Stress-Life and Crack Growth Calculations on an
Contents
1. da dN m cycle 1E 9 1E 10 OO 1E 11 1EO 1E1 1E2 Delta K Apparent MPa m1 2 Figure 55 NASGRO 7050 T74 Apparent Delta K da DN data Delta K Effective Plot 7050 T74 mvision Environment AIR C 1 11E 9 m 3 97 1E 6 PN 0 0 1 7 gt 0 S E 1E 8 V Z D 3 1E 9 1E 10 621 OZ A E s e eo 1 1E1 1E2 Delta K Effective MPa m1 2 Figure 56 NASGRO 7050 T74 Effective Delta K da DN data 27 Delta K Effective Plot 7050 T74 mvision Environment High Humid Air C 7 12E 9 m 3 31 1E 6 0 0 1E 7 gt 0 ES E 1E 8 Vw 2 2 1E 9 D 1E 10 1E 11 1 1 2 1 1 Delta K Effective MPa m1 2 Figure 57 NASGRO 7050 74 data for High Humidity Air Delta K Effective Plot 7050 T74 mvision Environment salt fog C 1 05E 8 m 3 31 1E 6 aN P 0 1E 7 gt 0 E 1E 8 Z J 1E 9 3 T H 1E 10 1E 11 i 1 1E1 1E2 Delta K Effective MPa m1 2 Figure 58 NASGRO 7050 T74 data for Salt Fog Figure 59 The FE elements used to calculate an average reference stress 28 DISPLAY OF SIGNAL NEIL_GROWTH_TRY1 DAC 124 points 20 pts Secon Displayed T 124 points 1 from pt 1 2 Full file data 16 11 X at 52 Seconds Min 128 3 0 x at 1 Secon2. CU axo irae F Figure 18 The Solution Parameters form The second of the 3 main forms is the Materials form see Figure 19 In this form the location of the materials database is defined and the various material properties applied to each region are defined For this S N part of the project the region fatiguecalc included the whole of the plate model shown in Figure 2 minus the MPC s Also in this form any surface finish or surface treatments can be defined not available for aluminium Two sources of S N material data were available Firstly an S N curve source nol in the following form see Appendix 1 was used 1056005 max R 402 n S max 1 R 200 40 2 source nol was the material Databank of Alenia Aerospazio Divisione Aeronautica Pomigliano D Arco Napoli This was produced for a Kt value of 3 1 and with R 0 06 The S N curve for these conditions is shown in Figure 20 This plot shows both the above S N curve equation and the single linear line fitted through it in MSC Fatigue A bilinear line could also have been used An S N curve for the same material for Kt 1 0 was obtained from MSC MVision for an value of 0 This is shown in Figure 21 In order to make a comparison the Source nol supplied curve was normalised to a Kt 1 0 value and a comparison between these 2 sets of data for Kt 1 0 is shown in Figure 22 The last of the three main forms is the Loadi
3. Estimated Life 46560 Flight uo Figure 32 Fatigue calculated with Source nol 7050 T74 Kt 3 1 data and reference stress time signal Sensitivity to Loading Level In order to assess the influence of load stress magnitude the Design Optimisation form can be run by choosing Job Control gt Interactive gt Design Optimisation buttons see Figure 33 From this form a sensitivity analysis can be run for varying load levels For instance 1 0 2 5 0 1 returns results from 1 0 to 2 5 in steps of 0 1 The result of this is shown in Figure 34 So for instance the fatigue life for a load stress increase of 1 7 1s 6600 flights The results are summarized in Table 1 Table 2 Summary of Stress Life results S N data used Fatigue life in flights 253E3 Mvision 7050 T74 data with stresses increased by 1 7 15 FEFAT Desen Jobname MEILS GN _ Made 10155 Anales Single calculation Denga Lite 1500 Change Paramebers T results Display ed nes Hoda Elman select nos dob f Ureoeieereg ngona parameter C Becsculsie ect lo main menu Leah Feck Pisan RER A 1 ZER L LA GE LE gen VC Ll ERU LN A i1 7414 de TEH 1 5d E Figure 34 Load levels varied from 1 0 to 2 5 Investigation of Stress Conditions Marc amp Nastran The stress conditions in the reg
4. original stress vy bass Crmch Fu eres E Lenag nir Lrech Lew Final Caci Figure 44 The MSC Fatigue crack growth form 23 FTTTITTITIT Figure 46 Standard configurations available for computing a Compliance Function Figure 48 Graphical plot of single crack at hole in tension 24 PESOL Calculation Definition Figure 49 Options for solving the Fracture Mechanics Triangle PKSOL Solution for Stress Intensity F I EZ 1 20 1 Figure 50 Solving the Fracture Mechanics Triangle for K 30 H 25 u lt e 1 2 d 15 10 5 15 20 Crack size mm Figure 51 A typical result showing K versus crack size 25 Ez cade Figure 52 The materials form in Fracture Fracture Mechanics Data Figure 53 Editing the Materials form 26 Delta K Effective Plot Alenia 7050 T73652 LT Environment AIR C 3 438E 9 m 3 372 Alenia 7050 T73652 Environment AIR C 9 225E 10 m 3 659 da dN m cycle 1E 10 1 1E1 1E2 Delta K Effective MPa m1 2 Figure 54 A comparison of 7050 1773652 da dN souce nol data in LT and TL directions Delta K Apparent Plot 7050 T74 mvision Ratio O 1 Environment AIR C 1 11E 9 m 3 97 25 DO O 1 D1 0 1 Hc 0 6
5. geometries Mode II and Mode III crack growth data are scarce Mode I is the most common type of in service failure The curve in Figure 41 is sometimes called the apparent AK curve There are many effects that the Paris equation does not take into account such as crack closure corrosive environments the influences of a notch and static fracture mode contributions One way to model these effects is to derive an effective AK curve modifying the apparent AK curve through all three of its regions This effective AK is then used in the Paris equation to determine crack growth 20 Stresss Intensity Factor K Versus Compliance Function Y The factor Y is sometimes called the Compliance Function In physical terms it is the change in stiffness or flexibility as the crack grows 1 e the structure becomes more compliant as the crack gets longer Y is unity for a central through thickness crack in an infinite body and 1 12 for an edge crack For more realistic geometries the Compliance Function Y is normally more complex Many hundreds of K solutions are available The designer s task is not to derive new expressions for Y but to identify the geometry and loading present and find an existing formula The relationship between stress intensity stress and crack length is known as the fracture mechanics triangle Figure 42 If two of the corners are known the other can be derived Stress Intensity Fracture Mechanics Triangle Crack Size
6. nominal stress from the uncracked body and the crack length The value of 15 further modified by the K solution or Compliance Function this is a function of crack ratio The crack ratio varies from uncracked to 1 fully cracked This Compliance takes into account two effects Firstly as the crack grows the stresses may re 21 distribute and secondly the crack may be growing into higher or lower stressed areas So it is very important to use the correct nominal stress Using Fracture Mechanics in Damage Tolerant Design In one version of Damage Tolerant design the initial crack length a is determined by the longest crack likely to be missed at inspection and the final crack length ay 15 the one which would cause catastrophic failure If the applied fatigue loading is constant amplitude the steps in the calculation are 1 Estimate the size of crack likely to be present in the component when it is first put into service dj ii From a measured value of Kyr estimate the maximum crack length af which the component will tolerate when the applied stress reaches maximum tension An expression for crack tip stress intensity factor will be needed iii Using the same expression for crack tip stress intensity factor calculate AK Substitute AK into the Paris equation to obtain a crack propagation rate This will put da dN in terms of crack length a v Integrate this equation between a a and a af to
7. of expressions have been published such as the well known Rooke and Cartwright publication Most of these are included in the MSC Fatigue database measured from tip Figure 38 The concept of stress intensity Controlling Force Around the Crack Tip s zw d h i F ES Fracture i Zone h d Plastic E EN Zone n s Figure 39 Crack tip yielding Mode Mode H Mode lli Figure 40 The 3 modes of cracking used in fracture mechanics Fatigue Crack Propagation and LEFM Static LEFM provides a numerate criterion for the onset of catastrophic failure in a fatigue test If a crack is propagating under repeated loading a will steadily increase and the value of K when the dynamic load is a maximum will also increase When this value Kuax reaches a material property the crack will extend catastrophically LEFM contributes more than this to fatigue though In a constant amplitude fatigue test ranging from Omax to Omin values of K can be computed for the extremes of load say Kya and Kmin The difference between these is the range of crack tip intensity factor say AK As the rate of crack propagation da dN depends on AK its value can be calculated The rate will depend on and on crack length a which will increase as the crack extends To carry out tests at constant AK crack length must be monitored and the range of load decreased proporti
8. E L 0 L i 168 0 L 0 L 2 1E2 E E 1EO 1E1 1 2 1 1E4 1E5 1E6 1E7 1E8 1E9 1E10 Life Cycles Figure 22 A comparison of the Source nol supplied curve normalised to Kt 1 0 with the MVision curve 11 Figure 23 The Loading form showing the cross referencing of Nastran load case load case ID and time history P t REUS Ee sf Sie See EE Figure 24 The Loading form showing load magnitude must be set to 1 scale factor and mean offset 12 Identify Critical Location Once the Full Analysis option was processed the results were read back in to Patran with the Read Results button The result for damage using the MVision 7050 T74 S N data is plotted in Figure 25 Figure 26 and Figure 27 The critical location corresponds with node 10186 The fatigue life was recalculated at the critical location using the alternative Source nol 7050 T74 Kt 1 0 S N Curve Both these results use the peak stress at node 10186 to calculate fatigue damage and hence life By choosing Job Control gt Interactive the form shown in Figure 28 is spawned which provides a number of useful post processing options including a Results Processing option see Figure 29 which reads in the FEF results file Using this option the table of most damaged nodes Figure 30 and single shot result for node 10186 Figure 31 are shown for the MVision 7050 74 data Note that there is a slight differe
9. Stress Figure 42 The fracture mechanics triangle The fracture mechanics triangle Figure 42 allows a designer to compute any one of the three parameters given the other two Using AK and the Paris equation the instantaneous rate of crack propagation at a given value of a can then be calculated An extension of this using some form of integration will give the number of cycles needed to propagate a crack from an initial to a final length This leads to the fatigue crack propagation rectangle of Figure 43 where knowing any three corners allows the fourth to be computed When considering crack growth then there is a relationship between stress range and life just as there is with the Stress Life S N method In crack growth though life 15 closely related to initial and final crack lengths This forms the basis of a life estimation method that underlies the Damage Tolerance philosophy Final Crack Cycles to Size Failure Initial Stress Crack Size Range Figure 43 The fatigue crack propagation rectangle What is the Meaning of Nominal Stress as Used With a Compliance Function in FE Based Crack Growth Calculations The definition of nominal stress for crack growth calculations is similar to that used in component S N curves Rather than try to consider the stress in the region of the crack tip the stress conditions around the crack tip are characterised using K the stress intensity factor This value is a function of the
10. Stress Life and Crack Growth Calculations on an Aircraft Main Frame Section Using MSC Fatigue Neil Bishop Marco Veltri and Andy Woodward Date 21 August 2001 Report Number RLDO10801 Please note that this work was supported by Alenia Aerospazio Divisione Aeronautica Pomigliano D Arco Napoli a Al enla EROSPAZIO Divisione Aeronautica RLD Ltd Engineering Analysis And Design Hutton Roof Eglinton Road Tilford Farnham Surrey GU10 2DH Tel 01252 792088 Fax 01252 794165 MS C SOFTWARE Registered Company Number 2953415 Stress Life and Crack Growth Calculations an Aircraft Main Frame Section Using MSC Fatigue Neil Bishop Marco Veltri and Andy Woodward 21 August 2001 Summary The main objective of this project was to perform Stress Life and crack growth calculations on a typical aircraft main frame section using MSC Fatigue Thereby demonstrating the possible usefulness of MSC Fatigue as a general purpose fatigue analysis tool The project was based on a medium range passenger aircraft This fatigue analysis software was used in conjunction with Nastran Patran and Marc The following tasks were undertaken Set up model and check model quality mesh density etc Perform Stress Life fatigue analysis with MSC Fatigue Identify critical location Investigate stress conditions In this region MARC Nastran Demonstrate current state of the art techniques for dealing with fracture stress intensity function cal
11. T CHROMIC ACID ANODIZE Experimental S N Curve equation mean value 600 5 1 402 Y 10 Smax I R 200 40 2 CRACK PROPAGATION DATA Forman 7050 T73652 Forg Tk 2 6 mm grain dir LT Units of measurement m Mpa Mpa Vm Inches Ksi Ksivin 9 972 3 372 3 438485 09 1 692889 07 70 98972 64 60432 7050 T73652 Forg Tk 6 mm grain dir TL Mat 7050 T74 5 Curve R 0 06 Kt 3 1 1 E 03 Smax MPa 1 02 1 01 1 03 1 E 04 1 05 CYCLES N 1 06 32 Appendix 2 Marc Results Appendix 3 Nastran Results zs i PPB Re o g i ER Min Principal 0 Nastran a 0 Min Principal a 1 Nastran 1 Min Principal a 2 Nastran a 2 Nastran a 3 Min Principal a 3 33 Min Principal a 4 5 Min Principal a 4 F Min Principal a 6 D Min Principal a 7 d Min Principal a 8 34 Nastran 4 Nastran a 5 Nastran a 6 Nastran a 7 Nastran a 8 Appendix 4 Stress distribution across critical crack plane Plate in Figure 2 Plate in Figure 2 with hole removed hole climb no hole climb 1 hole cruise 1 no hole cruise 1 hole fdapp 1 no hole fdappl 35 hole no hole flare T gt 15 no hole GT 15 hole init des 1 no hole init des 1 hole rota
12. and D1 in the form see Figure 53 have to be set to very low values say 0 1 the reader is referred to the MSC Fatigue User Manual for more details one major difference in the Material form is that the region defined here is the region from which the reference stress 1s to be calculated Figure 54 to Figure 58 show the various da dN curves used In order to perform a crack growth calculation an appropriate reference stress has to be calculated form the model This should be representative of the nominal stress in the model 22 if the feature being modelled hole was not there In order to assess this the stress distributions shown in Appendix 4 were carefully scrutinised and the element area shown in Figure 59 was subsequently chosen in order to calculate an average reference stress The stress history calculated form this region is shown in Figure 60 In the usual way Figure 61 and Figure 62 show the Loading form Figure 63 and Figure 64 show typical final results for the critical location node 10186 Finally in order to assess the effect of corrosion the NASGRO data for 7050 T74 corrosion supplied on the MSC Fatigue CD was used to assess the effect on crack growth rates These results and all other results are summarised in Table 3 These results clearly show the detrimental effects of corrosion and increased load level Table 3 Summary of crack growth results for different da dN data NASGRO 7050 T74 in air
13. culations and crack propagation analysis Perform crack growth calculation with MSC Fatigue e Perform sensitivity studies related to load level An Overview of FEA Based Fatigue Design In fatigue design three core fatigue methodologies have become established The first two techniques that were developed do not model the crack growth process at all Instead they use the concept of similitude to determine the number of cycles to failure Failure being defined as some predetermined crack length or loss of stiffness or separation of the component being designed This means that the relationship between component life and load level in a test specimen can be compared directly with that expected in service assuming the component is tested under identical conditions The first of these two methods is based on stress the so called Stress Life S N nominal stress or total life method The second and more recent technique is based on strain the so called Strain Life Local Stress Strain Crack Initiation Manson Coffin or Critical Location Approach CLA method The third and most recently developed method deals with Crack Propagation and relies on the observation that once cracks become established they have a stable growth period This 15 usually described using linear elastic fracture mechanics It further relies on the assumption that crack growth rates are proportional to the applied stress intensity a function of crack length geomet
14. ds lt Mean 13 36 5 0 43 98 140 RMS 45 79 Time Seconds 123 Figure 60 The reference stress calculated from the elements shown in Figure 59 Figure 61 The Loading form 20 Figure 62 The Loading form showing the same 12 5 scale factor PCRACK Final Situation Figure 63 An example of a final result from a crack growth analysis 30 mam 2 037E4 8 0001 2 9646 2 9992 3 981 ZE e MODIFYING Life Repeats EFFECTS 1 4 1 5 4 2EA CLOSURE 7 0 6 HISTORY N 0 5 gt 0 4 ENVIRON 2E5 4E5 6E5 1 STAT FRAC Life cycles Figure 64 A typical da DN final crack growth curve Conclusions and Recommendations For Future Work Stress Life and crack growth calculations have been performed on the main frame panel shown in Figure 2 Various sensitivity studies have been performed which show the effect on fatigue life of for instance increased loading levels 31 Appendix 1 S N and Crack Growth data supplied by Source nol Source nol was the material Databank of Alenia Aerospazio Divisione Aeronautica Pomigliano D Arco Napoli FATIGUE DATA MAT ALUMINIUM ALLOY AND TEMPER 7050 T74 FORM DIE FORGING GEOMETRY OPEN HOLE DIA 4 8 mm Kt 3 1 HOLE CONDITION DRILLED AND DEBURRED THICKNESS WIDTH 8 mm FATIGUE CYCLE CONSTANT AMPLITUDE R 0 06 ROUGHNESS 3 2um GRAIN DIRECTION LONGITUDINAL CHEMICAL TREATMEN
15. give the number of cycles needed to grow a crack from a to This is the predicted life of the component A classical integration is adequate if the Compliance Function is constant Other Compliance Functions will require a numerical integration as will any non constant amplitude signal Implementation in MSC Fatigue Again the starting point for an MSC Fatigue analysis is the MSC Fatigue form spawned from the tools top bar menu as shown in Figure 44 Now because Crack Growth has been chosen there is a new button Compliance Function at the top of the form This allows PKSOL to be accessed which 16 a useful tool for generating Compliance Functions from a standard library for entering externally defined CF s and also for solving the Fracture Mechanics Triangle to obtain for instance K from crack length and stress level Examples of this are shown in Figure 45 to Figure 51 Once a Compliance Function is available the rest of the MSC Fatigue forms can be generated in a very similar way to the S N approach Figure 52 shows the Materials form In this form the appropriate da dN curve 15 specified da dN data is somewhat more complicated than S N data allowing a number of modifications to be made to deal with for instance history effects crack closure etc These were all turned off in the analysis so that a standard Paris type crack growth calculation was performed In order to ensure that all these effects are turned off the values for DO
16. ion of the crack were investigated with both Marc and Nastran Based on these results it was concluded that principal stresses rather than shear stresses were driving crack behaviour Typical results are shown in Appendix 2 and Appendix 3 Stress Distribution Across Critical Crack Plane Appendix 4 shows the stress distributions across the critical crack direction These results show some very strange behaviour in the region of the panel stiffener and should be investigated further Investigation of Compliance Function with Marc 16 limited amount of work was done with Marc on a 2D model to generate and hence a Compliance Function Y for the panel The results are shown in blue in Figure 35 Again this shows very strange behaviour in the region of the stiffener and it is recommended that this be investigated further with a 3D model The comparison curve generated with the MSC Fatigue Compliance Function generator see later is shown in red In addition some work was done to check the possibility of the crack diverting away from the pre determined directions In order to check this the J Integral value was plotted against divergence angle and this confirmed that the least line of resistance at a crack length of 8mm was straight ahead see Figure 36 Compliance Functions Compliance Figure 35 Blue curve represents result from Marc normalized by 55Mpa Red curve is from MSC Fatigue f
17. ms of mesh refinement a small cut from the critical region in the basic mesh model provided was refined to the order of 4x 8x and 16x The stress results in the critical locations were observed to converge to a value 25 higher than from the standard mesh For all subsequent analysis the standard mesh was used and the stresses obtained were multiplied by 25 ie by 1 25 during the mission profile definition Figure 8 Mesh x 1 Figure 9 Mesh x 4 Figure 10 Mesh x 8 Figure 11 Mesh x 16 Definition of Mission Profiles in MSC Fatigue It 15 not obvious with MSC Fatigue how to set up and apply multiple loadings of the form normally applied to aircraft structures Table 1 lists the various base load stress cases which must be applied These loadings should be applied sequentially one at a time However MSC Fatigue expects multiple loadings to be applied simultaneously linear superposition of these loadings is then usually achieved with the following equation G t Zb d S k fea where P t is the force time history P 15 the magnitude of the force used to produce the static load case usually unity and is the Nastran static stress result at point 1j for load case For the purpose of the work reported in this study the mission profile was easily defined by setting up for each load case a time series of zeros and ones with the base load case being applied by specifying 1 and bei
18. nce between the result in Figure 31 and Figure 32 caused by a very small change in the S N material specification used As a comparison a reference stress was calculated near the critical location see Figure 59 and Figure 60 The location for this region was determined after careful scrutiny of the stress distributions shown in Appendix 4 The fatigue calculation was then repeated using this reference stress and the Source nol 7050 T74 data with Kt 3 1 The result is shown in Figure 32 Figure 27 Plot of total life zoomed 2 13 Figure 28 form spawned from Job Control gt Interactive a PFPOST Options Figure 29 The form spawned by the Results Processing button 1815 Listing al FE wawala ale MEILS _SN_INIT_TRAY FEF Figure 30 Table of fatigue life results for MVision 7050 T74 data 14 MOIE Time Series Single Shot Results Ox Input Filename MEILS 5M IMIT TH r110185 DAC Lycles Filename MEILS SM IMIT TAYT10196 5LF Material Mean Stress Correction Mone Humber af cycles counted Estimated Life 2E Flights Eee Figure 31 Fatigue life calculated with MVision 7050 74 data MOIE Time Series Single Shot Results Input Filename HEIL GROWTH Th D Cycles Filename NEIL GROWTH TRYT SLF Material ALENIA GN Mean Stress Correction Mone Number af cycles counted zn
19. ng form shown in Figure 23 and Figure 24 Here the time histories used to define the mission profile definition are associated with the correct Nastran base stress result and other scale factors and offsets are defined if required Excel was used to create asci load histories which were then read in to MSC Fatigue using the asci to binary conversion utility in the tools pull down menu This requires tools_pulldown plb file to be installed on the system see MSC Fatigue installation notes This completes the solution set up procedure The final task is to run Full Analysis from the Job Control button Once this is finished the results then have to be read back in using the Results button at the bottom of the MSC Fatigue form Figure 19 The Materials form 1000 100 10 1000 10000 100000 1000000 10 Figure 20 A comparison between the equation form of the source no 1 S N curve 7050 74 shown in blue and that fitted with a single linear line in MSC Fatigue shown in pink S N Data Plot 7050 T74 mvision SRH 1774 b1 0 1435 b2 0 1435 E 7 08E4 UTS 510 1E4 1E2 1E1 1 1 1 1E2 1E3 1E4 1E5 1E6 1E7 1E8 1E9 1E10 Life Cycles Figure 21 S N data 7050 T74 obtained from MVision Source no 1 S N data Kt 1 0 7050 T74 mvision SRI1 1774 b1 0 1435 b2 0 1435 7 03E4 UTS 510 T 1 1E4 2
20. ng turned off by specifying 0 These time series P t to P t are shown in the following figures The resultant stress history at critical node 5 10186 is shown in Figure 16 It is important to note that there is always 1 and only 1 load case applied at any given time step Figure 12 Applying load cases in MSC Fatigue Load cases 1 8 Figure 13 Applying load cases MSC Fatigue Load cases 9 16 Figure 14 Applying load cases in MSC Fatigue Load cases 17 24 Figure 15 Applying load cases in MSC Fatigue Load cases 25 32 Stress Life Fatigue Analysis The basic set up procedure for performing a stress based fatigue calculation is given below Most of these calculations can be done from within Patran or stand alone from the command prompt Most descriptions below assume the calculation is being done from within Patran unless otherwise stated If a job has already been set up then a saved file FIN will probably have been created in which all the job set up parameters will have been recorded and this can be read back in using Job Control gt Read Saved Job DISPLAY OF SIGNAL NEILS SN_INIT__TRY110186 DAC 124 points 1 pts Secon NTT ew Displayed 124 points 1 from pt 1 2 0 Full file data Max 19 75 A at 52 Seconds gt Min 261 4 at 1 Seconds lt Mean 30 41 300 RMS 90 36 Time Seconds 423 Figure 16 Principal stress obtained from critical l
21. ocation as a result of applying the 32 load cases simultaneously The starting point is to run Patran read in the appropriate model file and then spawn MSC Fatigue using the tools top bar menu This will spawn the form shown in Figure 17 This is the basic analysis form and should be worked through from top to bottom Firstly an S N analysis type must be set nodal rather than element averaging specified global rather than group averaging chosen and finally MPa chosen Once these basic factors have been determined the 3 basic forms can be filled in Figure 17 The basic MSC Fatigue form Firstly the Solution Parameters form needs to be filled out as in Figure 18 In this form it must be decided if any mean stress correction is to be applied Since all mean stresses in this analysis are compressive it was decided to take a conservative approach and assume no beneficial effect no mean stress correction was performed The Max Abs Principal was used to compute stress results This option picks the biggest principal stress whether 1t is compressive or tensile thus ensuring ranges of stress are properly defined A 5046 certainty of survival on material properties was also defined in this form mm bE ee Mes TE Bii D d ae feet Emir fee eee F Sg amun UU Eigen ind um Leg ped Gee bun U eent be Y 2 Dem U pacem I miy Tae Pam oo la
22. on to a ie 19 Figure 41 shows typical results for tests carried out at constant AK There are three regions Over the middle range of AK the relationship is linear Both scales are logarithmic which means that an expression for this middle portion is da dN C AK where da dN current rate of crack propagation current crack length and C are material properties This is the most used expression called the Paris Erdogan equation For high values of AK the graph diverges from a straight line This is not particularly important in most practical cases because the crack is growing so rapidly that big variations in the formula used here make little difference to the predicted life Much more important is the deviation from the straight line at low AK values If the line becomes vertical as it does in many reported data there is a threshold value of AK below which the crack growth rate is zero Region 1 Region 2 Possible Simple linear threshold relationship region 2 da o dN m cycle 10 wv Region 3 Static tearing 10 Re Log mN Figure 41 Crack propagation rates at constant AK The majority of fatigue crack propagation studies have been associated with long cracks 1 of order 10 mm and low cyclic stresses which are well described by linear elastic fracture mechanics Since Mode I cracking is the most easily studied using standard specimen
23. or an edge crack in center hole R 15 and W 245 0 14000 ET 0 13000 0 12000 D 1 Figure 36 The J Integral value plotted against crack direction 17 Crack Growth Calculation With MSC Fatigue The Concept of Stress Intensity Modern calculations use the concepts of Fracture Mechanics These were originally developed to compute the static loads that can be carried by components containing cracks before being extended to cover fatigue crack propagation The difficulties can be illustrated by referring to Figure 37 A circular hole in a plate carrying uni axial tension has of 3 which increases if the hole 15 elongated a direction perpendicular to the principal stress A possible model of a crack is an ellipse like this but with finite length a and zero width b The simple formula given in the figure then predicts that will be infinite so that any value of the nominal stress o will cause an infinitely high tension at the crack tip This implies that the crack will propagate catastrophically by tearing Experiments show that this does not happen Cracked bodies will carry some load so the analysis must be faulty and an alternative is needed a o K G K 3 K 1 27 K Very large plate O A M f 2b 4 2a gt 2 Circular or hale Elliptical hole Hale Crack Figure 37 Elastic stress concentrations Early theories concentrated on the energy absorbed when the crack move
24. rsd Final Climb Lateral Gust 4 Fullyreversd Cruise Vertical Gust 24 Fullreversd LateralGust_ 24 Fullreversd nitial Descent Vertical Gut 24 Fullyreversed Initial Descent LateralGust_ 4 Fullyrevered Flaps Down Approach Vertical Gust 3 Fullyreversd Flaps Down Approach Lateral Gust 3 Fully reversed The objective of any mission profile definition is to ensure that these loads are applied with the correct magnitude and in the correct sequence In order to get the results in to SI MPa units it was necessary to multiply all stress results by 10 This was done in the mission profile definition see later One very important issue was the nature of the stress conditions For instance was the crack being driven by tensile or shear cracking This issue 1s also addressed in more detail later U3 02 pa JS I HS HR kim WS ui hi Figure 3 Static stress response GT 15 Figure 4 Static stress response GT 15 LA Mari KE Mee 19 EP DH TTE Us HES r a Figure 5 Static stress response Taxi 1 3 Figure 6 Static stress response Flap Down Dep IL i 2 TTL im d HES Figure 7 Static stress response Cruise Lateral Gust Mesh Refinement In order to check model quality in ter
25. ry and stress level An Overview of the FEA Based Fatigue Environment MSC Fatigue is the leading tool for FEA based fatigue design and Figure gives an overview of the MSC Fatigue FEA based fatigue environment The three plots on the left indicate the FEA results applied loading and materials information The three plots on the right show the types of result visualisation that are possible The centre box indicates the types of fatigue calculations that can be done All of the fatigue techniques specified in Figure 1 are completely or substantially based on one of the three standard life estimation methods 1 Stress Life Strain Life or Crack Propagation described in detail later Analysis Options Fatigue Life Contours Geometry amp FEA Results Stress Life TN TT MR Saas Tq i I Crack Propagation Vibration Fatigue Service Loading Multi axial Fatigue Sensitivity Analysis Spot Weld Analyzer and Optimization IN m US 2 LL TTS Materials Data MM Damage Distributions Figure 1 An overview of the MSC Fatigue FEA based fatigue environment In aircraft applications subjected to mainly High Cycle Fatigue HCF situations the data widely available is of the S N form This st
26. s forward but we now concentrate on the stress field around the tip of the crack Westergaard showed that this field can be expressed in such a way that all terms normal stresses and shear stresses on all elements Figure 38 can have a common factor G Ta 2 extracted Geometry form of loading and the way the crack will extend also have effects that it may be possible to quantify for the whole field Combining these into a factor Y we can identify a parameter that characterises the whole stress field near to the crack tip Calling this the crack tip stress intensity factor K we have K Yola If the crack extends when K reaches a critical value we will have a criterion for determining the stress which will extend a crack of length a when Y has a certain value Tests show that this is the case Continuing to limit the discussion to the case of static loading the critical value that K must reach is a material property called fracture toughness symbol Ky Analysis is often limited to the case where the plastic zone near to the crack tip 15 small Figure 39 and the topic is then called Linear Elastic Fracture Mechanics LEFM The three modes of extension that can take place are identified as Mode I Mode II and Mode III as shown in Figure 40 and solutions for Y will depend on the mode as well as on component geometry Closed form solutions for Y exist in many cases and numerical solutions using FEA are common Several 18 compendia
27. tion no hole rotation 36 hole taxi 07 no hole taxi 0 7 hole TDI no hole TDI x hole unloaded no hole unloaded LEGEND hole 1 no hole yaw 1 37
28. udy therefore concentrates on the Stress Life rather than Strain Life approach in conjunction with a crack growth analysis The modules of MSC Fatigue used in this study are therefore Basic S N Fracture crack growth analysis and Utilities for all manipulation of data This report contains only a limited amount of theory relating to fracture fatigue and crack propagation Any readers wishing to obtain more detailed information are referred to any one of the standard textbooks on the topic Set Up Model The FE model used to represent a typical main frame section is shown in Figure 2 This is a small part from the complete main frame positioned approximately in line with the main wheels The model included all of the boundary conditions and Nastran base load case stress results Altogether 32 load cases were required in order to define the complete mission profile and Table 1 lists these base load cases Most of the loads have 2 elements that together create a fully reversed loading sequence Figure 3 to Figure 7 show some typical base load case stress results obtained with Nastran Figure 2 FE model showing critical plane Table 1 Unit Stress Loading Cases to be Used in Fatigue Analyses GroundTurn 6 Fulyrevesd Tai 17 Fulyrvesed Flaps Down Departure Vertical Gust 2 Fully reversed Flaps Down Departure Lateral Gust 2 Fully reversed FinalClimb Vertical Gust 44 Fulyreve
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