Estimation of Tearing Energy for Fatigue Life Prediction of Rubber Material

匶笾昪律

­

: 㹸ₖ㠦⍞㰖

°

: ⼖䡫⮶ 㠦⍞㰖

ƕ : ┾㥚㼊㩗╏ ⼖䡫⮶ 㠦⍞㰖 Ļ : ⼖䡫⮶

Ɓ : ‶㡊₎㧊 Ɠ : ⼖㥚

§

: ⹮⽋䞮㭧 㭒₆

1. 昢 嵦

ನ

E-mail : [email protected]

TEL : (033)252-6317 FAX : (033)242-6013

*

ἶⶊ㦮 䕢ᾊ 㧊⪶㦖 1950 ⎚╖⿖䎆 㔲㧧♮㠊 Ⱔ 㦖 ⹲㩚㧊 㧞㠞㰖Ⱒ 㩲㞞♲ 䕢ᾊ 㧊⪶㧊 䡚㨂㦮 ἶⶊ Ṳ⹲㠦 ₠Ợ 㩗㣿♮㰖 㞠㦖 ộ㦖 ἶⶊ㦮 䕢 ᾊ 㧊⪶㦖 㔺䠮㩗㧎 ㎇ỿ㧊 ⰺ㤆 ṫ䞮ἶ 䕢ᾊ㦮 䡚㌗㠦Ⱒ 䂮㤆㼺₆ ➢ⶎ㠦 㔺㩲㩗㦒⪲ ㌂㣿㧊 Ṗ

⓻䞲 㧊⪶㩗㧎 ✍⹱䂾㧊 ⿖㫇䟞㠞₆ ➢ⶎ㧊┺.

ἶⶊ 䕢ᾊ ₆㭖㦒⪲㍲㦮 㧎㧦⓪ 1952 ⎚ Rivlin

㠦 㦮䟊 “ 㹸ₖ㠦⍞㰖 (tearing energy)” Ṗ 㩲 㞞♮㠞㦒Ⳇ Andrew ❇

㦖 䌚㎇ὒ 㩦䌚㎇Ṛ㦮 㹸 ₖ㠦⍞㰖 㹾㧊⯒ “ 䧞㓺䎢Ⰲ㔲㓺 ㏦㔺Ἒ㑮 (hysteris

⪲ ⋮䌖⌊㠞┺ 㩦䌚㎇ ㎇㰞㠦 㦮䞲 loss factor)” .

䧞㓺䎢Ⰲ㔲㓺 ㏦㔺㦖 䤚䃊㡺Ⰲ

㠦 㦮䟊 㩫㎇ 㩫 ,

⨟㩗㦒⪲ 䘟Ṗ ♮㠞ἶ 㧚Ἒ㹸ₖ㠦⍞㰖(critical 㦮 Ἒ㌆㦚 䌚㏢ 䌚㏢ ἆ䞿㦮 ⿚䟊㠦 tearing energy) -

⍞㰖⯒ 㧊㣿䞮㡂 㩲㞞䞮㡖┺ 㹸ₖ㠦⍞㰖⯒ 㧊㣿 . 䞲 ἶⶊ㦮 ⌊ῂ 㑮ⳛ 䘟Ṗ㔳㦖 1958 ⎚ Thomas

㠦 㦮䟊 㔺䠮㔳㦒⪲ 㩲㞞♮㠞┺ ⁎㦮 ⏒ⶎ㠦㍲ . ἶⶊ㦮 㹸ₖ㦚 㩫㩗‶㡊㰚㩚 (static cut growth) ὒ

☯㩗‶㡊㰚㩚 (dynamic cut growth) 㦒⪲ ῂ⿚䞮㡖㦒 Ⳇ Ệ䂲‶㡊㰚㩚 (rough cut growth) 㡗㡃㠦 ╖䟊 㰚

ἶⶊ㦮 䞒⪲ 㑮ⳛ 㡞䁷㦚 㥚䞲 㹸ₖ㠦⍞㰖 㑮㔳䢪 ἶⶊ㦮 䞒⪲ 㑮ⳛ 㡞䁷㦚 㥚䞲 㹸ₖ㠦⍞㰖 㑮㔳䢪 ἶⶊ㦮 䞒⪲ 㑮ⳛ 㡞䁷㦚 㥚䞲 㹸ₖ㠦⍞㰖 㑮㔳䢪 ἶⶊ㦮 䞒⪲ 㑮ⳛ 㡞䁷㦚 㥚䞲 㹸ₖ㠦⍞㰖 㑮㔳䢪

Estimation of Tearing Energy

for Fatigue Life Prediction of Rubber Material

Ho Kim, Heon-young Kim

Key Words: Tearing Energy(㹸ₖ㠦⍞㰖), Fatigue Life(䞒⪲㑮ⳛ), Rubber(ἶⶊ), Virtual Crack(Ṗ

㌗䋂⧯), Energy Release Rate(㠦⍞㰖䟊⹿㥾), Fracture Criterion(䕢ᾊ₆㭖) Abstract

Fatigue life prediction is based on fracture mechanics and database which is established from

experimental method. Rubber material also uses the same way for fatigue life prediction. But the

absence of standardization of rubber material, various way of composition by each rubber company

and uncertainty of fracture criterion makes the design of fatigue life by experimental method almost

impossible. Tearing energy which has its origin in energy release rate is evaluated as fracture criterion

of rubber material and the applicability of fatigue life predicition method are considered. The system

of measuring tearing energy using the principal of virtual crack extension method and fatigue life

prediction by the minimum number of experiments are proposed.

㩚⨟ὒ 㰚㩚㏣☚㠦 ╖䞲 㔺䠮㔳㦚 ‶㡊㰚㩚㌗㑮

⯒ ㌂㣿䞮㡂 ⋮䌖⌊㠞┺.

㹸ₖ㠦⍞㰖Ṗ 㩲㞞♲ 䤚 㔺㩲 ἶⶊ 㩲䛞㠦㍲ ,

‶㡊 㰚㩚⨟ 䁷㩫㦮 ⳾䢎䞾ὒ 㠦⍞㰖㦮 ⼖䢪 Ἒ

㌆ ⹿⻫㧊 㩲㞞♮㰖 㞠㞚 ἶⶊ 䕢ᾊ ₆㭖㦮 㧎㧦

⪲㍲⓪ 㡃䞶㦚 ╊╏䞮㰖 ⴑ䞮㡖┺ . 1972 ⎚ Blackburn

㦖 ‶㡊㍶┾㣪㏢(crack tip special

⯒ 㧊㣿䞮㡂 㠦⍞㰖 䟊⹿⮶㦚 Ἒ㌆䞮⓪ element)

Ṗ㌗䋂⧯㰚㩚 (VCE, Virtual Crack Extension) ⻫㦚 㩲㞞䞮㡖┺. Rice

⓪ ‶㡊㍶┾㣪㏢㦮 ṫ㎇⺆㡊

⪲⿖䎆 㠦⍞㰖 䟊⹿㥾㦚 Ἒ㌆䞮㡂 (stiffness matrix)

䟊㍳㔲Ṛ㠦 ⿞Ⰲ䞲 㩦㧊 㧞㠞㦒⋮ Hellen

㦮 ἓ 㤆 ‶㡊㍶┾㣪㏢㦮 㠦⍞㰖 ⼖䢪⯒ 㰗㩧 ἶ⩺䞮₆

➢ⶎ㠦 䟊㍳㦮 㔲Ṛ㦮 ㏦㔺㧊 Ệ㦮 㠜㠞┺.

㹸ₖ㠦⍞㰖⯒ 㧊㣿䞲 ἶⶊ 䕢ᾊ⋮ ⌊ῂ 㑮ⳛ 䘟Ṗ㠦 ὖ䞲 ⏒ⶎ㦖 䢲⹲䧞 ⹲䚲♮㰖 㞠㞮㦒Ⳇ 㭒⪲ 㔺䠮㠦 㦮䞲 䘟Ṗ

⋮ 䌖㧊㠊㦮 䃊䃊㓺 㢖 ṯ㦖 ἶⶊ 䘟䕦㠦 㻶㕂㧊 㧒㩫䞲 Ṛỿ (cacas)

㦒⪲ ⺆㡊♮㠊 㧞⓪ 㩲䛞㠦 ╖䟊 䘟‶ 㠦⍞㰖⯒

㧊㣿䞮㡂 㠦⍞㰖䟊⹿㥾㦚 Ἒ㌆䞮ἶ 㔺䠮㩗㦒⪲

‶㡊㦮 㰚㩚㏣☚⯒ 䁷㩫䞮㡂 㠦⍞㰖䟊⹿㥾ὒ ‶ 㡊㦮 㰚㩚㏣☚ ὖἚ⯒ ⿚㍳䞲 Lake

㦮 ⏒ⶎὒ ṯ㧊 Ṛ㩧㩗㦒⪲ 㹸ₖ㠦⍞㰖⯒ 㧊㣿䞮⓪ ⏒ⶎ㧊 㭒⯒ 㧊⬾ἶ 㧞┺.

⽎ ⏒ⶎ㠦㍲⓪ 㹸ₖ㠦⍞㰖㦮 ἶⶊ 㨂⬢ 䕢ᾊ

₆㭖㦒⪲㍲ 㩗㣿㎇ὒ 㹸ₖ㠦⍞㰖⯒ 㧊㣿䞲 㑮ⳛ Ἒ㌆㔳㦮 㩗㣿㎇㦚 䘟Ṗ䞮㡖ἶ 㑮䞯㩗㦒⪲ Ἒ㌆

Ṗ⓻䞲 㧚Ἒ㹸ₖ㠦⍞㰖㦮 Ἒ㌆ ⹿⻫㦚 ㏢Ṳ䞮㡖

┺ 㧒⹮㩗㧎 . 2 㹾㤦 ⹥ 3 㹾㤦 㩲䛞㠦㍲ 㹸ₖ㠦⍞

㰖⯒ Ἒ㌆䞮₆ 㥚䟊 㥶䞲㣪㏢䆪✲㠦 㩗㣿 Ṗ⓻䞲 㩫㔳䢪⯒ 㑮䟟䞮㡖㦒Ⳇ 㾲㏢ 㔲䠮 䣵㑮⯒ 㧊㣿䞲 ἶⶊ 㑮ⳛ 㡞䁷 ⹿⻫㦚 㩲㞞䞮㡖┺.

焨卆櫖嘎滆汞 処怺 洇殯昷 2.

処怺 沲巒 砒刺 匶渆 2.1

⁞㏣㦮 ㍶䡫 䌚㎇ ⻪㥚⌊㠦㍲⓪ 㦧⩻䢫╖Ἒ㑮, 㠦⍞㰖䟊⹿⮶ 㦧⩻ ⼖䡫⮶㧊 ㍲⪲ ὖἚ㔳㦚 Ṗ , , 㰖Ⳇ 䕢ᾊ ₆㭖㦒⪲ ㌂㣿㧊 Ṗ⓻䞮㰖Ⱒ ἶⶊ㦮 ἓ㤆 㦧⩻䢫╖Ἒ㑮⓪ ⹎㏢⼖㥚㢖 ㍶䡫䌚㎇㦚 ₆

⽎Ṗ㩫㦒⪲ 䞮⓪ Irwin 㦮 ῃ⿖㦧⩻㔳㦒⪲ ⿖䎆 㥶

☚ ♮㠞ἶ 䡫㌗Ἒ㑮㢖 ṯ㦖 㔲䘎㦮 䡫㌗㠦 ╖䞲 , 㩲㟓㧊 ➆⯊⸖⪲ ╖⼖䡫 ゚㍶䡫㦮 ㎇㰞㦚 Ṗ㰖 , , ἶ 㧞㠊 ⽋㧷䞲 䡫㌗㦮 㩲䛞㧊 ╖┺㑮㧎 ἶⶊ㠦

⓪ 㩗㣿㧊 ⿞Ṗ⓻䞮┺ . ⁎⩂⋮ , 㠦⍞㰖䟊⹿㥾㦮 ἓ㤆 㨂⬢㠦 ╖䞲 㩲㟓 㠜㧊 ‶㡊㦮 㰚㩚㠦 ➆⯎

㠦⍞㰖 Ṧ㏢⧒⓪ 㧒⹮㩗㧎 ㌂㔺⪲⿖䎆 㥶☚Ṗ ♮ 㠞㦒⸖⪲ ㍶䡫 ゚㍶䡫 䌚㎇ ㏢㎇ 䡫㌗㠦 ㌗ὖ , , , , 㠜㧊 㩗㣿㧊 Ṗ⓻䞮Ⳇ ἶⶊ㠦☚ 㩗㣿㧊 Ṗ⓻䞮

┺ . J 㩗⿚☚ 㠦⍞㰖䟊⹿㥾ὒ ☯㧒䞲 Ṳ⎦㦚 Ṗ㰖 ἶ 㧞㰖Ⱒ ‶㡊 ㍶┾㦮 㦧⩻㧻㠦 ╖䞲 Ṳ⎦㧊 䞚 㣪䞮ἶ 㔲䘎㦮 䡫㌗㠦 㦮㫊㩗 㧊⸖⪲ ἶⶊ㠦⓪ 㩗㣿㧊 䧮✺┺ 㠦⍞㰖䟊⹿㥾 㧊⪶㦚 ἶⶊ㠦 㩗 . 㣿䞮㡂 Rivlin 㠦 㦮䟊 㩲㞞♲ 㹸ₖ㠦⍞㰖 㔳㦖 (1) 㔳ὒ ṯ┺.

­

_{áà ć} ƒ Î ć ŞƁ

Ş

ۊۍ à ć Ş

Ş

ڃڌڄ

ƒ⓪ 㔲䘎㦮 ⚦℮⯒ 㦮⹎䞮ἶ 㞚⧮㻾㧦 , Ɗ㦖 㔲 䘎㦮 ἶ㩫♲ 㔶㧻 ₎㧊⯒ 㦮⹎䞲┺ . Rivlin 㦖 NR 㻲㡆ἶⶊ 㨂⬢ 㭧 䞲Ṗ㰖 ⺆䞿 ㌗䌲㠦㍲ ㍲⪲ ┺

( )

⯎ 䡫䌲㦮 ‶㡊㔲䘎㦚 㧊㣿䞮㡂 㹸ₖ㠦⍞㰖⯒ 䁷 㩫䞮㡖㦒Ⳇ  ỿ䞲 㹸ₖ (catastrophic tearing) ㌗䌲 㢖 㽞₆ 㹸ₖ (incipient tearing) ㌗䌲㠦㍲ ṗṗ ÎíÐ Z Î×

, ÐíÔ Z Î×

ƃƐƅƑîƁƋ

㦮 ☯㧒䞲 㧚Ἒ㹸ₖ 㠦⍞㰖 Ṩ㧊 䁷㩫♾㦚 ⽊㡖┺ ⡦䞲 . , (2) 㔳㦮 㑲㑮 㩚┾ ‶㡊 㔲䘎㠦 ╖䞲 㧊⪶㩗 㹸ₖ㠦⍞㰖 Ἒ㌆

㔳ὒ ┾㿫 㧎㧻 㨂⬢ 㔲䠮㦮 㦧⩻ ⼖䡫⮶ ἷ㍶㦒 -

⪲⿖䎆 ἆ㩫♲ (3) 㔳㦮 㼊㩗╏ ⼖䡫⮶ 㠦⍞㰖㔳㦚

㍲⪲ ┺⯎ ⺆䞿 㫆Ị㦮 NR 㨂⬢㠦 㩗㣿䞮㡂 㹸 ₖ㠦⍞㰖⯒ Ἒ㌆䞲 ἆὒ 㧊⪶㔳㦒⪲⿖䎆 㹸ₖ㠦

⍞㰖 Ἒ㌆㧊 Ṗ⓻䞾㦚 ⋮䌖⌊㠞┺ . (2) 㔳㠦㍲ Ɗ

㢖 ƕ

⓪ ṗṗ ‶㡊 㔲䘎㦮 㔶㧻♲ ₎㧊㢖 㩖㧻

♲ 㼊㩗╏ ⼖䡫⮶ 㠦⍞㰖⯒ ⋮䌖⌎┺ . (3) 㔳㠦㍲

œÎ

㦖 㨂⬢ ㌗㑮㧊Ⳇ Ł⓪ 㔶㧻㥾㦚 ⋮䌖⌎┺.

㠦 Ṗ㰖 㨂⬢㠦 ╖䞲 㔶㧻㥾㠦 ➆⯎

Fig. 1 2 NR

㹸ₖ㠦⍞㰖⯒ 䁷㩫♲ ἆὒ㢖 㧊⪶㔳㦮 䞾㑮⯒ ☯ 㔲㠦 ⋮䌖⌊㠞┺.

­

á ƕ

Ɗ

ڃڍڄ

ƕ

á

^Ł

^{â ć} Ł

Î à Ï

^ڃڎڄ

㠦㍲ 㔺㍶㦖 㧊⪶㔳㦚 ⋮䌖⌊Ⳇ 㤦䡫ὒ Fig. 1

㕃㧦Ṗ⪲ 䚲㔲♲ 㩦㦖 ㍲⪲ ┺⯎ ⚦ ⺆䞿㨂㦮 䁷

㩫Ṩ㦚 ⋮䌖⌎┺ . Rivlin 㦮 㔲䠮㦖 㹸ₖ㠦⍞㰖Ṗ

䡫㌗ὒ 䞮㭧㠦 ☛Ⱃ㩗㧊ἶ ㍲⪲ ┺⯎ ⺆䞿㦮 NR 㨂⬢㠦 ╖䟊 Ï~Ó Z Î×

㦮 㧚Ἒ㹸ₖ㠦⍞㰖 ⿚䙂⯒

⽊㡂 䋆 䘎㹾Ṗ 㠜㦢㦚 㯳ⳛ䞲 ộὒ ἶⶊ㦮 㽞 . 䌚㎇ 㠦⍞㰖 㔳㦒⪲⿖䎆 㹸ₖ㠦⍞㰖Ṗ Ἒ㌆♶ 㑮 㧞㦢㦚 ⋮䌖⌎ ộ㦖 䡫㌗㧊 ⽋㧷䞮Ⳇ 䚲㭖䢪Ṗ

♮㠊 㧞㰖 㞠ἶ ⺆䞿㫆Ị㠦 ➆⧒ 㓓Ợ ⹪≢⓪ ἶ ⶊ 㨂⬢㦮 䔏㎇㠦 ╖䞲 䕢ᾊ ₆㭖㦒⪲㍲ 㩗㣿 Ṗ

⓻㎇㦚 Ṗ㰖Ợ 䞲┺.

沊凊焨卆櫖嘎滆 凊斶 2.2

㧚Ἒ㹸ₖ㠦⍞㰖⓪ ⁞㏣㦮 㧚Ἒ㦧⩻䢫╖Ἒ㑮

¤_œ

㢖 ☯㧒䞲 㦮⹎⪲ ἶⶊ㦮 㹸ₖ ₆㭖㦚 ⋮䌖

⌎┺ 㯟 ἶⶊ㨂⬢㠦㍲ . ,

­

ð

ڃڏڄ

㧊Ⳋ ‶㡊㧊 㰚㩚♾㦚 㦮⹎䞲┺ . Rivlin 㠦 㦮䟊 㔺䠮㩗㦒⪲ 䁷㩫♲ 㹸ₖ㠦⍞㰖⓪ 㧚Ἒ㹸ₖ㠦⍞㰖 㧊Ⳇ NR 㨂⬢㠦㍲☚ ⺆䞿㫆Ị㠦 ➆⧒ 㟓Ṛ㦮 䘎 㹾⯒ Ṗ㰚┺ . NR 㨂⬢⯒ 䙂䞾䞮㡂 ┺⯎ ἶⶊ 㨂⬢

㠦㍲☚ 㩗㣿 Ṗ⓻䞲 㧚Ἒ㹸ₖ㠦⍞㰖⯒ 㧊⪶㩗㦒

⪲ Ἒ㌆䞮⓪ ⹿⻫㦚 䤚䃊㡺Ⰲ㠦 㦮䟊 (5) 㔳㦒⪲

㩲㞞♮㠞┺.

­_×

á ƀ

ļł

Î

ڃڐڄ

(5) 㔳㠦㍲ ļ⓪ ┾ἆ䞿 (monomer unit) 㦮 ₎㧊 , ł

⓪ cross link ㌂㧊㦮 ┾ἆ䞿㦮 㑮 , ƀ⓪ 㼊㩗╏ ┾

ƄÞ­ß Ł

Fig. 1 Experimental and theoretical relation between tearing energy and extension ratio

ἆ䞿㦮 㑮,

⓪ 䕢┾㩦㠦㍲ ṗ ┾ἆ䞿㠦 㦮䟊 㩖㧻♲ 㠦⍞㰖㦮 㟧㦚 ⋮䌖⌎┺ 㔺䠮㩗㦒⪲ 䁷 . 㩫♲ 㧚Ἒ㹸ₖ㠦⍞㰖㦮 Ṩὒ (5) 㔳㠦 㦮䟊 Ἒ㌆♲

Ṩ㦖 ṗṗ 0.4~1.0 㢖 0.004~0.01

îƁƋ

㦒⪲ Î×

㦮 㹾㧊⯒ ⽊㡖㦒Ⳇ Andrew 㢖 䤚䃊㡺Ⰲ⓪ 㩦䌚㎇㠦 㦮䞲 䧞㓺䎢Ⰲ㏦㔺Ἒ㑮 ij⯒ ㌂㣿䞮㡂 (6) 㔳ὒ ṯ 㧊 ⽊㩫䞮㡖ἶ NR 㠦㍲ Î×

~Î×

㌂㧊㦮 Ṩ㦚 Ἒ㌆

䞮㡖┺ ἶⶊ㦮 㹸ₖ 㔲㧧㦚 ἶ⩺䞮₆ 㥚䟊㍲⓪ . 㽞₆ 㧚Ἒ㹸ₖ㠦⍞㰖Ṗ 䌖╏䞮⸖⪲ Î×

㦚 ㌂㣿䟊 㟒 䞮Ⳇ 㧊⪶㩗 㧚Ἒ㹸ₖ㠦⍞㰖㦮 Ἒ㌆㔳㦖 㨂 , ἶⶊ 㨂⬢㦮 ⹎㔲㩗 䔏㎇㦚 ┺⬾ἶ 㧞㦒⸖⪲ ⺆ 䞿㧊⋮ ἶⶊ㦮 㫛⮮㠦 ➆⯎ Ệ㔲㩗 䔏㎇㠦 ╖䟊

☛Ⱃ㎇㦚 Ṗ㰚┺.

­_œ

á ij

ڃڑڄ

朞律凊斶柣 洇殯昷 磏儆 3.

処怺 沲巒汞 砒刺 笊旇 3.1

㧒⹮㩗㦒⪲ ἶⶊ 㨂⬢⓪ 䌚㏢㢖 䌚㏢Ṗ 㰖⁎㨂

⁎ (zigzag) 䡫䌲⪲ ἆ䞿♮㠊 㧞⓪ ἶ⿚㧦 ㌂㔂 ῂ 㫆㦮 䡫䌲⪲ 㧊⬾㠊㪎 㧞㠊 䞮㭧㦚 ⹱Ợ ♮Ⳋ ⿚ 㧦 ἶⰂṖ 㧎㧻 ⹿䟻㦒⪲ 㨂⺆㡊 ♮Ⳇ 㧎㧻 ㌗䌲 㦮 ἶⰂ⓪ 㨂⬢㦮 ⿞‶㧒㎇㦒⪲ 㧎䟊 ⿖⿚㩗㦒⪲

⊠㠊㰖Ợ ♲┺ 㧊⓪ 㡆㐚 ⊠㠊㰦 䡚㌗㦒⪲ 㧊㠊 . 㪎 ⹎㏢ 䋂₆㦮 Ὃ☯ (cavity) 㦚 䡫㎇䞮Ợ ♮ἶ Ὃ

☯㦮 䋂₆Ṗ 㧚Ἒ 䋂₆⽊┺ 䋂Ợ ♮Ⳋ ‶㡊

⪲㍲㦮 ₆⓻㦚 Ṗ㰖Ợ ♮㠊 ㎇㧻㦚 䞮⓪ (crack)

䕢ᾊ ὒ㩫㦒⪲ 㧊㠊㰚┺ 㔺Ⰶ▪ 䡫㦮 ἶⶊ 㟧Ⳋ . 㦚 ⁞㏣㠦 㩧㹿䞮㡂 䞮㭧㦚 Ṗ䟊 䕢ᾊ ┾Ⳋ㦚 ὖ 㺆䞲 Gent

㦮 ⏒ⶎ㠦㍲⓪ 㔲䘎㠦 㧎㧻䞮㭧㦚 Ṗ 䞲 䤚 ┾Ⳋ㦚 㩞┾䞮㡂 ὖ㺆䞲 ἆὒ ἶⶊ ⌊⿖㠦

⌊䙂䞮ἶ 㧞⓪ 䃊⽎な⧯ (carbon black) 㧊 㧚Ἒ䋂⧯

Fig. 2 Detailed section plot of cracked specimen

Fig. 3 Cross section plot of cracked specimen

㦮 㡃䞶㦚 䞮㡂 㭒㥚⪲ ‶㡊㧊 㩚䕢䞮⓪ ὒ㩫㦚 ὖ㺆䞮㡖ἶ ┾Ⳋ 㩚㼊㠦 Ỏ㼦 ‶㡊㧊 ⿚䙂♲ 䡫

㌗㦚 䢫㧎䞮㡖┺ . Fig. 2 㠦 䃊⽎な⧯㦚 ₆㩦㦒⪲

‶㡊㧊 㩚䕢♲ ┾Ⳋ㦮 䡚⹎ἓ ㌂㰚㦚 ⋮䌖⌊㠞ἶ 㠦 ⚦℮㠦 ➆⯎ ‶㡊 ㌳㎇ 㟧㌗㦚 ⋮䌖⌊㠞 Fig. 3

┺ 㩲㫆♲ ἶⶊ 㨂⬢㦮 ⌊⿖㠦⓪ 䃊⽎ な⧯㦚 . 䙂䞾䞲 Ⱔ㦖 㫛⮮㦮 ἆ䞾㧊 ⌊䙂♮㠊 㧞㦒Ⳇ 㧚 Ἒ䋂₆ 㧊㌗㦮 ‶㡊㧊 ὉὉ㠦 㫊㨂䞶 Ṗ⓻㎇㧊 㧞┺ 㧊⪲ 㧎䟊 Ὃ☯㦮 ㎇㧻㠦 㦮䞲 ‶㡊㦮 ㌳ .

㎇ὒ㩫㧊 ㌳⨋♮ἶ ‶㡊㦮 ㎇㧻 ⡦⓪ Ⲟ㿺㦚 ἶ ⶊ 㨂⬢㦮 䕢ᾊ ὒ㩫㦒⪲ ㌳ṗ䞶 㑮 㧞┺.

勦櫺 昷沫暓壊柣 3.2

ἶⶊ 㨂⬢㦮 ☯㩗 ‶㡊 ㎇㧻(dynamic cut 㦖 ⿖✲⩂㤊 ‶㡊㎇㧻

growth) (smooth cut growth) 㡗㡃ὒ Ệ䂲 ‶㡊㎇㧻 (rough cut growth) 㡗㡃   ,

Fig. 4 Dynamic cut growth curve

Fig. 5 Relation between rate of cut growth and T for various mix

ỿ䞲 ‶㡊㎇㧻 (catastrophic cur growth) 㡗㡃㦒⪲

ῂ⿚䞲┺ . ⼖䡫ὒ 䛖㠊㰦 (relaxing) 㦮 ⹮⽋䞮㭧㦚 Ṗ䞮Ⳋ  ỿ䞲 㹸ₖ 䞮㭧⽊┺ 㧧㦖 䞮㭧㠦㍲☚ , 䋂⧯㦮 ₎㧊Ṗ 㯳Ṗ䞮Ⳇ 㽞₆㦮 ザ⯎ ㎇㧻⮶㧊 *

⺇ cycle 㧊䤚 㧒㩫䞮Ợ ⓦⰆ ㎇㧻⮶⪲ ⼖䢪䞮⓪ ộ㦖 䋂⧯ 䕗㦮 Ệ䂶㠊㰦 (roughening) 㠦 㦮䞲 ộ 㧊┺ . Fig. 4 㠦 ☯㩗 ‶㡊 ㎇㧻 ἷ㍶㦚 ⋮䌖⌊㠞

┺ 㔲䠮㠦 ㌂㣿♲ ㍲⪲ ┺⯎ ἶⶊ 㨂⬢㦮 䋂⧯ .

㎇㧻⮶ ὖἚ㔳㦖 Fig. 5 㠦㍲ ⽊⓪ ộὒ ṯ㧊 Ệ㦮 㹾㧊Ṗ 㠜㦒Ⳇ 㔺䠮㩗㦒⪲ 䋂⧯ ㎇㧻⮶㦖 , ­

^㠦

゚⪖䞲┺ . Thomas ⓪ 㔺䠮㠦 㦮䞲 㩫㩗 (static) ὒ

☯㩗 ‶㡊㎇㧻㔳㦚 㩲㞞䞮㡖┺.

(7), (8) 㔳㠦㍲

㢖

⓪ ṗṗ 㩫㩗 ☯㩗 ‶ , 㡊㎇㧻Ἒ㑮⯊ ⋮䌖⌊Ⳇ ╖⨋

î

á Î×㦮 ὖἚ

⯒ Ṗ㰚┺ . Thomas Ṗ 㩲㞞䞲 ㎇㧻㏣☚㔳㦖 ⁞㏣

㠦㍲㦮 Paris law 㢖 㥶㌂䞲 䡫䌲⪲ ‶㡊㦮 㞞㩫

㎇㧻㡗㡃㠦 䟊╏䞲┺ ⁞㏣㦮 ἓ㤆 ‶㡊 ㌳㎇₢ . ĢƁ á ć

Î

(7)

ć Ƃ

ƂƁ á ć

Î

(8)

Fig. 6 Relation between rate of cut growth for various type of specimen

Ł Ɓ

ÞZ Î×

ß

, kcycles Observed Calculated

2.36 36 3.0 4.4

2.08 46 6.5 7.2

1.47 43 78 88

1.205 70 700 760

1.098 78 8600 9500

Table 1 Calculated and observed fatigue lives

㰖㦮 㑮ⳛ㧊 㞞㩫㩗 ㎇㧻 㡗㡃㦮 㑮ⳛ㠦 ゚䟊 䋆

゚㭧㦚 㹾㰖䞮㰖Ⱒ ἶⶊ㦮 ἓ㤆 ‶㡊㦮 㞞㩫㩗 ,

㎇㧻 㡗㡃㧎 Ệ䂲 ‶㡊㎇㧻 㡗㡃㧊 Fig. 6 ὒ ṯ㧊

‶㡊 ㎇㧻㦮 ╖⿖⿚㦚 㹾㰖䞮Ⳇ ‶㡊 ㎇㧻㔳㠦 㦮䟊 Ἒ㌆♲ 㑮ⳛ㦮 ἆὒ㢖 㔺䠮㩗㦒⪲ 䁷㩫♲

㑮ⳛ㧊 䚲 1 ὒ ṯ㧊 20% ⹎Ⱒ㦮 㹾㧊⯒ ⽊㡖┺ .

⡦䞲 㹸ₖ㠦⍞㰖⯒ ⼖㑮⪲ ㌂㣿䞮㡖₆ ➢ⶎ㠦 䡫

㌗㠦㍲☚ ☛Ⱃ㎇㦚 ⋮䌖⌊㠞┺ 㧊⓪ 㤦⪶㩗㦒⪲ . 㧚㦮㦮 䡫㌗㦮 㔲䘎㠦 ╖䞲 䋂⧯ ㎇㧻⮶㦖 ┺⯎

䡫㌗㦮 㔲䘎㦒⪲⿖䎆 䁷㩫㧊 Ṗ⓻䞾㦚 ⋮䌖⌎┺.

焨卆櫖嘎滆 凊斶 4.

‶㡊₎㧊㦮 ⼖䢪㠦 㦮䟊㍲ 㹸ₖ㠦⍞㰖⯒ 㩫㦮 䞮㡖₆ ➢ⶎ㠦 㹸ₖ㠦⍞㰖㦮 Ἒ㌆㦖 ‶㡊㧊 㫊㨂 䞮ἶ ‶㡊㦮 ₎㧊Ṗ 㯳Ṗ䞶 ἓ㤆㠦 Ṩ㧊 㫊㨂䞲

┺ ➆⧒㍲ 㩲䛞㠦 㧚Ἒ ‶㡊㧊 㧊⹎ 㫊㨂䞲┺⓪ . Ṗ㩫ὒ 㽞₆ ‶㡊 ₎㧊㦮 ⁏ ⹎㏢ 㯳Ṗ⧒⓪ Ṗ㩫 㦚 䟊㟒 䞲┺ 㩲䛞㦮 㩲㫆 ὒ㩫㠦㍲ 㧚Ἒ‶㡊䋂 .

₆ Ɓ

㧊㌗㦮 ‶㡊㦖 㫊㨂䞮⓪ ộ㦒⪲ Gent 㦮 ⏒ ⶎ㠦㍲ 㯳ⳛ䞮㡖㦒⸖⪲ 㩲䛞㦮 㩚㼊㩗㧎 㑮ⳛ㦖

‶㡊㦮 ㎇㧻ὒ ⹖㩧䞲 ὖ⩾㧊 㧞┺ ⡦䞲 . Ɓ

䋂₆ 㧊䞮㦮 Ὃ☯Ⱒ㧊 㫊㨂䞮⓪ 㩲䛞㦮 ἓ㤆 Ɓ

䋂₆㦮

⹎㏢Ὃ☯㧊 㫊㨂䞮⓪ 㩲䛞⽊┺ 㑮ⳛ㧊 ₎ ộ㧊⸖

⪲ 㡂⩂ ㌮䝢 (sample) 㠦㍲ 䁷㩫♲ 㑮ⳛ 㭧 㾲㩖 ‘ 㑮ⳛ 㧊⧒⓪ Ṳ⎦㠦㍲ 㦮⹎Ṗ 㧞┺ 䁷㩫♲ 㧚Ἒ ’ . 㹸ₖ₎㧊 㭧 Ệ䂲 㹸ₖ㡗㡃㠦㍲⓪ 10 łƋ㧊ἶ 䤚 䃊㡺Ⰲ⓪ ‶㡊㧊 ⚻⁒ 䡫㌗㠦㍲⓪ 100 łƋ 㩫☚

⯒ 㧚Ἒ䂮⪲ ㌳ṗ䞮㡖┺ 㾲㏢Ṩ㧎 . 10 łƋ 㧊㌗

㦮 ‶㡊㧊 㿿⿚䧞 㫊㨂䞮⸖⪲ 㧚Ἒ ‶㡊㦮 㫊㨂 Ṗ㩫㧊 㦮⹎Ṗ 㧞┺ ⽎ ⏒ⶎ㠦㍲⓪ Ṗ㌗ 䋂⧯ . Ṳ⎦ὒ 㧒⹮㩗㧎 㣪㏢⯒ 㧊㣿䞮㡂 㹸ₖ㠦⍞㰖⯒

Ἒ㌆䞮⓪ ⹿⻫㠦 ╖䟊 ⏒㦮䞮Ⳇ 㧊⯒ 㥚䟊 ⳝ Ṗ 㰖 Ṗ㩫㦚 ㌂㣿䞲┺ Ⲓ㩖 ἶⶊ㦮 ἓ㤆 㩲㫆㌗㦮 . 䔏㎇㌗ 10

㦮 ‶㡊㦚 ⌊㨂䞮ἶ 㧞㦒Ⳇ 㧊⯒ 㽞

₆ ‶㡊 䋂₆ Ɓ

㧚㦚 Ṗ㩫䞲┺ Ệ䂲 㹸ₖ㡗㡃㦮 . 䔏㰫㧎 Ệ䂲 䕢┾Ⳋ ‶㡊㦮 㰚㩚㦖 㽞₆㰚㩚㠦 , 䟊╏䞮⓪ 㧚Ἒ㹸ₖ㠦⍞㰖⯒ ₆㭖㦒⪲䞮Ⳇ , ㌗╏

⨟㦮 㹸ₖ㠦⍞㰖㠦 䟊╏䞮⓪ NR 㦮 ĢƁṨ㦚 㽞₆ Ṗ㌗ 䋂⧯ 㰚㩚⨟㦒⪲ ㌂㣿䞲┺.

㠦⍞㰖 䙂䎦㍂㦚 Į ⧒ἶ 䞮Ⳋ ┾㥚₎㧊╏ 㠦 ,

⍞㰖 Ṧ㏢㥾

⓪ (9) 㔳ὒ ṯ㧊 㝎 㑮 㧞┺ .

­

_{áà ć} ƂƁ ƂĮ ڃڔڄ

㩫㩗 Ệ☯㠦 㧞㠊㍲ Į ⓪ 㧒⹮㩗㦒⪲ 㥶䞲㣪㏢

䡫䌲⪲ (10) 㔳ὒ ṯ┺ . Į á ć Ï

Î Ɠ Ɠ Ɠ Ɠ

Ɠ Ɠà Ɠ Ɠ Ɠ Ɠ Ɠ Ɠ

ڃڌڋڄ

ŸŸ

ŸŸ

⓪ ❇Ṗ㦮 㩞㩦 ⻷䎆, Ɠ Ɠ Ɠ Ɠ⓪ ⼖㥚⻷䎆,

⓪ ṫ

㎇䟟⪂㧊┺ 㼁 ⻞㱎 䟃㧊 ⌊⿖ 㠦⍞㰖 䟃㦚 㦮 .

⹎䞮⸖⪲ ⳾◎ ⌊⿖ 㧚㦮㦮 㩦

^{㠦㍲㦮 ⼖䡫⮶}

㠦⍞㰖

^{⯒ 㧊㣿䞮㡂 (10) 㔳㦚 ┺㔲 㝆ἶ}

^⯒ 㩫Ⰲ䞮Ⳋ

Į á

^{à Ɠ Ɠ Ɠ Ɠ}

^ڃڌڌڄ

㔳㠦㍲ 㠦⍞㰖 䘟䡫 㫆Ịὒ

(11)

㢖 ὖ⩾♲ 䟃 㦖 䋂⧯㧊 ⹲㌳䞮⓪ 㩦 㭒⼖㠦 䞮㭧㧊 㩫㦮♮㠊 㧞㰖 㞠Ệ⋮ 㧒㩫䞮┺⓪ Ṗ㩫 䞮㠦 (12) 㔳ὒ ṯ㧊 㩫Ⰲ䞶 㑮 㧞┺.

ć ĺƁ

ĺĮ á

^{ć Ş} _ŞƁ

^ڃڌڍڄ

‶㡊㰚㩚㧊 ♮㰖 㞠⓪ ⳾✶ 㩦㠦㍲ ‶㡊 㰚㩚

⨟ ĢƁ㠦 ╖䞲 㠦⍞㰖 ⼖䢪⓪ 㠜┺ 㧎◇㓺 .

⓪ 䋂⧯㧊 㰚㩚♮⓪ 㩦㠦Ⱒ 䟊╏♲┺ . (12) 㔳㦚 ⹎⿚

䡫䌲Ṗ 㞚┢ 䟊㍳ ὒ㩫㠦㍲㦮 㯳⿚ 䡫䌲⪲ ⹪∪

㝆Ⳋ (13) 㔳ὒ ṯ┺ .

ć ĺƁ

ĺĮ á

^ć ĢƁ Ģ

ڃڌڎڄ

➆⧒㍲ 㹸ₖ㠦⍞㰖⓪ 㧒⹮㩗㦒⪲ ‶㡊 㯳⿚㠦 ,

➆⯎ ‶㡊 䚲Ⳋ㩗 ⹎㏢㯳⿚ ĺ

⡦⓪ 㯳⿚ Ģ

⯒ 㧊㣿䞮㡂 (14) 㔳ὒ ṯ㧊 䚲䡚 Ṗ⓻䞮┺ .

­

_{á ć} ĺ

ĺĮ á

^{ć Ģ} _Ģ

^ڃڌڏڄ

㧚㦮㦮 㩦 Ƈ⯒ 㥶䞲㣪㏢㠦㍲ ṗ 㩗⿚㩦㦮 㥚䂮

⪲ ╖㔶䞮ἶ 㩗⿚㩦㠦㍲㦮 Ṗ㌗ ‶㡊 㼊㩗 , Ɣ

㢖

㼊㩗╏ ⼖䡫⮶㠦⍞㰖 ƕ

⯒ 㧊㣿䞮㡂 (14) 㔳㦚 㩫

Ⰲ䞮Ⳋ (15) 㔳ὒ ṯ㧊 䚲䡚㧊 Ṗ⓻䞮Ⳇ Ɣ

㢖

⓪ ĢƁ㦮 䞾㑮㧊⸖⪲ (16) 㔳ὒ ĢƁ㦮 㧒㹾䞾㑮 䡫 䌲⪲ 㝎 㑮 㧞┺.

­

^á

^ć _Ģ ^Ɣ

^ƕ

⁽¹⁵⁾

­

á

^ƆÞĢƁßƕ

⁽¹⁶⁾

Ṗ㧻 Ṛ┾䞲 䡫䌲㧎 ㌗㑮 ὇㦮 䡫䌲⯒ 䀾䞮㡂 㾲㫛㩗㧎 㹸ₖ㠦⍞㰖 Ἒ㌆㔳㦖 (17) 㔳ὒ ṯ㞚 㩗

⿚㩦㠦㍲㦮 㼊㩗╏ ⼖䡫⮶ 㠦⍞㰖㢖 Ṗ㌗ ‶㡊 㰚㩚⨟㦮 ὇㦒⪲ 䚲䡚䞶 㑮 㧞┺.

­

á

^{ķĢƁ ƕ}

^ڃڌڒڄ

㦮 ⏒ⶎ㠦㍲ 㹸ₖ㠦⍞㰖⯒ Ἒ㌆䞮₆ 㥚䟊 Rivlin

㌂㣿♲ 㧎㧻㔲䘎㦚 ⳾◎Ⱇ䞮㡂 㔲䠮ὒ ☯㧒䞲 䞮 㭧 㫆Ịὒ ἓἚ㫆Ị㦚 ⿖㡂䞮㡂 ⼖䡫䟊㍳㦚 㔺㔲 䞲 ἆὒ 㔺䠮㩗㦒⪲ 䁷㩫♲ 㹸ₖ㠦⍞㰖⓪ 1.3

£

îƁƋ

㧊Ⳇ 䟊㍳㩗㦒⪲ 0.5 㦮 ‶㡊㰚㩚⨟㦚 ㌂㣿 䞮㡖㦚 ἓ㤆 1.38

îƁƋ

㦮 㹸ₖ㠦⍞㰖⯒ ⋮䌖⌊㠞

┺.

4. 冶 嵦

㹸ₖ㠦⍞㰖㦮 䡫㌗ὒ 䞮㭧㠦 ╖䞲 ☛Ⱃ㎇ὒ 㨂

⬢㠦 ╖䞲 䘎㹾Ṗ 㩗㦖 㩦㦖 ἶⶊ 㨂⬢ 䕢ᾊ ₆ 㭖㦒⪲㍲ Ṗ⓻㎇㦚 Ṗ㰖Ⳇ 㧚Ἒ㹸ₖ㠦⍞㰖㦮 㧊

⪶㩗 䘟Ṗ㔳㦖 㨂⬢㦮 ⹎㔲㩗 䔏㎇㦚 ┺⬾ἶ 㧞 㦒⸖⪲ ⺆䞿㧊⋮ ἶⶊ㦮 㫛⮮㠦 ➆⯎ Ệ㔲㩗 䔏

㎇㠦 ╖䟊 ☛Ⱃ㎇㦚 Ṗ㰚┺ ἶⶊ 㨂⬢㦮 㑮ⳛ䘟 . Ṗ⓪ Ệ䂲 㹸ₖ㡗㡃㦮 ‶㡊 ㎇㧻 ㏣☚㔳㦚 㧊㣿 䞮㡂 20% 㦮 㡺㹾⪲ 㡞䁷㧊 Ṗ⓻䞮Ⳇ 䡫㌗ὒ 㨂 ,

⬢㠦 ╖䞲 ☛Ⱃ㎇㦚 Ṗ㰖ἶ 㧞┺ 㧒⹮ ἶⶊ 㩲 . 䛞㦮 㑮ⳛ䘟Ṗ⯒ 㥚䟊 㹸ₖ㠦⍞㰖㦮 䘟Ṗ ⹿㞞㦚 㥶䞲㣪㏢ 㩫㔳䢪 ⌊㦮 㑮㔳䢪 ὒ㩫㦒⪲ 㩫Ⰲ䞮㡖 㦒Ⳇ Rivlin 㦮 ‶㡊 㧎㧻㔲䘎 ⳾◎㠦 ╖䟊 㹸ₖ㠦

⍞㰖㦮 㔲䠮Ṩὒ Ṛ㧊 Ἒ㌆Ṩ㦚 ゚ᾦ䞮㡂 Ṗ⓻㎇

㦚 㩦Ỗ䞮㡖┺.

焾処怾竒

(1) R. S. Rivlin, A. G. Thomas, 1952, "Rupture of Rubber. I. Characteristic Energy for Tearing", Journal of Polymer Science, Vol. 10, No. 3, pp.

291-318

(2) E. H. Andrews, 1974, "A generalized theory of fracture mechanics", Journal of Materials Science, Vol. 9

(3) Y. Fukahori, 1998, "Fatigue failure of elastomers", Nippon Gomu Kyokaishi, No. 11 (4) A. G. Thomas, 1958, "Rupture of Rubber. V.

Cut Growth in Natural Rubber Vulcanizates", Journal of Polymer Science, Vol. 31, pp. 467-480, (5) A. N. Gent, P. B. Lindley, A. G. Thomas,

1964, "Cut Growth and Fatigue of Rubbers. I. The Relationship between Cut Growth and Fatigue", Journal of Applied Polymer Science, Vol. 8, pp.

455-466

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