trend exists with the pore size of the samples structural features like grain size or filament size does not provide such a correlation To estimate the yield strength at the fully dense condition the yield strength versus porosity plot of Figure 1 11 at every strain rate is extrapolated to P 0 to provide an intercept value with a linear fit 200 t o 180 95 P 153 28 R 0 9427 0 1000 5e0 a oy 182 79 P 145 74 R 0 9247 e 0 0100 sec 0 isene o 155 91 P 127 85 R 0 9602 0 0010 sec iso oy 161 25 P 129 01 R 0 8986 e 0 0001 sec Ls Yield strength o MPa 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Porosity P Figure 1 11 The yield stress versus porosity plot of different membranes at different strain rates The intercept values at P 0 range from 127 to 153 MPa as the strain rate increases from 10 per second to 10 per second The average tensile strength of annealed silver wire is reported to be 125 MPa 53 The strength values at each strain 19 Texas Tech University H S Tanvir Ahmed December 2010 rate
49. the image on page 58 of the NA 2 manual Put the left marker on 0 174 Texas Tech University H S Tanvir Ahmed December 2010 and the right marker at the beginning of the section where it approaches the set amplitude value 100 Then click on Get from Curve button Am nm Am_Corr nm Figure I 6 Amplitude versus Amplitude correction curve LD 12 The probe is now ready to be used Place a soft sample for example Polycarbonate under the probe and do incremental indentations and record the Fz values with UMT software If the recorded normal force is considerably less than the nominal load values at input the load correction factor that controls creep of the probe cantilever needs to be adjusted from the Device Settings menu Please refer to section 3 2 16 on page 37 of the NA 2 manual A higher load correction factor indicates more creep compensation and therefore applies smaller biasing load on the cantilever To bring the actual load closer to the 175 Texas Tech University H S Tanvir Ahmed December 2010 applied nominal load the correction factor needs to be increased and subsequent indentation tests are needed to justify the change 176 Texas Tech University H S Tanvir Ahmed December 2010 REFERENCE FOR APPENDIX I 141 E mail communication with I Hermann CETR 14 Feb 2008 142 E mail communication with I Hermann CETR 21 Oct 2009 143 Training at CETR with I Hermann Summer 200
50. the use of the NA head will only be reviewed here This section will detail instructions beyond the CETR Inc manual on how to operate the hardware Before proceeding with this section the user should first read the instruction manual and become familiar with the software interface in the off line mode It will better enable the user to follow the controls and instructions of the CETR NanoAnalyzer interface of the Universal Materials Tester UMT that is documented in this section LA Starting up the NanoAnalyzer LA 1 Begin with the machine in stop mode and with no software running Double click on the UMT icon shortcut on the desktop and select Options Load from the menu bar By default the command opens the C NanoAnalyzer TRIB folder where a folder named Option files is located at Each option file is written for specific purpose only and will only work with a specific head mounted on the UMT machine The reader should consult the manual about how to write an option file See section 6 Calibration Procedures on page 96 of the UMT user s manual 151 Texas Tech University H S Tanvir Ahmed December 2010 LA 2 From the folder Tanvir_Option files select the option file named NanoAnalyzer_Fl 0326 opt This option file was written to give output of Fz and Fx in micro Newtons from the FL 0326 force sensor LA 3 After selecting the option file click on the automatic panel button on the menu bar a
51. to be in good agreement The implication is that strain rate sensitivity exponent will increase as the filament size decreases and will increase more rapidly as porosity increases 2 Interrupted tensile tests are done on porous silver membranes at different strain rates to show the stiffening behavior of porous materials under tensile loading It is observed that the membranes show an elastic modulus close to the G value However as deformation progresses an upper plateau in the elastic modulus is approached that is different than modulus found in monotonic loading conditions This upper plateau in the modulus measurement is more indicative of a value close to that measured for fully dense silver foils It is anticipated that elastic modulus can increase for materials that strain harden by as much as 10 15 i e Figure 1 22 data Thus it is postulated that the filaments or struts are linked with each other with ball joints that would in essence realign to each other in the direction of applied load This realignment of the load bearing filaments gives the membrane more elasticity provided that necking is not yet formed 3 Rate dependent tensile testing has been conducted on nanocrystalline electro deposited nickel to provide the strain rate sensitivity The as deposited condition provides the necessary shape for the test specimens The thickness and width of the samples are better estimated using optical microscopy The activatio
52. value to adjust the actual Fz force either by adding them together or by subtracting the later from the former depending on the sign in front of the values These actual load values need to replace the corresponding nominal load values on the calibration file that was saved by the NA software s Measure gt Hardness calibration function Consult the manual for details about how to create a calibration file Calibration files also sample data files can be opened with the built in software and can be edited for correct load values Once this is done the calibration file is ready to be used as standard of measuring the hardness of an unknown material On the sample surface similar scratches of nominal loads 200UN to 1500UN need to be produced After the scan is done on the scratches the width needs to be calculated using the scratch width measurement tool on the menu bar The 163 Texas Tech University H S Tanvir Ahmed December 2010 values need to be transferred to the Measure gt Hardness measure window The actual values of loads as recorded by UMT software need to be put on the respective field of nominal loads highlight a cell first and then edit it For hardness calculation an appropriate calibration file that was saved earlier needs to be loaded and a comparing value of hardness as measured with the following formula is automatically calculated by the software Hardnessknown Forcenown Hardnessyunknown Forceunkno
53. 00 4725 750 4775 4500 4525 Length 166 6 a u Height 31 316 kHz Figure IL 6 Frequency shift plot of Polycarbonate 183 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sapphire_200 1200Hz_Q30_Apr 02763 015 Line 1 filter 3 square dV 3 47 au dF r 1 67 E5 H z Fr E 4 Hz 30 AD v au Channel 2 P r35_Sapphire_200 1200Hz_Q30_Apr 02763 015 Line 1 dv 3 417 a u dAm 2 52 nm Am pm 5000 400 4000 3500 3000 Am 2500 2000 1500 1000 30 32 Length 23 7 au Height 362 697 kHz Figure II 7 Frequency shift plot of Sapphire 184 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Si 100 _200 900Hz_Apr 03443 011 Line 1 flter 3 square dv 3 76 a u d Fr 5 68 E 4 Hz Fr E 4 Hz 384 354 AD Channel 2 Pr35_Si 100 _200 900Hz_Apr 03443 011 Line 1 dV 3 76 a u dAm 533 96 pm 5000 Am N a Oo Oo o Length 44 1 au Height 300 091 kHz gt Z Figure IL8 Frequency shift plot of Silicon 100 185 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Ta_200 900Hz_Apr 03388 032 Line 1 filter 3 square dV 516 a u d Fr 1 69 E 5 Hz Fr ES Hz dv 6 16 au dam 2 89 nm ika 40 50 60 70 80 20 100 110 Length 82 3 a u Height 1659 938 kHz Figure II 9 Frequency shift plot of Ta 110
54. 1 A 6 Verify that the stage motors are initialized by clicking on the Automatic Panel button and check for motions Load the NanoAnalyzer_FI 0326 opt from the Tanvir_Option files folder Then click the Semi Automatic Panel and the Plot icons on the menu bar The Plot should show Fx and Fz in micro newtons Click on the Data tab on the Semi Automatic Panel and from the menu bar unbias all the channels 1111 and then bias them 0000 This will bring the Fx and Fz on the center of the Plot window LA 7 Now start the NanoAnalyzer NA software NA viewer go to Device from the menu bar and click on Show Device Window This will pop up another window Every function on this window is designated for controlling the hardware of the NA head LA 8 From Device click on Change Probes and select the appropriate probe that is installed on the machine every probe is recognized with a number which is written on the base of the probe as well as on the cover of the probe LA 9 Then from Device click on Run and it will start up the NA head From the move panel check the responses of the stage motors with the corresponding arrow buttons right clicking on any button will show a balloon help 153 Texas Tech University H S Tanvir Ahmed December 2010 1 A 10 Assuming that the correct probe is loaded go to the Probes tab and click on Aut
55. 1 filter 3 square dy 10 95 a u d Fr 1 04 E5 Hz Fro E 4 Hz AD Channel 2 Pr35_Sample 6_200 1000Hz_Apr 03040 022 Line 1 dV 10 95 au dAm 1 37 nm Am pm 30 4 Length 70 4 a u Height 315 210 kHz Figure II 16 Frequency shift plot of Au Ni d 15 2 nm A 4 5 nm Sample 6 193 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 7_200 900Hz_Apr 03766 036 Line 1 filter 3 square dY 6 75 a u d Fr 1 51 E 5 Hz Fr E 4 Hz T a Vi au Channel 2 Pr35_Sample 7_200 900Hz_Apr 03766 036 Line 1 dv 6 75 a u dAm 1 58 nm Am pm 10 15 20 Length 67 8 au Height 386 098 kHz Figure IL 17 Frequency shift plot of Au Ni A 1 9nm Sample 7 194 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 8_200 900Hz_Apr 03787 020 Line 1 filter 3 square dV 6 43 a u d Fr 1 32 E5 Hz Fr E 4 Hz v au Channel 2 Pr35_Sample 8_200 900Hz_Apr 03787 020 Line 1 dV 6 43 a u dAm 1 11 nm Am pm Length 77 5 au Height 339 527 kHz Figure IL 18 Frequency shift plot of Au Ni A 1 6nm Sample 8 195 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample_10_200 1300Hz_Apr 01683 007 Line 1 filter 5 square dV 1 65 a u d Fr 1 67 E4 Hz Fr E 4 Hz 9 8 A a Y au C
56. 10 tests conducted at each strain rate It can be seen that the modulus values increase with a decrease in porosity Also the modulus is found to increase with increasing plastic deformation up to a certain limit wherein the stress level starts to drop because of localized necking The maximum modulus value is found in Figure 1 20 in the upper plateau regions for each level of membrane porosity irrespective of the associated strain rates In a similar fashion intermittent tests have been conducted on dense silver specimens over 10 10 and 107 per second strain rates Figure 1 21 shows an example of the resulting elastic modulus after each successive plastic deformation that the sample goes through Like the porous samples the dense silver specimens also show an increase in modulus at higher amount of plastic deformation This increment in modulus too plateaus out after certain amount of work hardening Figure 1 22 plots all the data on elastic modulus of dense silver as a function of the applied engineering stress over all the strain rates The average of the maximum modulus values i e the plateau region is shown with a horizontal line These maximum elastic modulus values independent of strain rate determined from the incremented tensile tests are plotted as a linear function of membrane porosity in Figure 1 23 36 Texas Tech University H S Tanvir Ahmed December 2010 100 7 45 load
57. 19 2008 435203 8 8 H Drings R N Viswanath D Kramer C Lemier J Weissmiiller R Wiirschum Tuneable magnetic susceptibility of nanocrystalline palladium Applied Physics Letters 88 2006 253103 5 9 S Ghosh C Lemier J Weissm ller Charge dependent magnetization in nanoporous Pd Co Alloys IEEE Transactions on Magnetics 42 2006 3617 3619 135 Texas Tech University H S Tanvir Ahmed December 2010 10 J D Morse A F Jankowski R T Graff J P Hayes Novel proton exchange membrane thin film fuel cell for microscale energy conversion Journal of Vacuum Science and Technology A 18 2000 2003 2005 11 M Hakamada M Mabuchi Mechanical strength of nanoporous gold fabricated by dealloying Scripta Materialia 56 2007 1003 1006 12 M H Lee K B Kim J H Han J Eckert D J Sordelet High strength porous Ti 6AI 4V foams synthesized by solid state powder processing Journal of Physics D Applied Physics 41 2008 105404 8 13 C A Volkert E T Lilleodden D Kramer J Weissmuller Approaching the theoretical strength in nanoporous Au Applied Physics Letters 89 2006 061920 2 14 E W Andrews G Gioux P Onck L J Gibson Size effects in ductile cellular solids Part II experimental results International Journal of Mechanical Sciences 43 2001 701 713 15 Z Liu C S L Chuah M G Scanlon Compressive elastic modulus and its relationship to the struc
58. 3 030 Line 1 Am pm dV 7 50 a u dAm 3 40 nm Length 82 2 au Height 582 112 kHz Figure IL 45 Frequency shift plot of Ta V A 10 12 nm Sample 5 222 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Ta V 6_200 900Hz_Apr 04300 004 Line 1 filter 3 square Fr E 4 Hz dV 5 51 au d Fr 1 84 E 5 Hz AD 12 Pr35_Ta V 6_200 900Hz_Apr 04300 004 Line 1 Am pm Length 79 2 au Height 481 382 kHz Figure 11 46 Frequency shift plot of Ta V A 3 16 nm Sample 6 223 AD Am Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Ta V 9_200 900Hz_Apr 04466 022 Line 1 flter 3 square dv 14 80 au d Fr 1 22 E 5 Hz Fr E 4 Hz 504 4 Channel 2 Pr35_Ta V 9_200 900Hz_Apr 04466 022 Line 1 dV 14 80 a u dAm 1 26 nm Am pm o 25 so 75 100 125 150 Length 158 2 au Height 511 474 kHz o Z Figure IL 47 Frequency shift plot of Ta V A 2 26 nm Sample 9 224 AD Am Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Ta V 10_200 900Hz_Apr 04547 029 Line 1 filter 3 square dV 3 98 a u d Fr 6 08 E 4 Hz Fr E 4 Hz Channel 2 Pr35_Ta V 10_200 900Hz_Apr 04547 029 Line 1 dv 3 98 a u dAm 951 90 pm Am pm 5000 60 65 70 75 60 85 90 95 100 105 Length 66 3 au Height 3
59. 34 Texas Tech University H S Tanvir Ahmed December 2010 shown in time sec to clearly demonstrate the succession of loading unloading cycles with increased load 20 0 2 micron 1E 2 18 E 8 0 2 micron 1E 3 A 0 2 micron 1E 4 16 C 20 45 micron 1E 2 K 0 45 micron 1E 3 44 L 8 0 45 mciron 1E 4 g t 0 8 micron 1E 2 12 E X 0 8 micron 1E 3 2 0 8 micron 1E 4 3 10 L 6 3 mone E 2 3 micron 1E 3 2 L A 3 micron 1E 4 8 amp Ww 6 F 4 A 2 eg 0 E 1 i 1 f L L f 1 i 1 i f f 0 20 40 60 80 100 120 140 Strength MPa Figure 1 20 The elastic modulus of porous silver membranes as measured through incremented tensile loading are plotted as a function of the applied engineering stress The variation in the elastic modulus with the measured engineering stress assuming the cross sectional area being constant is plotted in Figure 1 20 This figure includes all of the modulus values from the onset of initial yielding through the final yield point i e the ultimate stress as measured from each interrupted loading interval It can be seen from this figure that some modulus values decrease at a stress level beyond the ultimate strength indicating the loading regime wherein the specimens undergo localized necking Average modulus values are plotted for all the 35 Texas Tech University H S Tanvir Ahmed December 20
60. 44 83 Au Ni 2 6 0 365 4 13 0 40 152 75 149 53 Au Ni 1 6 0 365 4 14 0 39 153 47 150 32 Au Ni 0 9 0 365 4 05 0 40 147 08 143 29 Au Ni 3 4 0 365 3 36 0 35 102 45 96 19 Au Ni 1 2 0 365 4 4440 48 175 72 175 43 Au Ni 1 9 0 365 4 25 0 55 161 46 159 23 Au Ni 1 6 0 365 4 57 0 28 185 82 187 14 Au Ni 8 9 0 365 4 79 0 47 203 52 208 19 Au Ni 2 0 0 365 3 19 0 24 92 66 86 31 Au Ni 0 8 0 365 3 02 0 22 83 34 77 05 Au Ni 2 9 0 365 3 52 0 41 112 11 106 09 Au Nb 1 6 0 42 2 97 0 21 80 69 70 73 Au Nb 3 2 0 42 4 48 0 30 178 80 170 07 Cu NiFe 6 7 0 32 5 76 0 41 290 83 333 88 Cu NiFe 4 0 32 4 84 0 32 207 66 220 78 Nb 0 4 4 14 0 29 153 47 145 68 Au Nb 0 46 0 42 3 66 0 31 120 90 109 50 Ta V 8 07 0 355 6 04 0 59 318 82 366 21 Ta V 3 14 0 355 4 41 0 46 173 43 174 24 Ta V 8 07 0 355 5 47 0 29 263 16 286 55 Ta V 3 14 0 355 3 85 0 35 133 34 129 49 Figure 4 11 and 4 12 show the plots of the relationship between elastic modulus and layer pair spacing Even though the modulus is plotted against the layer pair spacing it is better to correlate the change of elastic modulus with the amount of elastic strain energy in the ncnl thin film during their deposition process 87 Different amount of strain energy put into the system could result is different amount 130 Texas Tech University H S Tanvir Ahmed December 2010 of twinning or different type of grain boundary structure within the same grain and or layer pair size Prob
61. 576 732 43 45 13 0 014 0 0008 2 76 0 33 739 801 29 24 36 0 01340 0004 2 94 0 17 In a similar fashion scratches are conducted on a Au Ni nanolaminate sample 87 with a grain size of 6 9 nm and a layer pair spacing of 1 8 nm Figure 3 15 shows scratches at 100 m sec This experiment was done using the CETR NA 1 whereas the CETR NA 2 was used for testing the hydroxyapatite coating Figure 3 16 shows the profiles of the scratches at different scratch velocities and Table 3 2 lists scratch parameters at this particular scratch speed Table 3 3 lists the measured values of strain rates and hardness Figure 3 17 shows the log log plot of hardness versus strain rate for 1 5 mN loading 111 98 Texas Tech University H S Tanvir Ahmed December 2010 Figure 3 15 Scratches at 100 m sec on Au Ni nanolaminate surface Table 3 2 Scratch parameters at 100 um sec for the sample shown in Figure 3 15 Nominal Load Actual Load Width No UN N UN w nm 100 534 80 318 60 25 81 200 171 25 459 45 49 52 800 889 46 529 87 58 11 1000 899 95 536 12 53 16 1500 981 16 584 50 91 67 2000 1017 42 606 10 87 40 99 Texas Tech University H S Tanvir Ahmed December 2010 Height nm 27 25 23 21 UE SN ge ri FRE fe pf N sa t pram ee yee L i WA qi rl ps j C dy E 50ms um L a W o Jean 10ms um 1 1 5ms um
62. 6 and Dao et al 19 respectively The plot of Figure 3 18 indicates that the 6 9 nm grain size measured for the Au Ni nanocrystalline nanolaminate is consistent with the trend with the results obtained for nanocrystalline face centered cubic metals as Ni and Cu In addition the predictive equation suggested by Gu et al 26 is also plotted here for simulating the trend The equation given in 26 can be represented by m c In c Va al 3 14 102 Texas Tech University H S Tanvir Ahmed December 2010 where c1 C2 and c3 are constants depending on the shear modulus of rigidity G and burger s vector b Here c1 c2 and c3 are taken to be 0 018 3 0 and 1 65 respectively 66 It must be noted here that the range of strain rates covered by nanoscratch experiments are in general within region II and may not be comparable with tensile test results obtained from the mentioned references 0 12 0 1 Niandits alloys from Gu et al Cu and its alloys from Dao et al O Ni from tensile test Predicted by equation 0 08 Au Ni sample grain size o Au Ni sample layer pair size 0 06 0 04 Strain rate sensitivity exponent m 0 02 0 1 po ii jui 1 oo oe ee ee pa iii n dir rit n tut gt pal 1 fit fas 1 R E 1 E 00 1 E 01 1 E 02 1 E 03 1 E 04 1 E 05 1 E 06 1 E 07 Grain size d nm Figure 3 18 Strain rate sensitivity of the Au Ni sample as a function of
63. 8 144 Phone conversation with I Hermann 13 Mar 2008 145 E mail communication with I Hermann CETR 21 Feb 2008 146 E mail communication with I Hermann CETR 28 Feb 2008 177 Texas Tech University H S Tanvir Ahmed December 2010 APPENDIX IT APPROACH CURVES FOR ELASTIC MODULUS MEASUREMENTS II A Frequency shift curves for Calibration samples Channel 1 Pr35_Ag_200 900Hz_Apr 03063 007 Line 41 filter 3 square dV 2 25 au d Fr 4 63 E4 Hz Fr E 4 Hz 74 76 78 80 62 54 86 66 90 Length 20 7 a u Height 141 695 kHz Figure II 1 Frequency shift plot of Ag 111 178 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Au 25_200 900Hz_Apr 0301 4 033 Line 1 filter 3 square Fr E 4 Hz 33 dV 5 83 a u dF 1 71 ES Hz AD Channel 2 Pr35_Au725_200 900Hz_Apr 03014 033 Line 1 Am pm dv 5 83 a u dAm 1 40 nm Length 38 5 a u Height 307 282 kHz Figure IL 2 Frequency shift plot of Au 111 179 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_FusedQuatrz_200 900Hz_Apr 02963 028 Line 1 filter 3 square Fr E 4 Hz dV 10 72 au d Fr 7 28 E 4 Hz AD dV 10 72 au dAm 399 73 pm 4500 Am 1000 190 200 210 220 230 240 250 260 270 280 290 Length 132 6 a u Height 325 200 kHz Figure II 3 Frequency shift plot of
64. 87 866 kHz Figure IL 48 Frequency shift plot of Ta V Sample 10 225 Texas Tech University H S Tanvir Ahmed December 2010 APPENDIX III PROGRAM AND OUTPUT FOR BOUNDARY INTERFACE AREA CALCULATION OF NANOLAMINATES II A MATLAB program IIL A 1 Grain Boundary Intercept Area Calculation close al clear all r 50 w 1 2 3 4 5 6 1 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 40 50 60 70 80 90 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 1250 dg 15 2 Scircular grain size hg sqrt pi 2 sqrt 3 dg 2 Shexagonal grain size layer_size 4 5 theta 65 3 pi 180 Sface angle see geometry phi 115 13 pi 180 angle on the face see geometry alpha 77 049 pi 180 Sdetermined from geometry very Simportant for measuring height beta 30 pi 180 Shalf angle of equilateral triangle 60 2 30 deg w_crit 2 r cos alpha cos beta vol_sphere 2 3 pi r 3 pi r 3 cos asin w_crit 2 r sin asin w_crit 2 r 2 pi r 3 2 cos 3 asin w_crit 2 r 3 cos asin w_crit 2 r vol_grain sqrt 3 2 hg 2 layer_size 100 layer_size 100 is the step size ror 1 17 55 area i 0 Sarea initialization if w i gt w_crit vol_ind sqrt 3 12 w i 2 w i 2 tan phi 2 cos theta sqrt 3 12 w_crit 2 w_crit 2 tan phi 2 cos theta vol_sphere number_of_grain_c vol_ind vol_sphere vol_grain Sif
65. 900 950 1000 1050 1100 1150 1200 1250 dg 16 7 layer_size 2 6 dAB layer_size 2 Suse half the layer pair thickness theta 65 3 pi 180 Sface angle see geometry phi 115 13 pi 180 Sangle on the face see geometry alpha 77 049 pi 180 Sdetermined from geometry Svery important for measuring height beta 30 pi 180 Shalf angle of euilateral triangle 60 2 30 deg w_crit 2 r cos alpha cos beta for i 1 55 area_c 0 Sconical indentation area initialization area_s 0 Sspherical indentation area initialization if w i gt w_crit checking if the indent goes to conical part he_f 1 2 tan phi 2 w i w_crit hc hc_f cos theta h r r sin alpha Sonly one height for spherical indentation ht_c_f w i 2 tan phi 2 sprojected total height along the face of conical part nc_real hc dAB 228 Texas Tech University H S Tanvir Ahmed December 2010 nc_int floor hc dAB ht i hc h Stotal vertical height sum_c 0 for j l inc_int sum_c sum_c sqrt 3 4 2 tan phi 2 ht_c_f j dAB cos theta 2 end area_c 1 sum_c 1 is for 1 layer in the interface ZRKEKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKK spherical indentation starts here ZRKEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK if floor ht i dAB gt nc_int spherical upper fraction h h dAB dAB nc_real nc_int sum_s pi 2 r h h 2 else sum_s 0 end sum_s 0 n_int floor h dABj for j 1 n_int sum_s sum_s pi 2 r h j dAB h j d
66. AB 2 end area_s 1 sum_s else h r sqrt r 2 w i 2 2 for spherical indent there is only one height ht i h n_int floor h dAB sum 0 for j 1 n_int sum sum pi 2 r h j dAB h j dAB 2 end area_s 1 sum end area_layer i area_ctarea_s end 229 Texas Tech University H S Tanvir Ahmed December 2010 II B Program Output for Au Ni Samples Characteristic dimension h nm 0 1 4 1000 o o 000000200600 60000 0 0500000000 100 Na e o 0 4 10 as Volume GB area e Volume LP area o Depth i 5 L J a 2 eo hd a o 4 0 1 e een e AO J L 2 s e E 0 01 6 a 0 001 1 10 100 1000 Width of indentation nm Figure IIL 1 Program output for Au Ni d 16 0 nm A 0 8 nm 230 Texas Tech University H S Tanvir Ahmed December 2010 Characteristic dimension h nm 0000000000000 OOOO 6000000000000000 Volume GB area Volume LP area 10 Width of indentaiton 100 1000 Figure IIL 2 Program output for Au Ni d 15 2 nm 4 5 nm 231 Texas Tech University H S Tanvir Ahmed December 2010 Characteristic dimension h nm 45 40 35 30 25 20 15 oO i ee On DS RE EE PS or CR 000000000000 000060 Volume GB area Volume LP area
67. Ahmed December 2010 are used to serve as tensile test specimens Because of the deposition condition the test pieces are thinner at the middle while thicker at the ends This as deposition condition is utilized to make the dog bone shaped test pieces from the thin films Tensile testing is conducted at different rates on these specimens to provide the strain rate sensitivity 20 pm 49 68 uml 51 45 um Figure 1 3 Cross section of a dense silver foil measured with an optical microscope Texas Tech University H S Tanvir Ahmed December 2010 Figure 1 4 Detachable serrated grips used for tensile tests 1 3 Experimental methods and Analysis 1 3 1 Tensile test of Ag foils The tensile test specimens are mounted on a TestResources universal testing machine using detachable clamps with serrated grip surfaces Figure 1 4 Rate sensitive testing is done on the specimens by moving the linear actuator of the machine over the displacement of 10 mm while varying the displacement time from 10 sec to 10 sec The strain rate is given by a AH E 1 4 where Al is the displacement of the actuator up to 10 mm is the initial length of the specimen 10 mm and Af is the associated displacement time Thus the associated strain rates will range from 10 sec to 10 sec The data acquisition system logs the normal load from a load sensor as the displacement sensor Linearly Variable Differential Transducer LVDT record
68. F 1 ms um E M 4 0 5ms um L NG 1 ari L F io C y 500 1000 1500 2000 x distance nm Figure 3 16 Scratch profiles with 1 5 mN force at different scratch velocities on the Au Ni sample surface 100 Texas Tech University H S Tanvir Ahmed December 2010 Table 3 3 Hardness values calculated as per strain rates for the Au Ni sample Scratch Velocity Nominal load Actual Load Strain rate Hardness um sec N N H UN UN 1 sec GPa 1000 923 73 36 34 20 1500 977 59 34 34 3 5 0 26 2000 1089 57 30 81 1000 899 95 186 53 100 1500 981 16 171 09 39920 07 2000 1017 42 164 99 800 682 43 491 96 1000 742 87 451 94 ay 1500 774 04 433 74 ere 2000 901 21 372 53 800 615 51 2727 25 1000 663 29 2530 69 1009 1500 740 70 2266 29 R F 2000 771 86 2174 81 1500 646 26 5194 94 Hs 2000 872 78 3846 6 rain 101 Texas Tech University H S Tanvir Ahmed December 2010 y 5 2135x 48 R 0 8699 D Hardness GPa 5 10 100 1000 10000 Strain rate 1 sec Figure 3 17 Strain rate sensitivity plot of Au Ni nanolaminate for 1 5 mN load The strain rate sensitivity value computed from Figure 3 17 yields a value of m equal to 0 0848 111 112 This value is plotted in Figure 3 18 as a function of the grain size along with the rate sensitivity values for nanocrystalline Cu and Ni found in Gu et al 2
69. Figure 4 2 Approach curve on top and corresponding amplitude on bottom are shown for a nanocrystalline Au coating on silicon substrate Once the linear regime is defined the slope of the curve can be determined which can be used to measure the localized elastic modulus The measurement of elastic modulus can be done in two ways using calibration method and using analytical method The following derivation arrives at the final form of the elasticity equation from basic dynamics and Hertz s 127 equation of contact mechanics 114 Texas Tech University H S Tanvir Ahmed December 2010 The radius a of surface of contact between two spheres of radius R and Ro when pressed against each other by a constant force P was first studied by Hertz 127 and is given by 127 3x P K K 4 Magia R R 4 1 where K and K are related to the elastic properties Young s modulus and E and Poisson ration v of the spheres as given by For contact between a sphere R R and a flat surface R the equation 4 1 reduces to 4 2 432 ge ee 4 3 E E E By substituting equation 4 3 into equation 4 2 a e R 4 4 4E 115 Texas Tech University H S Tanvir Ahmed December 2010 a b Figure 4 3 Contact between a sphere and a flat surface on the application of load P For a point at a distance z from the plane of the surface of contact Figure 4 3a that is n
70. Fused Quartz 180 Am Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_FusedSilica_200 900Hz_Apr 2 0291 6 018 Line 1 filter 3 square dV 13 45 a u d Fr 3 86 E 4 Hz Fr E 4 Hz AD Channel 2 Pr35_FusedSilica_200 900Hz_Apr 2 02916 018 Line 1 dv 13 45 au dAm 325 69 pm 2000 1500 1000 500 520 530 san 550 560 570 580 590 600 610 620 Length 105 3 au Height 258 691 kHz Figure IL 4 Frequency shift plot of Fused Silica 181 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 P r35_Ni_200 900Hz_Apr 03429 035 Line 1 filter 3 square dV 5 34 au d Fr 1 06 E5 Hz Fr E 4 Hz 404 30 204 A V aul Channel 2 P r35_Ni_200 900Hz_Apr 03429 035 Line 1 dv 5 34 a u dAm 2 39 nm Am pm 5000 4500 4900 3500 3000 2500 2000 1500 1000 500 o1 25 30 35 4 45 so ss 60 65 70 75 60 Length 59 2 au Height 401 859 kHz Figure II 5 Frequency shift plot of Nanocrystalline Ni 111 182 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_P olycarbonate_200 1200Hz_Apr 02145 015 Line 1 filter 5 square dV 19 47 au d F r 8 85 E3 Hz Fr E3 Hz 504 AD Channel 2 P r35_P olycarbonate_200 1200Hz_Apr 02145 015 Line 1 dV 19 47 au dAm 198 63 pm Am pm 47
71. KR model is reported 130 to be a better estimation of the contact radius which is given by we z P 3y0R 6YTRP 3YTR 4 26 where yis the surface energy term of the sample Assuming a VRZz from equation oP lt 4 5b and solving for z from equation 4 18 yields the sample surface stiffness z Ks ap 2E VR lt 6yeRP Gyr tee 4 27 dz 37rR 67TRP 3YTR The frequency shift is then given by ff E NR NGYERP 6R Af k 4 28 2k k 3yrR J6yrRP GTR This equation can be used to determine the elastic modulus of soft materials and even conceivably liquids with the tapping mode frequency shift in which materials surface energy plays a significant role resulting in the change of contact area from the Hertz model A similar model can be determined 132 from the Derjaguin Muller Toporov DMT equation P z P 2YrR 4 29 a 124 Texas Tech University H S Tanvir Ahmed December 2010 It must be noted here that these equations equation 4 28 and 4 29 are derived based on only the first two terms of the Taylors expression of equation 4 14 For a higher accuracy model more terms need to be included in the derivation 4 4 Results A calibration curve was established for versus E with several known materials including polycarbonate fused silica Au Ni and sapphire 34 40 133 134 135 136 Table 4 1 represents the elastic modulus and cor
72. Radius nm III C 1 Berkovich tip 140 lal kah E 80 l pG E 2 t r 50 nm A 60 r 100 nm r 150 nm X r 200 nm 40 4 x r 250 nm g 4 r 300 nm 5 r 500 nm 20 0 100 200 300 400 500 600 700 800 900 1000 Width of indentation nm Figure IIL 7 Change in depth of indentation as a function of the tip radius of a Berkovich tip 236 Texas Tech University H S Tanvir Ahmed December 2010 III C 2 Conical tip 1200 6 L 1000 a L A os r 50 nm j x F mr 100 nm A x 800 r 150 nm R TOA X r 200 nm 4 x r 250 nm a A x x F r 300 nm a x x 900 r 500 nm a ae a s A p x x i a a e 400 a as z x he s a e a 200 nu a a L x xX o i x x e O mesasa t i 0 200 400 600 800 1000 Width nm Figure IILS8 Change in depth of indentation as a function of the tip radius of a Conical tip with 90 angle 237 Texas Tech University H S Tanvir Ahmed December 2010 III C 3 Cube Corner tip 400 p 350 F 2 L L 300 x e 6 2 x o 6 250 5 4 L e o 6 r 50 nm B e o 6 m r 100 nm ry 200 2 r 150 nm gt 2 e o X r 200 nm a a e o L x r 250 nm 3 a
73. TS ACKNOWLEDGMENTS pesscccisexscincesanicc cosceaesousnedes cobcveascosavacecasseessessovasacsasdesscssessssdancodescaces ii PR FACE sescsescesescsccsesesesveveentcscosssssiedevessesasessecesssussasesescsdossvessenesessscosesutsevesessstevssvsseseseses iv ABSTRACT iisecusaubicadavesossbacnctcccacuss sutiensbasusentcentatsssactusseddsssussosaadentecada oceuacecpsvessdencausececse ix LIST OB TABLES Sidiictescssdesdiessicisectesevanssscsicessutesdecsdessedscebereneseedsedevessdbentecdcceseeesaeessecacesese X LIST OF FIGURES siscssiesscessccscsessesvessencesssdsssuesdeeectasssseguensseccssscdssaentseocascsssssvenssescacscosseees xi CHAPTER 1 TENSILE TESTING OF NANOMATERIALS 660000000000000000000000000000000 00000000000000 0000000000000000 0000 1 Nl ntroductionze ts A aaa a Nga Na ns 1 1 2 Material Sirene pa gag ga wa a a TAPE ANG KAN GE GE Kg a E este dda ting sash nas Rte 3 1 3 Experimental methods and Analysis 8 131 Tensile testo Aa fOUS na RES TS RS cr eden es 8 1 3 2 Intermittent test of Ag foils coca mr de ten n anane 31 1 3 3 Tensile test of electrodeposited nanocrystalline Ni 40 1 3 4 Tensile test of nanocrystalline Au Cu foils an anane nane 47 PAR SUMMMANY PR EE PR ae BAO Oe Ee 50 CHAPTER 2 MICRO SCRATCH TESTING OF POROUS MEMBRANES 66000000000000000000 00000000000000 00000 0000 53 Dal ANTE LEC HOME 8 5 1 e Ga Bg a wah Deg veer eae eed WPT a a Rene a aa a a aa 53 De Background RE RE an aaa 55 2 3 Experim
74. Tanvir Ahmed December 2010 Load N 13 14 15 16 17 18 19 20 Time sec Figure 1 30 Load time plot for a Au Cu sample WD 8 4mm 2 Okv x180 250um Figure 1 31 SEM image is used on failed cross section of a Au Cu sample for measuring the width 48 Texas Tech University H S Tanvir Ahmed December 2010 500 450 400 y 810 14x R 0 8514 350 300 Tensile strength MPa 1 00 L 1 L L 1 L 1 if 1 1 1 0 0001 0 0010 0 0100 Strain rate 1 sec Figure 1 32 Strain rate sensitivity plot for the Au Cu samples Figure 1 32 shows the log log plot of tensile strength versus strain rate The data points are fitted with a power law relationship to determine the strain rate sensitivity exponent The grain size of the samples used in this experiment is calculated 27 28 29 to be 10 33 nm The strain rate sensitivity exponent value 1 e m 0 1393 from this experiment is in a very well agreement with the micro scratch results obtained by Nyakiti and Jankowski 66 and is shown in Figure 1 33 as a function of log scale grain size d Equation 1 33 has been used to predict the behavior of these nanocrystalline Au Cu samples The constants c1 c2 and c3 are taken to be 0 080 3 0 and 1 65 respectively 66 49 Texas Tech University H S Tanvir Ahmed December 2010 0 25 Results from Nyakiti and Jankowski L This experiment 0 2
75. Use of Dynamic Test Methods to Reveal Mechanical Properties of Nanomaterials by H S Tanvir Ahmed B S M E M S M E A Dissertation In MECHANICAL ENGINEERING Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Approved Alan F Jankowski Ph D Chairperson of the Committee Jharna Chaudhuri Ph D Alexander Idesman Ph D Michelle Pantoya Ph D Shameem Siddiqui Ph D Fred Hartmeister Dean of the Graduate School December 2010 Copyright 2010 H S Tanvir Ahmed Dedicated to my parents my family and friends Texas Tech University H S Tanvir Ahmed December 2010 ACKNOWLEDGMENTS Then which of the favors of your Lord will you deny Al Quran 55 Praise be to the most merciful the most gracious who created heavens and earth and everything in between It is the almighty God who taught human beings how to read and write Without His will kindness and mercy the completion of this work would have never been possible I would like to express my sincere gratitude and appreciation to my thesis advisor Dr Alan F Jankowski not only for his keen supervision and valuable suggestions but also for teaching me how to work on solving the riddles of everyday life I enjoyed talking with him not only about research but also exchanging views about socio cultural events politics and history of human evolution His continuous suppo
76. _200 900Hz_Apr 03129 036 Line 1 dv 7 74 a u dAm 2 12 nm Am pm 20 30 40 50 60 70 50 Length 75 0 au Height 315 272 kHz 7 Figure IL 22 Frequency shift plot of Au Ni d 16 7 nm A 2 6 nm Sample 13 199 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 14_200 900Hz_Apr 03901 018 Line 1 filter 3 square dV 6 40 a u d Fr 1 68 E5 Hz Fr 7E 4 Hz 45 Channel 2 Pr35_Sample 14_200 900Hz_Apr 03901 018 Line 1 dV 6 40 a u dAm 1 63 nm Am pm Length 54 8 a u Height 456 876 kHz Figure II 23 Frequency shift plot of Au Ni A 8 9 nm Sample 14 200 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 15_200 900Hz_Apr 03956 036 Line 1 filter 3 square dV 22 42 a u d Fr 2 84 E5 Hz Fr E4 Hz AD Vi au Channel 2 Pr35_Sample 15_200 900Hz_Apr 03956 036 Line 1 dV 22 42 a u dAm 2 19 nm Am pm 20 30 4 50 60 70 80 90 100 110 120 130 149 Length 128 8 a u Height 641 332 kHz gt Z Figure IL 24 Frequency shift plot of Au Ni A 2 1 nm Sample 15 201 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 16_200 900Hz_Apr 03979 022 Line 1 filter 3 square dv 17 80 au d Fr 1 57 E 5 Hz Fr E 4 Hz AD Channel 2 Pr35_Sample 16_200 900Hz_Apr 03979 022 Line 1 dv
77. a 0 7 um tip 60 Illustrating the measurement of the scratch width for porous materials 63 A comparative study of the width of scratches at different velocities on 0 45 MACON AO RS mata antenne A Mist 64 Rate sensitivity plot of 0 2 micron pore size membrane 66 Rate sensitivity plot of 0 45 micron pore size membrane 67 Rate sensitivity plot of 0 8 micron pore size membrane 68 Rate sensitivity plot of 3 0 micron pore size membrane 69 Rate sensitivity plot of fully dense silver foil 0 eee eeeeeseeeseeesneeeeeeeeneeeees 70 Schematic of the Rockwell tip used for micro scratch experiment 00 71 xii Texas Tech University H S Tanvir Ahmed December 2010 2 13 Comparison between hardness values using projected indentation area and actual indentation AT en ester aaa ba aa a a n 72 2 14 Measurement of a scratch at 5mm sec on the nc Ni with an optical HUET OS COG Rom ne Rte 74 2 15 Comparison of tensile hardness with micro scratch hardness and associated strain rate sensitivity of nanocrystalline Ni 75 3 1 a Side view and b top view of the schematics of indentation with a pyramidal Berkovich tip on a nanocrystalline nanolaminate the columnar grain size d is the diameter of the circular equivalent of the hexagonal grain and A4 is the layer pair size 79 3 2 Densely packed hexagonal grains are incrementally placed according to the numbers to find out the number of interf
78. ably that is why materials with same layer structure show different elastic properties From these Figures 4 11 and 4 12 it is apparent that there exists a general trend that with decreasing layer pair spacing the elastic modulus decreases In comparison for in plane elastic moduli measurments 100 an increase is found as the layer pair spacing decreases The decrease in elastic modulus correlates with an increase in the interface spacing for Au Ni when tension is present 116 This is seen for inter planer spacings normal to the film surface 114 115 for layer pairs between 1 to 4 nm Thus the film modulus normal to its surface should decrease between 1 to 3 nm 200 Average E 111 of Au Ni oa oO T Actual Elastic modulus E GPa e Oo oa T 0 1 2 3 4 5 6 7 8 9 10 Layer Pair 4 nm Figure 4 11 Elastic modulus of Au Ni nanolaminates 131 Texas Tech University H S Tanvir Ahmed December 2010 IN wo oa oO T wo Q T N O1 oO T Average E 110 of Ta V Actual Elastic Modulus E GPa N ol Oo oO Oo T oa T 0 1 2 3 4 5 6 7 8 9 Layer Pair nm Figure 4 12 Elastic modulus of Ta V nanolaminates 4 5 Discussion Nanolaminate materials are reported 87 137 to have super lattice effects where layers have an alternate distribution of residual tension and compression The materials tested he
79. aces eeeeeereeeeerereeeeee 80 3 3 Relationship of number of coincident boundaries with number of hexagonal grains in a densely packed CONITON 22 8 Men cous 81 3 4 Plot of coincident boundary per cell versus number of cells shows a plateau value around 2 8 boundaries per cell 82 3 5 The relationship between columnar grain size dg and hexagonal grain size hg SCA the model sasa aa aa AN a pagan nn Stan anah 83 3 6 Geometry left and SEM image right of a diamond Berkovich tip The length of the marker is 500 um on the SEM image ee eeeeeeeeee 84 3 7 Exaggerated model geometry the hemisphere is not tangent to the sidelines TP THIS PICHING 55 ass ag A a bah a ENG aa A en Sao eA 84 3 8 Characteristic dimension for grain boundary and layer pair intercept area as computed for a 16 nm grain size d and 0 8 nm layer pair size laminate Sn EN GG Da a wa Rte Sr A gah 86 3 9 Characteristic dimension for grain boundary and layer pair intercept area as computed for a 15 2 nm grain size d and 4 5 nm layer pair size larninat s Ste ne sas nn Se ent en nn Ce a 87 3 10 Depth of indentation as a function of width for different tip radius for a Berkovich type tip ix sean men dan ua di ne 88 3 11 A typical probe cantilever arrangement is shown on left figure while a Berkovich tip is shown on the right 89 3 12 Scratches on Hydroxyapatite 4991012 Ti at 50 nm sec with 1 mN force 95 3 13 Scratch profiles
80. ach sample sek nn Rd Pa ga ant aa 24 Strain rate sensitivity as a function Of grain Size 25 Strain rate sensitivity as a function of filament size 299 Porosity effect in strain rate Sensitivity 30 Typical stress strain curve 20 point average of the original curve for 0 2 micron membrane at 10 sec strain rate and positions of terr ONS sasa saa lens enter nn cond E Testes ed nie 33 Interrupted tensile test of 0 2 micron nominal pore size membrane at 10 sec strain rate to show the change in elastic modulus with PFOSTESSION Ol LOA RSA AR RE AS a A RES 34 The elastic modulus of porous silver membranes as measured through incremented tensile loading are plotted as a function of the applied engineering Stress sapaa E immenses AN E aa aa Ng tar 35 Change in elastic modulus of dense silver with progression of load at a strain rate of 10 PET seconde asang na aaa a a i 37 xi 1 22 1 23 1 24 1 25 1 26 1 27 1 28 1 29 1 30 1 31 1 32 1 33 2 1 22 2 9 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 Texas Tech University H S Tanvir Ahmed December 2010 Elastic modulus from interruted test of dense silver as a function of applied engineering stress over different strain rates 38 Variation of elastic modulus with porosity for silver membranes as measured using tensile test initial onset of yieldin
81. amp cos n seca tan 1 4 where N is the normal actual load H is the hardness r is the radius of the tip typically about 100 to 500 nm for Berkovich tips s is the shear stress The is the angle related to the tip radius r and scratch width w such as a sin 1 5 2r The second term in the equation 1 4 is usually very small By using the expression for a the equation for hardness can be simplified to 1 6 Since 8 7 equals the area under the leading half of the surface area for a spherical indenter tip that is on contact with the surface Note that equation 1 6 and equation 1 2 are similar However the major assumption in this analysis is that the indenter tip does not pass beyond the spherical regime of 165 Texas Tech University H S Tanvir Ahmed December 2010 the tip For shallow and narrow scratches this is true However for sharp tips this assumption becomes questionable and may not be the case Moreover the hemispherical part on the top of the tip is not always perfectly hemispherical So it is recommended to keep w lt 2r 66 I C Elastic Modulus Measurement I C 1 Producing approach curves In approach curve experiments the UMT software does not need be open All the necessary operations and data acquisitions can be done from the Nano Analyzer software For an elastic modulus measurement the surface of the sample needs to be scanned first for the presence of any
82. anned using Probe 41m The height histogram command will return a dx value at top right corner of the plot that will pop up A height histogram plot for TGZI is shown in Figure 1 4 From Device Calibration gt ADC z feedback this dx value needs to be put into the measured z step field while the actual value TGZ1 20 5 1 nm TGZ2 104 542 nm TGZ3 510 4 nm needs to be put into the reference z step field For example if the TGZ2 grid is being used and the height histogram on the 171 Texas Tech University H S Tanvir Ahmed December 2010 processed z image returns a dx value of 101 2 nm then on the reference z step field put 104 5 the actual height difference for using TGZ2 grid and on the measured z step field put 101 2 the measured value for height difference with the yet to be calibrated probe Figure I 3 AFM grid TGZ1 scanned with Probe 41m N Histogram dX 21 62 nm dY 0 16 Length 33 98 nm Height 3 3 Figure I 4 Height histogram on the z image of TGZ1 after processing 1 D 6 Follow the same procedure stated on I D 4 and I D 5 with the ZOpt image In the Device gt Calibration gt ADC ZOpt optic sensor put the measured value of dx from height histogram in the measured ZOpt step and the actual value which is the same as the z height of the grids as stated above in the reference ZOpt step field 172 Texas Tech University H S Tanvir Ahmed Decemb
83. anoscratch experiments Corrections for interfacial shear stress and elastic recovery Journal of Materials Research 18 2003 2150 2162 104 C Feldman F Ordway J Bernstein Distinguishing thin film and substrate contributions in microindentation hardness measurements Journal of Vacuum Science and Technology A 8 1990 117 122 105 V Blank M Popov N Lvova K Gogolinsky V Reshetov Nano sclerometry measurements of superhard materials and diamond hardness using scanning force microscope with the ultrahard fullerite C o tip Journal of Materials Research 12 1997 3109 3114 106 N Gitis M Vinogradov I Hermann S Kuiry Comprehensive Mechanical and Tribological Characterization of Ultra Thin Films Mater Res Soc Symp Proc Vol 1049 2008 107 A Gouldstone N Chollacoop M Dao J Li A M Minor Y L Shen Indentation across size scales and disciplines Recent developments in experimentation and modeling Acta Materialia 55 2007 4015 4039 146 Texas Tech University H S Tanvir Ahmed December 2010 108 J Mencik M V Swain Errors associated with depth sensing microindentation tests Journal of Materials Research 10 1995 1491 1501 109 T G Nieh A F Jankowski J Koike Processing and characterization of hydroxyapatite coatings on titanium produced by magnetron sputtering Journal of Materials Research 16 2001 3238 3245 110 H S T Ahmed A F Jankowski
84. as Tech University H S Tanvir Ahmed December 2010 sensitivity exponent values are close to each other the trend line for dense silver is positioned above in Figure 1 14 compared to that of the h line of the porous silver which means the dense silver has higher strength compared to porous silver at a particular strain rate This means that the particular dense silver foils used in these experiments have smaller grain size compared to the rest of the porous membranes This difference in the strength plot may originate from work hardening of the samples as well perhaps during their production as films So the rate sensitivity exponent m may follow the grain size trend higher m with decreasing hg but the yield strength may not 215 X0 2 micron A 0 45 micron 195 F 0 8 micron 3 0 micron y 201 1x 5 R 0 8983 175 Qhg 2 47 micron O Fully dense Ag 155 a a g SE y 162 920 R 0 8636 S f 115 z 2 F gt 95 y 111 81x 7 R 0 9977 Me y 97 635022 R 0 5161 75 gg Y57980 RE 0 9989 D f 5 d ka AE a a 6 y 57 012x 8 R 0 6612 35 L bi i ee ed ont Lu E fi pui fe ies ef ep i fe et 1 0E 05 1 0E 04 1 0E 03 1 0E 02 1 0E 01 1 0E 00 Strain rate 1 sec Figure 1 14 The log log plot of yield strength versus strain rate The values are fit with a power law relationship to produce the strain rate exponen
85. ased on the radius of the hemisphere the overall size i e volume of the indenter can either increase or decrease For example with a sharper tip radius the overall volume will be less compared to a dull tip larger tip radius indenter As the schematic of Figure 3 1 suggests the amount of intercept area for both grain boundary and layer pair would increase as the indenter goes deeper into the system Figure 3 5 shows the relationship between actual grain size ds and the structural dimension A of the hexagonal grain that is used in the simulation Figure 3 6 shows the geometry and SEM image of a Berkovich tip Figure 3 7 shows an exaggerated geometry that is used for modeling gt Figure 3 5 The relationship between columnar grain size d and hexagonal grain size h used in the model 83 Texas Tech University H S Tanvir Ahmed December 2010 WD 5 5mm 2 0kV x80 500um Figure 3 6 Geometry left and SEM image right of a diamond Berkovich tip The length of the marker is 500 um on the SEM image Figure 3 7 Exaggerated model geometry the hemisphere is not tangent to the sidelines in this picture With simple geometrical calculation from Figure 3 5 it can be shown that i gt h d 3 1 z 2 3 ed The expression from equation 3 1 is used in the MATLAB model to calculate the intercept area with d being a structural input parameter for a particular nenl Figure 3 8 shows a plot of grain boundar
86. at Zero porosity may be representative of shortest structural dimension 1 e the in filament grain size which is the average of the grain size values listed in Table 1 1 and is calculated to be 2 47 0 19 um The grain size information of the annealed silver wire is not available and hence the strength of 125 MPa may not be an appropriate value to do the comparison with Moreover the associated purity of silver plays a big role on its strength 54 For another comparison the fully dense Ag samples are tested in the same strain rate range i e 10 to 10 per second and is plotted in Figure 1 11 at P 0 representing the fully dense state In this case the yield strength at fully dense condition is higher compared to the extrapolated values The fully dense samples are assumed to be cold rolled during their production as 50 um foils and hence could have higher strength compared to annealed samples Since the yield strength of samples depends on the grain size the information of that structural feature on the fully dense samples is yet to be investigated which would enable their characterization in a better way Nevertheless the overall trend of the increase of strength estimation at P 0 seems reasonably satisfactory From Figure 1 11 a zero intercept yield strength is estimated at an average porosity of 81 8 1 8 which appears to be invariant with the change in strain rate The general trend of the yield strength appears to decrease in a
87. ates with the findings by Dao et al 19 for many fully dense metals like nickel and copper For porous materials it is proposed 1 that the filament size i e the width of the filament can be considered as a measure of characteristic length instead The reason proposed is that the filament size is the medium for deformation and porosity is the free space With similar grain sizes different membranes may possess different porosity with different filament sizes and hence should have different plasticity characteristics Whereas the grain size based deformation will only be able to explain the overall general trend the filament size based deformation should allow for more detailed characterization of the behavior To evaluate this the strain rate sensitivity data of the 28 Texas Tech University H S Tanvir Ahmed December 2010 membranes as a function of the filament size are plotted in Figure 1 16 Furthermore the final form of equation 1 28c is used with filament size hy as the variable to simulate a trend line for the m values 1 m c m c h c 1 29 The constants c6 c7 and cg are taken to be 0 03 8 4 and 2 1 respectively The trend line is plotted as a dashed dot line on Figure 1 16 It becomes very apparent from this figure that the filament size based trend line better predicts the rate sensitivity behavior of the membranes Based on this trend line it is also apparent that the rate sensitivity value rises mor
88. ave the cantilever bending stiffness ko tip radius R and frequency of natural oscillation fo which are usually only approximately known To have an estimate for these values the analytic curve was plotted with the calibration curve and was tried to match up the slope of the calibration curve see Figure 4 8 The significant difference between the experimental and 133 Texas Tech University H S Tanvir Ahmed December 2010 analytic equation 4 21 is attributable to the inherent error of the Taylor series expansion If the ke R and fo values can be determined with significant accuracy it will probably give better results if the equation is used with more terms from the expansion as shown with equation 4 24 Another significant source of error can generate from the estimation of Poisson ratio As seen in Figure 4 10 higher Poisson ratios have bigger impact on estimation of the actual modulus of the sample For determining the exact Poisson ratio the same sample can be tested with for elastic modulus with frequency shift technique both in plane and in cross section The frequency slopes of these results need to be numerically solved for Poisson ratio and has to be validated using equation G 2 1 v 4 31 Even though there exists a general trend for the elastic modulus with layer pair spacing of the nanolaminates the total crystal energy of the synthesized laminated structure has 87 117 a higher correlation wi
89. brane It is noticeable that no significant accuracies are achieved in the strain rate sensitivity by using actual area under the tip The slope of the power law fit remains fairly constant for both data sets 71 Texas Tech University H S Tanvir Ahmed December 2010 10000 r Using projected area A Using actual area y 1003 8x2 1516 R 0 8804 La A g ii y 670 05x R 0 8755 1000 L P Oo I 100 p E p 4 1 0E 01 1 0E 02 1 0E 03 Strain rate 1 sec Figure 2 13 Comparison between hardness values using projected indentation area and actual indentation area And the changes in the slope values are well within the error limits as calculated from the associated correlation coefficients However there are significant difference in the rate sensitivity values as found from tensile test and scratch test Figure 2 7 2 11 At strain rates higher than certain critical value there is a discretely observable upturn in the yield stress dependence on strain rate This change in strain rate sensitivity at high strain rates is seen for all porosity membranes Gu et al showed that the strain rate sensitivity value found using different test techniques may vary significantly 26 However he used nanoindentation and tensile test to compare his results and for nanoindentation experiments a significant source of error may originate from the 72 Texas Tech University H S
90. by the model equation 1 33 The strain rate sensitivity of these nanocrystalline nickel samples is found to be higher than the conventional coarse grained samples 43 Texas Tech University H S Tanvir Ahmed December 2010 Figure 1 25 A typical thickness of the nanocrystalline nickel as viewed under the optical microscope at 600X magnification 1400 1200 Engineering Stress MPa 200 1000 800 600 400 7 79E 02 sec 9 20E 03 sec 8 28E 04 sec 3 37E 05 sec 0 01 0 015 0 02 0 025 0 03 0 035 0 04 0 045 0 05 Engineering Strain Figure 1 26 Engineering Stress strain curves of NC nickel at different strain rates 44 Texas Tech University H S Tanvir Ahmed December 2010 10000 F y 1116 8x R 0 7466 a 1000 D TD gt 100 aus Is Ins Ine 1 00E 05 1 00E 04 1 00E 03 1 00E 02 1 00E 01 1 00E 00 Strain rate Figure 1 27 Power law fit of the stress versus strain rate to provide the strain rate sensitivity of nanocrystalline nickel 45 Texas Tech University H S Tanvir Ahmed December 2010 y 0 0177x 20 73 R 0 7708 In Strain rate 40 aor 300 400 500 600 700 800 900 1000 1100 1200 1300 Yield stress MPa Figure 1 28 Activation volume is calculated from the slope of linear fit of In strain rate versus yield stress 46 Texas Tech U
91. cause of the associated high surface roughness For measuring the width using the contact profilometer the tilt of the scan is adjusted first using wide left and right markers to sample a considerable segment of the background as shown in Figure 2 4 using red and green marker colors Then a horizontal line is drawn at the average step height of the membrane accompanied by two other horizontal lines which define at least 90 confidence level of covering the roughness Figure 2 5 illustrates the methodology The width of the scratch is measured at these three horizontal lines and an average of those widths is taken to be representative of the particular scratch 1 e w w w wee 2 3 2 1 2 1 The scratch hardness H is computed by dividing the scratch load by the projection of half of the area of the tip leading in the direction of the scratch The empirical expression is given by 61 Texas Tech University H S Tanvir Ahmed December 2010 H c 2 2 where H is the hardness F is the scratch load and w is the associated width of the scratch The constant c is a geometric function related to the indenter tip shape Assuming that the scratch does not go beyond the initial hemispherical region of the tip c equals 8 7 for the projection of the leading half area of the indenter The deformation path of the scratch is represented by the measured scratch width w And usually the depth of scratch is much less compar
92. ch Hardness transition Micro Scratch Hardness region Il y 574 46x 8 R 0 9825 y 977 23x R 0 8405 1000 4 A y 243 21x R 0 9949 100 i isali GENE isana oa aiii oa anasino print iaaa 1 0E 05 1 0E 04 1 0E 03 1 0E 02 1 0E 01 1 0E 00 1 0E 01 1 0E 02 1 0E 03 1 0E 04 Strain rate 1 sec Figure 2 9 Rate sensitivity plot of 0 8 micron pore size membrane 68 Texas Tech University H S Tanvir Ahmed December 2010 10000 r Tensile Hardness region A Micro Scratch Hardness transition E Micro Scratch Hardness region Il y 231 81x R 0 9264 Q 1000 oO b P 0 0418 R y 469 24x R ui rl y 156 68x 8 R 0 6612 100 1 piri po a iit po iit 1 t ot tint po TEH po bit 1 Loia to g tyit 1 E 05 1 E 04 1 E 03 1 E 02 1 E 01 1 E 00 1 E 01 1 E 02 1 E 03 Strain rate 1 sec Figure 2 10 Rate sensitivity plot of 3 0 micron pore size membrane 69 Texas Tech University H S Tanvir Ahmed December 2010 10000 p Tensile Hardness region A Micro Scratch Hardness region II O Scratch on cross section 1000 Hardness MPa phe y 445 2x 0848 e a R 0 8897 y 603 3x gt R 0 8983 100 1 0E 05 1 0E 02 1 0E 01 1 0E 00 1 0E 01 1 0E 02 1 0E 03 Strain rate 1 sec 1 0E 04 1 0E 03 Figure 2 11 Rate sensitivity plot of fully dense sil
93. comparable Similar trend lines were reported by Harding 72 in a study on commercial purity aluminum i e the higher strain rate exponents 65 Texas Tech University H S Tanvir Ahmed December 2010 are alike Table 2 1 lists the strain rate sensitivity exponents obtained for different regimes of all the specimens 10000 p Tensile Hardness region A Micro Scratch Hardness transition E Micro Scratch Hardness region Il y 1003 8x 3 R 0 8804 y 1488402886 R 0 8357 a T HF a 1000 L 2 G x y 335 54x0 18 R 0 9971 1 0E 05 1 0E 04 1 0E 03 1 0E 02 1 0E 01 1 0E 00 1 0E 01 1 0E 02 1 0E 03 1 0E 04 Strain rate 1 sec Figure 2 7 Rate sensitivity plot of 0 2 micron pore size membrane 66 Texas Tech University H S Tanvir Ahmed December 2010 10000 p Tensile Hardness region A Micro Scratch Hardness transition Micro Scratch Hardness region Il 1000 Hardness MPa 100 y 810 2x 9 R 0 7882 y 1057 2x0 0927 R2 ae att y 299 43x R 0 5161 p 1 0E 05 1 0E 04 1 0E 03 1 0E 02 1 0E 01 1 0E 00 1 0E 01 1 0E 02 1 0E 03 1 0E 04 Strain rate 1 sec Figure 2 8 Rate sensitivity plot of 0 45 micron pore size membrane 67 Texas Tech University H S Tanvir Ahmed December 2010 Hardness MPa 10000 Tensile Hardness region A Micro Scrat
94. cratch line information From this new window position the left marker at the beginning of the scratch left click and position the right marker at the end of the scratch right click The width of the scratch will be shown as dx value in nanometers on the top right corner The setting is set up to provide 7 scratch widths on a single window If necessary particular scratch 161 Texas Tech University H S Tanvir Ahmed December 2010 sections can be omitted from measurement Click on Graph Manager GM from the menu bar and particular scratches can be de selected from the new window with left mouse click This operation is particularly necessary when all the 7 sections of the same scratch do not provide meaningful data LB 1L r After the number of sections and their respective widths are defined open the Hardness Measurement window from Measure on the menu bar and create a new sample with a name Then from the scratch width window click Apply from the bottom right corner This will transfer the width information from the Scratch Measurement window to the Hardness Measurement window in a tabulated form Please refer to section 4 8 on page 70 of the NA 2 manual L B 2 Scratch Hardness Analysis Hardness as a function of the scratch width can be measured using both the calibration method and the direct method LB 2 a In calibration method several reference materials with known hardness values ar
95. ctro deposition process and are available in fully dense condition Many researchers 20 21 22 23 24 25 are studying for the room temperature strain rate sensitivity of fine grained submicron Ni because of its high strain rate sensitivity exponent m and its excellent prospect in terms of functionality in the MEMS NEMS area 26 In addition the rate sensitivity behavior of nanocrystalline gold copper Au Cu is being investigated here The free standing Au Cu foils are obtained from pulsed electro deposition process 27 28 29 and are available in fully dense condition Texas Tech University H S Tanvir Ahmed December 2010 Micron thick film of Au Cu alloy is considered to be an attractive option for use as a high pressure vessel 30 for laser fusion experiments where high strain rates occur with a low rise time As such the strain rate sensitivity of these alloys is important to be examined Previously tensile testing 31 was conducted on Au Cu alloys but the rate sensitivity behavior is yet to be investigated 1 2 Materials Porous silver membranes of 25 mm diameter of varying nominal pore sizes i e 0 22 um 0 45 um 0 8 um and 3 0 um are procured from General Electric Osmonics The purity of the silver membranes is stated to be 99 97 32 The average thickness of the foils ranges from 57 to 79 um as measured from a stack of ten foils with a micrometer Average cross section of the membranes is measured using a microm
96. d using a probe with a vibrating cantilever This technique is fairly new and is widely known as the tapping mode frequency shift Yet the method is based on Hertzian contact mechanics developed over a century ago This technique measures the modulus in the normal to plane direction of the thin films Texas Tech University H S Tanvir Ahmed December 2010 The first three chapters are to show that scratch test can measure the hardness in a wide range of strain rates and can be correlated with the more common tensile test Of course scratch test is less prone to brittle fracture and stress concentration because of its shear type of deformation With scratch technique it is possible to measure hardness of a specific area for example the hardness of either the fiber or the matrix or both in a fiber matrix composite Tensile micro and nano scratch can be used in conjunction to describe mechanical behavior of a material for a significant loading rate range The fourth chapter is to provide the details of the underlying formulations of the tapping mode technique which essentially has the ability to measure elastic anisotropy of the material With the increase of use of nanomaterials foreseen for this century the author believes that this research will enable to correctly characterize the mechanical properties of such materials in a wider range of applications vi Texas Tech University H S Tanvir Ahmed December 2010 TABLE OF CONTEN
97. d strength come out to be lower than that predicted by the linear fit The experimental values of yield strength of fully dense foils are not presented here and will be ignored in further plots because there is an apparent distinction of grain sizes between the fully dense and porous samples In Figure 1 13 on the other hand the cosine term of equation 1 15 is neglected In fact for pure tension the terms in the MacCauley brackets of equation 1 15 become zero and hence the cosine term disappears 45 In the resulting equation equation 1 16 x is assumed to be 4 5 with the critical porosity at 80 and the trend lines are fitted to the existing experimental data Even though the overall fit for the experimental data seems to be very good the prediction for intercept values at P 0 are lower with these trend lines compared to those with linear fit Figure 1 11 or with equation 1 15 Figure 1 12 21 Texas Tech University H S Tanvir Ahmed December 2010 140 0 1000 sec 120 0 0100 sec jon cape ce 0 0010 sec ii 0 0001 sec 100 FT gt 6 80 5 o L D 60 5 L S gt L 40 20 0 L 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 Porosity Figure 1 12 Strength as a function of porosity equation 1 15 Strain rate sensitivity is the ability of the material to uniformly plastically deform under load without the localized concentration of st
98. dium Physical Review Vol 119 1960 1532 1535 134 F H Featherston and J R Neighbours Elastic constants of Tantalum Tungsten and Molybdenum Physical Review Vol 130 No 4 1963 1324 1333 135 B T Bernstain Elastic constants of synthetic sapphire at 27 C Journal of Applied Physics Vol 34 No 1 1963 169 172 136 W A Brantley Calculated elastic constants for stress problems associated with semiconductor devices J Applied Physics Vol 44 No 1 1973 534 535 137 A F Jankowski The strain wave approach to modulus enhancement and stability of metallic multilayers Journal of Physics and Chemistry of Solids Vol 50 1989 641 649 138 J Drelich Adhesion forces measured between particles and substrates with nano roughness Minerals and Metallurgical Processing Vol 23 No 4 2006 226 232 139 M M McCann Nanoindentation of Gold single crystals PhD Thesis Virginia Polytechnic Institute and State University 2004 140 L E Goodman Contact stress analysis of normally loaded rough spheres Journal of Applied Mechanics 1962 515 522 150 Texas Tech University H S Tanvir Ahmed December 2010 APPENDIX I EMAIL WITH DR ILJA HERMANN HOW TO SETUP THE NANOANALYZER The aim of this section is to target the user of the NanoAnalyzer tool and hence information that relates to the scratch hardness measurement and tapping mode modulus measurement with
99. dness of the ncnl s are revealed 3 2 Experimental Approach Nanocrystalline nanolaminates are described by to primary structural features which are the characteristic layer pair spacing and the grain size The layer pair spacing is also known as the composition wavelength for the alternating sequence of the laminas A schematic for a typical nanocrystalline nanolaminate structure is shown in Figure 3 1 a The two types of interfaces that originate from such structuring are from the grain boundaries and from the layering of the laminates Figure 3 1 The grain boundary interfaces impede dislocation motions for strengthening the solid and possibly the interfaces formed between the layers do the same During the hardness measurements using nanoscale probing techniques it is postulated that the mechanical 78 Texas Tech University H S Tanvir Ahmed December 2010 response of the sample comes from both these interfaces The contribution from these interfaces can vary significantly depending on the size of the indentation That is at a certain depth the grain boundary effect may contribute more or less than the layering effect Thus it is important to quantify the contribution from both these two effects on the measurement From this quantification a particular depth or width of indentation Figure 3 1 can be chosen to obtain responses from both layer pair and grain boundary interfaces a b Figure 3 1 a Side view and
100. e and tungsten Those values from the standards are plotted as a function of the corresponding modulus values which can then be fitted with a power law relationship as shown in Figure 4 7 122 Texas Tech University H S Tanvir Ahmed December 2010 Sapphire Nickel WE Fused Silica E Figure 4 7 General trend of amp to elastic modulus The greater the number of calibration materials the better the trend line fit will be and the better the accurate calculation of the modulus of unknown sample will be Once the trend line in Figure 4 7 is fully established the modulus of unknown sample is calculated using the power law fit a a E 4 25 where a is a constant From equation 4 22 it is clearly observed that this is a quadratic equation of the reduced modulus EF and hence a power law fit of versus E would yield a value of 0 5 for the exponent n for the ideal case Equation 4 25 is derived from equation 4 22 as the fo k and R values remain same for measurements with the same probe for the analytic derivation The Hertz equation equation 4 4 is reported 129 130 131 to hold true for large loads and sometimes overestimates the elastic modulus of the sample for low loads because the effect of surface energy at such small loads is neglected assuming no contact surface at zero load In the small load regime Johnson Kendall Roberts 123 Texas Tech University H S Tanvir Ahmed December 2010 J
101. e calculated as follows c11 123 99 GPa c12 93 67 GPa and c44 46 12 GPa 5 t ___ 9 923058 GPa 1 6 ci Co Mey 2Cn s 2 0 009923 GPA 1 7 Ci T Ci On 2Cn 1 1 su 0 02168 GPa 1 8 C44 With the stiffness constants the directional surface elastic modulus E for the cubic system is given as 40 1 TE Ha sa mg SuN m mn P 1 9 where m and n are the direction cosines For 100 110 and 111 directions the direction cosines are 1 0 0 0 and respectively Thus the F F F F i surface moduli E 100 E 110 and E 111 are calculated to be 43 37 GPa 83 42 GPa and 120 51 GPa respectively The Ag samples used in this experiment do not have any 11 Texas Tech University H S Tanvir Ahmed December 2010 specific orientation of grains and are polycrystalline in nature So the elastic modulus of these foils does not necessarily have any preferential direction and is obtained by experiment The multiple monotonic tensile tests conducted over a strain rate range of 10 sec to 10 l sec yield an average Young s modulus E of dense silver to be around 36 GPa The shear modulus G and bulk modulus K are calculated here for reference using the following equations l 15 16 GPa 1 10 205 T Sn K EC 103 87 GPa 1 11 3 3G E 400 10 sec 107 sec amp 10 sec 10 sec Engineering Stress o MPa 0 0 005 0 01 0 015 0 02 0 025
102. e ceramic cantilever A general rule to follow is not to 160 Texas Tech University H S Tanvir Ahmed December 2010 decrease the set point by more than 2 as based on current setting For highly inclined surfaces the z limit of initial surface approach may need to be decreased from the default value of 50 145 since decreasing the value determines the z level at which the surface is found but not less than 30 from Device gt Settings gt Find Surface gt Critical Z level In the event of imaging distortion due to some surface artifacts a built in snipping tool or scissor tool is available to cut the black image from the rest of the shiny yellow image and then processing the black image with auto pallet 146 Also it is recommended to scan at the very beginning of the scratches and to scan only a small area associated with the scratch A high resolution large area scan will take hours as well as introduce thermal drift However it is advisable to choose an area that will cover about 5 to 10 times the width of the scratch on both sides I B 1 q Once the scan is complete process the z image line tilt step correction etc Then click on the Scratch Measurement tool from the menu bar of the NA viewer This will show the scratch lines on the z image Left click on the image and dragging will produce a box around the scratch Please refer to the images on page 74 of the NA 2 manual A new window will also appear with the s
103. e rapidly as filament size gets smaller as compared to the grain size based trend line 0 14 0 12 L O Ag filament size Ag m hg eq Ag m hf eq 2 2 o 2 a Strain rate sensitivity m o K 0 02 0 1 1 10 100 Filament Size h um Figure 1 16 Strain rate sensitivity as a function of filament size 29 Texas Tech University H S Tanvir Ahmed December 2010 As stated earlier porosity may have an additional effect on deformation Porosity is a portrayal of the void space contained in the structure and also is the available space for the filaments or struts for deformation Thus it is proposed that porosity is a measure of the activation volume Porosity may couple with the filament size and may consequence different rate sensitivity for membranes having same filament size but different amount of available void space or porosity Equation 1 25 is adopted to use filament size as activation length and porosity as activation volume and is given by 1 5 3 0 5 h h m amp ln 6 1 30 P P 0 14 Ag m hg eq 0 12 F Ag m hf eq Agm hf p eq L p 0 25 0 1 F P 35 E Sens 0 08 2 L o a 2 g 0 06 E 7 0 04 VA 0 02 0 1 LT 0 1 1 10 100 Filament Size h um Figure 1 17 Porosity effect in strain rate sensitivity 30 Texas Tech University H S Tanvi
104. e rate sensitive nature of materials Among those tensile 1 27 31 57 62 71 and compression tests 11 12 13 are probably the most common method of testing specimens for about 10 to 10 per second strain rates 1 20 27 69 At the slower end of strain rate experiments with tensile tester has a difficulty of not being able to deform the sample in a highly continuous or monotonic fashion In most cases the linear actuator of the instrument for tensile deformation moves in a discrete manner in slower rates which become evident from the plot of load versus time recording Clusters of data points can be seen in the load time curve as the actuator moves and tries to keep up with the input signal at such slower speeds At faster rates the major problem lies with the speed of data acquisition In spite of these practical issues associated with the hardware of the experimental setup tensile test provides highly accurate estimates of the stress strain plots of the materials Faster rate tests for example 10 to 10 per second strain rates are mostly reported to be conducted by Split Hopkinson Pressure Bar SPHB technique 72 73 74 75 76 In this setup a gas driven projectile hits an incident bar while the 53 Texas Tech University H S Tanvir Ahmed December 2010 specimen is situated between the incident bar and a transmitter bar Both these incident and transmitter bars have significantly large dimensions compared to the
105. e strain rate sensitivity and activation volume fcc versus bec metals Materials Science and Engineering A 381 2004 71 79 71 A F Jankowski Mechanics and Mechanisms of Finite Plastic Deformation 14 Int Symp on Plasticity Proc A S Khan and B Farrokh eds NEAT Press Fulton MD 2008 187 189 72 J Harding The effect of high strain rate on material properties in TZ Blazynsky Ed Materials at High Strain Rates Elsevier Applied Science 1987 73 L D Oosterkamp A Ivankovic G Venizelos High strain rate properties of selected aluminium alloys Material Science and Engineering A 278 2000 225 235 74 R W Armstrong S M Walley High strain rate properties of metals and alloys International Materials Reviews 53 2008 105 128 75 N N Dioh A Ivankovic P S Leevers J G Williams The high strain rate behavior of polymers Journal De Physique Colloque C8 4 1994 119 124 142 Texas Tech University H S Tanvir Ahmed December 2010 76 N N Dioh A Ivankovic P S Leevers J G Williams Stress wave propagation effects in split Hopkinson pressure bar test Porc R Soc Lond A 449 1995 187 204 77 F Mohs Grundriss der Mineralogie 1824 English Translation by W Haidinger Treatise of Mineralogy Constable Edinburgh Scotland 1825 78 L B Freund J W Hutchinson High strain rate crack growth in rate dependent plastic solids J Mech Phys Solid
106. e tip whereas during scratch the deformation volume remains in front of the tip along the scratch direction Mostly because of this reason a simpler equation is used in the direct method of hardness measurement by omitting the second term x T gon a pao sin 3 10 Substituting equation 3 9 into equation 3 10 scratch hardness H is given by 92 Texas Tech University H S Tanvir Ahmed December 2010 H 3 11 The coefficient 8 7 in front of equation 3 11 is an approximation for the projection of the leading half of the spherical region of the tip A more exact equation can be developed by using the actual area instead of the projected area under the tip based on the scratch width and tip geometry If the scratch is within the spherical part then the actual area of the leading half is given by 1 cos sin A xr sin ee eae 3 12 If the scratch is beyond the spherical regime then the coefficient which is 8 z for this instance will be different and will depend on the tip geometry as for example pyramidal for Berkovich Cube corner tip and conical for Rockwell conical tip This is why it is better to use a generalized expression for equation 3 11 as H C 3 13 where C is a coefficient that may be calibrated depending on the overall geometry of the tip The major controversy in using the direct method of hardness measurement lies within the tip itself The actual shape of the tip varie
107. e used as standards for comparison with unknown materials Most common reference materials are Polycarbonate hardness 0 28 0 02 GPa Fused Silica hardness 9 5 0 5 GPa and Sapphire hardness 2741 GPa At a particular scratch speed which can be changed from Device gt Settings gt Sclerometry Scratch Speed several scratches of nominal loads starting from 200UN to 1500uN need to be done on a reference material Using scratch width measurement tool found on NA software s menu bar the widths of 162 Texas Tech University H S Tanvir Ahmed December 2010 the scratches need to be transferred to the hardness calibration window Measure gt Hardness Calibration and the calibration file needs to be saved cbr The actual load values of scratches will be found from the load versus time plot which was recorded using UMT software s Blackbox tab of Semi Automatic Panel Open that file using the Viewer software and select Fz from the box on the middle right of the software s start page Use the scroll arrows to find a particular scratch and position the left and right marker on the start and end of the scratch load both by right clicking This will give an output of the average and standard deviation of Fz in a lower left field Record this data and then position both the left and right markers on a place where there was no scratch 1 e the curve looks flat Take note of this average value and use this
108. ed to the width of the scratch Even though the depth and width of the scratch are geometrically related to each other for a well defined tip the depth of the scratch involves some level of elastic rebound of the material Scratch test involves primarily a shear type of deformation because the material is sheared along the direction of the scratch During this shear type of deformation the scratch width remains unchanged Hence the width of the scratch offers a better measurement of the actual volume of the material that undergoes the deformation For this reason the width of the scratch is used to determine the scratch hardness in equation 2 2 The strain rate for micro scratch experiments are empirically derived 66 to be 2 3 where v is the velocity of the stylus producing the scratch and w is the resultant scratch width Strain rate sensitivity of strength o for a material is given by famous Dorn equation o c 2 4 62 Texas Tech University H S Tanvir Ahmed December 2010 where m is the strain rate sensitivity exponent and c is a constant Thus m is derived from this equation by taking logarithm on both sides of equation 2 4 as olno m oln 2 5 3 2 2 L i 4 L 5 L 6 z E 20 40 60 80 100 120 140 Distance x um Figure 2 5 Illustrating the measurement of the scratch width for porous materials 63 Texas Tech Universi
109. ember 2010 Channel 1 Pr35_Ta V 2_200 900Hz_Apr 04094 023 Line 1 filter 3 square Fr 2 E 4 Hz PE Hz dY 6 67 au d Fr 1 10 E5 Hz AD Channel 2 Pr35_Ta V 2_200 900Hz_Apr 04094 023 Line 1 Am pm dv 6 67 au dAm 2 21 nm Length 68 5 a u Height 399 576 kHz Figure IL 42 Frequency shift plot of Ta V A 3 14 nm Sample 2 219 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Ta V 3_200 900Hz_Apr 041 25 01 4 Line 1 filter 3 square d 3 32 a u d Fr 1 05 E 5 Hz Fr E 4 Hz AD Channel 2 Pr35_Ta V 3_200 900Hz_Apr 041 25 014 Line 1 dY 3 32 au dA Am pm Am m 1 47 nm 15 20 25 30 35 4 45 so 55 Length 50 9 au Height 237 710 kHz 7 Figure IL 43 Frequency shift plot of Ta V A 8 07 nm Sample 3 220 Texas Tech University H S Tanvir Ahmed December 2010 Channel 4 Pr35_Ta V 4_200 900Hz_Apr 04180 032 Line 1 filter 3 square dV 1 72 a u d Fr 2 46 E 4 Hz A Fr E 4 Hz v au Vi au Length 25 6 au Height 89 581 kHz Figure IL 44 Frequency shift plot of Ta V A 3 14 nm Sample 4 221 AD Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Ta V 5_200 900Hz_Apr 04363 030 Line 1 filter 3 square dV 7 50 a u d Fr 2 31 E5 Hz Fr E4 Hz Channel 2 Pr35_Ta V 5_200 900Hz_Apr 0436
110. endent micro scratches are done on the cross section of these polished samples The widths of the scratches are measured with an optical microscope Figure 2 14 shows an optical image of a scratch done at 5 mm sec The data from scratch on cross section is shown in Figure 2 15 For reference the tensile test data of the nc Ni foils from section 1 3 3 is plotted with the micro scratch data It is observed that the strain rate sensitivity exponent of 73 Texas Tech University H S Tanvir Ahmed December 2010 nanocrystalline Ni increases from 0 0561 0 01 to 0 085 0 01 as the strain rate increases Figure 2 14 Measurement of a scratch at 5mm sec on the nc Ni with an optical microscope 74 Texas Tech University H S Tanvir Ahmed December 2010 1 0E 04 Tensile Hardness m Microscratch hardness y 3306 1x 8 R 0 8835 y 3350 3x R 0 7466 0 1 P 9 I 1 0E 03 A A Per 1 0E 05 1 0E 04 1 0E 03 1 0E 02 1 0E 01 1 0E 00 1 0E 01 1 0E 02 1 0E 03 Strain rate 1 sec Figure 2 15 Comparison of tensile hardness with micro scratch hardness and associated strain rate sensitivity of nanocrystalline Ni 2 4 Summary Strain rate above 10 l sec in general are not achievable with tensile testing because of the limitations to conducting tensile test method In addition a ductile brittle transition in tensile behavior can occur at higher strain rates due to the
111. enough energy to overcome these barriers and flow stress becomes dependent on temperature and strain rate At higher rates of strain a significant increase in the rate sensitivity exponent is observable as shown in segment III and as will be seen in the micro scratch experiments of the porous foils Harding 72 reported this transition from segment II to segment III at about 5x10 strain rate for annealed mild steel at room temperature Freund and Hutchinson 78 reported a similar transitioning strain rate between 105 and 10 strain rate however did not show the intermediate zone region IT as a separate section Armstrong and Walley 74 collected a numerous results of research conducted in this area in the review paper and stated that additional deformation features such as deformation twinning adiabatic shear banding and dislocation or twin generations play very important roles in very high strain rate regime for shock loading They also reported that behavior of shock loading as obtained from SHPB and shockless loading with a continuous increase in load in a very small rise time may differ significantly and may be more governed by drag resisting velocities of dislocations for shockless loading This phenomenon is widely known as phonon drag whereas the original dislocation density is required to move at the upper limiting speed i e the speed of sound and rate exponent increases most likely because of the saturation of the m
112. ental methods and analysis 58 2 3 1 Micro scratch experiment of porous silver foils eeseeeeseeeeereeereeerereese 58 2 3 2 Micro scratch experiment of nanocrystalline N1 73 2A SUIS SSSR Se RTS Baga ad van v tose D a a as ba aa a a a a Da aa 75 CHAPTER 3 NANOSCRATCH TESTING OF AU NI THIN FILMS AND HYDROXYAPATITE CERAMICS Seite A cae sus cous cosa a AG EEEE a a seuss ist aa ein ras cel 77 6 l MTOdHCNON Sen tente dass ae Res Nn EAE L 77 3 2 Experimental Approach nina 78 3 3 Experimental methode nonini a E EREE ct ets 88 JA Experimental TESules sa nsen aE en nd N N 94 3 5 SUNMA APAN A E EER A T RE E POM a 106 CHAPTER 4 TAPPING MODE ELASTICITY OF NANOCRYSTALLINE THIN FILMS see 107 eV troduction eena n a rene sale Gang a GN Kg shew a ga 107 AD Background inin oe n nn E E vant eo xa eo NER OTR 108 Texas Tech University H S Tanvir Ahmed December 2010 4 3 Experimental Technique sisi sanateed casveune sabe evebaraeulaaesvvdeedipanavgea 109 4 ACR OSUIS Ress nn wots cant ace pide dena aa A A Ga poeta Ne de GN 125 45 DISCUSSION ER ARR nn RS AN YG pa aa A Tag nt lode Aste a R we eh aie 132 RERPRENCR indiennes ie entrent dresse 135 APPENDIX I EMAIL WITH DR ILJA HERMANN HOW TO SETUP THE NANOANALYZER 6000000 151 LA Starting up the NanoAnalyzer ss 151 LB Hardness Measurement by Nano Scratch eceeesccceeseeeeseeeeesneeeeseeeeeneeeesaes 154 LB 1 Producme Nano SCratthis ses nt de eet dee ee 154
113. equency fo since it is available from the tuning of the probe at the beginning of a tapping test and is fairly constant The modulus values of calibration materials can help in assuming k and R Figure 4 8 plots the experimental calibration curve along with the fits using different analytic equations i e equation 4 21 and 4 4 The reduced elastic modulus of the samples are plotted in Figure 4 9 with the experimental calibration curve Table 4 2 represents the frequency shift data of the calibration materials and Table 4 3 represents all the data of the samples from the experimental calibration curve Table 4 1 Elastic modulus of calibration materials Sample Elastic modulus Poisson Reference Reduced elastic modulus E GPa ratio V E GPa Polycarbonate 3 0 1 0 37 3 47 Sapphire 495 10 0 27 40 135 381 25 Silicon 100 130 1345 0 27 34 40 126 99 Fused Silica 72 1 0 17 70 24 Fused Quartz 72 1 0 17 70 24 Ta 110 192 345 0 34 40 134 186 95 V 110 124 7 5 0 37 40 133 130 35 Ag 111 120 51 5 0 37 35 40 126 39 Ni 111 305 10 0 31 40 269 28 Hydroxyapatite 100245 0 27 109 93 02 Determining the actual elastic modulus may vary abit depending on the assumption of the Poisson ratio especially for materials having Poisson ratio from 0 3 to 0 5 Figure 4 10 shows a generic relationship between actual elastic modulus and reduced elastic modulus depending on vari
114. er 2010 LD 7 Once these steps are complete it is appropriate to begin the load non linearity test First retract the probe from the sample i e the AFM grid surface and move it a few millimeters above the surface Next run the test from Device calibration manager load nonlinearity Since this load non linearity test uses ZOpt as input parameter it is extremely important to finish the ZOpt calibration 1 D 6 first and then to run the test This test may take 15 to 30 minutes depending on the existence of previous non linearity tests Load non linearity tests are important for the probe to apply a load on a sample close to the nominal input load value The load non linearity tests are probe specific and have to be done for every new probe installed for the first time LD 8 After the load non linearity test is completed the x and y distance calibration is performed next Bring back the processed z image file of the AFM grid used in step I D 3 and using a horizontal marker from the menu measure a section of the image with a left and right click The resulting plot uu Figure I 5 A horizontal section of the scanned TGZ1 after processing with line tilt should appear like Figure 5 X um and step correction 173 Texas Tech University H S Tanvir Ahmed December 2010 I D 9 On the figure from step I D 8 put the right marker at the beginning of a cycle and after 10 cycles or 20 cycles dependi
115. erialia 51 2004 119 124 96 A F Jankowski Diffusion mechanisms in nanocrystalline and nanolaminated Au Cu Defect and Diffusion Forum 266 2007 13 28 97 D M Makowiecki A F Jankowski M A McKernan R J Foreman Magnetron sputtered boron films and Ti B multilayer structures Journal of Vacuum Science and Technology A 8 1990 3910 3913 98 A F Jankowski M A Wall J P Hayes K B Alexander Properties of boron boron nitride multilayers NanoStructured Materials 9 1997 467 471 99 A F Jankowski J P Hayes D M Makowiecki M A McKernan Formation of cubic boron nitride by the reactive sputter deposition of boron Thin Solid Films 308 309 1997 94 100 100 A F Jankowski J P Hayes C K Saw Dimensional attributes in enhanced hardness of nanocrystalline Ta V nanolaminates Philosophical Magazine 87 2007 2323 2334 145 Texas Tech University H S Tanvir Ahmed December 2010 101 N Tayebi T F Conry A A Polycarpou Reconciliation of nanoscratch hardness with nanoindentation hardness including the effect of interface shear stress Journal of Materials Research 19 2004 3316 3323 102 N Tayebi A A Polycarpou T F Conry Effects of substrate on determination of hardness of thin films by nanoscratch and nanoindentation techniques Journal of Materials Research 19 2004 1791 1802 103 N Tayebi T F Conry A A Polycarpou Determination of hardness from n
116. ersity H S Tanvir Ahmed December 2010 Channel 1 Pr35_Au Nb 626_200 900Hz_Apr 06682 029 Line 1 filter 3 square dv 6 57 au d Fr 7 94 E 4 Hz Fr E 4 Hz AD Channel 2 Pr35_Au Nb 626_200 900Hz_Apr 05682 029 Line 1 dY 6 57 au dAm 296 19 pm Am pm 5000 4500 4 3500 4 3000 Am 2500 2000 4 1500 4 1000 4 4 50 60 70 80 90 100 110 120 Length 94 9 a u Height 584 565 kHz Z Figure IL 31 Frequency shift plot of Sample Au Nb 626 A 0 46 nm 208 130 Texas Tech University H S Tanvir Ahmed December 2010 II D Frequency shift curves of Cu NiFe samples Channel 1 Pr35_Cu NiFe 302_200 900Hz_Apr 05310 035 Line 1 filter 3 square dV 7 33 aux d Fr 1 67 E5 Hz 2 Fr 2 E 4 Hz ao4 35 N 304 25 204 15 104 Vi au Channel 2 P r35_Cu NiF e 302_200 900Hz_Apr 05310 035 Line 1 dY 7 33 a u dAm 2 91 nm Am pm 45 so Length 45 8 au Height 427 377 kHz Figure IL 32 Frequency shift plot of sample Cu NiFe 302 A 4 0 nm 209 AD Am Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Cu NiFe 303_200 900Hz_Apr 05243 005 Line 1 filter 3 square Fr E 4 Hz Channel 2 Pr35_Cu NiFe 303_200 900Hz_Apr 05243 005 Line 1 Am pm Dit dV 5 02 a u d Fr 2 01 E5 Hz dV 5 02 a u dAm 2 19 nm Length 64 4 au
117. est Acta Metallurgica 38 1990 2695 2700 53 F Saeffel G Sachs Zeitschrift Fur Metallkunde 17 1925 33 54 K C Goretta W E Delaney J L Routbort J Wolfenstine W Zhang E E Hellstrom Creep of silver at 900 C Superconductor Science and Technology 9 1996 422 426 55 M Aubertin L Li A porosity dependent inelastic criterion for engineering materials International Journal of Plasticity 20 2004 2179 2208 56 Y M Wang A V Hamza E Ma Temperature dependent strain rate sensitivity and activation volume of nanocrystalline Ni Acta Materialia 54 2006 2715 2726 57 R D Emery G L Povirk Tensile behavior of free standing gold films Part II Fine grained films Acta Materialia 51 2003 2079 2087 140 Texas Tech University H S Tanvir Ahmed December 2010 58 J Lian C D Gu Q Jiang Z Jiang Strain rate sensitivity of face centered cubic nanocrystalline materials based on dislocation deformation Journal of Physics 99 2006 076103 1 3 59 J Lian B Baudelet A modified Hall Petch relationship for nanocrystalline materials Nanostructured Materials 2 1993 415 419 60 J W Cahn F R N Nabarro Thermal activation under shear Philosophical Magazine A 81 2001 1409 1426 61 H S T Ahmed A F Jankwoski Tensile deformation of micro to nanoporous metal membranes 16th International Symposium on Plasticity ed Akhtar S Khan Proceed
118. eter from a stack of 10 foils SEM images on cross section of the foils validate this measurement The weight of the sample is measured using a microbalance and sample density pis calculated using the formulation w zr h p 1 1 where h is the average thickness of the foil and w is the weight of the foil Porosity p is given by p 1 1 2 Prag where pag is the density of fully dense silver and is 10 5 gm cc A die is designed Figure 1 1 following ASTM standards length is equal to or greater than three times Texas Tech University H S Tanvir Ahmed December 2010 the width to produce two test specimens from a single disc and was made through NC milling Tensile test specimens are cut from the foils using this die resulting in a gage length of 10 mm and width of 3 mm 10 0 Fi LEAI Figure 1 1 Design of die dimensions in mm SEM images are taken in plan view and in cross section of the samples to provide surface morphology and structural features Some definition of grain sizes within each filament is also available from these images Lineal intercept method is used to measure the filament sizes of the different foils wherein six different straight lines are drawn at equal angular spacing on the plan view SEM image of the foils The measurements of the filaments are taken between the intercept points along the lines The grain sizes are estimated to be the average of the shortest distances i e the
119. f 81 Texas Tech University H S Tanvir Ahmed December 2010 3 0 is very close to the actual number Figure 3 4 as well as to the theoretical approx imation However this simplification overestimates the number of coincident boundaries for up to first 150 grains The volume of indentation that is necessary for quantifying the boundary effects of nanocrystalline nanolaminates involves much higher number of grains and hence this error up to 150 grains is insignificant 2 5 Coincident boundary per cell 0 5 150 Number of cells 50 100 200 250 300 Figure 3 4 Plot of coincident boundary per cell versus number of cells shows a plateau value around 2 8 boundaries per cell A MATLAB program Appendix II is written to simulate the intercept area of the indenter for layer pair and grain boundary contributions In the program the geometry of Berkovich tip is considered to have a triangular base and a spherical tip with a transition in between In the transition part the sphere is considered to be 82 Texas Tech University H S Tanvir Ahmed December 2010 tangent on the three common side lines of the faces of the tip The orientation of the tip with respect to the cantilever hence with respect to the direction of the scratch is not considered in the model Tip radiuses of 50 nm and 500 nm are used for simulation to find out possible affect of change in the intercept area on tip shape B
120. f scratches is changed from set to set to induce a strain rate effect 66 Generally at least three scratches are done at each combination of load and velocity to obtain a sound statistical correlation After each set of scratches the coating surface is scanned perpendicular to the scratch in order to measure the width without any effect from thermal drift Each scratch is measured at several positions typically at 5 positions or more to provide a statistical average of the scratch width Figure 3 11 A typical probe cantilever arrangement is shown on left figure while a Berkovich tip is shown on the right 89 Texas Tech University H S Tanvir Ahmed December 2010 The strain rate is calculated using the following formula 66 3 2 w where V is the velocity of the scratch nm sec and w is the width of the scratch nm The relationship between Strength and Strain rate can be found using the Dorn relationship as Cee 3 3 where m is the strain rate sensitivity exponent Rewriting equation 3 2 after taking the natural logarithm we find that _ olnd dln 3 4 From equation 3 4 a plot of dIn versus dln o will yield a linear curve with a slope equal to the strain rate sensitivity In our case the hardness H is plotted rather than the strength 0 since hardness and strength are related according to o cH where c is a constant having a typical value of 1 3 81 82
121. fficient essentially remains the same and thus equation 3 6 can be written for this case as H H 3 7 R This is the governing equation for measuring hardness of a sample using calibration method In the direct method the scratch hardness is measured independently based on the physical parameters 83 101 102 103 used during the 91 Texas Tech University H S Tanvir Ahmed December 2010 scratch experiment The equation for hardness of the sample in this method is given as F SH sin sr sin a cos a In sec a tan a 3 8 where F is the normal load of scratch H is the hardness r is the radius of the tip is the contact angle of the indenter tip with the sample surface and s is the shear stress or surface traction 83 If the scratch is within the upper hemispherical region of the tip see Figure 3 6 and 3 7 contact angle can be found from simple geometrical relationship r La Qa sin 2 3 9 However it must be noted here that Tayebi et al 101 102 103 tried to make the indentation hardness and scratch hardness same in terms of magnitude Hence he incorporated the second term in equation 3 8 in addition to the projected area of the leading half of the indenter tip during scratch However these two types of hardness values are not really the same because of their associated type of deformations In the indentation hardness the volume of deformation is located beneath th
122. first two terms of the Taylor s expression in equation 4 14 This simplified formula is usually not used because of the error associated with it A third term in the Taylor s expression gives better accuracy and the formula for is given by NG k k Cc a asda 4 22a FNR gt E 4 22b hha JRE a gt NS k Cc The formula provided by the manufacturer CETR simplifies equation 4 22b by introducing a constant C given by 121 Texas Tech University H S Tanvir Ahmed December 2010 CE 4 22c Hence equation 4 22b is simplified to g p 1 4 23 k 1 CVRE Solving for the reduced modulus E yields only positive sign is taken into consideration CVR CHENE ER ee eae aes 4 24 E ak Using this formula of equation 4 24 the reduced elastic modulus E 5 of sample can be derived from the slope of frequency shift versus probe displacement plot provided that the values of free standing frequency of oscillation of the cantilever Jo cantilever bending stiffness k and tip radius R is exactly known However in reality these values can only be determined with limited accuracy Hence calibration method for measurement of elastic modulus is more frequently put into use In the calibration method a values are measured for a number of materials with known elastic modulus for example materials with standard values are used such as fused silica gold nickel sapphir
123. g and interrupted test at ultimate strength 39 Serrated grips for mounting the nanocrystalline Ni foils 40 A typical thickness of the nanocrystalline nickel as viewed under the optical microscope at 600X magnification 0 0 eee eeeeeseeeeeeeeeeeseeesaeeeseeees 44 Engineering Stress strain curves of NC nickel at different strain rates 44 Power law fit of the stress versus strain rate to provide the strain rate sensitivity of nanocrystalline nickel 45 Activation volume is calculated from the slope of linear fit of In strain rate Versus yield STESS asana AN nan ar here Ritter 46 Strain rate sensitivity of Cu 19 and Ni 26 as a function of grain size 47 Load time plot for a Au Cu sampl ssssies anses teen 48 SEM image is used on failed cross section of a Au Cu sample for measuring the Widhi sasae TE MO EN REA PR aaa Ta aa aa an a Re a I EE VE 48 Strain rate sensitivity plot for the Au Cu samples ce eeeeeseeeseeeseeeeeeeaees 499 Strain rate sensitivity as a function of grain size for nanocrystalline Au RE LI DL RE inside ote Senco a Set hoe Ba nai Coie 50 Schematic of different regions of rate sensitivity eas0eo0eenenonanoenen ena n een ene 56 Microseratch test BiG Gagang A asec eas AT cerivastatin een 59 Scratches at different velocities on a single membrane mounted on plan view 60 A sample scan on one of the scratches using the profiler using
124. grain size and layer pair size It has already been noted earlier that the characteristic dimension of nanocrystalline nanolaminates can be a sum of the contributions from layer pair interfaces and grain boundary interfaces An average separation of the interfaces can 103 Texas Tech University H S Tanvir Ahmed December 2010 be computed as a diameter of a sphere where the spherical volume is equal to the hexagonal volume created by the grain size dg and layer pair interfaces A 113 Figure 3 19 Schematic of equating the hexagonal grain volume with a spherical volume to find out the average separation of interfaces The volume of the hexagonal grain V with 21 height as shown in Figure 3 19 is given by v Has 3 15 Equating equation 3 15 with the volume of a sphere with arbitrary diameter d yields 3 v3 pige da 3 16a A BF A 2 3 da _393 2 3 16b 2 loz A 3 d aa 3 160 27 104 Texas Tech University H S Tanvir Ahmed December 2010 Using this expression equation 3 16c the average interfacial separation for the stated Au Ni sample becomes 4 138 nm Thus the hardness value of this sample should be corresponding to this average separation dimension of 4 138 nm instead of the gain size 6 9 nm or the layer pair size 1 8 nm Figure 3 20 is the plot of the rate sensitivity exponent where this consideration has been taken into account 0 12 Niandits alloys fr
125. hannel 2 Pr35_Sample_10_200 1300Hz_Apr 01683 007 Line 1 Am 5000 em dV 1 65 a u dAm 327 50 pm 66 68 Length 202 au Height 81 912 kHz Figure I1 19 Frequency shift plot of Au Ni d 6 9 nm A 1 8 nm Sample 10 196 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 11_200 900Hz_Apr 03206 036 Line 1 filter 3 square dV 8 01 a u d Fr 1 09 E 5 Hz Fr E 4 Hz AD Channel 2 Pr35_Sample 11_200 900Hz_Apr 03206 036 Line 1 Am pm 30 45 50 60 70 80 30 100 110 Length 80 9 a u Height 400 263 kHz 7 Figure IL 20 Frequency shift plot of Au Ni d 13 1 nm A 2 5 nm Sample 11 197 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 12_200 900Hz_Apr 03157 024 Line 1 filter 3 square dV 6 51 au d Fr 117 E5 Hz Fr E 4 Hz 30 a 20 15 10 Vi au Channel 2 Pr35_Sample 12_200 900Hz_Apr 03157 024 Line 1 dV 6 51 au dAm 1 36 nm Am pm 40 50 60 70 80 90 100 110 Length 83 3 au Height 400 228 kHz Figure IL 21 Frequency shift plot of Au Ni d 11 4 nm A 1 2 nm Sample 12 198 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 13_200 900Hz_Apr 03129 036 Line 1 filter 3 square dv 7 74 au d Fr 1 36 E 5 Hz Fr E 4 Hz 30 a 20 41 GG lt Vi au Channel 2 Pr35_Sample 13
126. he National Academy of Sciences 104 2007 3031 3036 87 A F Jankowski Vapor deposition and characterization of nanocrystalline nanolaminates Surface and Coatings Technology 203 2008 484 489 88 A F Jankowski D M Makowiecki M A Wall M A McKernan Subnanometer multilayers for x ray mirrors Amorphous crystals Journal of Applied Physics 65 1989 4450 4451 89 A F Jankowski R M Bionta P C Gabriele Internal stress minimization in the fabrication of transmissive multilayer x ray optics Journal of Vacuum Science and Technology A 7 1989 210 213 90 A F Jankowski Deposition optimization of W C multilayer mirrors Optical Engineering 29 1990 968 972 91 A F Jankowski SPIE conf Proc 1738 1992 10 21 92 J R Childress C L Chien A F Jankowski Magnetization Curie temperature and magnetic anisotropy of strained 111 Ni Au superlattices Phys Rev B 45 1992 2855 2862 144 Texas Tech University H S Tanvir Ahmed December 2010 93 A Simopoulos E Devlin A Kostikas A F Jankowski M Croft T Tsakalakos Structure and enhanced magnetization in Fe Pt multilayers Phys Rev B 54 1996 9931 9941 94 A F Jankowski T Tsakalakos Phase stability by the artificial concentration wave method Metallurgical and Materials Transactions A 20 1989 357 362 95 A F Jankowski C K Shaw Diffusion in Ni CrMo composition modulated films Scripta Mat
127. hod Journal of Colloid and Interface Science 208 1998 34 48 125 W C Oliver and G M Pharr An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments Journal of Materials Research Vol 7 1992 1564 1583 126 A S Useinov A nanoindentation method for measuring the young modulus of superhard materials using a NanoScan scanning probe microscope Instruments and Experimental Techniques Vol 47 2004 119 123 127 S P Timoshenko J N Goodier Theory of Elasticity grd edition McGraw Hill 128 K V Gogolinski Z Ya Kosakovskaya A S Useinov and I A Chaban Measurement of the elastic moduli of dense layers of oriented carbon nanotubes by a scanning force microscope Acoustical Physics Vol 50 2004 664 669 129 A D Roberts PhD Dissertation 1968 Cambridge University England 130 K L Johnson K Kendall and A D Roberts Surface Energy and the Contact of Elastic Solids Proc R Soc Lond A 324 1971 301 313 131 Ya Pu Zhao X Shi and W J Li Effect of work of adhesion on nanoindentation Rev Adv Mater Sci Vol 5 2003 348 353 132 B V Derjaguin V M Muller YU P Toporov Effect of contact deformations on the adhesion of particles J of Colloid and Interface Science Vol 53 1975 314 326 149 Texas Tech University H S Tanvir Ahmed December 2010 133 G A Alers Elastic moduli of Vana
128. ies originate from assuming a constant c value of 1 3 in strength hardness relationship These discontinuities are more evident in higher porosity membranes i e the slope of data points from region II moves higher in elevation At different level of indentations different tip geometry is active and hence it is necessary to consider different corresponding c values However for calculating strain rate sensitivity only the slope of the power law fit is important and the elevation of the plot corresponding to different c values can be neglected without any significant error From these figures it is also evident that for some specimens there may be little or no transitional zone between low region I and intermediate region IJ strain rate sensitivity These phenomena can be observed for high porosity membranes 0 8 and 3 0 micron nominal pore size as well as for fully dense foil To investigate any possible difference similar rate dependent micro scratches are done on the cross section of the dense samples The samples were prepared using epoxy mount in cross section and involved grinding and polishing at different smoothness levels to remove surface roughness and other possible artifacts from the vacuum casting process The data from scratch on plan view and on cross section overlaps as it can be seen from Figure 2 11 It is also found that at intermediate regime region II the rate sensitivity exponents of all porosity membranes are somewhat
129. ine 1 filter 3 square dv 216 a u dF ne 462 E4 Hz Fr E 4 Hz 354 AD Vi au Channel 2 Pr35_Au Nb 606_200 900Hz_Apr 05431 036 Line 1 Am pm dv 2 16 au dAm 397 04 pm 3500 4 Am 91 Length 61 5 a u Height 345 455 kHz Figure IL 28 Frequency shift plot of Sample Au Nb 606 205 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Au Nb609_200 900Hz_Apr 04788 035 Line 1 flter 3 square dV 11 71 au d Fr 1 08 E 5 Hz Fr E4 Hz AD Channel 2 Pr35_Au Nb609_200 900Hz_Apr 04788 035 Line 1 dv 11 71 au dAm 935 60 pm Am pm 5000 2 4500 3500 3000 2500 Am 2000 1500 Length 73 5 a u Height 341 190 kHz Figure IL 29 Frequency shift plot of Sample Au Nb 609 A 1 6 nm 206 AD Am Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Au Nb615_200 900Hz_Apr 04835 026 Line 1 filter 3 square Fr E4 Hz Channel 2 P r35_Au Nb615_200 900Hz_Apr 04835 026 Line 1 Am pm 3500 3000 2500 2000 1500 dV 4 23 au d Fr 9 22 E 4 Hz A 7 AN WI IN v au dV 4 23 a u dAm 1 24 nm 1000 500 0 Vi au 210 215 220 225 230 235 240 Length 34 3 au Height 211 280 kHz Z Figure IL 30 Frequency shift plot of Sample Au Nb 615 A 3 2 nm 207 Texas Tech Univ
130. ing the deposited nickel Free standing test pieces are laser cut to have a nominal width of about 1 4mm while the thickness of the specimens is determined by the as deposited condition being nominally about 50 microns The test specimens are mounted on the tensile tester using heavy duty serrated grips Figure 1 24 Figure 1 24 Serrated grips for mounting the nanocrystalline Ni foils 40 Texas Tech University H S Tanvir Ahmed December 2010 Rate sensitive tensile testing 1s done on the samples using the same technique as described in section 1 3 1 Tensile test of Ag foils The tests are carried out at strain rates of 10 to 10 For each strain rate at least two or three samples are tested to failure and the data is recorded as a function of time Optical microscopy of the cross sections of the samples after failure is done at various magnifications to provide more accurate measurements of the thickness and width and also to provide some identification of ductile or brittle failure A typical optical image of the thickness of such a foil at about 600X magnification is shown on Figure 1 25 The yield strength is measured from the engineering stress versus engineering strain curve at a point where the linearity of loading starts to deviate The linear loading regime is defined using a 20 point moving average and a linear fit The highest correlation coefficient of the linear fit provides the limits of the linear part while the 20 poin
131. ings Plasticity 10 NEAT Press 2010 118 120 62 R D Emery G L Povirk Tensile behavior of free standing gold films Part I Coarse grained films Acta Materialia 51 2003 2067 2078 63 G D Hughes S D Smith C S Pande H R Johnson R W Armstrong Hall Petch strengthening for the microhardness of twelve nanometer grain diameter electrodeposited nickel Scripta Metallurgica 20 1986 93 97 64 http en wikipedia org wiki Nickel 65 D Hull D J Bacon Introduction to dislocations Ae Edition ISBN 0750646810 66 L O Nyakiti A F Jankowski Characterization of strain rate sensitivity and grain boundary structure in nanocrystalline Gold Copper alloys Metallurgical and Materials Transactions A 41 2010 838 847 141 Texas Tech University H S Tanvir Ahmed December 2010 67 Y M Wang E Ma Three strategies to achieve uniform tensile deformation in a nanostructured metal Acta Materialia 52 2004 1699 1709 68 R J Asaro S Suresh Mechanistic models for the activation volume and rate sensitivity in metals with nanocrystalline grains and nano scale twins Acta Materialia 53 2005 3369 3382 69 L Lu R Schwaiger Z W Shan M Dao K Lu S Suresh Nano sized twins induce high rate sensitivity of flow stress in pure copper Acta Materialia 53 2005 2169 2170 70 Q Wei S Cheng K T Ramesh E Ma Effect of nanocrystalline and ultrafine grain sizes on th
132. is nt 179 II 3 Frequency shift plot of Fused Quartz 180 IL 4 Frequency shift plot of Fused Silica co cc secs sui nm 181 ILS Frequency shift plot of Nanocrystalline Ni 182 II 6 Frequency shift plot of Polycarbonate 183 II 7 Frequency shift plot of Sapphire 4m has hea wa MEANS Ale em 184 II 8 Frequency shift plot of Silicon 100 ins sen nn ne cade awanane anana nne 185 1 9 Frequency shift plot Of Ta siciecvisiicad vives eis Gitacrantacdend peace eee eee 186 ITO Frequency Shire plot of Mis nds ne RTE a Tee Net 187 IL 11 Frequency shift plot of Au Ni A 1 7 nm Sample 1 188 IL 12 Frequency shift plot of Au Ni d 16 0 nm 2 0 8 nm Sample 2 189 IL 13 Frequency shift plot of Au Ni A 4 0 nm Sample 3 190 IL 14 Frequency shift plot of Au Ni A 0 9 nm Sample 4 191 IL 15 Frequency shift plot of Au Ni A 1 2 nm Sample 5 192 IL 16 Frequency shift plot of Au Ni d 15 2 nm 4 5 nm Sample 6 2 2 193 I1 17 Frequency shift plot of Au Ni A 1 9nm Sample 7 194 IL 18 Frequency shift plot of Au Ni A 1 6nm Sample 8 195 IL 19 Frequency shift plot of Au Ni d 6 9 nm A 1 8 nm Sample 10 196 II 20 Frequency shift plot of Au Ni d 13 1 nm 2 2 5 nm Sample 11 197 IL 21 Frequency shift plot of Au Ni d 11 4 nm 2 1 2 nm Sample 12 198 11 22 Frequency shift plot of A
133. is selected beforehand In the later case a calibration file needs to be loaded from the Elastic modulus measurement window Calibration files can be made in a similar way for known materials for example fused silica sapphire polycarbonate etc I D Probe Tuning For probe tuning it is necessary to copy an existing probe file with the extension prm and rename it for the new probe Probes with ceramic cantilever have suffixes CW and probes with metallic cantilever have suffixes M The UNMT hardware should be turned on only after the physical installation of the new probe So press the red Stop button on the front of the machine before proceeding and press the green Reset button after the new probe has been installed Before starting up the NA hardware from the software environment i e Device Run the new renamed probe should be selected from the Change probe menu Please refer to the image on page 43 of the NA 2 manual The standard procedures to follow are 169 Texas Tech University H S Tanvir Ahmed December 2010 I D 1 Run the Auto Setup from Probe tab to see if the probe is tunable The Auto Setup operation will return a curve which should look like a bell shaped see Figurel 2 If the probe does not have any physical or other type of damages the maximum point on the bell shaped curve will be close to the set amplitude value Am nm D Fr KHz Figure I 2 A typical Auto Setup c
134. lease refer to the image on page 28 of the NA 2 manual I C 1 f Once all the lines are aligned put the left marker and right marker on the linear portion of the Af versus z plot left and right mouse clicks respectively Click on the slope button that will plot the slopes of all the lines with an average and standard deviation value This command will not work if the lines are not squared If automatic curves processing does not square the curves the squaring has to be done manually from the graph manager panel from Process tool on the menu bar If the standard deviation is too high gt 10 deselect some of the lines with high deviating values using the graph manager panel 168 Texas Tech University H S Tanvir Ahmed December 2010 I C l g Once this task is completed open the elastic modulus measurement window from Measure Elastic Modulus Create a new material file If you are measuring a calibration material create a new calibration material file give it aname and its elastic modulus Otherwise create a new sample file I C 1 h On the slope calculation window click on the Add value button Please refer to the images on page 79 of the NA 2 manual This will add the average slope of all the curves in the elastic modulus calculation window If you are measuring a calibration material make sure that material is selected before clicking on Add value Similarly for measuring a sample make sure that sample
135. lidation at room temperature Journal of Materials Science 36 2001 1219 1225 43 H X Zhu J F Knott N J Mills Analysis of the elastic properties of open cell foams with tetrakaidecahedral cells Journal of the Mechanics and Physics of Solids 45 1997 319 343 44 W E Warren A M Kraynik Linear elastic behavior of a low density kelvin foam with open cells Journal of Applied Mechanics 64 1997 787 794 45 L Li M Aubertin A general relationship between porosity and uniaxial strength of engineering materials Canadian Journal of Civil Engineering 30 2003 644 658 46 E O Hall The deformation and ageing of mild steel III Discussion of results Proceedings of the Physical Society B64 1951 747 753 139 Texas Tech University H S Tanvir Ahmed December 2010 47 E O Hall The brittle fracture of metals Journal of Mechanics and Physics of Solids 1 1953 227 233 48 N J Petch The cleavage strength of polycrystals Journal of the Iron and Steel Institute 174 1953 25 28 49 N J Petch The fracture of metals Progress in Metal Physics 5 1954 1 52 50 N J Petch The upper yield stress of polycrystalline iron Acta Metallurgica 12 1964 59 65 51 R M Douthwaite N J Petch A microhardness study relating to the flow stress of polycrystalline mild steel Acta Metallurgica 18 1970 211 216 52 N J Petch R W Armstrong The tensile t
136. lotted as a function of the grain size and compared with the data available from literature for nc Cu and Ni It is found that m increases with decreasing value of grain size A model has been established to predict the rate sensitivity as a function of grain size assuming that Hall Petch is still valid Another model has been suggested to find out the average distance of dislocation travel which could be more appropriate in correlation with the rate sensitivity It must be noted here that strain hardening effects were not considered in this analysis More points however are needed under 10 nm dimension to understand the complete trend of the behavior of strain rate sensitivity exponent m 106 Texas Tech University H S Tanvir Ahmed December 2010 CHAPTER 4 TAPPING MODE ELASTICITY OF NANOCRYSTALLINE THIN FILMS 4 1 Introduction Structural features for example grain size and layer pair spacing can affect the mechanical properties of materials e g strength amount of plastic deformation strain rate sensitivity elasticity etc in diverse ways 116 117 As grain sizes get smaller and smaller the dislocation motions get confined before pile up occurs at the grain boundary thereby increasing the strength as governed by Hall Petch relationship dislocation based strengthening Thus nanocrystalline materials in general show higher strength up to a certain limit after which dislocation based strengthening breaks down and softening occu
137. m sec with 1 mN force 95 Texas Tech University H S Tanvir Ahmed December 2010 35 30 F N o Elevation nm 20 F 100 nm sec 1000 nm sec 50 nm sec 0 3000 6000 9000 Distance nm Figure 3 13 Scratch profiles with 1 mN force at different scratch velocities on Hydroxyapatite 4991012 Ti The scratch profiles at three different scratch velocities on the hydroxyapatite 110 ceramic film are seen in Figure 3 13 As this plot suggests the width as well as the height of scratches tends to be larger as the scratch speed decreases Figure 3 14 plots the hardness value computed for this film at scratch velocities ranging from 10 nm sec to 5 um sec on a log log plot Hence the strain rate sensitivity is obtained as the slope of the power law fit of the data The hardness of the film is calculated using equation 3 13 and for simplicity C is taken to be 8 7 Prior ramp load testing by Nieh et al 109 at constant scratch speed shows a linear variation of the scratch width with respect to increasing scratch load This result suggests that the hydroxyapatite coating 96 Texas Tech University H S Tanvir Ahmed December 2010 does not strain harden The strain rate sensitivity exponent found from this experiment is found to be 0 0159 which also shows almost no strain hardening behavior of the coating Table 3 1 presents the data from this scratch experiment on this artificial
138. mage on a 0 8 um membrane is given in Figure 1 2 which shows that the pores on plan view and on thickness are of nearly equivalent structure hence implying that the value of n to be Texas Tech University H S Tanvir Ahmed December 2010 1 5 The plan view is taken prior to deformation and the cross sectional image is taken after the sample was tested to failure As it is seen from this figure the pre versus post deformation images are quite similar and do not show significant difference in pore size or filament width except for some locations where cup and cone formations may have generated Figure 1 2 SEM images of plan view on left pre deformation and of cross section on right post deformation of a 0 8 um foil For comparison of the mechanical properties of these porous structures fully dense silver foils with 99 95 reported purity are procured from SurePure Chemetals 33 Tensile test specimens are die cut from this foils using the same die as shown in Figure 1 1 to produce test pieces of 10 mm gage length and 3 mm width The thickness of these dense foils is 50 3 um as measured with a micrometer and verified with an optical microscope Figure 1 3 shows a representative cross section of the dense silver In addition to the Ag foils electrodeposited nanocrystalline Au Cu thin film foils 27 28 29 are available for study Segments from these as deposited thin films 6 Texas Tech University H S Tanvir
139. ments decreases as loading goes up very quickly and interruption at an estimated load level which has to be higher than the preceded load becomes difficult For membranes with higher porosity the interruption is difficult even for lower strain rates mostly because of their unpredictable strength 33 Texas Tech University H S Tanvir Ahmed December 2010 after the yielding and or because of quick necking and fracturing For this reason more than one test is done at each strain rate to achieve sufficient confidence level The incremental load curve for a 0 2 micron nominal pore size membrane tested at 10 per second strain rate is shown in Figure 1 19 With each successive interval of time the load is seen to increase 22 20 F e load N amp Elastic modulus GPa m Ave Modulus from Tensile test 4 12 ee ye a Load N Elastic modulus GPa a90 0 ap e ome 99 so a oeo o o OE EESE D sie iii a 500 Time sec Figure 1 19 Interrupted tensile test of 0 2 micron nominal pore size membrane at 10 sec strain rate to show the change in elastic modulus with progression of load The modulus is measured using corrected cross sectional area as the slope of the linear portion to the loading curve for each increment The elastic regime is identified using a linear fit and a 20 point average trend line The abscissa in Figure 1 19 is
140. n 51 Texas Tech University H S Tanvir Ahmed December 2010 volume is found to be about 0 07 nm which is suggestive of a grain size below 10 nm The rate sensitivity is plotted as function of the grain size and is found to follow the similar trend from literature data for Hall Petch strengthening mechanism The experimental data is modeled based on an analytical model of bow out of an edge dislocation 26 59 and has good correlation with the plotted trend line 4 Nanocrystalline Au Cu samples are tested in tension at different strain rates Strain rate sensitivity exponent of the samples has been obtained through a log log plot of the strength versus strain rate The 10 33 nm grain size samples show a strain rate exponent of 0 1393 This value is very close to projected value by the trend line obtained by Nyakiti and Jankowski 66 through micro scratch testing of Au Cu samples with different weight percent of Cu 52 Texas Tech University H S Tanvir Ahmed December 2010 CHAPTER 2 MICRO SCRATCH TESTING OF POROUS MEMBRANES 2 1 Introduction Mechanical behavior of materials on a wide range of strain rates has been of interest to many researchers e g 19 20 57 62 67 68 69 70 Most materials are known to have different strength at different rate of loading hence exhibits at least some level of strain rate sensitivity Many testing methods for example tension compression torsion etc can be applied to reveal th
141. n of the tip rises A frequency feedback system moves the probe further into the material until a predefined frequency shift i e change of the recorded frequency from its free standing natural 109 Texas Tech University H S Tanvir Ahmed December 2010 frequency is achieved 106 A number of frequency shift curves are produced on the surface to achieve higher repeatability and accuracy Elastic modulus is measured from these frequency shift curves with some approximations usually within 5 of the actual modulus value Elastic modulus ranging from 50 GPa to about 1000 GPa are reported to be measured using this technique The frequency shift curve as shown in Figure 4 1 has four major parts 126 1 The tip oscillates freely without contact with the surface 2 The tip oscillates in contact with the viscous top layer present on the surface This viscous layer is mainly present due to the existence of moisture from the air Afr Figure 4 1 A typical frequency shift curve 3 This part represents direct interaction with the sample surface This segment in the frequency shift curve has two sections namely 3 and 3 Even though the probe tip is fully in contact with the sample surface at 3 section the 110 Texas Tech University H S Tanvir Ahmed December 2010 probe base is still far from the surface and hence there might be some point during the oscillation while the tip is not in full contact with the s
142. nd check that the UMT motors are initialized by pressing CTRL left or right arrow for the slider i e x direction movement CTRL up or down arrow for carriage 1 e z direction movement CTRL lt or gt key for the spindle 1 e y direction movement The ALT key can also be pressed instead of the CTRL key but make sure the head is far from the specimen stage because pressing the ALT key will move the stages very fast and can damage the probe by unintended contact if not done with care LA 4 If the motors are not initialized the stages will not move Check if the emergency button was pressed Press the reset button and try again If it does not work then load the option file named Micro opt click on the semi automatic panel on the menu bar wait for about 10 seconds close the semi automatic panel and click on Tools gt Setup motor controllers and check that the values in the Carriage Slider Spindle fast and Spindle Slow are set at 2000 20000 5000 and 100000 respectively Then click on Set motor controller defaults and wait until the initialization process is complete LAS Once complete a popup message will be displayed which asks to restart the UMT software Click Ok and close the UMT software Double 152 Texas Tech University H S Tanvir Ahmed December 2010 click on UMT icon again to start the software Click Options Save as and save the opt file under the same name to overwrite the existing one
143. nel 1 Pr35_Sample 3_200 900Hz_Apr 03697 004 Line 1 filter 3 square Fr E 4 Hz dV 7 52 a u d Fr 1 88 E 5 Hz AD Channel 2 Pr35_Sample 3_200 900Hz_Apr 03697 004 Line 1 Am pm dV 7 52 a u dAm 1 24 nm 45 50 Length 54 5 a u Height 334 096 kHz Figure IL 13 Frequency shift plot of Au Ni A 4 0 nm Sample 3 190 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 4_200 900Hz_Apr 03589 009 Line 1 filter 3 square dV 7 29 a u d Fr 1 07 E 5 Hz Fr E 4 Hz w a AD Channel 2 Pr35_Sample 4_200 900Hz_Apr 03589 009 Line 1 dY 7 29 a u dAm 1 18 nm Am pm 5000 4500 4000 3500 3000 2500 2000 1500 1000 Length 48 2 au Height 371 819 kHz Figure IL 14 Frequency shift plot of Au Ni A 0 9 nm Sample 4 191 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 5_200 900Hz_Apr 03687 032 Line 1 filter 3 square Fr 2 E 4 Hz 254 dv 3 67 au d Fr 7 32 E 4 Hz AD Channel 2 Pr35_Sample _200 900Hz_Apr 03687 032 Line 1 Am pm dV 3 67 au dAm 773 84 pm 40 45 50 Length 54 4 a u Height 245 479 kHz Figure IL 15 Frequency shift plot of Au Ni A 1 2 nm Sample 5 192 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Sample 6_200 1000Hz_Apr 03040 022 Line
144. ng R Si_200 900Hz_Apr 05490 005 Line 1 4500 Texas Tech University H S Tanvir Ahmed December 2010 dV 4 83 au d Fr 4 33 E 4 Hz V au Am pm dv 4 83 a u dAm 383 91 pm YV au 60 70 Length 72 6 au Height 370 542 kHz 20 95 100 105 110 115 120 125 Figure IL 36 Frequency shift plot of sample 4991012 R Si 213 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Hydroxy Coating Ti Si_200 900Hz_Apr 05540 018 Line 1 filter 3 square dV 8 72 a u d Fr 5 07 E 4 Hz Fr 7E 4 Hz AD au dAm 417 00 pm Am 20 30 ao so 60 70 80 90 100 110 120 130 Length 1213 a u Height 429 568 kHz gt Z Figure IL 37 Frequency shift plot of sample 4991012 Ti Si 214 Texas Tech University H S Tanvir Ahmed December 2010 I F Frequency shift curves of Silicon wafers Channel 1 Pr35_Si 111_200 900Hz_Apr 04579 024 Line 1 filter 3 square Fr 7E 4 Hz 45 dV 8 68 a u d Fr 1 08 E 5 Hz AD Channel 2 Pr35_Si 1411_200 000Hz_Apr 04579 024 Line 1 dv 8 68 a u dAm 725 85 pm Am pm Am 4 8 2500 Length 90 3 a u Height 451 627 kHz 7 Figure IL 38 Frequency shift plot of Silicon 111 215 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Si base_200 900Hz_Apr 04682 016 Line 1 filter 3 square dV 7 58 a u d Fr
145. ng on the size of the area scanned place the right marker Take note of the dx value on the top right corner of the plot Now from the Device gt Calibration gt xy scanner window put 3 0 the width of a cycle in microns as stated on the AFM grid box in the reference x step width field and the measure dx value from the mentioned figure divided by 10 or 20 depending on how many cycles you counted on the measured x step width field Press OK to exit the window You may check the calibration by scanning an area again on the grid and measuring a number of cycles 1 D 10 Rotate the AFM grid by 90 degree and scan in the y direction radio button on the scan panel After processing the z image take a vertical marker measure 10 cycles and note the dx value This time put the dx value divided by 10 on the measured y step width field in the xy scanner window The reference value is 3 0 as stated earlier If you like you may check the calibration by scanning the area again The xy scanner calibration is not probe specific and hence needs to be done only once Even if new probe is installed the xy calibration will still hold true as opposed to z and z opt calibration and the load non linearity I D 11 Once all of these tests and calibrations are done run the amplitude correction test from the Device gt Calibration gt Amplitude Correction menu After the test is complete a window will appear see Figure I 6 Also please refer to
146. niversity H S Tanvir Ahmed December 2010 0 08 r Niandits alloys from Gu et al 0 07 L Cu and its alloys from Dao et al A This study Predicted by equation 0 06 0 05 0 04 L 0 03 Strain rate sensitivity exponent m 0 01 o L i i i bevit 1 Li ji pit i i bt bent 1 fe ti i ti 1 iy evil 1 ff riirii 1 it stiit 1 E 00 1 E 01 1 E 02 1 E 03 1 E 04 1 E 05 1 E 06 1 E 07 Grain size d nm Figure 1 29 Strain rate sensitivity of Cu 19 and Ni 26 as a function of grain size 1 3 4 Tensile test of nanocrystalline Au Cu foils The nanocrystalline Au Cu alloys have a composition of Au 100 Cut where x lt 20 weight percent and are about 20 um in thickness The free standing foils are synthesized 27 28 29 using electrodeposition through pulsed current The laser cut foils are tested to failure in tension using the TestResources tensile testing machine and are mounted using wire grippers Rate sensitivity experiments are performed by moving the linear actuator over a constant distance while varying the test time Figure 1 30 shows a representing load time plot for a Au Cu sample SEM images are taken of the failed cross section to determine the width Figure 1 31 shows such an image from which the width of the corresponding sample was determined Highest load value from the load time plot is taken to obtain the ultimate strength of the sample 47 Texas Tech University H S
147. nvir Ahmed December 2010 E Ee 1 13 where E is the elastic modulus of the fully dense solid E is the elastic modulus of porous material P is the porosity and k and kz are fitting coefficients As discussed earlier the E value of fully dense silver is measured to be 36 35 GPa Taking this value as E and taking k and ko to be 1 25 and 3 45 respectively equation 1 12 and 1 13 are plotted on Figure 1 10 In these cases the critical porosity P porosity at which the strength becomes zero is derived from the prediction of the linear fit of the strength plot and is approximated to be 80 The assumption of zero strength at 80 porosity originates from the strength plot and is discussed later in this section Gibson 2 proposed a relative approach for the estimation of the Young s modulus of the open cell porous membranes 2 E P cle 1 14 Eef a Ss where E and pare the elastic modulus and density of the membrane respectively The E relative modulus is plotted as a function of the relative density 2 in Figure 1 9 and the data are fitted with a power law As a crosscheck to the reported value of the coefficient C which is a constant related to the cell geometry to be 0 98 43 44 and the exponent to be 2 2 the values found here are 0 9946 and 2 6714 respectively 15 Texas Tech University H S Tanvir Ahmed December 2010 1 2 4 E Es 0 9946 p p R 0 9765 0 8
148. o set up After this you are ready to work with the NA I B Hardness Measurement by Nano Scratch LB 1 Producing Nano Scratch At this point you will be running two software programs NA and UMT simultaneously It is better for the user to keep the UMT software running on one monitor and NA software running on the other monitor The standard operating procedure for producing scratches is as follows I B 1 a The optical microscope attached with the NA head needs to be initialized From the UMT menu bar click on the light icon which will turn on the illuminator You will have two choices to select the one that best suits your need Then click on the Run microscope button that looks like a green arrow button on the menu bar which will initialize the microscope Note that only for the microscope of the NA head the extra piece of extension cable has to be plugged in to the microscope I B 1 b Place a sample on the Y stage and look it under the optical microscope You can focus the microscope from the NA software by moving the carriage z height Then using the x and y movement control from the NA on the Move tab place an area of interest in the middle of the microscope window LB 1 c From the Move tab on the NA device controller click on Run an icon next to the x and y movement arrows and click on the Indentation icon The Run button will only work if the probe is far from the sample
149. oad level beyond the yield load of the previous cycle Figure 1 18 shows a typical stress strain curve for a 0 2 micron nominal pore size membrane at 10 sec strain rate wherein the loading curve will be interrupted at positions marked by horizontal dashed lines beyond the initial yield point and up to the ultimate stress It is suggested that an increase in the elastic modulus will progress with the amount of plastic deformation until the ultimate strength level is reached Thereafter localized necking will reduce the cross section so that further deformation will provide a decrease in the engineering stress and computed elastic modulus 32 Texas Tech University H S Tanvir Ahmed December 2010 150 125 Engineering Stress MPa I ol a 25 0 0 01 0 02 0 03 0 04 0 05 Engineering Strain Figure 1 18 Typical stress strain curve 20 point average of the original curve for 0 2 micron membrane at 10 sec strain rate and positions of interruptions As it is seen from Figure 1 18 for incremented tensile load tests beyond the initial yield point there are approximately five additional modulus measurements as this porous sample is subjected to further plastic deformation at 10 sec strain rate However such number of additional measurements is not always possible For slower strain rates there is enough time to manipulate the loading system For increasing strain rates the number of measure
150. obile dislocations average velocity 20 Dioh et al 75 76 studied the high strain rate properties of materials using SHPB and demonstrated that in some case the higher rate sensitivity above certain strain rates is the outcome of generalization of the impact problem by assuming 57 Texas Tech University H S Tanvir Ahmed December 2010 equality of stress all over the deforming specimen In reality he showed that the stress wave form generated by high impact velocity of the pressure bar induces stress and strain gradients and thus is different from uniform stress assumption that neglects the dynamic effect Today many researchers can now use scratch technique as a comparable method for investigating mechanical properties of materials Nyakiti and Jankowski 66 studied rate sensitivity behavior of gold copper alloys using micro scratch experiments The range of micro scratch strain rates was comparable with the limits of tensile testing and thus reported values of sensitivity exponents were consistent with values as obtained by tensile tests 2 3 Experimental methods and analysis 2 3 1 Micro scratch experiment of porous silver foils Membranes of varying nominal pore sizes 0 2 0 45 0 8 and 3 0 micron are procured from General Electric Osmonics The porosity of the membranes is characterized using the same procedure as stated in Chapter 1 The estimation of grain size is obtained with lineal intercept method also e
151. om Gu et al 0 1 Cu and its alloys from Dao et al Nifrom tensile test Predicted by equation 0 08 Au Ni sample average separation 0 06 0 04 Strain rate sensitivity exponent m 0 1 bob iii 1 ib titi 1 pot wets 1 i hit 1 i i HEE b p et 1 irii 1 E 00 1 E 01 1 E 02 1 E 03 1 E 04 1 E 05 1 E 06 1 E 07 Grain size d nm Figure 3 20 Strain rate sensitivity of Au Ni as a function of average separation length However this model is subject to the consideration whether or not the dislocations actually move towards the interfaces between layers It has been observed 114 115 that edge dislocations in Au Ni ncnl move in the direction parallel to the layer interfaces Also if the layer interfaces are not coherent the resultant stress strain 105 Texas Tech University H S Tanvir Ahmed December 2010 fields produced by the lattice misfit may not be sufficient to resist dislocation motion 113 3 5 Summary Micro length scratches have been made on the surface of a Au Ni nenl and on Hydroxyapatite coating with constant loads at different scratch velocities The scratches have been measured with the Nanoanalyzer tool and software The hardness of the materials is calculated by measuring the scratch width and the actual load The strain rates have been measured as the ratio of the scratching velocity to the width of the scratch The strain rate sensitivity exponent m has been p
152. ope 118 4 6 Probe in contact with a surface having a stiffness of ks 119 4 7 General trend of amp to elastic Modus din nee nines 123 4 8 Power law fit for the known samples to obtain the calibration curve 127 4 9 Reduced elastic modulus of samples determined from calibration curve 128 4 10 Variation of reduced elastic modulus with respect to actual elastic modulus as a function Of POISSON rAfO 25 nse ceeseehiedeateescecelbeesdeecdbendeceweneens 129 4 11 Elastic modulus of Au Ni nanolaminates s0esseeseeoneeoeeoe anana eee n anna a nen 131 4 12 Elastic modulus of Ta V nanolaminates es0eeseeseeeneoeeoeen anna a aane nane 132 4 13 Schematic of a complete cycle of nano indentation 0esseeseeo0eeseneeoeo 133 I 1 A typical square of frequency shift versus vertical distance curve 0 0 eee 167 RADICAL Auto Setup CULV C50 NE nord ceo ola ee ee eR 170 1 3 AFM grid TGZ1 scanned with Probe 41m 172 1 4 Height histogram on the z image of TGZ1 after processing eeeeeeeeeeeeees 172 1 5 A horizontal section of the scanned TGZ1 after processing with line tilt and Step CONTE CEOM s osiris iit ene n Ea e nn er Ba rites ee 173 1 6 Amplitude versus Amplitude correction CUr ve 175 XIV Texas Tech University H S Tanvir Ahmed December 2010 II 1 Frequency shift plot of Ag iii 178 II 2 Frequency shift plot of Ali sens min
153. ous Poisson ratios 126 Texas Tech University H S Tanvir Ahmed December 2010 In determining the Poisson ratio of the sample nanolaminates a rule of mixture formula is used 0 VU V v 4 30 where Vi and V are the volume fractions generally 0 5 each and v and v are the Poisson ratios of the constituents of the sample 8 Equation 4 25 a 0 3074 E R 0 9564 FA L 6 Equation 4 24 a 0 3777 E 4 R 1 5 Equation 4 21 0 0148E R 1 a 4r 8 2 L Calibration materials from experiment oO Analytical Calculation equation 4 21 1 O Analytical Calculation equation 4 24 0 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 50 100 150 200 250 300 350 400 450 500 Reduced elastic modulus E Figure 4 8 Power law fit for the known samples to obtain the calibration curve 127 Texas Tech University H S Tanvir Ahmed December 2010 8 E Calibration materials 7 Samples e 5 a 0 3074 E R 0 9564 0 50 100 150 200 250 300 350 400 450 500 Reduced elastic modulus E Figure 4 9 Reduced elastic modulus of samples determined from calibration curve 128 Texas Tech University H S Tanvir Ahmed December 2010 700 600 gat Na e ee 500 22 iy 9 v 0 1 5 400 v 02 8 v 0 3 0 2 X v 0 4 6 300 NG X v 0 5 eae
154. ow within the surface of contact after application of normal load P z is given by Z 4 5a 2 a R a VRz 4 5b By substituting equation 4 4 into equation 5b we get Jea ER 4 6a 4E 2 3 1 3 ats 4 66 4E R The dynamic equivalent of the probe cantilever with a tip can be represented with a spring mass system 128 as shown in Figure 4 4 For a displacement x the equation of motion of this system is given by mx k x 0 4 7a 116 Texas Tech University H S Tanvir Ahmed December 2010 satak X x 0 4 7b where the spring constant of the cantilever k is given by k _ 3EI 4 70 ih Figure 4 4 Cantilever with bending stiffness ke and mass m is represented with a spring mass system So the natural oscillation frequency of the system is given by Q JE 2xf 4 8a m m k 4 8b CTA 117 Texas Tech University H S Tanvir Ahmed December 2010 Piezoelectric Cantilever Figure 4 5 Actual probe as imaged by an optical microscope An actual probe cantilever system with diamond Berkovich tip is shown in Figure 4 5 When the probe is in contact with the surface the dynamic system can be modeled 128 as shown in Figure 4 6 For a displacement x the equation of motion of the system is given by mit k k x 0 4 9a fete 4 9b m 118 Texas Tech University H S Tanvir Ahmed December 2010 Elastic response of the surface
155. owever this accuracy of prediction remains valid for only up to several thousand grains At high number of grains the calculation by higher order polynomials deviates highly from the actual number of interfaces Figure 3 2 Densely packed hexagonal grains are incrementally placed according to the numbers to find out the number of interfaces 80 Texas Tech University H S Tanvir Ahmed December 2010 800 r 700 y 2E 12x 1E 09x 5E 07x 1E 04x 0 01x 2 2725x 4 3681 R 1 Maximum coincident boundary No of hexagonal cells Figure 3 3 Relationship of number of coincident boundaries with number of hexagonal grains in a densely packed condition Figure 3 4 shows a plot where number of interfaces per cell is plotted with increasing number of cells on the x axis As the number of cells increases the intercept boundary per cell decreases and plateaus out about a value of 2 8 Theoretically the maximum number of intercept boundary per cell that is possible is less than 3 0 Figure 3 2 and 3 4 The polynomials and other logarithmic fits that were used to fit the data could not simulate this asymptotic behavior of the intercept boundary per cell All the equations apparently overestimate this asymptotic value by a factor of at least 2 for high number of grains Because of this reason a general value of 3 0 is used to model the behavior of the intercept boundary per cell This value o
156. oy and bulk nanocrystalline nickel These tensile test results establish the baseline for comparison with other test results iv Texas Tech University H S Tanvir Ahmed December 2010 such as micro and nano scratch Different modeling equations are proposed in this section to predict the experimental data from tensile tests This chapter also describes potential change of elastic properties of porous materials as can be seen with intermittent tensile test experiments The micro scratch techniques are described in Chapter 2 where epoxy mounted porous and dense silver as well as nanocrystalline Nickel foils are scratched on cross sections at different strain rates The hardness properties of the foils are measured from the dimensions of the produced scratches An optical microscope is used to scan the surface to measure the necessary scratch dimension As it is seen in this section there is good agreement between the tensile data and the micro scratch data Nano scratch technique is quite like the micro scratch however done on a much smaller scale and requires more precise control of the equipment Artificial ceramic bone and a Au Ni nanocrystalline nanolaminate nenl are tested with this technique as documented in Chapter 3 This chapter introduces how the grain boundary and layer pair area of a nenl can be included in the analysis for hardness measurement Chapter 4 describes how the elastic properties of thin films can be measure
157. r all the produced frequency shift curves should be aligned on the same plot and for that also the zero amplitude can provide guidance for alignment Another strategy to position the right marker that bounds the onset of plasticity is to conduct a range of frequency shift experiments from lower frequency to upper frequency and image the area If for a particular frequency an indentation can be observed on the imaged surface the right marker position should not go beyond the square of that frequency shift input value See Figure 4 2 For positioning the left marker that bounds the onset of the elastic response care must be taken to avoid the preceding non linear section of the curve One potential way of determining the linear section could be the use of correlation coefficient for a linear fit for a particular position of the left and right markers Then the maximum correlation coefficient for the maximum part of the curve would best determine the linear regime This option however is yet to be implemented in the commercially available software 113 Texas Tech University H S Tanvir Ahmed December 2010 Channel 1 Pr35_Au725_200 900Hz_Apr 03014 033 Line 1 filter 3 square dV 5 83 au d Fr 1 71 ES Hz aah FE 4 Hz Vi au Channel 2 P r35_Au725_200 900Hz_Apr 03014 033 Line 1 dv 5 83 a u dAm 1 40 nm Am pm 4 60 Length 38 5 au Height 307 282 kHz
158. r Ahmed December 2010 Equation 1 30 is plotted as filled circle markers in Figure 1 17 for the specific cases of the four different membranes used in this experiment taking co and cjo to be 0 000367 and 2 21 respectively Furthermore trend lines for three different porosity P 0 25 P 0 35 and P 0 5 average porosity of 0 8 micron and 3 0 micron membranes are quite close to 0 5 are also plotted in Figure 1 17 to show the general effect of porosity on rate sensitivity These trend lines are completely different from those general trends plotted for grain size and filament size being the only variable As seen from this figure the prediction of rate sensitivity governed by the solid trend lines using filament size and porosity as inputs seems to be more accurate and representative of the experimental data It is also suggested that higher rate sensitivity exponent may be achievable for porous materials with larger filament sizes larger than 5 um where the local minima takes place if the porosity is kept at a constant value At constant filament size membranes with lower porosity will have higher rate sensitivity 1 3 2 Intermittent test of Ag foils The continuous loading of the porous membranes in tension produces typical engineering stress strain curves as shown in Figure 1 5 The linear elastic regime of the loading curves is linearly fitted with highest correlation coefficient to obtain the elastic modulus It is seen from these tension
159. racteristic dimension computed for the grain boundary intercept area is little less than 50 of the grain size This factor of 50 is associated with the coefficients of the predictive equation modeled from Figure 3 2 and 3 4 85 Texas Tech University H S Tanvir Ahmed December 2010 Characteristic dimension h nm 0 1 000000000000000 60000 1000 00000000000000 3 100 e Nai e e e e o ee 3 10 e Volume GB area 4 Volume LP area AS Depth P a 3 oe e A oo eee 0000000000 e AC e 4 0 01 iof 0 001 10 100 1000 Width of indentation nm Figure 3 8 Characteristic dimension for grain boundary and layer pair intercept area as computed for a 16 nm grain size d and 0 8 nm layer pair size laminate At a very small indentation depth or width the indenter tip does not reach the first layer interface and hence contribution of intercepted area only comes from the grain boundaries provided the grains are small enough As the indentation increases this layer interface contribution increases almost at a continuous fashion except where the shape of the indenter changes from hemispherical to pyramidal However since the indenter meets with layer pair interfaces intermittently the initial part of the curve fluctuates before the die out of fluctuations occurs This fluc
160. rate loading 76 Texas Tech University H S Tanvir Ahmed December 2010 CHAPTER 3 NANOSCRATCH TESTING OF Au Ni THIN FILMS AND HYDROXYAPATITE CERAMICS 3 1 Introduction Strain rate sensitivity of the flow stress is one of the key parameters to understand the deformation kinetics in nanocrystalline materials Literature studies show that the strengthening of nanocrystalline materials with increasing strain rate as the grain size decreases to about 10 nm 70 The dependence of material plasticity on grain size has been of interest to many researchers The nanometer grain size structures compared with conventional coarse grained materials offer high strengths and better wear resistances 19 26 83 High strain rate sensitivities appear 19 84 to be governed by grain boundary deformation processes as grain boundary sliding and grain boundary rotation The strategy to make materials with ultra high strength is to limit the dislocation movements required for plastic deformations 85 86 However the ability to change shape without failure ductility is often reduced as a compromise to the high strength nc materials In addition to grain size laminating or layering is a method of reducing size to the nanoscale in order to change the mechanical properties of the materials 87 Therefore nanocrystalline nanolaminates ncnl may come with the high strength and the potential for flexibility and ductility at the same time Relevant industrial
161. re are nanocrystalline nanolaminates and are highly non homogeneous and anisotropic because of the structure they have Conventional analysis of nano indentation experiments assumes the material to be homogenous and isotropic to compute the elastic modulus Thus such techniques have limitations to assess this kind of nanolaminate materials Tapping mode frequency shift measurement of thin films is a technique that has been useful for several decades and the basics of that technique have been discussed here However this technique 132 Texas Tech University H S Tanvir Ahmed December 2010 assumes Hertzian contact and thereby neglects the effects of pull force or surface adhesion in forming the analytical model This results in some error in calculation of the elastic modulus of the materials To eliminate that both JKR and DMT contact mechanics have been used to develop a similar model to determine the modulus from frequency shift experiments To have a measure of the surface adhesion nano indentation can be done on the sample to make a complete load displacement curve from which the amount of pull off force can be determined see Figure 4 13 below 138 139 From the pull off force surface adhesion ycan be determined which can be used in the JKR or DMT model Load P A Pull off force Po S Figure 4 13 Schematic of a complete cycle of nano indentation Displacement 6 For using analytic form it is necessary to h
162. responding reduced elastic modulus for all the calibration samples In these calculations the reduced elastic modulus of diamond tip is back calculated from Ta and V data and is taken to be 0 00075 Even though there are reports of Diamond modulus being 1140 GPa and corresponding Poisson ratio being 0 07 126 these values are not consistent and hence back calculation was necessary to find the appropriate value Figure 4 8 shows the plot for the experimental calibration curve and the analytic equations 4 21 and 4 24 Once the calibration curve was formed reduced elastic modulus of the unknown samples were calculated from the curve It is worth noting that all the calculations were done assuming Hertzian contact mechanics wherein the effect of adhesion was neglected Even though the work of adhesion can play a significant role in low load contacts we see from the calibration plot that this error may not be too high i e the correlation coefficient for the power law fit is above 95 Using this calibration curve the modulus of sputter deposited nanocrystalline nanolaminate Au Ni and Ta V 87 100 118 samples were determined from corresponding frequency shift experiments 125 Texas Tech University H S Tanvir Ahmed December 2010 Instead of using calibration the reduced elastic modulus can also be calculated analytically from values using equation 4 24 with values of k and R There is no need to assume natural oscillation fr
163. ress and originates in the formula given by Dorn o c 1 20 where cis the stress c is a constant is the strain rate i e 47 and mis the strain rate sensitivity exponent Thus from the power law fit the strain rate sensitivity is obtained as the slope of the fit and is given by m 0 Ino dIn 1 21 22 Texas Tech University H S Tanvir Ahmed December 2010 The measured yield strength from the engineering stress versus engineering strain curves of different porosity samples are plotted in Figure 1 14 as a function of strain rate in a logarithmic scale The overall strain rate dependent behavior of the porous membranes having similar grain size hg is also plotted in this figure i e the intercept values of linear fit on Figure 1 11 And finally the experimental data set of the dense silver is plotted for comparison The data points are fitted with power law relationship from which the strain rate sensitivity is obtained for each sample set 120 0 1000 sec SSS 0 0100 sec 0 0010 sec ne 0 0001 sec Yield strength o MPa Porosity Figure 1 13 Strength as a function of porosity equation 1 16 The analysis for variation of yield strength of the porous samples with strain rate for the grain size case hz yields a strain rate exponent of 0 0281 0 00383 and that for the fully dense samples yields 0 0215 0 00219 Even though these two rate 23 Tex
164. rs For nanocrystalline nanolaminates competing effects of grain size and laminate size can limit dislocation movement Furthermore because the layers of different materials having different lattice parameters try to match up the resulting phenomenon can be a strained layer effect or superlattice effect 116 117 In such a laminate the lamina having smaller lattice parameter matches up with the lamina having larger lattice parameter Thereby residual tension is induced on the lamina having smaller lattice parameter and residual compression is induced on the alternate layers having larger lattice parameter The resulting elastic modulus of the laminate is likely to be different from each of the individual laminas There can be a significant effect to the presence of a buffer layer and its lattice parameter on the super lattice effect of the laminated structure Au Ni Ta V Au Nb and Cu NiFe nanocrystalline nanolaminates 87 100 118 of different grain sizes and layer pair spacing are coated on Silicon 200 wafers 107 Texas Tech University H S Tanvir Ahmed December 2010 with a Au or Ti buffer epitaxial layer for the Au Ni nanolaminates and Ta buffer layer for the Ta V nanolaminates Elastic modulus of these nanolaminates is measured using Hertzian contact mechanics The optically flat surfaces of the nanolaminates are point loaded with a highly stiff material as e g Diamond where surface adhesion effects are neglected
165. rt made my stay at the mechanical engineering department full of joy and excitement and guided me to achieve my career goals I am also thankful to my doctoral committee Dr Jharna Chaudhuri Dr Alexander Idesman Dr Michelle Pantoya and Dr Shameem Siddiqui for their continual support and inspiration None of this would have possible without the love and encouragement of my parents my brother and sister and my friends Their constant back ups from a land half around the world has always been like a beacon to me I thank my uncle Engr Nazmul Hasan who inspired me to pursue this higher study when I was about to let the opportunity go away in order to take care of a difficult situation Thanks to my wife for her patience and support il Texas Tech University H S Tanvir Ahmed December 2010 I thank the graduate school of Texas Tech University for granting the travel support in the Fall 2008 and the dissertation award in the Summer 2010 I am thankful for the J W Wright Endowment for Mechanical Engineering for supporting me during my study I also thank the mechanical engineering department and Texas Tech University for all the supports towards the completion of my PhD ill Texas Tech University H S Tanvir Ahmed December 2010 PREFACE This dissertation is based upon the research conducted in the Nanomaterials Lab of Mechanical Engineering Department at Texas Tech University The purpose of this dissertation is to find sui
166. s 33 1985 169 191 79 R W Armstrong F J Zerilli Dislocation mechanics based analysis of material dynamics behavior Journal De Physique Colloque C3 1988 529 534 80 P S Follansbee High strain rate deformation mechanisms in copper and implications for behavior during shock wave deformation APS topic of Shockwaves in Condensed Matter 1987 edited by S C Schmidt and N C Holmes Elsevier Science Amsterdam 1988 249 81 J T Burwell C D Strang Metallic wear Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences 212 1952 470 477 82 J T Burwell C D Strang On the empirical law of adhesive wear Journal of Applied Physics 23 1952 18 28 83 K M Lee C D Yeo A A Polycarpou Nanomechanical property and nanowear measurements for sub 10 nm thick films in magnetic storage Experimental Mechanics 47 2007 107 121 84 G Li J Lao J Tian Z Han M Gu Coherent growth and mechanical properties of AIN VN multilayers J Applied Physics 95 2004 92 96 143 Texas Tech University H S Tanvir Ahmed December 2010 85 Y Wang J Li A V Hamza T W Barbee Jr Ductile crystalline amorphous nanolaminates Proceedings of the National Academy of Sciences vol 104 2007 11155 11160 86 T Zhu J Li A Samanta Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals Proceedings of t
167. s from manufacturer to manufacturer and may not have a perfect geometrical shape with a well defined tip radius or symmetry of revolution 105 Even the blunt conical tips are found to be 93 Texas Tech University H S Tanvir Ahmed December 2010 parabolic in the axis of revolution This uncertainty mainly lies with the synthetic diamond used in the tip and the associated machining technique For example 107 the high resolution SEM image of a Berkovich tip reveals lack of smoothness on the indenter tip Figure 1 in the reference Manufacturers data on the radius of the tip is not sufficient and is found be quite blunt compared to their advertised values Also the sharp radius of the tip becomes dull very quickly as subsequent experiments are done with the same tip In such nano regime hardness tests the tip geometry is extremely important to be accounted for 108 and hence researchers using nanoscratch technique mostly use the calibration method 105 106 However in the present study strain rate sensitivity of the material is looked for and using exact coefficient C in equation 3 13 would move the fitted curve up or down without any change in the slope Thus direct measurement method is employed here to find out rate sensitivity exponents 3 4 Experimental results For producing a nano scratch the surface of the sample is first cleaned with alcohol and then a small area is scanned with the cantilever tip to find out possible
168. s the crosshead position as a function of time at a user specified frequency The displacement measured load curves are fit with a 8 Texas Tech University H S Tanvir Ahmed December 2010 twenty point moving average Engineering stresses for the specimens are calculated using corrected cross sectional area Ac 150 10 sec 10 sec 10 sec 125 oO Engineering Stress MPa a N Oo a 25 0 0 02 0 04 0 06 0 08 0 1 Engineering Strain Figure 1 5 Engineering stress versus engineering strain curves for a 0 2 um sample for different strain rates A sample engineering stress versus engineering strain curve is shown on Figure 1 5 for 0 2 um foil for different strain rates The yield stress o is determined at a point on the loading curve beyond which the linearity of the elastic regime is lost correlation coefficient at least 95 The linear elastic part of the loading curve is determined using best available linear fit as indicated by the corresponding correlation coefficient R The elastic modulus E is determined from the slope of the linear fit with an error bar calculated from the corresponding R value as 9 Texas Tech University H S Tanvir Ahmed December 2010 of error E 1 R x 100 1 5 From Figure 1 5 it appears that the elastic modulus measured at the onset of yield point of the engineering stress versus engineering strain curve of the Ag foils
169. se the second comment line instead of the first for my approximation else vol_ind 2 3 pi r 3 pi r 3 cos asin w i 2 r sin asin w i 2 r 2 pi r 3 2 cos 3 asin w i 2 r 3 cos asin w i 2 r number_of_grain vol_ind vol_grain Sif number_of_grain lt 43 0 area_const 2e 8 number_of_grain 6 3e 6 number_of_grain 5 0 0002 number_of_grain 4 0 0056 number_of_grain 3 0 0861 number_of_grain 2 0 7155 number_of_grain 0 6003 number_of_grain else area_const 0 2056 log number_of_grain 1 7013 number_of_grain area i 2 sqrt 3 hg 6 layer_size 100 227 Texas Tech University H S Tanvir Ahmed December 2010 3 0 number_of_grain area_const 2 0e 12 number_of_grain 6 1 0e 9 number_of_grain 5 5 0e 7 number_of_grain 4 1 0e 4 number_of_grain 3 0 01 number_of_grain 2 2 2725 number of _grain 4 3681 end end IIL A 2 Layer Pair Intercept Area Calculation To calculate the layer pair intercept area all dimesnions are in nm Swidth w grain size dg layer pair dAB radius r face inclination angle theta 65 3 deg sface crest angle phi 115 13 deg sface depth h_f scratch depth h therefore h h_f cos theta Area of the face A 0 5 w h_f close all clear all r 50 w 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 40 50 60 70 80 90 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850
170. specimen size and are equipped with strain gauges Data are recorded from these strain gauges from these bars as the specimen is compressed in the in between position Despite its popularity there are some reports that indicate that SHPB results may sometimes be misleading 75 76 The major postulations behind SHPB experiments rises from assuming uniform deformation of the sample i e stress equilibrium and no frictional response of the system which sometimes are not the actual case As an alternative scratch hardness measurements originally introduced by Mohs in 1824 77 have evolved as a method for measuring mechanical properties of bulk materials and thin films Rate sensitive scratch tests can be done to reveal the strain rate sensitivity of a material Inherent rise time for scratch velocity prohibits the sample from being shock loaded Also the scratch test method is not as sensitive to the internal flaws and defects present the material as it is for tensile experiments at high rates In tensile tests the internal defects present in the test material often lead to premature failure through the stress concentration effect Significant variation 31 60 71 can result in the measurement of strength from such high rate tensile tests As such scratch testing can be utilized as a better option for testing materials at high strain rates The aim of this research is to conduct micro scratch experiments on porous silver foils to high strain ra
171. t average shows an overall behavior Figure 1 26 shows a comparative plot of the engineering stress versus engineering strain curves at different strain rates measured at room temperature The measured yield strengths of the samples are plotted on Figure 1 27 as a function of the applied strain rate on a logarithmic scale The exponent of the power law fit of the data points provides the strain rate sensitivity of the nickel specimens A linear relationship is fitted on plot of In strain rate versus yield stress in units of MPa to reveal the activation volume Figure 1 28 The activation volume V is given by 60 dln 06 V k T 1 31a 41 Texas Tech University H S Tanvir Ahmed December 2010 nee 1 31b oo kT where kg is the Boltzman constant 1 381x10 J K and T is the temperature The V slope of In strain rate versus yield stress would give a value equal to At room B temperature T 300K the value of kgT equals to 4 142x107 J Thus the activation volume in nm is given by 4 142 times the slope of the linear fit of the above mentioned plot if yield stress is plotted in the units of MPa Higher activation volume means larger grain size and vice versa The activation volume for this case becomes 0 0733nm which implies that the grain size of the nanocrystalline nickel is about 10 nm 26 assuming Burger s vector for perfect dislocation The atomic radius of nickel is 124pm 64 and hence
172. t for each sample set 24 Texas Tech University H S Tanvir Ahmed December 2010 The variation of rate sensitivity exponent m generally depends on some measure of structural feature size and generally increases with decreasing dimension 19 26 56 Most reports present the variation of m with the change in grain size hg The rate sensitivity of the porous membranes as a function of the grain size fig is plotted on Figure 1 15 In addition strain rate exponents of nanocrystalline submicron gold computed from the tensile tests 57 are plotted in this figure for comparative reference of m to the dependency on grain size dimension of the porous membranes 0 14 gt Au grain size 0 12 L D Ag grain size ad Ag m hg eq 0 1 E L 0 08 i o 0 2 0 06 L 5 o 0 04 0 02 o 0 1 1 10 100 Grain Size h um Figure 1 15 Strain rate sensitivity as a function of grain size For nanocrystalline materials an expression of rate sensitivity m with respect to activation volume V for plastic deformation with a characteristic activation length or dislocation line length L is found in the references 26 58 59 Firstly the critical 25 Texas Tech University H S Tanvir Ahmed December 2010 stress o for bow out of an edge dislocation from Frank Read source in the slip planes is expressed as 59 o S m rss 1 22a L 1
173. table test methods to measure the mechanical properties of nanomaterials Different chapters in this dissertation describe different techniques for testing nanomaterials In general the mechanical characterization of nanomaterials has been limited to small range of strain rates with available static techniques Even though some of the dynamic techniques have originated a long time ago for example the scratch technique was developed by German mineralogist Friedrich Mohs during the early 1800s not many improvements have been made towards developing the details of the techniques as well as analyzing the outcome results Nanomaterials show a great promise as future materials to be used in various industrial applications like MEMS NEMS band gap engineering etc In such prospective applications these materials may go through different strain rates as induced by either mechanical or thermal load For this reason it is very important to find out their elastic and plastic properties over a wide range of strain rates The methodologies developed in this dissertation will enable us to measure the elastic properties of thin films as well as the plastic properties in terms of the strain rate sensitivity of strength as described by the Dorn equation Chapter 1 introduces how a tensile testing machine can be used in a dynamic manner and thereby measure strain rate sensitivity exponents for micro to nano porous silver dense silver bulk Au Cu metallic all
174. tes and compare the results with tensile tests to generate a longer range strain rate sensitivity plot for the porous silver membranes 54 Texas Tech University H S Tanvir Ahmed December 2010 2 2 Background Several researchers documented a change in the sensitivity exponent for various material systems as they compared uniaxial compression test with Split Hopkinson Pressure Bar SHPB test for a wide range of strain rates Freund and Hutchinson 78 studied the problem of crack growth in plastics in high strain rate and reported the existence of a transition shear stress at a transition plastic strain Below that transition stress the dislocation motion is controlled by lattice resistance or discrete obstacles and above that transition stress the regime is controlled by phonon drag Armstrong and Zerilli 79 reported similar transitioning behavior towards high rate sensitivity for copper and o iron Follansbee 80 speculated that limited dislocation mobility by phonon drag could lead to higher rate sensitivity A general description of the mechanical response associated with rate sensitivity is given by Harding 72 He summarized the strain rate response of materials into three major categories with corresponding rate controlling mechanisms These three regions are shown in the following schematic Figure 2 1 labeled as I II and II 55 Texas Tech University H S Tanvir Ahmed December 2010 Yield Stress Log strain
175. tests that the elastic modulus of the membranes does not change with the strain rate and remains fairly constant for each porosity samples However for deformation of the membrane it is postulated that the porous membrane will first plastically deform as an open cell structure and then continue to deform wherein the open cell structure collapses through shear 31 Texas Tech University H S Tanvir Ahmed December 2010 deformation under tensile loading as the filaments or struts realign with the load direction through a bending shearing mode primarily at the junctions between the filaments 61 Generally speaking the junctions between filaments can be visualized as ball joints with three degree of rotational freedom and the filaments align themselves with the direction of the tension as loading starts and become parallel to each other as the test specimen is loaded to its ultimate strength Once the filaments are aligned with the direction of the load the structure will stiffen and the deformation mechanism will change from shear towards uniaxial For the deformation mode to change the elastic modulus measured from the tensile loading should also change as the open filament structure condenses under tensile elongation One way of assessing this postulate is to do the intermittent tensile test wherein the loading curve will be interrupted after initial yielding by complete unloading and reloading 57 62 The reloading should go up to a l
176. th the elastic constants and film modulus More experiments are necessary on almost continuously varying layer spacing samples to obtain a better curve Also the roughness factors of both the sample and the tip 140 need to be considered for higher accuracy 134 Texas Tech University H S Tanvir Ahmed December 2010 REFERENCE 1 H S T Ahmed A F Jankowski The mechanical strength of submicron porous silver foils Surface and Coatings Technology 204 2009 1026 1029 2 L J Gibson Mechanical behavior of metallic foams Annual Review of Material Science 30 2000 191 227 3 A F Jankowski J P Hayes Sputter deposition of a spongelike morphology in metal coatings Journal of Vacuum Science and Technology A 21 2003 422 425 4 J Weissmiiller R N Viswanath D Kramer P Zimmer R Wiirschum H Gleiter Charge induced reversible strain in a metal Science 300 2003 312 315 5 J Biener A Wittstock L Zepeda Ruiz M M Biener D Kramer R N Viswanath J Weissm ller M Baumer A V Hamza Surface chemistry driven actuation in nanoporous gold Nature Materials 8 2009 47 51 6 M Sagmeister U Brossmann S Landgraf R Wiirschum Electrically tunable resistance of a metal Physical Review Letters 96 2006 156601 4 7 S Dasgupta S Gottschalk R Kruk H Hahn A nanoparticulate indium tin oxide field effect transistor with solid electrolyte gating Nanotechnology
177. the elastic modulus of the samples Error in strain measurement cross section measurement and alloy impurity plays a significant role in mechanical properties of the material Also for polycrystalline samples there is a possibility of mixed mode deformation comprising of shear bending and tension between the grains which may lead to lower elastic modulus The linear extrapolated value of elastic modulus of dense silver from Figure 1 6 and the actual value obtained through experiments are close 25 07 GPa as opposed to 36 35 GPa but not in good agreement with each other There can be several underlying reasons for this In open cell foams the initial deformation occurs through bending 2 which may lower the elastic moduli of the porous samples as well as the extrapolated value The validity of the linearity of the elastic regime of the stress strain curve of porous samples is limited due to the early plastic deformations 41 as random pores essentially work as micro cracks in the sample These reasons suggest that a linear extrapolation may not be ideal for estimating elastic modulus at varying porosity For estimation of the fully dense elastic modulus and critical elasticity several researchers proposed specific equations other than using a linear curve fit Yeheskel et al 42 used two different equations to predict the elastic modulus of fully dense solids which are E E GP 1 12 14 Texas Tech University H S Ta
178. this step document the procedure of scanning a scratch The scan is done horizontally by default if not changed The direction of scan can be changed from x to y and vice versa from the Scan tab shown as radio buttons below the imaging area Please refer to the image on page 16 of the NA 2 manual I B 1 0 To scan the scratch it is very important to click on the Go to Scan button on the Measure tab do not click on the Scan tab directly from the top which would move the probe to the start of the existing scan area by keeping the co ordinates same and would show the line trace of the scratch on the to be scanned area It is recommended to produce a low resolution scan of the scratched area and perform a high resolution scan thereafter During nano 158 Texas Tech University H S Tanvir Ahmed December 2010 indentation scratch tests the surface roughness plays a major role in the uncertainty of the scratch width calculations Thus a step size of about 5 of the width of the scratch is fully sufficient in resolving the width 143 i e there should be twenty or more data points to define the scratch geometry in cross section Higher resolution scans can be done on the area but the amount of time and associated tip wear would not add up to the resolution of the width by much The accuracy of the test can instead be improved by doing more than one scratch at same condition at more locations It is very well possible
179. tic Regime Figure I 1 A typical square of frequency shift versus vertical distance curve I C 1 b Go to Device Settings Approach Curves and make sure that the automatic curve processing box is checked This option will automatically filter the measured curves user defined generally the filter coefficient is 3 and square them before plotting I C 1 c Check that the Add button on the Menu bar is pressed This will plot all the approach curves on a single plot 167 Texas Tech University H S Tanvir Ahmed December 2010 I C l d With a value in the Frequency shift field click on the scanned image shown on the measurement panel A cross hair would appear on the image which denotes the position of the measurement The table below would also show this value position and the amount of frequency shift You may also edit those values from the table in case of need Once you have positioned all the points according to your need with corresponding frequency shift values click on Run Wait until the experiment is finished L C 1 e When all the approach curves are measured all the lines on the Af window need to be aligned with each other i e overlay the individual curves For this there is a function on the graph manager GM panel named Align However individual lines can also be aligned by selecting them individually from the graph manager panel and moving them with the arrow keys on the keyboard P
180. to scan and click on Scan button Please refer to the image on page 16 of the NA 2 manual 155 Texas Tech University H S Tanvir Ahmed December 2010 I B l g After the scan is finished click on the z image This will have z at the end of the name of the image Other images will have Am or Z opt or Fr at the end of their respective names Process this image e g line tilt step correction filter gt average etc from the Process on the menu bar of the NA viewer according to your need I B 1 h Move this processed z image to the measurement panel by clicking on M gt icon on the menu bar Both scratches and elasticity measurement has to be done from the measurement panel 1 B 1 1 This version of the NA i e the NA 2 can produce both vertical scratches and horizontal scratches as seen on the computer screen However horizontal scratches will move the probe in a lateral direction perpendicular to the axis of the probe cantilever which can put the cantilever under heavy torsional load This may reduce the life of the ceramic probe and can break it It is NOT recommended to produce horizontal scratches 141 From the measurement panel choose Scratch from the dropdown list Then click on the image that was imported to this panel earlier and draw vertical lines by dragging the left mouse button Note that once the line has been drawn a table on the bottom of the panel shows the properties of the scratch
181. ts are conducted to better understand the operative deformation mechanisms in the evaluation of strength as the scale of the porous structure changes from the micro to nano regime 1 Texas Tech University H S Tanvir Ahmed December 2010 Commercially available free standing silver Ag membranes with constituent micron to submicron porosity and fully dense foils are evaluated here for their rate dependency of strength Preliminary findings 19 indicate that the strain rate sensitivity of tensile tested specimens is found to increase as length scale decreases The trends are similar to those experimental results reported for bulk nanocrystalline metals Underlying structural features that can contribute to this mechanical behavior include pore size filament or strut size and the grain size within These features of length scale are evaluated through monotonic and interrupted tensile testing In this study the effect of pore size filament size and grain size on yield strength of commercially available porous Ag subjected to different strain rate are investigated Different pore sizes of the porous Ag i e 0 2 um 0 45 um 0 8 um and 3 um are studied For testing the specimens we have applied tensile testing which is free from the bending and buckling problems associated with compression testing The strain rate sensitivity behavior of nanocrystalline nickel Ni is also being researched here The nickel foils are obtained from the ele
182. tton at the bottom of the measurement panel and wait until the scratch experiment is finished The machine is highly prone to external noise and it is extremely important that the surrounding of the machine is kept to the best possible quietness during the experiments are running I B 1 m Once the experiment is finished a window will pop up in the NA software environment to confirm that Now go to the UMT software and click on the Stop button on the menu bar of the UMT software This will stop data 157 Texas Tech University H S Tanvir Ahmed December 2010 collection from the force sensor Allow it some time for the system to response Typically it takes about 30 seconds sometimes less before the data acquisition system actually stops the data collection You will see that the number count the number field next to Sample on the Blackbox Please refer to section 6 7 on page 28 of software operating manual part of UMT user s manual stops once the data collection is ended You can later open this file with Fz and Fx information with the Viewer software The Viewer software can either be opened independently or from the UMT panel s menu bar LB 1 n After a scratch is produced vertical scratch it is recommended to scan the area horizontally perpendicular to the direction of the scratch to reduce the influence of thermal drift on the calculation of scratch width The following steps including
183. tuation is dominantly observable if the layer pair size is considerably higher compared to the grain size Figure 3 9 shows such a case where the grain size is 15 2 nm and the layer 86 Texas Tech University H S Tanvir Ahmed December 2010 pair size 1s 4 5 nm Figure 3 10 shows the dependency of the depth with the width of indentation as the radius of the tip increases from 50 nm to 500 nm for a Berkovich tip 10 0000000000000 66060 0 000000006000 lt Volume GB area Volume LP area a m D p u o LC 2 2 Sa hah NG 6 g G O 1 1 10 100 1000 Width of indentaiton Figure 3 9 Characteristic dimension for grain boundary and layer pair intercept area as computed for a 15 2 nm grain size and 4 5 nm layer pair size laminate 87 Texas Tech University H S Tanvir Ahmed December 2010 140 120 L 4 e o 100 ee o e g 0 era r 50 nm E e r 300 nm 60 L j r 500 nm o o 40 ee o gt o 20 oo 0 100 200 300 400 500 600 700 800 900 1000 Width of indentation nm Figure 3 10 Depth of indentation as a function of width for different tip radius for a Berkovich type tip 3 3 Experimental method The use of nanoscale probing techniques makes the mechanical propert
184. ture of a hydrated starch foam Acta Materialia 51 2003 365 371 16 U Ramamurty M C Kumaran Mechanical property extraction through conical indentation of a closed cell aluminum foam Acta Materialia 52 2004 181 189 17 Y Toivola A Stein R F Cook Depth sensing indentation response of ordered silica foam Journal of Materials Research 19 2004 260 271 18 M Wilsea K L Johnson M F Ashby Indentation of foamed plastics International Journal of Mechanical Sciences 17 1975 457 460 136 Texas Tech University H S Tanvir Ahmed December 2010 19 M Dao L Lu R J Asaro J T M De Hosson E Ma Toward a quantitative understanding of mechanical behavior of nanocrystalline metals Acta Materialia 55 2007 4041 4065 20 R Schwaiger B Moser M Dao N Chollacoop S Suresh Some critical experiments on the strain rate sensitivity of nanocrystalline nickel Acta Materialia 51 2003 5159 5172 21 F D Torrea H V Swygenhoven M Victoria Nanocrystalline electrodeposited Ni microstructure and tensile properties Acta Materialia 50 2002 3957 3970 22 Y M Wang E Ma On the origin of ultrahigh cryogenic strength of nanocrystalline metals Applied Physics Letters 85 2004 2750 2752 23 C D Gu J Lian Z Jiang Q Jiang Enhanced tensile ductility in an electrodeposited nanocrystalline Ni Scripta Materialia 54 2006 579 584 24 X Z Liao A R
185. ty H S Tanvir Ahmed December 2010 10 mm sec 8 mm sec 5 mm sec 1 mm sec 7 l 0 5 mm sec 0 3 mm sec Height um fon a IN A D a 2 mm sec 0 20 40 60 80 100 120 Distance um Figure 2 6 A comparative study of the width of scratches at different velocities on 0 45 micron foil A plot of In versus Ino will yield a linear curve with a slope m equal to the strain rate sensitivity For the scratch test data the hardness H is plotted rather than the strength since hardness and strength are related according too cH where c is a constant having a typical value of 1 3 81 82 The rate sensitivity plots of 0 2 0 45 0 8 and 3 0 micron pore size membranes are shown in Figures 2 7 2 10 respectively For reference the yield strengths obtained from the tensile tests as a function of strain rate are plotted as well Material deformation under scratch is mostly of shear type and hence to compare the scratch hardness with the tensile hardness 1 3 times the tensile strength the scratch hardness 64 Texas Tech University H S Tanvir Ahmed December 2010 values are multiplied by V3 These hardness values which are uniaxial in essence are plotted in the aforementioned figures Figure 2 11 shows the rate sensitivity plot for fully dense silver From these figures it can be seen that the slope of the data points from different regions lie at different elevations These discontinuit
186. u Ni d 16 7 nm 2 2 6 nm Sample 13 199 II 23 Frequency shift plot of Au Ni A 8 9 nm Sample 14 200 IL 24 Frequency shift plot of Au Ni A 2 1 nm Sample 15 201 11 25 Frequency shift plot of Au Ni A 1 3 nm Sample 16 202 II 26 Frequency shift plot of Au Ni A 2 9 nm Sample 17 203 II 27 Frequency shift plot of Sample B1119 204 II 28 Frequency shift plot of Sample Au Nb 606 0000 ee eee eesecereceneeeeeeeeeeeeneen 205 11 29 Frequency shift plot of Sample Au Nb 609 A 1 6 nm 206 11 30 Frequency shift plot of Sample Au Nb 615 A 3 2 nm 207 11 31 Frequency shift plot of Sample Au Nb 626 A 0 46 nm 208 XV IL 32 11 33 IL 34 IL 35 11 36 IL37 11 38 11 39 IL 40 IL 41 IL 42 11 43 11 44 IL 45 11 46 IL 47 IL 48 III 1 IL2 IL3 III 4 ILS II 6 II 7 III 8 II 9 Texas Tech University H S Tanvir Ahmed December 2010 Frequency shift plot of sample Cu NiFe 302 A 4 0 nm 209 Frequency shift plot of sample Cu NiFe 303 A 6 7 nm 210 Frequency shift plot of sample 4991105 R S1 nenen nen 211 Frequency shift plot of sample 4991105 Ti S1 anana eaaa 212 Frequency shift plot of sample 4991012 R S1 213 Frequency shift plot of sample 4991012 Ti S1 nenen nen 214 Freq
187. uency shift plot of Silicon 111 cic cesa teen dis castle oheaec nn setae cols hades 215 Frequency shift plot of Silicon base itunes dinde 216 Frequency shift plot of Sapphire 00 2 vs nie nent ceeds 217 Frequency shift plot of Ta V A 8 07 nm Sample 1 218 Frequency shift plot of Ta V A 3 14 nm Sample 2 219 Frequency shift plot of Ta V A 8 07 nm Sample 3 220 Frequency shift plot of Ta V A 3 14 nm Sample 4 221 Frequency shift plot of Ta V A 10 12 nm Sample 5 222 Frequency shift plot of Ta V A 3 16 nm Sample 6 223 Frequency shift plot of Ta V A 2 26 nm Sample 9 224 Frequency shift plot of Ta V Sample 10 225 Program output for Au Ni d 16 0 nm 0 8 nm 230 Program output for Au Ni d 15 2 nm 4 5 nm 231 Program output for Au Ni d 6 9 nm 1 8 nm 232 Program output for Au Ni d 13 1 nm 2 5 nm 233 Program output for Au Ni d 11 4 nm 1 2 nm 234 Program output for Au Ni d 16 7 nm 2 6 nm 235 Change in depth of indentation as a function of the tip radius of a Berkovich HDi one ner et 236 Change in depth of indentation as a function of the tip radius of a Conical tip With DES LEA Le PR RTE a ease yee NG EN gam ed le Leute 2371 Change in depth of indentation as a function of the tip radius of a Cube COMER tp with 90 anglesi serinus E KN IN ENE ag a PN EE eg egen en 238 XVI Texas Tech University H S Tanvir Ahmed December 2010 CHAPTER 1
188. urface This part occurs immediately after the tip starts to contact the surface passed the viscous top layer The tapping mode contact between sample and probe starts from this section In 3 part the amplitude deceases as the probe is further pushed against the surface 1 e loading increases At this point the surface atoms and probe tip begin to oscillate without separation This part is well recognized in the square of frequency shift curve as a linear regime and hence represents the working part of the curve and serves for the measurement of the elastic properties of the material under study 4 This segment represents the damping of probe frequency of oscillation primarily due to the plastic deformation of the material Some other associated effects of damping are surface adhesion due to stiction In any case this portion represents initiation of material failure and is evidenced by a deviation of frequency shift from the linear regime usually with a short horizontal jump in the Figure 4 1 plot This horizontal feature in the curve represents that no further frequency shift is achievable with an increase in loading This part may be an indication of the cyclic fatigue of the material under study and is yet to be developed for research purposes which could contribute to the formation of S N curve in a very short time at frequency loading of about 10 Hz However extraction of the S N curve from this 4 part of the frequency shift
189. urve LD 2 Next it is necessary to find a set point at which the Z nm indicator starts to increase Start from the lower set point and work your way to a higher set point with an increment of 0 05 by clicking on the arrows below the set point indicator Once that unstable set point z indicator starts to increase 170 Texas Tech University H S Tanvir Ahmed December 2010 rapidly is found decrease the set point by 0 5 and save it It is necessary to do this only for the first time installation of a new probe LD 3 Next one of the AFM grids depending on the tip radius needs to be mounted on the NA for scanning The grid needs to be placed in such a way that the grid lines lie perpendicular to the x axis scanning direction 1 2 degrees misalignment is acceptable About 20 30 lines typically in the dimension of 60 um by 10 um need to be scanned along the x axis direction on the grid I D 4 Process the z image with the line tilt and step correction I D 5 Next click on Process gt Height histogram from the menu This will reveal the height difference for the whole scanning area If the probe is not calibrated the height histogram value returned by the program will be very different compared to the actual height of the grid being used TGZ1 20 541 nm TGZ2 104 5 2 nm TGZ3 510 4 nm These height difference values and the period 3 00 0 01 um for the grids are listed on the AFM grid box Figure I 3 shows the TGZI grid sc
190. ver foil Table 2 1 Strain rate sensitivity exponents for different regimes of all specimens Specimen Porosity Strain rate sensitivity exponent Region I Transition Region II 0 2 micron 0 258 0 008 0 0318 0 002 0 0586 0 009 0 1316 0 016 0 45 micron 0 341 0 017 0 0249 0 012 0 0927 0 005 0 1319 0 028 0 8 micron 0 482 0 019 0 0498 0 003 0 0396 0 006 0 1864 0 003 3 0 micron 0 502 0 045 0 0278 0 009 0 0418 0 005 0 2519 0 019 Fully Dense 0 0215 0 002 0 0546 0 006 To investigate any possible higher accuracy in the strain rate sensitivity an attempt has been taken to calculate the hardness using actual area under the tip during scratch as opposed to using the projected area 1 e AWIS Assuming the side wall of 70 Texas Tech University H S Tanvir Ahmed December 2010 the conical tip is tangent to the hemispherical region the actual area of deformation during the scratch with the tip is given by a For scratch within the spherical region 1 cos sin A xr sin Le Al 2 6 b For scratch beyond the spherical region a 30 2 ARR ne 2 7 4 2cosa 2 Figure 2 12 Schematic of the Rockwell tip used for micro scratch experiment Figure 2 12 shows a schematic from which the geometrical area is formulated to these expressions In Figure 2 13 the hardness values calculated using projected area and actual area are shown for 0 2 micron pore size mem
191. with 1 mN force at different scratch velocities on Hydroxyapatite 4991012 Ti rninenentanaennent 96 3 14 Strain rate sensitivity of the Hydroxyapatite coating 4991012 Ti 97 xiii Texas Tech University H S Tanvir Ahmed December 2010 3 15 Scratches at 100 m sec on Au Ni nanolaminate surface sees0ee0eeoeenei 99 3 16 Scratch profiles with 1 5 mN force at different scratch velocities on the Au Ni sample SUrTaG nn nn ni ent 100 3 17 Strain rate sensitivity plot of Au Ni nanolaminate for 1 5 mN load 102 3 18 Strain rate sensitivity of the Au Ni sample as a function of grain size and layer palf SIZES AL sense tn fre al ee 103 3 19 Schematic of equating the hexagonal grain volume with a spherical volume to find out the average separation of interfaces 104 3 20 Strain rate sensitivity of Au Ni as a function of average separation length 105 Als Ae bypieal frequency Shift CULV st omis nt de bem at nee Rite 110 4 2 Approach curve on top and corresponding amplitude on bottom are shown for a nanocrystalline Au coating on silicon substrate 0 0 0 114 4 3 Contact between a sphere and a flat surface on the application of load P 116 4 4 Cantilever with bending stiffness kc and mass m is represented with a spring ASS Syste se sede ag a NE ga a a Ga NGA E NG TEN TAA olan E A ANE aa a a ne ea a 117 4 5 Actual probe as imaged by an optical microsc
192. wn 1 1 It is noted here that by connection only similar width scratches should be compared to each other For example if a scratch on an unknown sample produces 200 nm width only a scratch width of 200 nm or similar on calibration standards should be compared with it 105 In sclerometry method the hardness value is calculated as H k F w L2 where ks is the coefficient of the tip shape F is the actual normal load to produce scratch and w is the width of the scratch The shape of the indenter is very important in determining ks 108 and in reality is very difficult to characterize with sufficient accuracy For similar widths if the normal load is F on a known material and is F on an unknown material then the hardness of the unknown sample H is computed from equation 1 2 that is a rewrite of equation 1 1 and is given by H F 1 3 164 Texas Tech University H S Tanvir Ahmed December 2010 Since for the same scratch width the volume of the tip submerged into the specimens are same the coefficient of tip shape remains unchanged Thus comparing similar widths alleviates the necessity of accurately knowing the tip shape coefficient 1 B 2 b In the direct method of measuring hardness only width and actual load values are necessary to be known from the scratch testing Using the following equations 101 102 103 the hardness of the sample H can be determined as 2 2 Ft 2 N mo sin sr sin
193. xplained in Chapter 1 on the plan view images of the samples using a Hitachi S 4300 SE N SEM The samples are cut in rectangular sizeable dimensions using an X acto knife and are mounted on plan view on a steel stub using epoxy glue on all four corners of the samples The micro scratch experiments are conducted using a Universal Micro Tribometer M UMT mounted on a mechanical vibration isolation table A spheroconical diamond Rockwell tip of 12 5 um radius having 60 deg angle is used to produce the scratches on the mounted samples Figure 2 2 shows a typical set up for 58 Texas Tech University H S Tanvir Ahmed December 2010 conducting the micro scratch test nominal load of 10 gm 98 mN normal to the sample surface is used to make the constant load scratches During a scratch test the Y stage of the UMT that contains the sample on it moves in the direction of the scratch and the tip remains constant at its position applying the load on the surface A force feedback system that records the applied force as a function of time is used to measure the actual force and scratch velocity To induce different velocities of scratches associated time is varied while the lengths of scratches remain same Seven different scratch velocities i e 0 3 mm sec 0 5 mm sec 1 mm sec 2 mm sec 3 mm sec 5 mm sec and 10 mm sec are used to produce all the scratches on the foils At least three scratches are produced at every scratch speed to obtain a good
194. y H S Tanvir Ahmed December 2010 LIST OF FIGURES Design of die dimensions MM 460g sae ates a eee 4 SEM images of plan view on left pre deformation and of cross section on right post deformation of a 0 8 um foil nne neen ne 6 Cross section of a dense silver foil measured with an optical microscope 7 Detachable serrated grips used for tensile tests 0eesenonenoeseon anana anan ne eaaa 8 Engineering stress versus engineering strain curves for a 0 2 um sample for diff rent SANT TALES oa n es a E aaa NG nt AE ere ne ne ae 9 Average elasticity plot for different porosity samples ces eeeeeeeeeeeeeneeeeeeeees 10 Engineering stress strain plot of fully densesilver at different strain rates 12 Elastic modulus of fully dense silver measured at different strain rates 13 Relative elastic modulus as a function of relative density 16 Trend lines for prediction of elastic modulus of Ag at different porosity 18 The yield stress versus porosity plot of different membranes at different Strain TAS a naak an D RER NS aye ay tear ae 199 Strength as a function of porosity equation 1 15 22 Strength as a function of porosity equation 1 16 nenen n ane 23 The log log plot of yield strength versus strain rate The values are fit with a power law relationship to produce the strain rate exponent for e
195. y measurement of ultra thin films accessible which is otherwise not quite possible with macroscopic techniques such as tensile or compression tests Static nanoindentation analysis generally assumes a homogeneity and isotropy of the test material which is seldom the case Moreover nanoindentation is limited to 10 depth of film thickness as the technique is highly prone to sensing substrate effect 104 as the pressure volume during loading lies directly beneath the indenter tip In nanoscratch technique the pressure volume lies in front of the scratch and hence much thinner films can be tested with scratch technique which otherwise are not possible with nanoindentation 88 Texas Tech University H S Tanvir Ahmed December 2010 103 For these reasons nanoscratch technique has evolved as an advantageous measurement procedure for testing thin films deposited on substrates 102 A NanoAnalyzer M trade mark of Center for Tribology CETR Inc is capable of making micro length nano width scratches A number of scratches are produced on the coated surface of the optically flat samples These scratches are made with a diamond Berkovich tip conical and cube corner tips are also available for producing scratches mounted on a ceramic cantilever some tips are mounted on metal cantilevers A typical probe cantilever arrangement is shown on Figure 3 11 A normal load ranging from 100 UN to 2 mN is applied to produce the scratches The velocity o
196. y and layer pair intercept area on a laminated film as 84 Texas Tech University H S Tanvir Ahmed December 2010 the width of indentation increases In this case the modeling has been done for a structure that has densely packed hexagonal columnar shaped grains with grain size de being 16 nm and layer pair spacing 4 being 0 8 nm The characteristic dimension 1 e volume of the indent divided by the intercept area is plotted as the indent goes deeper into the system A Berkovich tip as shown in Figure 3 6 and 3 7 with a 50 nm tip radius is used in this model As mentioned earlier the shape of the tip does not have continuity in all directions as the geometry goes from the hemispherical section to the triangular section This discontinuity is observable in the computation of the interface area as it can be seen in Figure 3 8 at about 20 nm of indentation width The depth of indentation also goes through a fluctuation due to the change of shape of the indenter Other than this discontinuity the penetration depth can be assumed to be linear until the spherical penetration as well as for the pyramidal penetration with different slopes The asymptotic characteristic length computed for the layer pair intercept area is half of the layer pair size as each interface of the layer pair contributes to the calculation However for the grain size all sides of the hexagonal grain does not contribute to the intercept area and thus the asymptotic cha

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