卒業論文 フラクタル解析による シャルピー衝撃破断面
Contents
1. 0 00000000000000000000000000000000000 000000000000000000000000000000000 0 0000000000000000000000000000000000 000000000000000000000000000000000000 000000000000000000 00000000000000000000000000000000000 0000000000000000000000 1 12 00000000000 00000000000000000000000000 0 0000000000000000000000000000000000000 00000000000000000000000000000000000000 1 101 0 000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0 000000000000000000 0 000000000000000000000000000000000000 00000000000000000000 0 000000000000000000000000000000000000 0 0000000000000000000000000000000000 400 O0O000000000000000000000000000000000000 O0O000000000000000000000000000000000000 O0O0000000000000000000000000000000000000 000000000 0 0000000000000000000000000000000000000 OOOO0O0O000000000000000000000000 OOO00000000000000000000000000000000000 OOO00000000000000002. 00000004 1000000000000 4 10000000000000 0 0000000000000000000000000000000000000 0 0000000000000000000000000000000 A r4 27 2 3 21 4 000000000000000000 0000000000000 060 lt 1 4 00000000000000000 1 lt d lt 2 dr 10 000000000000000 260 gt dr 20 0000000000000000 3 lt d lt 4 dr 3 0000000000000000 00000000000000000000000000000 233 0000000000000 U l LI ED AH AH Ud 1 0000000000 2 J0000000000000000000 3 0000000000000 800000 0000000000 000000000000000000000000000 20000000 50 0 0000000000000000000000000000000000000 0000000600000 40 4 slope 1 2 8 0000000000000000000000000000000000000000 0000000000000000000000000000000000000000 HEE 000000000000000000000000 0000 70000 S f x f 2 9 800000000 0000000000000 8 5 2d 2 10 2 3 22 00000000000000000 210 000 00000000000000000000000000000000000000 0 0000000000000000000000000000000000000 00000000000 200000000 00000000000000000 146 Coe D 2 11 0 000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0 0000000000000000000000000000000000000 00000000 3 420 000000000000
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4. U 5000000000000 0000000000000000 r 1 O E BEG JG dE L1 0000000 000000000000000000000000000 0 0000000000000000 Fractal dimension of brittle fracture e average Fractal dimension mag1500magi000maggoo mag3000 4 _ 7 mag600 mag1200 mag2000 0 5 10 15 20 25 30 Number of facet observation range 4 39 0000000000000000000000000 4 2 31 Fractal dimension of ductile fracture mag1000 DT E j mag mag2000 mag800 2 Iasz 1 S E average 0 10 20 30 40 50 60 Fractal dimension Number of minimum size of dimple in observation range 440 0000 00000 000 0 000 00 060 000 000 e 400000 1000 000 e 4 3 52 43 0000000000000 0000000000000000000000000 000000000 000 00000000000000000 06 0000000000000000000000000000000 000000000000000000000000000000000000 0004 200000000000000000000000000000000 000000000000000000000000000000000000 000000000000000000
5. 0000 00000 0000 00000 0000 00000 0 00 0 0 age 00000000000000000000000000000000 5 1 100000000000000000000000000 facet 0 000000000000000000000000000000000000 1 0 111 10 1 1 0000000000000000000 void 000000000000 0 000000000000000000000000000000000 20 0 000000000000000000000000000000000 0 5 2 1000000000000000 0000000000000 0000 20000000000000000000000000000000 0000 000000 00000000000000000000000000 0 0000000000000000000000 0 0 4 37 4 381 00000000000 1 0 0000000000000000000 0000000000000000000 000000000000000000 0 000000000000000 4 37 4 38 581 OD L3 OD DI L3 EI EI O L L EG E E EG 0 0 0 0 0 5 1 64 00000000000000000000000000000000000000 0 0000000000000000000000000000000000000 000000000000000000000000000000000000000 00000000000000000000000000000000000000 0 0000000000000000000000000000000000 4390 0000000000000000000 00000000000000 0 00000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0 00000000
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7. Oan IPS ER eo ee drm S 61 DR 64 519 lee re utet eoe aee 64 PPE ees 65 54 TAR 04 65 EE 73 UL 3 1 3 2 3 3 3 4 EEE mass eM 30 Der cf ch 30 querela tat i een tora Ea 31 CH RT Sr ee er ee ei 37 1 1 8 Eh 111 000000000 0 000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0 0000000000000000000000000000000000000 Fractgraphy 0000000000000000000000 0 0000000000000000000000000000000000000 0000 5 0 0000000000000000000 15000000000 0 00000000000000000000000000000000000000 0 0000000000000000000000000000000000000 OOO000000000000000000000000000000000000 OOO00000000000000000000000000000000000 0 0000000000000000000000000000000000000 00000 300000000000000000000000000000000 0000000000000 2000000000000000000000000 0 0000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0 00
8. OOO000000000000000000000000X0000000000 0 3 5 0 Zi ot gt T48372 UI 18M 1 2KX 888112 ES 4 3 5 2000 000000000000 56000 0000000000000000 3 4 34 34 0000000000 341 000000000000 0000000000000000000000000000000000000 0000000000000 0000000000000000000000000000 05 00000000000000000 3 60000000000000 00000000000000000000000000000 00000 3 6 00000000000 00000000000 N n On 3 1 000000000000 0000000000 0000000000000 00000000000 9000000 2000000000000 0000006000000 233 00000000000000000000000 00000000000000000 000000000000000000000000 0 0000000000000000000000000000000000000 3 4 35 342 00 OOOO0000000000000000000000000000000000 342000000000000 7000000 00000000000000 00000000000 00000000 0 3 7 000000000000 00000 N n 32 000000 0 3 7700000000000000000 000000 PUOUUUUUUUUUUUUUUUUUUUUUUUUUUUDU 000000000000000000000000000000000000000 0 0000000000000000000000000000000000 200 80000 0000
9. 400000 500000000000000000000000000000 000 9000 00000000000000000000000000000 420000000000000000006 50000000000000000 0 0000000000000000000000000000000000000 000000000 Fractal dimension of brittle fracture average Bge Fractal dimension 1000 2000 3000 4000 5000 6000 Observation magnification 4 37 000000000000000000000 42 49 Fractal dimension of ductile fracture average Fractal dimension 0 1000 2000 3000 4000 5000 6000 Observation magnification 438 J000000000000000000000 0 00000000000000000000000000000 0000000000000000000 0 000000000000000000000000000000000000 1 1 1 00000000000000000000000000000000000000 0 000000000000000000000000 7000000000000 000000000000000000000000000000000 SEMUUU 00000000 124 0000 50 0 000000000000000000000000000000 00000000000000000000000000001000 0000000000000000000000000000000 OG L L rr ee 3 E
10. 75 18a 8KU 1 5KX 999123 U 411 0000 1500000000 410 0000 1200000000 8572 15 0908112 412 0000 1500000000 BE BBN ABS TW 375 0 16H 2 KX j 888123 413 0000 2000000000 44 8572 15 8KU 2 KX 888112 4 14 0000 20000 00000 TW0375 10 0KU 888123 415 0000 3000000000 TWOS7S 18 8KV SE S KX 888123 000112 3 80 186 5 860 8372 416 0000 3000000000 TW8372 15 8KU SE 5 KX 888112 4 17 0000 5000000000 418 0000 5000000000 42 0000000000000000000 45 82200 gt gt 4 19 000 400000000 4 20 0000 400000000 lt U 421 0000 600000000 4 22 0000 600000000 4 23 0000 800000000 4 24 0000 800000000 42 0000000000000000000 46 4 25 0000 1000000000 4 26 1000000000 p p 427 0000 1200000000 4 28 0000 1200000000 4 29 0000 1500000000 430 1500000000 42 0000000000000000000 47 431 0000 2000000000 4 32 0000 2000000000 4 33 0000 3000000000 4 34 0000 3000000000 gt lt gt 435 5000000000 4 36 0000 5000000000 4 2 42 2 50 48
11. 0 50 100 150 200 250 300 350 400 um 4 45 186400 000001 31000000000000000000000000000000 1 1 0300 14 42 00 00000000 00000001 43 JOO0000000000 56 OOO 100000000000000 1200 OOO 10 1200000000 5 mx 1004 4000000000000 XUUUUUU 0 a 1 1 01 1 02 1 03 1 04 1 05 1 06 1 07 Fractal dimension 446 OOOO 00000000000 1 800 5000 100 0000000000000 0000000000000 000 sou 0000000000000000000 00000000000000000 43 1 57 75 00 0 100000 20000 400000000 0000000000000 ine400 ine250 ine100 Fractal dimension 4 48 10000000 2 43 58 1 2 1 13 1 1 1 05 1 0 50 100 150 200 250 Fractal dimension um 449 line2500 0000 2 Fractal dimension 4 50 line400 2 800 OOO 1 1 03000000000 1 1 1 200000000 59 43 D HH EL EL EL D 1 1 1 EE OOO 200000000000000 8000 1000000000000000000000000000000000 00000 2000000000000000000000 00000000000 0 0000000000000000000000000000000000000 00000 OOOO
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13. ET dad 45 MW Bred Badge s mt uus 45 COO TN yasta per aeo Se 45 ETT TTC TIT 45 aaa 45 aces 46 OOO 46 FM e d d or des 46 HOT ee e 46 46 Fron HH PE E 46 M OOOO TMM See Gea Saad 47 5 2 47 B OOO rene 47 E ea 47 es 47 aene do 47 4 1 48 4 88964 49 50 440 00000000000000000000000000 51 441 0000 000000000001 53 125 nnn E EL 54 AAS b 54 444 Wy yl e bre emer 55 de 55 AA uo ea se a paie 56 44 57 AAS Scr erd 57 ATR OTM TERNI rsa qhata 58 TN NN 58 H o REINE 59 452 0000 YO00000000003 60 Ses 60 8 61
14. 0 40 1900000000000 MTT cica sok 42 ATT ME m de apen 4225 oet Rare 2 AOD Marr porer eere s e sssi 233 AI AI PTA E a ulaqa 239 RP EET e di Aita testen 050 51 00000000000000000000000000 52 110011 000 01010000 0000 060 E re ee 25 28 29 30 33 34 34 35 38 39 40 41 41 48 52 52 53 62 63 67 68 69 70 71 UL 1 1 2 1 2 2 2 3 2 4 2 5 2 6 2 2 6 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 4 1 4 2 4 3 4 4 4 5 4 6 9 x 14 area 15 CRT 16 ME a abil ae 18 19 20 EI ED EVEI EI Yeu a 26 nnd DT DD TT 27 E eS 29 0000000 Is 2 2202 1980 0 40000 30 4 lia Sy 31 sote za yu um 32 SEMA MT WMC MIU ana 33 2 2 i 34 00000000000000000 36
15. 0000000000 DI CI CI 2 3 E CI 23 431 UUUUUUUU 000000000000000 100 200 00 8000000 12000 0 000 200 00000003000000000000000000000000000 4000000000000000000000000000 3 5000 00000 2000000000000 00000000 0000000 5600000000000 100000 20000 4000000 3000 0000000000000 43 53 4 3 2 HOO 100000000000000 8000 000 20 800000000 112 54 m x 1504 0 000 4000000000 000 T 1 01 1 02 1 03 1 04 1 05 1 06 1 07 Fractal dimension 4 41 0000 1 0 000000000000000000000000000000000000 0000000000000 43 JOO0000000000 54 112 5 000 OA Y u 00 0 100000 250000 40000000 00000000000 Ya 000000000000000000000000 4 42 0000 00000000000 1 d n d 1 1 0 50 100 150 200 250 300 350 400 Y um 443 linet00 0000 1 43 55 122 d 2 1 15 H tue 5 fu 1 05 1 0 50 100 150 200 250 300 350 400 Y um 4 44 1 25000000000 1 1 2 Fractal dimension
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17. 800000000 11254 150 0000 4000000000000 XUUUUUU gm 8 8 He de 0 Fractal dimension 4 51 0000 00000000000 1 0 000000000000000000000000000 43 JOO0000000000 60 0000 10000 8 112 5 000 OA Y u 100000 2500 4000 000000000000 100 gt ine250 ine400 j 450 m Fractal dimension 4 53 line100 0000 3 4 3 61 Fractal dimension 454 116250 O 0 0 3 Fractal dimension m 0 50 100 150 200 250 300 350 400 um 4 55 line400 0000 3 00000000300000000000000000 00000000 00 62 5 1 63 51 O0O0000000000000000000000 ELE 4 37 4 381 000000000000000000000000000000 00000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0 0000000000000000000000000000000000000 00000 00000 000000000000000000000000000000000 0000000000000000000000000000000 BO 000000
18. 0 L L L L 0 1000 2000 3000 4000 5000 6000 Observation magnificant 5 4 0000000000000 00000 5 1 66 0000000000 000000000 00000 0 000000000000000000000000 0000000000000000 000000000 000000000 000000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0000000 3000000000000000000000000000000 52 0000000000000000000 67 2 1111 1 iii E 100000000000000000000000000000000 00 000000000000000000000000000000000 0 0000000000000000000 1 1 0300000000000000 0000000000000 1 1 1 2000000000000000000000 000000000000000000000000000000000000 01 000000000000000000 000000000000000000 E EJ 0 0 200000000000000000000 000000000000000000000000 0 000000000000000000000000 0 00000000000000000000000000
19. 0 28 2 4 24 000000000 241 0000 0 000000000000000000000000000000000000 00000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0 0000000 000000 0 00000000000000 00000000 2000000000 000 R 7 2 12 RMS 1 5 0 0000000000000000000000000000000 2 13 0000 Rt 0000 Ami 0000000000 RE Tiras 2 14 0 000000000000000000000000000000000000 0 0000000000000000 Ra 0 000000000000000000000000000000000000 2 4 24 R 2 15 111 Ra Riu 0000000000000000000000000000000000 A mu Rew 2 16 2 001 10101001010101001011010100100100000011001 4144 2442 E Ai EP HH 25 25 29 Top E 251 0000000000000000000000000000 1 0000000000000000006 000000000000 2 J00000000000000000000000000000000000 00000000000 252 OOOO0000000000000000000000000000000000 ductile fracture 0000 brittle fracture O00 00000000000000 2
20. 00000 210 90 750000000000 0000 b tan0 K x bn 2 1 210 5 0000 10 25 0000000000000 2 000000000000000000000000000 0500000000000 20000000000 90000000 20000 00 0 0 00000000000000000000 2 38 00000000 16 23 000 2 2 17 223 00000000 000000 00000000 2 40000 224 3000000000000 0000000000000000000000000000000000 005 00000000000000000000000000000 000000000000000000000000000000000000 00000000000000000000000000000000000 0 0 OO 0 OO 0 0 0000000000000000000000000 0 000000000000000000000000000000000 0101 r 3 O O 5 1 2 E E 22 22 18 een eee ORNS SERRE EER U 24 000 23 19
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26. 000000000000000 1007777 000000 880 11520000000 CRT OOO 10000000 100 x 1 1152 0 1 0 00000 000000000 0 10 02mm 000000 lt 8 00000000000000 00000000000000000000000000000000 0 000000 000000000000 00000000000000000000000000 0000000000 0000000000 lt 8 0000000000000 2 2 14 0 2 1 0000000000 000000000000000 0000000000000 000000000000000 00000000000000000000 0 0 0 0 0000000000000000000000 0 000000000000000000000 000 0 2 1 00000000000000000000 000000000000000 000000000000000000000000000000000000000 00000000000000000000000000000000000000 0 2 2 0 222 0000000000 0000 1 0 000000000000000000000000000000000000 000000000000000000000000000000000000000 22 15 RETR 0 2 2 000000000 0000000000000000000000000 0 00000000000 0000000 OOO 90000 0 00000000000000 00000000000 0000000000 al 0 00
27. 0000000000000000000 OOO0000000000000000 0000000000000000000000000000000000000 0 0000000000000000000000000000000000000 0 0000000000000000000000000000000000000 000000000000000000000 4 13 14 15 00000000000 000000 00000000 0000000 1994 0 00000000000 00000 00 0 0000 0000 1993 A J Paullay B B Mandelbrot D E Passoja Fractal character of fracture surfaces of metals Nature Vol 1308 pp 721 722 1984 Master s thesis O 1998 000 00000000000 0000000 1988 0000 00000 0000 1986 0000000 0000 1987 00000000 0000000000000 000000 1975 000 00000000 0000000 1970 00000000 00000000 00000000 0 20 1986 O00000 000000000000000000000000000000 U PhD thesis 1998 00000 00000 10000000 1991 00000 Benoit B Mandelbret 1 DO 1 00000000 1985 000 0000 00000 00000 1999 5 16 000000000 00000000000000000000000 6 UU pp LE ape 80238
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