DOI : 10.5228/KSTP.2011.20.3.222
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YYYGV穢剳暒昷儆击穟箒滆V洢YW劒G 洢Z笾SGYWXX噊G G
࣮犛ࣜ汾沫ࣜ柢竞ࣜ愯憛櫖ࣜ分穢ࣜ処然ࣜ
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愛滊匶
1· 橎塛焲
2· 單沲懻
2· 卆欇昣
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State of Art for Biaxial Tensile Test Systems
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J. G. Park, D. C. Ahn, J. B. Nam, Y. S. Kim
(Received December 17, 2010 / Revised April 28, 2011 / Accepted May 3, 2011) G
Abstract
This paper is a review of biaxial tensile test equipments and specimens. The stresses acting on a component in service are multiaxial in nature. Therefore, it is necessary to consider the mechanical properties of sheet materials not only under uniaxial but also under these multiaxial stress states. Biaxial testing of metal in industry becomes an important investigation tool for the evaluation of mechanical properties of sheet metals. In this paper, several types of biaxial tensile tests were reviewed, and their advantages and limitations were discussed.
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Key Words : Biaxial Tensile Test, Yield Loci, Material Properties, Cruciform Specimen
41# ⇆# ᤊG G
䕦㨂㎇䡫₆㑶㦖 㧦☯㹾, 䟃Ὃ, Ṗ㩚, ㌳䢲₆₆
❇ 㤆Ⰲ⋮⧒ ㌆㠛㦮 ⁒Ṛ㧎 ㈢Ⰲ㌆㠛㠦㍲ ⍦Ⰲ 䢲㣿♮ἶ 㧞⓪ 㭧㣪䞲 ₆㽞₆㑶㧊Ⳇ ╖⨟ ㌳㌆㠦 㥶Ⰲ䞲 㧻㩦㦚 Ṗ㰖ἶ 㧞┺.
⁎⩂⋮ 㧊⩂䞲 ㎇䡫Ὃ㩫㠦 ㌂㣿♮⓪ 㨂⬢✺㦖 㫛㫛 ㎇䡫㎇㠦㍲ ⶎ㩲⯒ 㟒₆㔲䋾┺. 㧊⩂䞲 ⶎ㩲
⯒ 䟊ἆ䞮₆ 㥚䟊㍲, 㨂⬢㦮 ₆Ἒ㩗 䔏㎇ ⼖䡫 䔏㎇㦚 㧊䟊䞮ἶ ㎇䡫䞲Ἒ㠦 ⹎䂮⓪ 㣪㧎✺㦚 䢫 㧎䞮⓪ ộ㧊 ⶊ㠝⽊┺☚ 㭧㣪䞮Ⳇ 㧊⯒ 䐋䟊㍲
㌳㌆┾Ṗ⯒ ⌄㿪ἶ ἶ䛞㰞㦮 㩲䛞㦚 ㌳㌆䞶 㑮 㧞┺ [1].
㨂⬢㦮 ₆Ἒ㩗 䔏㎇㦚 ⋮䌖⌊⓪ 䟃⽋㦧⩻, 㧎㧻 ṫ☚, ṖὋἓ䢪 㰖㑮 ❇㦖 㭒⪲ ┾㿫㧎㧻 㔲䠮㦚 䐋䟊㍲ 㠑㠊㰚┺. ⁎⩂⋮ Ệ㦮 ⳾✶ 䕦㨂 ㎇䡫Ὃ 㩫㦖 䘟Ⳋ㦧⩻ 㯟, 2㿫 㦧⩻ ㌗䌲㠦㍲ 㧊⬾㠊㰖₆
➢ⶎ㠦 ┾㿫㧎㧻 㔲䠮㦚 䐋䟊 㠑㦖 ◆㧊䎆 Ⱒ㦒
⪲ 䕦㨂㦮 ㎇䡫Ὃ㩫㦚 ⳾㌂䞮₆㠦⓪ 㫇䞲 㩦㧊
Ⱔ┺ [2].
⁎⧮㍲ ┺㿫 㦧⩻ ㌗䌲㦮 㨂⬢㦮 ㏢㎇⼖䡫䔏㎇
⼖䡫Ệ☯㦚 㧊䟊䞮₆ 㥚䞲 ⻫㦒⪲ 2㿫 㧎㧻 㔲䠮㧊 ⍦Ⰲ 䟟䟊㰖ἶ 㧞┺. ▪㤇㧊 ╖㦮 ⁞
㏣㨂⬢✺㦖 ㏢㎇ 㧊㎇㦚 Ṗ㰖ἶ 㧞㦒Ⳇ 㧊⓪ 2 㿫 㧎㧻 㔺䠮㦚 䐋䟊㍲ 㓓Ợ 䢫㧎♲┺ [3]. ⁎Ⰲἶ 2㿫 㧎㧻 㔺䠮㦖 䟃Ὃῂ㫆ⶒ㧊⋮, ┺Ⰲ㦮 㰖㰖╖
₆Ἒ 㣪㏢㦮 ₆Ἒ㩗 䔏㎇㦚 䘟Ṗ䞮₆ 㥚䞲
⻫㦒⪲ ⍦Ⰲ ㌂㣿♮ἶ 㧞┺.
Ⳋ, 㞚㰗₢㰖 2㿫 㧎㧻㔲䠮⻫㠦 ╖䞲 ′ỿ 䢪♲ 㔲䠮⻫㧊 㠜㠊 Ⱔ㦖 㡆ῂ㧦✺㧊 ┺㟧䞲 㔺䠮⻫㦚 ㌂㣿䞮ἶ 㧞⓪ 㔺㩫㧊┺. ⁎⩂⋮ 䞲Ṗ 㰖 ☯㧒䞲 ộ㦖 㔲䘎䡫㌗㧊 Makinde[4] ❇㧊 㩲㞞 䞲 ộὒ ṯ㦖 㕃㧦(+) 䡫䌲⪲ ♮㠊㧞┺⓪ ộὒ ⁎
䟻㦒⪲ 㧎㧻㦚 䞮㡂 㔺䠮㦚 䞲┺⓪ ộ㧊┺.
⁎Ⰲἶ 㔲䠮 ⻫ὒ 㔲䘎㦮 䡫䌲⓪ 㫆⁞㝿 ┺
⯊㰖Ⱒ 㕃㧦 㔲䘎㦮 㭧㞯㠦㍲ ⼖䡫⮶㦚 䁷㩫䞮 ἶ ⁎ ┾Ⳋ㩗㦚 㧊㣿䞮㡂 㦧⩻㦚 ㌆㿲 䞲┺⓪ ộ 㧊┺.
XUG ἓ╖䞯ᾦG ╖䞯㤦G YUGwvzjvG ₆㑶㡆ῂ㏢G
JG ᾦ㔶㩖㧦aG ἓ╖䞯ᾦSGlTaGgUUG
穢剳暒昷儆击穟箒滆V洢YW劒G 洢Z笾SGYWXX噊VYYZG
G
⁎⧮㍲ 㔲䠮㧊 㰚䟟♮⓪ ☯㞞 㔲䘎㦮 㭧㞯㠦
㍲ ‶㧒 ⼖䡫㧊 ㌳㎇♮☚⪳ 䞮⓪ ộ㦖 ⰺ㤆 㭧㣪 䞮┺. ⽎ ⏒ⶎ㠦㍲⓪ 㡂⩂ 㡆ῂ㧦✺㧊[4~8] 㩲㞞䞲 2㿫 㧎㧻 㔲䠮₆㢖 㔲䘎㠦 ╖䟊㍲ ㌊䘊⽊ἶ ⁎ 䔏㰫ὒ ⶎ㩲㩦 ╖㞞㦚 ⏒㦮䞮ἶ㧦 䞲┺.
#
51#5⸿# ⠢⡏# ⎆㚂#
514# 㘂⦻⣆♞# ᳓⎇#
2㿫 㧎㧻 㔲䠮㦚 䐋䟊㍲ 㠑㦚 㑮 㧞⓪ ╖䚲㩗 㧎 ἆὒⶒ㦖 䘟Ⳋ㦧⩻ ㌗䌲㠦㍲㦮 䟃⽋ἷⳊ㧊┺.
2㿫 㧎㧻 㔲䠮㦒⪲ ῂ䞲 䔏㩫 ㏢㨂㦮 㔺䠮㩗 䟃
⽋ἷⳊὒ 㡂⩂ 㫛⮮㦮 㧊⪶㩗 䟃⽋ 㫆Ị㔳㦚 ゚ ᾦ䞮㡂 ㏢㨂 ㏢㎇Ệ☯㦚 Ṗ㧻 㧮 ㌂䞮⓪ 㫆Ị 㔳㦚 ㍶䌳䞮Ợ ♲┺. Fig. 1㦖 㔲䘎㠦 㡂♮⓪ 㦧
⩻ ㌗䌲⯒ ⋮䌖⌊ἶ 㧞┺. 䟃⽋ἷⳊ㦮 1 ㌂Ⳋ㦖 㭒 㦧⩻(V1)ὒ 㦧⩻(V2)㧊 ⳾⚦ 㟧(+) 㧎 2㿫 㧎 㧻 ㌗䌲㧊ἶ, 2 ㌂Ⳋ㦖 㭒 㦧⩻㧊 㦢(-)㧊ἶ 㦧⩻㧊 㟧(+)㧎 㩚┾㌗䌲㧊Ⳇ 4 ㌂Ⳋ㦖 㭒 㦧⩻
ὒ 㦧⩻㦮 2 ㌂Ⳋὒ⓪ ╖㦮 ㌗䌲㧊┺. ⁎ Ⰲἶ 3 ㌂Ⳋ㦖 㭒 㦧⩻ὒ 㦧⩻ ⳾⚦Ṗ 㦢(-) 㧎 ㌗䌲⪲ 2㿫 㞫㿫 ㌗䌲㧊┺.
2㿫 㧎㧻 㔲䠮₆Ṗ ☚㧛♮₆ 㧊㩚㠦⓪ 䟃⽋ἷ Ⳋ㦚 㧧㎇䞮₆ 㥚䟊㍲⓪ Fig. 1ὒ ṯ㧊 1 ㌂Ⳋ㦮
₆㫊㦮 ❇2㿫 㧎㧻 ◆㧊䎆⓪ ⻢㰖㔲䠮㦒⪲ ῂ䞮 ἶ, 䘟Ⳋ⼖䡫 ῂṚ㦖 䘟Ⳋ⼖䡫 㔲䘎㦚 㧊㣿䞮㡖㦒 Ⳇ, 㭒· 㦧⩻ 㿫 ㍶㌗㦮 ◆㧊䎆⓪ ṗ 䟻⼚ ┾ 㿫㧎㧻 㔲䠮㦒⪲ ῂ䞮Ⳇ, 2 ㌂Ⳋὒ 4 ㌂Ⳋ㦮
◆㧊䎆⓪ 㩚┾ 㔲䘎㦚 㧊㣿䞮㡂 䢫⽊䞮㡖┺. ⡦䞲 ٻ
Fig. 1 Stress on each specimens
(a) Makinde[4] (b) Kuwabara[6]
(c) Park[3]
Fig. 2 Biaxial tensile test machine controlled by load
(a) Ferron[8] (b) Fraunhofer[9]
Fig. 3 Biaxial tensile test machine controlled by displacement
ṗ 䟻⼚ Ⳋ⌊(In-plane) 㞫㿫㔺䠮㦒⪲ 㭒· 㦧⩻
㿫 ㍶㌗㦮 㞫㿫 ◆㧊䎆⯒ 䢫⽊䞮㡖㦒Ⳇ 䕦㨂㦮 Ⳋ㣎(Out-plane) 㞫㿫 㔺䠮㦒⪲ 3 ㌂Ⳋ㦮 ❇ 2㿫 㞫㿫 ◆㧊䎆⯒ 䢫⽊䞮㡖┺. ⁎⩂⋮ 㧊 ⻫㦖 ⳾
⚦ ┾㿫 㧎㧻 㔲䠮₆⯒ 㧊㣿䞮㡂 ┺㿫 㧎㧻 ㌗䌲
⪲ ⼖䡫䞮㡂 㔲䠮䞮⓪ 㔳 㧊Ⳇ 㔲䠮 ὒ㩫㠦㍲
㑮䞯㩗 Ṗ㩫㦚 ⌊䙂䞮₆ ➢ⶎ㠦 㩫䢫䞲 ◆㧊䎆⯒
䢫⽊䞮⓪◆ 㠊⩺㤖㧊 ➆⯎┺.
㧒㩗㦒⪲ ┾㿫㧎㧻 㔲䠮㦖 ⼖㥚⯒ 㩲㠊䞮㡂 䞮㭧㦚 䁷㩫䞮⓪ ⻫㦒⪲ ⼖㥚Ṗ ☛Ⱃ⼖㑮㧊Ⳇ 䞮㭧㧊 㫛㏣⼖㑮㧊┺.
⁎⩂⋮ Fig. 1㠦 ⋮䌖⌎ ộ ṯ㧊 䟃⽋ἷⳊ㦖 㦧
⩻ὋṚ㌗㠦 㧧☚ ♮Ⳇ 㭒 㦧⩻ὒ 㦧⩻㧊 ㍲⪲
YY[GV穢剳暒昷儆击穟箒滆V洢YW劒G 洢Z笾SGYWXX噊G G
㡆☯♮㠊 㔺䠮㧊 㰚䟟♮㠊㟒 䞮₆ ➢ⶎ㠦 ⼖㥚㩲 㠊Ṗ 㞚┞⧒ 䞮㭧㩲㠊 ♮㠊㟒 䞾㧊 Ⱎ➛䞮┺. ⁎
⧮㍲ [3], Makinde[4], Kuwabara[6] ❇㧊 㧊㣿䞲 2 㿫 㧎㧻 㔲䠮₆⓪ ㍲⪲ ┺⯎ ⚦ Ṳ㦮 㿫㧊 ㍲⪲
㡆☯♮㠊 㧞㦒Ⳇ 㭒 㦧⩻ 㿫㦚 ₆㭖㦒⪲ 䞮㡂 䞮 㭧㦚 ㍶䡫㩗㦒⪲ 㯳Ṗ㔲䅲ṖⳆ ⼖㥚 ⼖䡫⮶㦚 䁷㩫䞮⓪ 㔳㦒⪲ 㰚䟟♲┺. 㯟 2 㿫 㧎㧻 㔲䠮 㦖 㦧⩻㧊 ☛Ⱃ⼖㑮Ṗ ♮ἶ ⼖䡫⮶㧊 㫛㏣ ⼖㑮 Ṗ ♲┺.
㾲㽞 Makinde[4] ❇㧊 ἶ㞞䞲 ⻫(Fig. 2(a))㦚
⁎ 㧊䤚㦮 㡆ῂ㧦[3, 5, 6] ✺㧊 ⽊㢚䞮㡂 ⋮Ṫ⓪◆, Makinde[4]㦮 㔲䠮㧻゚⓪ ㍲⪲ Ⱎ㭒⽊ἶ 㧞⓪ 㥶 㞫㔺Ⰶ▪㦮 㦧㏣☚Ṗ ╂⧒㍲ 㕃㧦 㔲䘎㧊 䞲㴓
䟻㦒⪲ ⊢⩺Ṗ⓪ ┾㩦㧊 㧞㠞┺. 㧊⯒ ⽊㢚䞮₆ 㥚䟊㍲ ṗ 㔺Ⰶ▪㠦 㢚㿿㧻䂮⯒ 㹿䞮㡖┺. 䞮㰖 Ⱒ 㢚㿿㧻䂮 Ⱒ㦒⪲⓪ 㢚⼓䞮Ợ ‶䡫㦚 㥶㰖䞶 㑮Ṗ 㠜㠞┺. Kuwabara[6] ❇㦖 ㍲⪲ Ⱎ㭒 ⽊ἶ 㧞
⓪ 䞲 㕣㦮 㥶㞫㔺Ⰶ▪㠦 䖂䏶⁎⧮䝚 (Pantograph) 䡫䌲㦮 ₆ῂ⯒ 㹿䞮㡂 Ệ㦮 㢚⼓䞮Ợ ‶䡫㦚 㧊
⬾Ợ 䞮㡖㦒Ⳇ Park[3]❇㦖 Kuwabara[6]Ṗ 㩲㞞䞲 㔲䠮₆㠦 㔏㡾㧻䂮㢖 CCD䃊Ⲫ⧒⯒ 㧊㣿䞲 ⼖䡫
⮶ 䁷㩫㧻䂮⯒ 㹿䞮㡖┺. ἓ╖䞯ᾦ[3]㠦㍲ ⽊ 㥶䞲 2㿫 㧎㧻 㔲䠮₆⓪ 700°C₢㰖 㔏㡾 㔺䠮㧊 Ṗ⓻䞮Ⳇ 㔲䠮₆㦮 㾲╖ 䞮㭧㦖 5䏺(ton)㧊┺. Fig 2(c)㠦 ἓ╖䞯ᾦ㠦㍲ ⽊㥶䞮ἶ 㧞⓪ 2㿫 㧎㧻 㔲䠮₆⯒ ⋮䌖⌊㠞┺.
䞮㭧㩲㠊 㔳㦖 䟃⽋ἷⳊ㦮 ₆⽎ Ṳ⎦㠦 㞚㭒 㿿㔺䞲 㔺䠮 ⻫㧎◆ 䟊 ⁎ 㔺䠮⻫㧊 ┺㏢
₢┺⫃ἶ ἶṖ㦮 㧻゚Ṗ 䞚㣪䞮┺.
515# ᵪ➮⣆♞# ᳓⎇#
┾㿫㧎㧻 㔲䠮㧊 㨂⬢ ⶒ㎇䘟Ṗ㠦 ⍦Ⰲ ㌂㣿♮
⓪ 㧊㥶⓪ ゚ᾦ㩗 Ṛ┾䞲 ⻫㦒⪲ ῂ⋮Ṗ 㑮 䟟䞶 㑮 㧞₆ ➢ⶎ㧊┺. ➢ⶎ㠦 ┾㿫㧎㧻 㔲䠮₆
⯒ 㧊㣿䞮Ệ⋮ ゚ᾦ㩗 Ṛ┾䞲 㔲䠮 ⻫㦒⪲ 䟃
⽋ἷⳊ㦚 䢫⽊䞮ἶ㧦 䞮⓪ 㡆ῂṖ 㧊⬾㠊㰖ἶ 㧞
┺[5, 8~10]. Lin[5]㧊 㩲㞞䞲 ⻫㦖 ₆㫊㦮 㧎㧻㔲 䠮₆㠦 ⼚☚㦮 ῂ☯㿫㦚 Ṗ䞮㡂 2㿫 㧎㧻 㔲䠮 㦚 ῂ䡚䞮㡖㦒Ⳇ, Ferron[8] ❇㦖 Fig. 2(a)㢖 ṯ㦖 䖂䏶⁎⧮䝚 ₆ῂ⯒ 㧊㣿䞮㡂 2㿫 㧎㧻㦚 ῂ䡚䞮㡖
┺. Fraunhofer[9]☚ Fig. 3(b)㢖 ṯ㦖 Ⱇ䋂(Link) ₆ῂ
⯒ 㧊㣿䞮㡂 2㿫 㧎㧻㦚 ῂ䡚䞮㡖㦒Ⳇ Geiger[10]
⓪ ㎇䡫䞲Ἒ☚ 㔲䠮㠦㍲ ❇ 2㿫 㧎㧻 ⳾✲⯒ ῂ 䡚䞮⓪ ộὒ ṯ㦖 ⻫㦒⪲ 䔏㑮䞲 䡫䌲㦮 㔲䘎 㦚 㧊㣿䞮㡂 2㿫 㧎㧻 㔲䠮㦚 ῂ䡚䞮㡖┺. ⁎⩂⋮
㧊㢖 ṯ㦖 ⻫㦖 ⼖㥚⯒ 㩲㠊䞮₆ ➢ⶎ㠦 䟃⽋
㩦₢㰖 ゚⪖䞮⯒ ῂ䡚䞮₆Ṗ 㠊⩺㤆Ⳇ ❇ 2㿫 㧎㧻 㧊㣎㦮 ἓ㤆☚ 㔲䠮䞮₆Ṗ 㓓㰖㞠┺. ⼖㥚㩲 㠊 㔳㦮 㔲䠮⻫㦖 㫆㧧㧊 㣿㧊䞲 㧻㩦㧊 㧞 㰖Ⱒ ┺㟧䞲 㔲䠮 ◆㧊䎆 䢫⽊㦮 㠊⩺㤖㧊 ➆⯎
┺.
61#5⸿# ⠢⡏# ⎆㑢#
䡚㨂㦮 2㿫 㧎㧻 㔲䘎㦮 䡫㌗㦖 㨂⬢㦮 䞒⪲
䕢ᾊ㡆ῂ[11, 12]㠦㍲䎆 㔲㧧 ♮㠊 㑮㩫 㩚
♮㠊 㢪┺. 㧊䤚 Makinde[4] ❇㦖 2㿫 㧎㧻 㔲䘎㠦
╖䟊 ₠㧊 㧞⓪ ἶ㺆㦚 䐋䟊 㔲䘎㦮 䡫㌗㦚 㾲㩗 䢪 䞮㡖┺. Makinde[4] ❇㦖 Fig. 4(a), (b)㢖 ṯ㧊 㔂 Ⱅ(Slit)㧊 㧞⓪ 㔲䘎ὒ 㠜⓪ 㔲䘎㦚 ゚ᾦ䞮㡖┺.
⁎Ⰲἶ ⚦ 㔲䘎 ⳾⚦ 㦧⩻ ⼖䡫⮶㦚 䁷㩫䞮⓪ 2㿫㧎㧻 㔲䘎㦮 㭧㞯Ⱒ㦚 ⚦℮⯒ 㟝Ợ ₆ἚṖ Ὃ 䞮㡂 ㌂㣿䞮㡖┺. Ṗ㤊◆ 㦮 ⚦℮⯒ 㟝Ợ 䞲 ộ㦖 䁷㩫 㥚㠦㍲ ⼖䡫㦚 㥶☚䞮₆ 㥚䞾㧊
┺. ⁎⩂⋮ Fig. 4(a) 㔲䘎ὒ ṯ㦖 ἓ㤆㠦⓪ 㔲䘎
⚦℮㦮 㡆㏣ὒ ⽋㧷䞲 㔲䘎䡫㌗㦒⪲ 㧎䟊 䁷㩫
㥚㦮 㦧⩻ ⼖䡫⮶㧊 ‶㧒 䞮㰖 㞠㦚 ㈦ 㞚
┞⧒ ⚦℮ ⼖䢪⪲ 㧎䟊 ₆㭖 ┾Ⳋ㩗㦚 㠒Ⱎ⪲ 䟊 㟒 ♮⓪㰖㠦 ╖䞲 ₆㭖㧊 ⳾䢎䞮┺. ⁎⧮㍲ 㔲䘎 㦚 Fig. 4(b)㢖 ṯ㧊 ┾Ⳋ㩗㧊 ⼖䞮⓪ 㦚 ㌂ṗ 䡫䌲⪲ Ⱒ✺㠊 ₆㭖 ┾Ⳋ㩗㦚 ⳛ䢫䞮Ợ 㩲㔲䞮㡖 ἶ 㔲䘎㦮 ⋶Ṳ㥚㠦 㔂Ⱅ㦚 ṖὋ䞮㡖┺. 㧊 㔂 Ⱅ㦖 㕃㧦 㔲䘎㠦㍲ 㞚㭒 㭧㣪䞲 㡃䞶㦚 ╊╏䞮
⓪◆, 㔲䘎㦮 ⋶Ṳ 㦮 ㎎㧻゚⯒ 䋂Ợ 䞮⓪ 㡃 䞶㦚 䞶 ㈦ 㞚┞⧒ 2㿫 㧎㧻 㔲 㔲䘎 䡫㌗㦒⪲
㧎䞲 㑮㰗 䟻 ⼖䡫㩖䟃㦚 Ṧ㏢ 㔲䅲 㦧⩻
⼖䡫⮶ 䁷㩫㥚㠦 ‶㧒 ⼖䡫㦚 㥶☚䞮㡂 㔺䠮㦮 㔶⬆☚⯒ 䟻㌗㔲䋾┺.
⁎ 䤚 Kuwabara ❇[6]㦖 Makinde[4] ❇㧊 㩲㞞 䞲 㔲䘎㦚 㑮㩫䞮㡂 Fig. 4(c)㢖 ṯ㦖 㔲䘎㦒⪲ 䕦 㨂㦮 ㏢㎇⼖䡫 Ệ☯ 㡆ῂ㠦 㩗㣿䞮㡖┺. 㔂Ⱅ㦮
⚦℮⓪ Ṗ⓻䞲 㾲㏢䞲㦒⪲ 䞮㡂 䡚㨂⓪ 0.2mm⪲
㩲㞞䞮ἶ 㧞㦒Ⳇ 䁷㩫㥚㦮 ⚦℮ Ṧ㏢ 㠜㧊 㧒 㩫䞮Ợ 㥶㰖 䞮ἶ 㧞┺. 㞴㍲ ㍲㑶䞲 㢖 ṯ㧊 㔂Ⱅ㦮 䣾ὒ⓪ ‶㧒 㦧⩻ ⼖䡫⮶ ㌳㎇㠦 㩫 㩗㧎 㡃䞶㦚 䞮㰖Ⱒ 㔲䠮㧊 㰚䟟♮Ⳋ 㔂Ⱅ㠦
⼖䡫 㦧⩻㧊 㰧㭧♮㠊 䕢┾㠦 㧊⯊Ợ ♮⸖⪲
╖ ⼖䡫㦚 㥶☚䞮₆Ṗ 䧮✺┺. ⁎⧮㍲ Fig. 4(c)㢖 ṯ㦖 㔲䘎㦚 㧊㣿䞮Ợ ♮Ⳋ ㏢㎇ ⼖䡫⮶㦚 10%㧊
㌗㦒⪲ 㥶☚䞮₆Ṗ 㠊⪋┺.
穢剳暒昷儆击穟箒滆V洢YW劒G 洢Z笾SGYWXX噊VYY\G
G
(a) Makinde[4] (b) Makinde[4](c) Kuwabara[6] (d) Geiger[10] (e) Ohtake
(f) Abu-Farha [14] (g) Gozzi[15] (h) Gozzi[15]
Detail of section A-A
(i) Zidane[21]
Fig. 4 Proposed geometry for cruciform specimens
YY]GV穢剳暒昷儆击穟箒滆V洢YW劒G 洢Z笾SGYWXX噊G G
Vx(MPa) Vy(MPa)
Hp 0.002 0.005 0.01
-400 -300 -200 -100 0 100 200 300 400
-400 -300 -200 -100 0 100 200 300 400
TD (y) RD (y)
Room temp.
200¶C
Vx(MPa) Vy(MPa)
Hp 0.002 0.005 0.01
-400 -300 -200 -100 0 100 200 300 400
-400 -300 -200 -100 0 100 200 300 400
TD (y) RD (y)
Room temp.
200¶C
(a) Aluminum alloy[2] (b) Magnesium alloy[3]
(c) Stainless steel[15] (d) CP titanium[20]
Fig. 5 Yield loci for various materials
㧒㩗㦒⪲ 䡚㧻㠦㍲ 10%㧊㌗㦒⪲ ㏢㎇⼖䡫㦚 䞮㡂 㩲䛞㦚 ㎇䡫䞮ἶ 㧞₆ ➢ⶎ㠦 㨂⬢㦮 ㏢㎇
⼖䡫 Ệ☯ 㡆ῂ☚ 10%㧊㌗㦮 ⻪㥚㠦㍲ 㧊⬾㠊㪎 㟒 䞮㰖Ⱒ, 䡚㨂⓪ ゚ᾦ㩗 ⌄㦖 ㏢㎇⼖䡫 㡗㡃㠦
㍲ 䢫㧎䞲 ⼖䡫Ệ☯㦒⪲ ╖ ⼖䡫 㡗㡃㦮 ⼖䡫Ệ
☯㦚 㥶㿪䞮ἶ 㧞┺. ⁎⧮㍲ 䕦㨂㔲䠮㦮 ἓ㤆㠦⓪ Ohtake [13] ❇㧊 㩲㞞䞲 Fig. 4(e)㢖 ṯ㧊 㡂⩂ 㫛
⮮㦮 㔲䘎 㭧㠦 㼁 ⻞㱎 ⻫㦒⪲ 䁷㩫㥚㦮 ┾ Ⳋ㩗㦚 Ṧ㏢㔲䋺⓪ 䡫䌲Ṗ Ṗ㧻 㥶㣿䞶 ộ㦒⪲
䕦┾♮Ⳇ, ゚ᾦ㩗 ⚦ℒ㤊 ῂ㫆㨂㔲䠮㦮 ἓ㤆㠦⓪ Abu-Farha [14]❇㧊 㩲㞞䞲 Fig. 4(f)㢖 ṯ㦖 ⻫㦒
⪲ ⚦℮⯒ Ṧ㏢㔲䅲 ┾Ⳋ㩗 Ṧ㏢⯒ 䢫⽊䞮⓪
⻫㧊 㥶㣿䞶 ộ㦒⪲ 䕦┾♲┺.
㞴㠦㍲ 㠎 䞲 㧊 ⚦ Ṗ㰖㦮 ἓ㤆 ⳾⚦ 㔂Ⱅ㦚 䙂䞾䞮⓪ 䡫䌲Ṗ ▪㤇 䞿╏䞮┺ἶ 䕦┾♲┺.
Gozzi[15]⓪ 㓺䎢㧎⩞㓺 䕦㨂㦮 ㏢㎇⼖䡫 䔏㎇㦚 㞢㞚⽊₆ 㥚䟊 Fig. 4 (g), (h)㦮 㔲䘎㦚 㧊㣿䞮㡖┺.
⁎Ⰲἶ Geiger[10]⓪ Fig. 4(d)㦮 㔲䘎㦚 㧊㣿䞮㡂
㏢㎇䟃⽋Ệ☯ 㡆ῂ⯒ 㑮䟟䞮㡖㦒⋮ 㭒⳿䞶 Ⱒ䞲 ἆὒ⓪ 㞚㰗 㠑㰖 ⴑ䞮㡖㦒Ⳇ Zidane ❇[21] 㦖 ㎇ 䡫 䞲Ἒ☚⯒ 㧧㎇䞮₆ 㥚䞮㡂 Fig. 4(i)㢖 ṯ㦖 㔲 䘎㦚 㧊㣿䞮㡖┺.
71#5⸿# ⠢⡏# ⎆㚂⠂# ⟻❓#
#
㽞₆㦮 2 㿫 㧎㧻㔲䠮㦖 㨂⬢㦮 䞒⪲䕢ᾊ[11, 12]
穢剳暒昷儆击穟箒滆V洢YW劒G 洢Z笾SGYWXX噊VYY^G
G
㡆ῂ㠦 㭒⪲ 䢲㣿 ♮㠞㰖Ⱒ, 㾲⁒㠦⓪ 㨂⬢㦮 ㏢㎇⼖䡫 Ệ☯ ′ⳛ㠦 㭒⪲ 䢲㣿♮ἶ 㧞┺. ⁎ 㭧 Kuwabara ❇[6]㧊 㡆ῂ䞲 ⻫㧊 ⍦Ⰲ 㧊㣿♮ἶ 㧞㦒Ⳇ Ⱔ㦖 ἆὒ✺㧊 ⽊ἶ♮ἶ 㧞┺. [2, 3, 16, 17] ❇㦖 Fig. 2(c)㠦 ⋮䌖⌎ 2 㿫 㧎㧻㔲䠮₆⯒ 㧊 㣿䞮㡂 Ⱎ⁎⍺㓮, 㞢⬾⹎ⓚ, 䌖㧊䌖ⓚ ❇ 㧊㎇
㨂⬢✺㦮 ㏢㎇⼖䡫 䔏㎇㠦 ╖䟊 㡆ῂ䞮㡖㦒Ⳇ, Fig.
5(a) 㢖 (b)㠦 ⋮䌖⌎ ộὒ ṯ㧊 㞢⬾⹎ⓚ Ⱎ⁎
⍺㓮 䞿⁞ 㨂⬢㠦 ╖䞲 䟃⽋ἷⳊ㦚 䢫⽊䞮㡖┺.
䔏䧞 ṫ䞲 㧊㎇ὒ ⌄㦖 ㎇䡫㎇ ➢ⶎ㠦 㭒⪲ ἶ 㡾㠦㍲ ㎇䡫䞮⓪ Ⱎ⁎⍺㓮[3]ὒ 䌖㧊䌖ⓚ[17]㠦 ╖ 䟊㍲⓪ 2 㿫 㧎㧻 㔲䠮₆㠦 㔏㡾 㧻䂮⯒ 㹿䞮㡂 ἶ㡾 䟃⽋ἷⳊ㦚 㧧㎇䞮㡖┺.
₆㫊㦮 2㿫 㧎㧻 㔲䠮₆㢖 㔲䘎Ⱒ㦒⪲⓪ Fig. 5 㦮 (a)㢖 ṯ㧊 1 ㌂Ⳋ㦮 ◆㧊䎆 㠦 䢫⽊䞮㰖 ⴑ䞲┺. ⁎Ⰲἶ Fig. 5(b), (d)㢖 ṯ㧊 Ⱎ⁎⍺㓮ὒ 䌖 㧊䌖ⓚ ❇ὒ ṯ㦖 㧊㎇ 㨂⬢✺㦖 Ⳋ⌊ 㑮㰗 㧊
㎇ ㈦Ⱒ 㞚┞⧒, 㧎㧻䟃⽋㦧⩻ὒ 㞫㿫䟃⽋㦧⩻
㦮 䋂₆Ṗ ┺⯎ 㧎㧻-㞫㿫 ゚╖䃃 䔏㎇☚ Ṗ㰖ἶ 㧞┺[3, 18, 19]. 㧊⓪ ┾㿫 㧎㧻 㔲䘎㦚 㧊㣿䞲 Ⳋ
⌊ 㞫㿫 㔲䠮㦒⪲☚ Ṛ┾䞮Ợ 䢫㧎 䞶 㑮 㧞┺.
Ishiki ❇[19]㦖 ₆㫊㦮 2㿫 㧎㧻 㔲䠮₆⯒ 㑮㩫 ⽊ 㢚䞮㡂 2, 4 ㌂Ⳋ㦮 㔺䠮 ἆὒ☚ 䢫⽊䞮㡖┺. 2, 4 ㌂Ⳋ㦮 㔺䠮 ἆὒ⯒ 㠑₆ 㥚䟊㍲⓪ 㭒 㦧⩻
䟻㦒⪲⓪ 㧎㧻, 㦧⩻ 䟻㦒⪲⓪ 㞫㿫㦧⩻㦚
㡂䟊㟒 䞮⓪◆, 䕦㨂⯒ Ⳋ⌊ 㞫㿫䞮Ợ ♮Ⳋ 㫢 Ὴ㧊 ㌳䞮⓪◆ 㧊⯒ 㰖䞮₆ 㥚䞮㡂 㔲䘎 ㌗
䞮㠦 㰖⁎⯒ 㧻㹿䞮㡖┺. Gozzi[15]⓪ 1, 2, 4 ㌂Ⳋὒ ❇ 2㿫 㞫㿫 㡗㡃㧎 3㌂Ⳋ㦚 䙂䞾䞮
⓪ 㩚 ῂṚ㦮 䟃⽋ἷⳊ㦚 䢫⽊䞮⓪◆ ㎇Ὃ䞮㡖┺.
㾲⁒㠦 2㿫 㧎㧻 㔲䠮₆⯒ 㧊㣿䞮㡂 䚲♮ἶ 㧞⓪ 㡆ῂ ἆὒ✺㦖 䕦㨂㦮 ㏢㎇⼖䡫 Ệ☯[3, 6, 15
~19]㧊 ╖㧊Ⳇ, ⁎ 㭧 Kuwabara ❇[6]㧊 㩲㞞 䞲 㔲䠮 㧻゚㈦Ⱒ 㞚┞⧒ 㔲䘎䡫㌗㦒⪲ 㑮䟟䞲 㡆ῂἆὒ✺㧊 Ṗ㧻 䢲䞮Ợ 䚲♮ἶ 㧞┺[16, 17]. 㧊⩂䞲 ἆὒ⯒ 䌫㦒⪲ 㧒⽎, 䞲ῃ ❇ 䞯㧦
⯒ 㭧㕂㦒⪲ 2㿫 㧎㧻㔲䠮㠦 ╖䞲 ISO ′ỿ 㩲㩫 㦚 㥚䞲 㭖゚Ṗ 㰚䟟 㭧㧊┺.
⁎⩂⋮ 㞴㍲ 㠎 䞲 ộὒ ṯ㧊 㨂⬢㦮 ㏢㎇⼖
䡫 䔏㎇㦚 ⳛ䢫䧞 ′ⳛ䞮₆ 㥚䟊㍲⓪ 2㿫 㧎㧻 㔲䠮㦒⪲☚ ┾㿫㧎㧻 㔲䠮ὒ ṯ㧊 䕢┾₢㰖 㔲䠮 㧊 Ṗ⓻䟊㟒 䞲┺. ⁎⩂Ⳋ, ⼖䡫 㽞₆㦮 ㏢㎇⼖䡫 Ệ☯㦚 䢫㧎 䞶 㑮 㧞㦚 ㈦Ⱒ 㞚┞⧒ ╖ ⼖䡫㦮
㏢㎇⼖䡫 Ệ☯ὒ ⍻(Neck) ㌳㔲㦮 ㎇䡫䞲Ἒ₢㰖 䢫㧎 䞶 㑮 㧞┺.
䞲䘎 Zidane ❇[20]㦖 䕦㨂㦮 䟃⽋ἷⳊ㦮 䘟Ṗ㠦 㩗㣿䞮₆ 㥚䟊 Ṳ♲ 2㿫 㧎㧻㔲䠮 ⻫㦚 䕦㨂 㦮 ㎇䡫䞲Ἒ☚ 䘟Ṗ㠦 㻮㦢 㩗㣿䞮㡖┺. 㞴㠦㍲
⏒䞲 ộ ṯ㧊 ₆㫊㦮 㭧㞯 ┾Ⳋ㦮 ⚦℮Ṗ 㔲䘎
⚦℮㢖 ☯㧒䞲 ἓ㤆⓪ 㔂Ⱅ㠦㍲ 㧒㹣 䕢┾㧊
㌳䞮⸖⪲ 㭧㞯 ┾Ⳋ ⚦℮⯒ Fig. 4(i)㢖 ṯ㧊 Ṧ㏢ 㔲䌊㦒⪲㖾 㨂⬢㦮 䕢┾䞲Ἒ₢㰖 ⼖䡫㧊 Ṗ
⓻䟊㰚┺. ⁎⩂⋮ 1mm ⁒㦮 䕦㦮 ἓ㤆㠦⓪
⚦℮㦮 㡗䟻㦚 ⶊ㔲䞮₆ 㠊⪋₆ ➢ⶎ㠦 ⚦℮ Ṧ
㏢ ⽊┺⓪ Fig. 4(g)㠦 ⋮䌖⌎ ộὒ ṯ㧊 䁷㩫㥚 㦮 ┾Ⳋ㩗 Ṧ㏢⯒ 䐋䟊 ╖ ⼖䡫㦚 㥶☚ 䞶 㑮 㧞 㦚 ộ㦒⪲ 䕦┾♲┺.
81# ൚# ᤊ#
Ⱔ㦖 ₆Ἒῂ㫆ⶒ㧊⋮ ⁎ 㣪㏢✺㦖 䟃㌗ ┺㿫 㦧
⩻ ㌗䌲 䞮㠦 㧞ἶ, 䕦㨂 ㎇䡫Ὃ㩫☚ 2㿫 㦧⩻ ㌗ 䌲㠦㍲ 㧊⬾㠊 㰖₆ ➢ⶎ㠦 ┾㿫㧎㧻 㔲䠮㦚 䐋䟊 㠑㦖 ◆㧊䎆 Ⱒ㦒⪲ 㨂⬢㦮 Ệ☯㦚 ⳾㌂ 㡞䁷 䞮₆ 㠦⓪ 㫇䞲 㩦㧊 Ⱔ┺. ⁎⧮㍲ ┺㿫 㦧⩻ ㌗䌲㦮 㨂⬢㦮 ㏢㎇⼖䡫䔏㎇ ⼖䡫Ệ☯㦚 㧊䟊䞮₆ 㥚䞲
⻫㦒⪲ 2㿫 㧎㧻 㔲䠮㧊 ⍦Ⰲ ㌂㣿♮ἶ 㧞┺.
⽎ ⏒ⶎ㠦㍲⓪ 㾲⁒ 䢲䧞 㡆ῂṖ 㰚䟟♮ἶ 㧞⓪ 2㿫 㧎㧻 㔲䠮₆㦮 㫛⮮㢖 䔏㰫 ⁎Ⰲἶ ⁎ 㔲䘎㦮 㡂⩂ 䡫䌲㦮 䔏㰫ὒ 㧻┾㩦㠦 ╖䟊㍲ 㞢 㞚⽊㞮┺.
2㿫 㧎㧻 㔲䠮₆㦮 㫛⮮⯒ 㩲㠊㔳㦒⪲ ⮮
䞮Ⳋ 䞮㭧㩲㠊㔳ὒ ⼖㥚㩲㠊㔳㧊 㧞┺. 䞮㭧 㩲㠊 㔳㦖 㨂⬢㦮 ㏢㎇⼖䡫 䔏㎇㦚 ′ⳛ䞮₆ 㥚䞲 ⻫㦒⪲ 㩗䞿䞮┺. ⁎⩂⋮ 㔲䠮⻫㠦 㧞㠊
┺㏢ 㑮ἶ⪲㤖㧊 ➆⯊₆ ➢ⶎ㠦 ⼖㥚㩲㠊㔳㦒⪲
㩚䢮䞮ἶ㧦 䞮⓪ 㡆ῂṖ 䢲䧞 㰚䟟 ♮ἶ 㧞┺.
⁎Ⰲἶ 2㿫 㧎㧻 㔲䘎㦒⪲⓪ 㕃㧦(+)䡫䌲Ṗ ╖
㧊Ⳇ, 㨂⬢㦮 ⍻ ㌳㎇ 䕢┾₢㰖 㔲䠮㦚 㰚 䟟䞮₆ 㥚䟊 㡂⩂ 㫛⮮㦮 㔲䘎㧊 㩲㞞♮ἶ 㧞┺.
゚ᾦ㩗 ⚦ℒ㤊 㨂⬢✺㦖 䁷㩫㥚㦮 ⚦℮ Ṧ㏢⪲
╖ ⼖䡫㦚 㥶☚䞮Ⳇ 1mm 㧊䞮㦮 䕦㦮 ἓ㤆㠦
⓪ 䁷㩫㥚㦮 䙃 Ṧ㏢⪲ ╖ ⼖䡫㦚 㥶☚䞶 㑮 㧞㦚 ộ㦒⪲ 䕦┾♲┺.
㝮
⽎ 㡆ῂ⓪ 2010 ⎚☚ 㩫(ᾦ㥷ὒ䞯₆㑶)㦮 㨂 㤦㦒⪲ 䞲ῃ㡆ῂ㨂┾㦮 㭧㩦㡆ῂ㏢㰖㤦㌂㠛㦒⪲
㑮䟟♲ 㡆ῂ㧚(2010-0020089).
YY_GV穢剳暒昷儆击穟箒滆V洢YW劒G 洢Z笾SGYWXX噊G G
Ⳣ ඊ ᯢ 㙶
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Process., Vol. 18, pp 416~421.
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138~144.
[5] S. B. Lin, J. L. Ding, 1995, Experimental study of the plastic yielding of rolled sheet metals with the cruciform plate specimen, Int. J. Plasticity, Vol. 11, pp. 583~604
[6] T. Kuwabara, S. Ikeda, K. Kuroda, 1998, Measurement and analysis of differential work hardening in cold rolled steel sheet under biaxial tension, J. Mater. Proc. Technol. Vol. 80-81, pp.
517~523.
[7] J. S. Welsh, D. F. Adams, 2002, An experimental investigation of the biaxial strength of IM6/3501-6 carbon/epoxy cross-ply laminates using cruciform specimens, Composites: Part A 33 (6), pp. 829~
839.
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Test. Eval., Vol. 16, pp. 253~256.
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