1p » 90p - 酒井・泉研究室
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1. 4 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU EEL ELE 15 22. 210 aun 5 20g a b in tanu K x 17 Image of Reflected Electron Specimen Reflected Electron Secondary Electron 0 22 0000000000 0210 0000 2 23 tel 23 3 24000 80 2 34 SEMQO0 3000000000000 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU
3. UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU ENSE e E E 10 a
4. 87 DO 40000000000000000000000000000000000 E LD
5. 5 5 Ha a UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU ils 4 5 60 E ER UUUUU
6. 16 HUUUUUUUUUUUUUUUUUUUO 2 0180 Image of Reflected Electron n T rj 2 z amp N x 1 y i j a r 1 Tr kB 4 E 3 x an m r E m 1 am Reflected Electron Secondary Electron 0 2 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU 0 22 68 2 3 2 1
7. 221 scanning electron microscope SEM LH LU D E E E EE OE U U U ETE Eee ET EEOC EET S ED transmission electron DEED ETE HE ER DESDE B p SEE EPIS EDS E EAE BTE ETE E ip 0 ti hi 13 Fe 5 2 4 2 E IUUUUUUUUUUUUUUUUUU EE E Ba AEE EE DR E E A RO E UA RR GR DER RR 1011111 D RR trans granular fracture L1 L HE E E E E EE FE 000000 integranular fracture IUUUUUUUUUUUUUUUUUUUUUU
8. j n W j a gt 8 5 1 n W hi a U 0 0 L 8 1 000 0 5 6 2 0000 0 5 7 be x 5 3 47 3 000000000 5 8 1 ld gw 5 6 nu 5 08000 58 UUUUUUnNUUUUUUUUUUUUUUUUUUUUUnNOUUUOUU tea A EE OA 0 85 8 Hursti iOD Hurtpo0O 0000000 5 9 5 10000 Charpy Hurst exponent 1 1 r 1 0 1 n ua 5 3 UW
9. 18 Secondary Electron Detector Secondary Electron Detector a signal 0 level b signal 0 level a b signal 0 level ax 0 2 3 0000 19 Power supplies for column Electron column D A converter Add subtract Secondary VJ circuit electron detectors Graphic display Micro computer 0 24 0000 20 24 2 4 1 200000000000 8 46 fractus D E UO D
10. 2 322 nn UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUUOUU 4 1 SM490B SM50B Q 00000000000 000 31320000 29 320000000 JIS Z 22021980 0 40000 0 3 1 9000 massq 32 00000 30 3 23 ductile fracture dg d 1 0000000 24 3 O00000 shear lip 32 0000000000000000
11. 9 A 2 000000 0 LOO00000000000 0000 4001 A2 a 058 amp 5000060 0 0000 0000 400 16 100 THb ab 201 10i 3 84 511 4 A 4 2 34 m0000 W x y 5 4 681m0 000 W x y a A 6 a 9 37 W x y 17 18 amp 8 amp m0 000 A 8 375 mGOOO 78 4007 Al a 9 40 B 0000 4000 000000 All a 1000 og 1 a 2 34 m HH HH J W x y a 0800000 000000 19 A13 6 3 W x ya D da dtt 080006060 Figo THb aL 7 poc 500 8 A16 a 3755m0000 03 080006060 80 0 UB OOOO L BAA E A E E E E Pe 40 44000 W hxo x J by 45000
12. 2 2 log 1 Ds log 2 3 uududgddddduddguuuluduuuuuuuuuuuululuuutlulll 0 c 23 242 hx 5 h x gt i h x 2 5 lt lt 10000 hO 10 000000000000 0 00000 2 D 2 6 2900000000000 0000000000 29000000 400000 2900000000000 0000000000000 29 2901020 JU 400000 20000000000 0000000 2500000 Hurst 2 7 10 2 9 00000000 Hurto 0000000000 9 lt H inpia
13. 37 1005 3 89g m gt 0 0 0 0 1480 a ig O D TI D i t 00 3 3 4 3 3 3 LODE 1 200000000000 300000000000000000 4000000000000000000000000 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU UU
14. 15 10 54 6 2 2 0 8208 0000000000060 0 5 210 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU 63 5 Hurst J L 6 3 1 00000080
15. 3190000 FA pL pr 106 x xj 7 05 RFE FRKU Ag x1 25 230 nik 4427722 2901198 316 3 17 Ex A 0 02 s JU if 3 18 LO ODDO 3 19 0000000 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUUUU TiAiQ00000000000000000000 2 163840 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUUUUUU 163840 0000000000000000006060 41 140 4 1 00 00000000 Hurst 000000 2640000000 2 500 xen t h x h xo x h xo 4 1 s x 4 2 22200 hx G b P 3W hs x br 4 3 no0000000 280004300000 Whxo x ba WIh x xo h xo b a
16. e 23 0000 3000000 2 31 00000000 0000 880 11520 0 0000 0 0 880 x 1152 1 000 000 5 HOU 5 100mm 1 1 D D 0 UO D D U U D U C 100 15000 2 0 880 115208 0000000 1000006060 20 m x 1152 20nm 000 5 20 20 TEI 880 11520000000 100 x 1 1152 0 lmmgO0000 010 02 HB Bh 0
17. Hurst 64 db 0000000 0000000000000 FustQUOO00000002610 00000000 2 0 Burst Hurstt 000 2 Hurst 6319 63300 00 AB 20000 0000000 0 344mmp 00000000000 0172mm 0 00000 HurBt exponent 1 508000000000 08 0 03
18. 48 5 10 000000000000000 0 H H 00000 5100000 1 60 17 000 0 59000 1 60 17 EP IG EET EEG EET ET E EP s 32 I I 5 120 5 140 DD 3 12 00000000000000008 Purse goo 2 150 27D D D L 49 Hurst exponent ductile Parlooo Hurst exponent brittle Parl00D c 1 I s 0 9 ME 0 7 l a zu D 3 0 4 0 6 D B 1 La M 0 6 0 8 a 514 000000000000000 H H Hurst exponent charpy Gault 1 1 1 E A LI C 5 6 i E 5 15 H Hurst exponent ductile Gaulooo Hurst exponent brittle Gaulooo 1 1 zd us 0 7 sl ii 0 3 0 4 0 6
19. AWC PE A l i B 1638400000000 6 1516 12 6 11 H 0 2000000 0 6 12 H 0 5000000 LU 6 13 H 0 80 000000 6 2 2 6 141 61400000 ig Till bi E BEBE PIGET T il 58 6 14 6 15 1095 wiaj 616 6 17 Haco FPSO 0 2 0 379 0 005 0 228 0 003 0 183 0 369 0 164 0 036 0 570 0 004 0 491 0 002 0 511 0 373 0 452 0 042 0 783 0 003 0 745 0 001 0 812 0 347 0 755 0 058 59
20. 3 1 AWC I D Hurstti c DIU 00000 0 823 0 058 0 760 0 071 0 848 0 058 5 2 2 000 Hurst UU 4 a b u D logWthi xo a logaQ 0 0000 540000 leg W h b al 21 12 10 T 4 5 4 b 344u log W h b a og a O O a 6 2 ta an en a a 5 4 46 5 5 Hurst exponent mm 0 5 1 1 5 2 2 5 055 OOOOOOO0000000000 XOO0000000D logwWihk xo a
21. NC 2 13 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUUOUU 0 00000000000 00000000000 Hurst Hurst HUUUUUUUUUUY 2 12 26 26 2 00 0000000 100000000000000 17 con C t h x t hix F 2 14 LI pon B 3 i ai i CIt S c 2 15 uggHgHuspnapgggmnagggaagggugaddgnmudtuaddiuc txthmt EE E S cria 2 16 NOt ooo Dr 2 H 2 17 26 3 ie
22. 4 39 34 34 DEN TID 3 5 000000000000 3 6 0000000000000 35 37 0000000 38 000000000 36 300000 UUODUUL I Stress 7 Stress Stress Stress E 29 9 ETT 310 00000 Lp SIE UU HOU 2 3 3 3 E HOU
23. UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUUOUU 24 210 0O000000 000 6 25 000000000 W f x AS jr x dx 2 8 2 0 0000000 0000 00 l bY dadb x Eff owi IE E 2 9 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU Cas f AU y La ee 2 10 ii D00040 0 21000 HUUUUUUUUUUUUUUUO f A x dx 0 2 11 20000 j k0 0000 6 1 2k 2 0 W f x 2 4k 211 2 f A 2 x k f x dx 2 12 25 ELIT EE GT 2 1000000 211 4 2 6 26 1
24. HurtO J ATJ JU Hurst O 16 6 27 6289 6300 000 AB 20000000000 Oe E mH Hurgt expornent 6 28 H 0 200 63 6 29 H 0 200 0800000000 6 30 H 0 500 080000000 651 6 240 6 26 64 00000000 641 00000000 0000000 Hurstg 0o00 6 4 26 Hurst 0000 6 4 HurstQGO000 00000 IU 0 853 0 008 0 679 0 006 0 427 0 404 0 823 0 058 JUD 0 861 0 013 0 500 0 003 0 249 0 499 0 760 0 071 0 908 0 008 0 532 0 003 0 352 0 652 0 848 0 024 10000000 10 10000
25. 3 24 00000000 LS 31 HOU UUUUUUUUUUUUUUUUUUUOUU B 0 B x100 3 1 200000 S0 F gt 7 100 86 3 2 E WR cos cos L 3 3 JUD L w 000000 N R 0000000000000000000 m 317111 M PU U LU DAL JL D U 330000000000000000000000000 9000 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU 32 His SE Bie ED gt PIHL y 5 tt I tf E 9 33 00000000000000000000000 3 2 5
26. 2 180 00000011 f h t e2 f tdt 2 18 i 1 2 19 LU DD UL BL IEEE OE UU S f of 2 19 27 t Hurst H 2H 2 20 5 2200000 26 4 Hurstp pn rn f 0000000000000 00000 eraged wavelet coetcient method AWC method L1 L L L L DDD D D U 12 28 1 2500 W h x ba h x br a 2 21 W h x b a M gt DOMI AW h x 2 22 4 0 h x a b 2 23 0000000 222000 a w h x a 2 24 0 28 130 0000000000000 L 1L 31 1 000000000000 2 3 2 0000000000 3 2 1
27. 32 4 E s ESI ET FE AT SIE 33 3 3 3 3 1 10 40 0 1 330000 44 97 75 0 05 3500000000000000000000 34000000000000 37380000 3 3 0000 wt Ti C Si Mn V 3 4 Bal 0008 001 001 lt 0 01 Fe Cu Nb Cr O 0 04 0 01 lt 0 01 lt 0 01 lt 0 01 0 029 N H 0 002 0 0006 34 000000 wt Temp C 8775 005 _ Waveform A 3 32
28. 0000000000 A UF Fa MEINEK 2 TIAIDQO0O 000000000000 5 5 72 OO DO L 2000 2 B B Mandelbrot D E Passoja Paullay Fractal character of fracture sur faces of metals Nature Vol 1308 pp 721 722 1984 3 R H Dauskardt F Haubensak R O Ritchie On the interpretation of the fractal character of fracture surface Acta metall mater Vol 38 No 2 pp 143 159 1990 41 No 470 pp 1611 1615 1992 F TEUER i thesis 1998 6b OOOOOO00 000000000000000000000000000 Vol 66 No 644 pp 7410747 2000 1 00000000 000000000 Vol 60 6 3981405 1990 91 0000 00000 0000 1986 10 H E Stanley Fractal Concept
29. E EEE 00000000 gt 4 5 W f x b a W f x 6 ca 4 8 048000000 0000 060 1 1 1 2 8 000000 0000 1 0 b 00000000 5 1 1 52 1 1 NOOOOOO f x k2 O000b 00000000000000000 0 00000 i0000000000000000 mm 0 38 42 0 1 0 1 TNI I After Original Translation 42 000000000 44 Il 51 mathematica3 0 Wolfram Research HL E EB E HE E E U 2 2 51 53 0 5 2 00000000000 33 00000000000 45 0 51000000 160 5 2 1 Hurst Hurst O O UO
30. 6 330 00000000 6 3 00 1 60 65 exponent exponent V gt M 2 mm mm 0 2 0 4 0 6 0 8 1 1 3 4 0 2 0 4 0 6 0 8 1 1 3 ex mnpnagugsBcnauggunagudgesxumnpnaud H H Charpy HursBt exponent 1 1 1 0 4 9 9 h ve 1 5 1 1 5 Hurst EXPONENT ductile Reclooo Hurst exponent brittle ReclDn00 1 11 V W Me IM 0 9 M 5 il 9 9 wa T Vi 0 41 Y 9 71 0 51 0 6 n hd 0 4 56 D B 1 1 2 1 4 0 6 0 8 1 4 6 35 00000000000000 0 6 36 0 0000000000000 H H 66 651 6 4 2 HurstO 0000 Hurst 0000 0000 TI
31. 2 7 2 4 1 41 T 0 2 1000000 2000000000000000000 e curve 1 lt 0 lt 2 e curved surface gt 2 lt D lt 3 UUUUUUUUUUUUUUUUUUUUUUUUOUUUUUUUUUOUU 8 22 line curve plane curved surface solid 28 0000000000 WOU
32. 624 626 1000000000 61 6 3 0000000 Hurstp rtu l 0 2 0 5 0 320 0 006 0 207 0 009 0 162 0 371 0 199 0 013 0 2 0 8 0 313 0 005 0 197 0 010 0 163 0 361 0 176 0 013 0 5 0 8 0 592 0 008 0 530 0 007 0 460 0 381 0 514 0 038 Hu rEL Exponent 6 24 H 0 20 0 Hurst Exponent Hurst Exponent d icd 2500 5000 7509 10000 12500 15000 2501 5000 7500 10000 12500 15000 6 25 0 20 p 0800000000 6 26 H 0 500 0800000060 62 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU E E e e e e E N N Hurst 000
33. 2 0000000000000 1225 0 000000000606060 3 38 34 000000000 3 4 1 E pl 34 22 1 00000000000 HOU
34. 412 ERA 4000 000000000 00 2000 3004 3 130 3 15 UJ 4 O 3160000000000 Image Pro PLUS3 0 Media Cyberenetics t E L L E E E ED E E EL EE EL EE EE 000 0 317 0000000 600 255 3180000 39 3 12 00000000000000 V NET charpy ductile fracture surface brittle fracture surface li ITI 3 14 315 40 25 gt
35. ASOS EE 9 9 TS BG H 0 20 0 H 0 20 0 H 0 50 0 8000000000000 DD TU DE A Be Se MEER iqi eee a eG EE BEBE BL BS piq Be HS 2 eX 25221512250 a asas n a IAT EVE ECE ED ELEC EEN p EME Say fo ES ONG OOD leeds I ae 6 V a gee ZU S10 n n SERO RTT T I s a A A Ts USITAS o eRe exc uam A 2 a 0 58 amp m0000 2 76 A 3 L1 mM OU 1 77 A 4 23
36. L Co LIL IL L Co 1 LIL IL LIL IL CJ CJ Co LIL IL LJ CJ Cd LIL IL L L IL 10 90 130 20 100 OL O0 UU UL 96159 1 1 1 2 1 3 20 21 2 2 2 3 2 4 2 5 2 6 5 3 1 3 2 Ne OCCO ke ee eee wo E E239 01 404 1240404332 1392509 22E 2 22 Wh 223 uL ILS CE oie See tee eee 1 231 B B B ded mE dd EO Shee Oe uae LE 234 SEM STOTT eA s O E hee a s qu 552522025545 55251 261 ae ge EA 2 6 5 S ce s a 264 iii P P 9 alee bole dale ek eke edb IMIG eve wes os te ae ee ce eee DM ye AE 3 3 3 4
37. fa n 4 0 6 DB 1 132 La M 5 24 55 53 UL 6 1 5 62 0000000000 6 2 1 Hurt OOO 0 8208 0000000000 0 0 5 100000 5 5 1 5 0 5 9 000 1
38. 0 2 0 5 0 30 0000 10241654 0 00000000000000000 1024400000000 6 6100 260 0000000000000 0000 FPSO N AWC U 6 0 61000000 99 100 IN l W n Wf 6 1 H 0 20 000000 1 6 2 H 0 20 000000 2 6 3 1 64 2 6 5 H 0 80 000000 1 6 6 H 0 80 000000 2 56 4 x 36 adr 1 a 1 14 a n 0 32 IC ss mume PES Que m a TB 3771 6 TEN 1 B 1 9 p au i apf 5 28 6 7 6 8 q Ef log Wia 1 5 e 1 1 4 al 4 0023 4 x 6 10 AWC d 6 9 5 UU ULL 0 er 0000000 Hurt D D U L 0 82 0 738 0 010 0 589 0 011 0 730 0 311 0 708 0 076 57
39. 1 A 5 2 2 A 6 9331 m JU 000000 2 2 22 77 A 7 188 18 A 8 3 2 32 18 m 134008 ete 10 0 58 amp m 0000 2 79 79 A 12a 2 321m JU HL 000000 1222512 79 A 13a 4609 m0000 1222112 1 80 A 14a 9331m J 2 80 15 18 8 2 2 2 2 80 A 16a 37 1m U DDD 21 1 80 3 1 3 2 3 3 3 4 5 1 5 2 6 1 6 2 6 3 6 4 6 5 U L RIS ICO HE ICED 120 w s a ers 0 55540 220224 24 A AWC HE a BE dob ar ee 5 AW Hurst uice eae ee ee ee ee ee eB BE TTS 97 59 l B yi O EHE EIFE Cee Gl a tal Jie ee 04 TIAN Shas eee ee ee 67 11 O00000
40. 5 HOU UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUUUU 88 99 i 9000 i O OUL JU1 20 100 96159
41. 40 4 1 4 2 5 2 5 3 en 6 1 6 2 6 3 6 4 6 5 70 Bae Se eee 2 2 9 53 292 Aa eee ESTIS 334 PP al p NOAM EMM te oe p qoe ge ge artis ee ge SL BOE i ip ee ee ee tee aa 5 5 EEN TA 521 Hurstt 00000 522 CIT OE u T0343 7208132707232 1219 531 Hurstt 00000 iB iS ala E BEEN oe a Aca ge oe 621 php TET USE ELE EE EE EM BERE REL ERIS RUSE EITC 65 2 i p ms B S TOT EET TT ECT DS ox Tina para as u 64 2 Sa a sus sa SEM TREO OR
42. y 22 20 s iC ee ud JA ATI Ve Me Ses EE SIS FAMED ETE Sees 40 SLO SEM DL CTD ee d S C12 29 02749040 ge b E cee ee M 257755525 puas a2 aE s F Bose u 5 4 b 344u ml U U U log 0 522 2 22 2 9 JT a E a 50 VEC irriter 5 9 MH EOD DS ee ee ee E EXP EPS Sd Pj P ECT Siz i hi s ph phi RE apa m mo mO eus o O PE 333 21552255 5 19
43. 41 522 2 6 2 1000000000 Hurst Exponent 2500 5000 7500 10000 12500 15000 6 18 H 0 200 000000000 H we H Exponent Hurst Exponent I A SY uM yw 6 19 620 IS D Dl UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU ERE N E EE UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU 60 6 3 2 000 0000000000 2 0 2116 22 6 22 H 0 200 0800000000 6 23 h 0500 080000000 0630 260 0000000000000000000000000 FO000 E
44. W h x a f deser T gt lt poc 2 gt lt gt lt um e gt lt x E T gt lt gt lt SS 7 2 e gt lt o gt lt O m A Jh X Xo h Xo dx x j h X dX b Xo 1 E 3 2 1 0000000060 23108 0000000 J mathematica3 0 Wolfram Research tj JU DD D mathematica 123113510 00000600 1 00000000000 2 3 1 1 UJ t ume 1 2 3 2 n 12 3 0 0000000000000000 DU EDGE RE Dp ee dp ATEN TEN TENET a bunkai data level 2 3 2 detan 4 1 4 110 000000 calcFS level tumeg bunkail data level t 0 0 0 4250 0000000000060 ET B Bip Bei E 44 1 9 21 d level 1 0 00000000000 4 wavana level
45. Wih x b Xo 8 4 4 0004300000 W hx x i b a b Xo a 4 5 04300000 44000 4300000 45000000000000000 W h x b xo a i i 2W h x X b Xo 8 4 6 4300 460 00000000000 00000 0000 000 1 5 E E E E HBHP LH 42 42 20000 jiko 0000 6 1 2152 WIF 692 Ik 211 2 AIX KIF 4 7 7 4 j M P di ee Eri j a 41 10 13 10 k 2 19000000 43 khi P
46. 0 8 1 1 4 58 1 i4 Bm 5 16 00000000000000 0 5 17 00 0000000000000 H H 50 53 TIATD D D LI LI U C 5 180 gt 1900000000000000000 5 TiAl creep height mm es Joh 1 NA p y v 0 2 0 3 ASe ii mu mmi EE 9 3 1 Hurst I I U J 5 2 Hurst 0 Hurst OO O 52 amp 51 5 3 2 JU DU Hurst ggg HurstQ O00 5 200 5 210 000 TiAl creep TiAl creepfatigue Hurst exponent Hurst exponent 1 1 1 1 1 0 1 0 E f Tug Ag s N
47. UU EE EVER BERGER EL EE BL EE ELE ee FIT PER EET IC CDL POI 519 U L Zoe pepa p ppp S n n ss Ao MAE El s S eee s 49 224 aaa E ee ee a AU 25 Sige eee TER 2 6 OM 2 9 D 23 Ses GA A 2 10 8 a ua a TAS BERE EFE RE 551622252520 2 12 ee 25 31 0154 2202 1980 0 40000 30 3 5 TS 39 5 9 nk exem 509 30 eee ee Se 39 6 O E el Els tees ee eee 15555 21 SEL IMG Vile ede RET M b
48. pp si TE SOO TS OT pcc PSY TE 522 DN P8 OTT TTT 15522542 5 23 TAINH DET ELE DT BERE D I EE ae 5 5 24 IAT IJ E S pak 525 TAS ETE BT P T T BE 555 ss 61 H O2Q 000000 62 H O2Q 000000 63 H O5Q0 000000 64 H O5Q0 000000 65 H O08Q 000000 66 H 0 80 000000 CF BGA a ee ee ee He DP ee ee ee Du e ee ee eee 0 10 AVEC eS ii a See 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 6 25 6 26 6 27 6 26 6 29 6 30 6 31 6 32 6 33 6 34 6 35 6 36 6 37 6 38 6 39 6 40 6 41 6 42 6 43 6 44 6 45 6 46 6 47 6 46 6 49 A 1 OLS MEMES 2 ee ence u os eee ee ees ETE ee 532 HHO ia Wel ee ee Peon EOD OP X esu ND ee Pp bp B P Ej WL dee cae i A Soe bres Es eer pu B Dip p ss TET ucc 6 sis tus H 02 J sO eh TE
49. 00000 00002000 15 000000 HOU 2 3 040 0000 0000000000 0000000000000000 Hurst UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU EP E EP E 11 5 12 121 0000 21 pO 1 00000006060 20000 30000000000 3000000000000000000 40000000000000 gt 0 00000000 2 2 5 HOU
50. 4 2 j error error Length fit Print N error 83 H TE EETA E I A NO UJ filterRect j n U 6 filterParzen j n 5 filterGaus j n 0 800000000j 0000000000 0000000000000 Uti data ReadList res Record RecordSeparators gt data ToExpression data datazdata 1 datar t t filterParzen j n Fit For isstart i send 1 fitzAppend fit data2 i DE 0 O00 level start Hurst n rtt data ReadList res Record RecordSeparators gt data ToExpression data data data 1 gradi ong For j l j lt Length data 10 filterGaus j 1000 For i l i lt 8 i 94 fitzAppend fit data2 i gradli ong Append Coefficient f x E ListPlot gradlong PlotStyle RG6BColor 0 0 0 Hurst C4 N
51. AI 0 880 0 014 0 656 0 003 0 473 0 430 0 823 0 045 0 789 0 015 0 578 0 002 0 513 0 353 0 764 0 094 0 10001Q0 000000 UUODUUL I Hurst LU L 632 Hurst 6379 6 380 0 OO AB 2000 0 172mm HOU 8 5 67 HurBt exponent li 595 A ta 2 95 0 91 9 86 y 85 TE 5 k i i i mm 0 2 0 4 0 6 0 8 1 0877 638 exponent c3 1 i UTI 0 2 0 4 0 6 0 8 1 2 TiAl creep
52. O makekoch n_ MO 1 2 21 takea k a m 4k 3 takeb b m 4k 2 b c 2atb 3 d a 2b 3 rote Cos PLI SIn Pi 3 CoSEPET SEES x 1 3 b a e C trot x top k takea k takeb k c d x e m lnsert m c 4k 2 mel nsert m e 4k 1 mel nsert m d 4k Koch fk 4 n 1 3 initm m 0 0 1 0 makekoch n initm koch t t 1 n ListPlot m Plot olned gt True Aspect Ratio gt 1 4 Axes gt False affine div Oop O 21000000 2 0000000000 RATNE soshika st en E O A 1 xo Yk HE 95 rnarrayall 000000 86 OO UUUUUUUUUUUOUUUUUOUUOUUUUUUU UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU
53. P RUM 0 81 hy S ie x P i Er a 0 W VAAT M 2 6 i rm 0 2 0 4 0 6 0 8 1 1 4 0 3 0 4 0 6 0 8 5 20 521 TAFE HE ELE E EL EE E EL CE EE E 00000000 5 220 5 230 0 00 Hurst XDOTGIPIA creep rot Parl000 HUTSE Creepfatigue rot parinbo 1 1 ji m B 8 14 A N 0 9 F Sa 8 wy x 0 81 1 0 71 d ER Ku Tow i y P Y i Fi eee Ix ee n 5 22 5 23 5 5 240 9 250 000 52 Hurst exponent Hurst creep rot Gaulooo TiAl creepfatigue GaulD0D z A l 1 f A A pw ju x on m ga JN W l i id 5 6 0 6 0 4 0 6 1 1 2
54. U U UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU 12 90 UUODUUL 25 _ Step 2 Step 3 Step 4 0 25 00000 22 21 iq p PED n D ET ESE ED EE n VEN 2 6 1 2 71 Ut PO f ET ee Po Bo r i b N IL us h A _ E n EA 74 Fou 4 j S k HA F ry Yo FO f w tA EON ME NIC SU ME NI Aor T MUS OU UL L 26
55. UUUUUUU U U 223 UUDUULD 1 14 O O L UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUUUOUU ELE EE E UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUUUOUU ENE BEEN E ee
56. UUUUUUUUUUUUUUUUUUUUUUUUUOUUUUUU E E ET E DE BEL EE UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU ga E E E 10 12 a Fl gl i ll UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUOUU HOU 1 2 0000 00000
57. exiglas block Phisical Review E Vol 60 No 2 pp 133711343 1999 TSS D00 0000000 68 000000000000 Vol A No 249 251 1991 Z3 000 000000000000000 000000000 159 241 0 000 00000000000000 000000000 0000 1993 25 B D Dempsey Schwoeble C S P ande L E Richards N Louat Fractal char acterization of fractured surface Acta metal Vol 35 No 7 pp 163311637 1987 26 I P rocaccia B I shraiman T C Halsey ensen L P Kadano amp Fractal mea sures and their singularities the characterization of strange sets Phys Rev A Vol 33 No 2 pp 114111151 1986 14 2710 000 0000000 0000 1987 28 Benoit B Mandeibrot OO 0000 00000000 00000000 1985 2910 000000000000000000 00000000000000 0 EL UO UO D UI UI O 1997 3010 0000 00 0000000000000000000 0000000 1996 BI HOOOO000 0000000000000 000000 1975 321000 00000000 0000000 1970 33 Gerard Valentin Stephane Morel ean Schumittbuhl M Lopez Anomalous roughening of wood fractured surface Phisical Review E Vol 58 No 6 pp 6999 7005 1998 B44 0000 000000000000000000000000000000 Master s thesis 2000 Mathematica A System for Doing Mathematics by Computer O Second Edition 1992 15 1 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU
58. fatigue Hurst exponent TiAl creep Hurgt exponent 1 1 Lal N Aw 0 9 4 0 8 1 1 2 1 4 1 04 6 9 N 9 7 TOME 0 6 i i i 0 2 0 4 0 6 0 8 1 1 4 1 4 639 640 68 o5 3 641 44000000000000 8000000000060 1684 x 561 0 0000 0 268 m 0000 4 y P L E P 1 EN k 4 Ern AE Spl wo ME et Ai i uF a ia Li a 5 t f i 1 E v 450 Hm 6 41 xXUUUUUUU vB UO DO XI T LG CL tL 42 64 n 400 107 Hurst Expornernt Hurst Exponernt Q 8 e n vtt 0 5 V 6 43 101 6 42 FH 69 Hurst Exponent Hurst Exponent g 644 2018 000000000000 0 5 3010 000000000000 H H Hurst Exponen
59. s Surface Growth Cambridge University Press 1995 11 William H Press Saul Teukolsky William T Vetterling Brian P Flannery NUMERICAL RECIPES inC Q7 D D B 00000 1993 12 Ingve Simonsen Alex Hansen Determination of the hurst exponent by use of wavelet transforms Physical Review E Vol 58 No 3 pp 277912787 1998 13 1994 141 0000 Master s thesis 1997 ERR 1 UUU UUUUUUU 060 Vol 61 No 591 2501 2507 1995 ee a ee 2000 17 ean Schmittbuhl ean P ierre Vilotte Reliability of self a ne measurements P hys Rev E Vol 51 No 1 pp 1314147 1995 18 L T Dougan P S Addison W M C M cK enzie Fractal analysis of fracture a com parison of dimension estimates M echanics Reaserch Communications Vol 27 No 4 pp 3831392 2000 19 A Arneodo G Grasseau Wavelet transform of multifractals Phys Rev Lett Vol 61 No 20 pp 228112284 1988 20 Matthias Holschneider On the wavelettransformation of fractal object J ournal of Statistical Physics Vol 50 963 993 1988 21 Arnaud Delaplace ean Schmittbuhl Knut J orgen Maaloy High resolution description of crack front in a heterogeneous pl
60. step 3 calc 5 000000 3 211 212 221 2221 O O U alldata resfilename test00l res ootrespn O O O EE test001 res testbol res 08 000000 0 0 test x 82 ISl D HOU 5 Sep 00000000 200000 30000000000000 step 30000 C 2 NO data ReadList res Record RecordSeparators gt data ToExpression data data data 1 sum Forli 1 1 zLenogth data 1 i sum Append sum 0 For izl i sLength data For jzl j sLength data i sum jl 42Abs data i j Sum sum Length data ListPlot Log 2 sum Fg L 5 109 1 9 lt end 1 fit Append fit sum ill p PE EO sumgggddstatOg error 0 For i 1 i lt Length fit I error Abs
61. t Hurst Expeonernt A duo Q MI 300 400 pm d d i iu 100 200 6 46 4018 000000000000 0 64 501 H H 70 5 E LE 6480000 6 48 H 0000 163840 0000 H HursBt exponent 1 1 0 9 HN E L V P 9 4 6 49 H 5 71 O0 7 70 BU e E pipi 111311 Hurst 1 Hurst OU U
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