A Finite Element Analysis for Near-net-shape Forming of Al6061 Powder under Warm Pressing

⾰ᖌ ⪹㾝 㻠⽘⪤ Al 㻱ថ ✌⍘ム ㆝█㆝㾝⽘ ᲈ㻤 エ㻤〜⬔㻼⪥

卆匶痢^ᅺ · 檗篎熦^*· 卆涋列^*

A Finite Element Analysis for Near-net-shape Forming of Al6061 Powder under Warm Pressing

KiTae Kim, HoonChul Yang, JongKwang Kim

Key Words : Rubber Mold (ἶⶊ ⴆ✲), Near-net-shape Forming (㩫⹖㩫䡫), Warm Die Pressing (㡾Ṛ ⁞䡫㞫㿫 ㎇䡫), Rubber Isostatic Pressing (ἶⶊ ❇Ṗ㞫 ㎇䡫), Finite Element Analysis (㥶䞲㣪㏢䟊㍳), Strain Energy Potential (⼖䡫⮶ 㠦⍞㰖 䙂䎦㎲)

Abstract

A finite element analysis for near-net-shape forming of Al6061 powder was performed under warm pressing. The advantages of warm compaction by rubber isostatic pressing were discussed to obtain parts with better density distributions. To simulate densification and deformed shape of a powder compact during warm pressing, the elastoplastic constitutive equation based on yield function of Shima-Oyane was implemented into a finite element program(ABAQUS). The hyperelastic constitutive equation based on the Ogden strain energy potential was employed to analyze nonlinear elastic response of rubber. Finite element results were compared with experimental data for Al6061 powder compacts under warm pressing.

1. 昢 嵦

㧒⹮㩗㧎 ⿚Ⱖ 㟒⁞ Ὃ㩫㦒⪲⓪ ⿚Ⱖ ┾㫆 (Powder Forging), ⿚Ⱖ ㌂㿲 ㎇䡫(PIM: Powder Injection Molding), 㡊Ṛ ❇Ṗ㞫 ㎇䡫(HIP: Hot Isostatic Pressing), ⁞䡫㞫㿫(Die Pressing) ❇㧊 㧞┺.

₆Ἒ㣪㏢⓪ 㧊⩂䞲 Ὃ㩫✺㦚 㧊㣿䞮㡂 ⿚Ⱖ㦚 ㎇ 䡫䞲 䤚 ㏢ἆ㧊⋮ 㾲㫛ṖὋ㦚 Ệ㼦 ㌳㌆䞲┺. 㾲 㫛⿖䛞㦮 ₆Ἒ㩗 ㎇㰞㦖 ⿚Ⱖ ㎇䡫㼊⯒ 㩲㫆䞮⓪ ὒ㩫㠦㍲ ⹲㌳䞮⓪ 㡂⩂Ṗ㰖 㣪㧎✺㠦 㦮䟊 ἆ㩫

♲┺. ⁎ 㭧㠦㍲☚ Ṗ㧻 㭧㣪䞲 㧎㧦㭧㦮 䞮⋮Ṗ

⁞䡫⼓ὒ ⿚Ⱖ㦮 Ⱎ㺆㧊┺. 㧊ộ㦖 ㎇䡫㼊 ⌊⿖

㦮 ⿞‶㧒䞲 ⹖☚ῂ⺆⯒ ⹲㌳㔲䋺ἶ, ㏢ἆ♲ 㾲㫛

⿖䛞㦮 ₆Ἒ㩗㧎 ⶒ㎇㩖䞮㢖 ⿞䞚㣪䞲 ṖὋ㦚 㽞

⧮䞲┺.

90 ⎚╖ 㧊䤚㠦⓪ ⿚Ⱖὒ ⁞䡫㦚 130~150^oC 㩫

☚⪲ Ṗ㡊䞮㡂 ㎇䡫䞮⓪ 㡾Ṛ ㎇䡫 Ὃ㩫⻫㧊 㡂⩂

㡆ῂ㧦✺㠦 㦮䟊 Ṳ⹲♮㠞┺.^(1~3) 㡾Ṛ ㎇䡫㦖 ₆ 㫊㦮 ㎇䡫Ὃ㩫㠦 ゚䟊 ⏨㦖 ㎇䡫⹖☚㢖 ṫ☚, ㎇ 䡫㼊 ⌊⿖㦮 ‶㧒䞲 ⹖☚⿚䙂, 㧦₆㎇㰞㦮 䟻㌗

⹥ 㩫⹖㩫䡫 ❇㦮 㧻㩦㦚 Ṗ㰖ἶ 㧞┺.

Rutz ❇⁽⁴⁾㦖 ⏨㦖 ㌗╖⹖☚⯒ 㠑㦚 㑮 㧞⓪ 㡾 Ṛ ㎇䡫Ὃ㩫㦚 㾲㽞⪲ 㩲㞞䞮㡖┺. Gagne⁽⁵⁾⓪ 㥺 䢲㩲Ṗ 㻾Ṗ♲ ⿚Ⱖ㦚 150^oC 㠦㍲ ㎇䡫䞮Ⳋ, ⁞䡫 ὒ ⿚Ⱖ㌂㧊㦮 Ⱎ㺆⩻㧊 Ṧ㏢䞮㡂 ㎇䡫㼊㦮 ⹖☚

⯒ 㯳Ṗ㔲䌂 ㈦Ⱒ 㞚┞⧒ 㞫㿲䞮㭧☚ 25~33%₢㰖 Ṧ㏢䞲┺⓪ ộ㦚 㯳ⳛ䞲 ⹪ 㧞┺. Chemlar ❇⁽⁶⁾ ὒ Miller ❇⁽⁷⁾㦖 䡂Ⰲ䅂 ₆㠊㢖 㧦☯㹾㦮 䎆ゞ 䠞 ぢ⯒ ⌟Ṛ ㎇䡫䞲 ἓ㤆㢖 㡾Ṛ ㎇䡫䞲 ἓ㤆㠦 ㏢ ἆ㼊㢖 㾲㫛⿖䛞㦮 䂮㑮⯒ ゚ᾦ䞮㡂 㡾Ṛ ㎇䡫 ♲ ἓ㤆Ṗ ⌟Ṛ ㎇䡫䞲 ἓ㤆㠦 ゚䟊㍲ ‶㧒䞲 ⹖☚ῂ

⺆㢖 䡫㌗⼖䢪⯒ Ṭ⓪┺⓪ ἆὒ⯒ 㠑㠞┺.

㾲⁒㠦⓪ 㧦㎇ 㨂⬢㦮 ㎇㰞㦚 䟻㌗㔲䋺₆ 㥚䟊

㍲ RIP(Rubber Isostatic Pressing)Ὃ㩫㧊 Sagawa ❇⁽⁸⁾ 㠦 㦮䟊 Ṳ⹲♮㠞┺. ἶⶊ ❇Ṗ㞫 ㎇䡫㦖 ┺⯎

Ὃ㩫㠦 ゚䟊 ἶⶊ ⴆ✲㦮 䡫㌗㦚 㩗㩞䧞 㩲㠊䞮㡂 㩫⹖㩫䡫㦚 䞶 㑮 㧞㦚 ㈦Ⱒ 㞚┞⧒ 㩗㦖 ゚㣿ὒ

ᅺ 䙂䟃Ὃ╖ ₆ἚὋ䞯ὒ ᾦ㑮 E-mail : [email protected]

TEL : (054)279-2164 FAX : (054)279-5899

* 䙂䟃Ὃ╖ ₆ἚὋ䞯ὒ ╖䞯㤦

㔲Ṛ㦒⪲ ㎇䡫㼊 ⌊⿖㦮 ⹖☚ῂ⺆⯒ 㭚㧒 㑮 㧞

⓪ 㧻㩦㧊 㧞┺. Shima ❇⁽⁹⁾㦖 RIP Ὃ㩫㠦 ╖䞲 㥶䞲㣪㏢䟊㍳㦚 㑮䟟䞮㡂 㩫⹖ 㩫䡫㧊 Ṗ⓻䞲 ἶ ⶊ ⴆ✲㦮 䡫㌗㦚 㾲㩗䢪 䞮㡖㦒Ⳇ, Kim ❇⁽¹⁰⁾ὒ Yang ❇⁽¹¹⁾㦖 ⌟Ṛὒ 㡾Ṛ 䞮㠦㍲ ἶⶊ ⴆ✲㦮 䔏

㎇㠦 ➆⯎ ⁞㏣ ⿚Ⱖ㦮 䂮⹖䢪 㡗䟻㦚 㫆㌂䞮㡖┺.

⽎ ⏒ⶎ㠦㍲⓪ 㞢⬾⹎ⓚ 䞿⁞ ⿚Ⱖ㦮 㡾Ṛ㠦㍲

㦮 ἶⶊ ❇Ṗ㞫 ㎇䡫㦚 㑮䟟䞮㡂 ㎇䡫㼊 ⌊⿖㦮

⹖☚ῂ⺆⯒ 㾲㏢䢪䞮ἶ, 㥶䞲㣪㏢䟊㍳㦚 䐋䞲 㾲 㩗䢪♲ ἶⶊ ⴆ✲⯒ 㧊㣿䞮㡂 ⻶⻾₆㠊 䡫䌲㦮 ⿖ 䛞㦚 ㎇䡫䞮㡖┺. ⡦䞲 㧒⹮㩗㦒⪲ Ṗ㧻 ⍦Ⰲ ㌂ 㣿♮⓪ ⁞䡫㞫㿫㠦 㦮䞲 ㎇䡫 ⹿⻫ὒ ゚ᾦ䞮㡂 ⿖ 䛞 ㎇䡫㔲㦮 ṖὋ㎇ ⹥ ㎇䡫㎇㦚 䘟Ṗ䞮㡖┺.

2. 柪 竞

⽎ ⏒ⶎ㠦㍲⓪ Ṗ㓺 ⿚㌂⻫㦒⪲ 㩲㫆♲ 䘟‶

㧛㧦㦮 䋂₆Ṗ 15 µm 㧎 Al6061 ⿚Ⱖ㦚 ㌂㣿䞮㡖

┺. ⿚Ⱖ㦮 ⶒⰂ㩗 ㎇㰞ὒ 䢪䞯㩗 㫆㎇㦖 ┺⯎

⏒ⶎ㠦㍲ 㓓Ợ 㺔㦚 㑮 㧞┺.⁽¹¹⁾

2.1ࣜ橒差惾垊ࣜ穯匎ࣜ把廖汞ࣜ微沲柢碾ࣜ

㞢⬾⹎ⓚ 䞿⁞ ⿚Ⱖ㦮 ⳾㨂㔲䘎⯒ Ⱒ✺₆ 㥚䞮 㡂 ⿚Ⱖ㦚 㰚Ὃ ⹖⽟䞮㡂 㡊Ṛ ❇Ṗ㞫 ㏢ἆ₆ (Kobelco System 30T, Japan)㠦㍲ 520^oC, 100 MPa㦮 㞫⩻㦒⪲ 2 㔲Ṛ☯㞞 㡊Ṛ ❇Ṗ㞫 ㏢ἆ㦚 䞮㡂 ㌗

╖⹖☚Ṗ Ệ㦮 1 㧎 㔲䘎㦚 㩲㫆䞮㡖┺. ㏢ἆ 䤚 䃪㦚 㩲Ệ䞮ἶ 㔲䘎㦚 㤦㭒䡫㦒⪲ ṖὋ䞮㡂 210^oC 㦮 㞚⯊Ἲ ⿚㥚₆㠦㍲ 2 㔲Ṛ☯㞞 㠊┦Ⱇ䞮㡖┺.

㔲䘎㦮 㾲㫛 䂮㑮⓪ 㰖⯚ 7 mm ⏨㧊 10 mm 㧊Ⳇ,

㌗╖⹖☚⓪ 0.995 㧊㌗㧊㠞┺.

2.2ࣜ微沲ࣜ柢碾汞ࣜ欮儊ࣜ沂犛ࣜ橛犛ࣜ柪竞ࣜ

㞫㿫ٻ 㔺䠮㦖ٻ ἶ㡾ٻ ⿚㥚₆㦮ٻ 㰚Ὃ⪲㠦㍲ٻ 10^oC/min 㦮ٻ 㔏㡾ٻ ㏣☚⪲ٻ 300^oCٻ ₢㰖ٻ Ṗ㡊䞲ٻ 䤚ٻ 㔲䘎㧊ٻ 㡊㩗ٻ 䘟䡫㌗䌲Ṗٻ ♮☚⪳ٻ 㔲䠮ٻ 㡾☚⯒ٻ 30

⿚Ṛٻ㥶㰖䞮㡖㦒Ⳇڇٻ0.1 MPa/s 㦮ٻ㧒㩫䞲ٻ䞮㭧㏣☚

⪲ٻ200 MPa 㦮ٻ㦧⩻ٻ⻪㥚㠦㍲ٻ䞮㭧㦚ٻṖ䞮㡖┺ډٻٻ

⡦䞲ٻSiCٻ㞫⹮ὒٻ㞫㿫㔲䘎ٻ㌂㧊㦮ٻⰞ㺆㦚ٻ㭚㧊₆ٻ 㥚䞮㡂ٻ㩧㽟Ⳋ㠦ٻ䌚䌞⮾ٻ⹫䕦(t=0.01mm)㦚ٻ㌓㧛䞮 㡖㦒Ⳇڇٻ 㔲䘎㦮ٻ 㞫㿫♲ٻ ⼖㥚⓪ٻ LVDT(Linear Variable Displacement Transducerڄ⪲ٻ䁷㩫䞮㡖┺ډٻٻٻ

2.3ࣜ処怺汞ࣜ恂昷ࣜ柪竞ࣜ

㡾Ṛٻ ❇Ṗ㞫ٻ ㎇䡫㦚ٻ 㥚䞮㡂ٻ ἶⶊٻ ⴆ✲ٻ 㨂⬢⓪ٻ 㔺Ⰲ䆮ٻἶⶊ⯒ٻ㌂㣿䞮㡖┺ډٻٻἶⶊ㠦ٻ╖䞲ٻ₆Ἒ㩗ٻ 䔏㎇㦚ٻ 㫆㌂䞮₆ٻ 㥚䟊㍲ٻ 㧒㿫ٻ 㧎㧻ڇٻ 㧒㿫ٻ 㞫㿫ڇٻ

⁎Ⰲἶٻ㼊㩗ٻ㞫㿫㔺䠮㦚ٻ㑮䟟䞮㡖┺ډٻٻ㧒㿫ٻ㧎㧻ٻ 㔺䠮㦚ٻ㑮䟟䞮₆ٻ㥚䞮㡂ٻἶⶊٻ㔲䘎㦖ٻ㰗ἓٻ10 mmڇٻ

₎㧊ٻ70 mm 㦮ٻ₊ٻ㤦㭒䡫ٻ㔲䘎㦚ٻ㩲㧧䞮㡖㦒Ⳇڇٻ

㧒㿫ٻ㞫㿫ὒٻ㼊㩗ٻ㞫㿫ٻ㔺䠮㠦㍲⓪ٻ㰗ἓٻ20 mmڇٻ

⏨㧊ٻ20 mm 㦮ٻ㤦㭒䡫ٻ㔲䘎㦚ٻ㌂㣿䞮㡖┺ډٻٻ㧒㿫ٻ 㧎㧻ٻ㔺䠮㠦㍲⓪ٻἶⶊ㦮ٻ䋆ٻ㡆㔶㥾⪲ٻ㧎䞲ٻ㑮㿫㥾 㧊ٻⰺ㤆ٻ䋂₆ٻ➢ⶎ㠦ٻ㔲䘎㦮ٻ⹎⊚⩂㰦㦚ٻ⹿㰖䞮₆ٻ 㥚䟊ٻ⁎ⰓڃGrip)㦚ٻ䔏⼚䧞ٻ㩲㧧䞮㡖㦒Ⳇڇٻἶⶊٻ㔲 䘎㠦ٻ 䞮㭧㦚ٻ 㻲㻲䧞ٻ 㯳Ṗ㔲䋺Ⳋ㍲ٻ㔶㧻⨟㦚ٻ䁷㩫 䞮⓪ٻ⹿⻫㦒⪲ٻ㔺䠮䂮⯒ٻῂ䞮㡖┺ډٻٻ㧒㿫ٻ㞫㿫ٻ㔺 䠮㦖ٻ㞫㿫㔲ٻἶⶊٻ㔲䘎ὒٻ㞫⹮㌂㧊㦮ٻⰞ㺆㦚ٻ㭚㧊

₆ٻ 㥚䞮㡂ٻ 䎢䝚⪶ٻ ⹫䕦ڃTeflon Sheetڄ㦚ٻ ㌓㧛䞮㡖

┺ډٻ ٻ 㼊㩗ٻ 㞫㿫㔺䠮㦖ٻ ἶⶊٻ 㔲䘎㦮ٻ 㣎ἓὒٻ ṯ㦖ٻ 䂮㑮㦮ٻ⁞䡫㞞㠦ٻ㌓㧛䞮㡂ٻ㔺䠮㦚ٻ㑮䟟䞮㡖┺ډٻٻ

2.4 欮儊 処怺 姷儆橛 昷笛 柪竞

ἶⶊٻ ❇Ṗ㞫ٻ ㎇䡫ٻ 㔺䠮㦖ٻ MTS 㨂⬢ٻ 㔲䠮₆㠦ٻ 䔏⼚䧞ٻ㩲㧧♲ٻṖ㡊⪲⯒ٻ㌂㣿䞮㡂ٻ300^oC 㠦㍲ٻ㑮 䟟䞮㡖┺ډٻٻ㔺䠮㦖ٻ㞢⬾⹎ⓚٻ䞿⁞ٻ⿚Ⱖ㦚ٻἶⶊٻⴆ

✲㞞㠦ٻ㿿㩚䞲ٻ䤚ٻ⌊ἓ㧊ٻ43 mm 㧎ٻ㽞ἓٻ⁞䡫ٻ㞞 㠦ٻ㌓㧛䞮㡂ٻٻ㧒㿫ٻ㞫㿫䞮㡖㦒Ⳇڇٻἶⶊٻⴆ✲㢖ٻ⁞

䡫ٻ㌂㧊㠦ٻⰞ㺆㦚ٻ㭚㧊₆ٻ㥚䟊ٻ䦧㡆ٻ㥺䢲㩲⯒ٻ㌂

㣿䞮㡖┺ډٻ ٻ 㿿㩚ٻ 㰗䤚ٻ ⿚Ⱖ㦮ٻ ㌗╖⹖☚⓪ٻ 0.5ٻ 㡖 㦒Ⳇڇٻ1 MPa/s 㦮ٻ䞮㭧㏣☚⪲ٻ170 MPa 㠦㍲ٻ㎇䡫䞮 㡖┺ډٻٻ

2.5ࣜ欮儊ࣜ匎笛橛犛ࣜ柪竞ࣜ

SKD11⪲ٻⰢ✶ٻ6 Ṳ㦮ٻ⁞䡫㦚ٻ㫆Ⱃ䞮㡂ٻ18.2g 㦮ٻ 㞢⬾⹎ⓚٻ䞿⁞ٻ⿚Ⱖ㦚ٻ⍹㠊ٻ300^oC 㦮ٻ㡾☚㠦㍲ٻ⁞

䡫㞫㿫㦚ٻ㑮䟟䞮㡖┺ډٻٻ⿚Ⱖὒٻ⁞䡫㌂㧊㠦⓪ٻⰞ㺆 㦚ٻ㭚㧊₆ٻ㥚䟊ٻ⁞䡫ٻ⼓Ⳋ㠦ٻ䦧㡆ٻ㥺䢲㩲⯒ٻ㌂㣿 䞮㡖㦒Ⳇڇٻ1 MPa/s 㦮ٻ㧒㩫䞲ٻ䞮㭧㏣☚⪲ٻ170 MPa 㦮ٻ㞫⩻㠦㍲ٻ㞫㿫䞮㡖┺ډٻٻ⿚Ⱖὒٻ⁞䡫ٻ⹥ٻ䗖䂮⓪ٻ

☯㔲㠦ٻ Ṗ㡊䞮㡖㦒Ⳇڇٻ 㔏㡾ٻ ㏣☚⓪ٻ 5^oC/min 㦒⪲ٻ 䞮㡖┺ډٻٻ㡊㩗ٻ䘟䡫㦚ٻ㥚䞮㡂ٻ㔲䠮ٻ㡾☚⯒ٻ30 ⿚ Ṛٻ㥶㰖䞲ٻ䤚ٻ㌗⿖ٻ䗖䂮㠦㍲ٻ䞮⿖ٻ䗖䂮⪲ٻ䧮㧊ٻ㩚

╂♮⓪ٻ㧒⹿䟻ٻ㞫㿫ڃSingle Action Pressingڄ㦚ٻ㑮䟟 䞮㡖┺ډٻٻٻ

2.6ࣜ把廖ࣜ昷笛熺汞ࣜ愆壊ࣜ把磲ࣜ

ἓ☚㢖ٻ ㌗╖⹖☚㦮ٻ ㌗ὖٻ ὖἚ⯒ٻ 㠑₆ٻ 㥚䞮㡂ٻ

⌟Ṛٻ㩫㑮㞫ٻ㎇䡫₆(ABB Autoclave Systems inc.)⯒

㧊㣿䞮㡖㦒Ⳇ, Al6061 ⿚Ⱖ㦚ٻ ₎㧊ٻ 25 mmڇٻ 㣎ἓٻ 15 mm,ٻ⚦℮ٻ2 mm 㧎ٻἶⶊٻⴆ✲㞞㠦ٻ㿿㩚䞮ἶٻ㰚 Ὃٻ⹖⽟䞲ٻ䤚ٻ50~300 MPa 㦮ٻ㩫㑮㞫㦚ٻṖ䞮㡂ٻ┺

㟧䞲ٻ⹖☚⯒ٻṬ⓪ٻAl6061ٻ⿚Ⱖٻ㎇䡫㼊⯒ٻ㎇䡫䞮㡖

┺ډٻٻ㎇䡫♲ٻ㔲䘎㦖ٻ480^oC 㦮ٻ㰚Ὃٻ⿚㥚₆㠦㍲ٻ㏢

ἆٻ㩚䤚ٻ⹖☚㦮ٻ⼖䢪Ṗٻ㠜☚⪳ٻ20 ⿚Ṛٻ㡞゚ٻ㏢ἆ 䞲ٻ 䤚ٻ ┺㧊㞚ⴂ✲ٻ 䥶ڃISOMET Low Speed Saw, BUEHLER, U.S.A.)⪲ٻ㭧㞯┾Ⳋ㦚ٻ㩞┾䞮㡖┺ډٻٻ㩞

┾♲ٻ㔲䘎㦖ٻ㰚Ὃٻ⿚㥚₆㠦㍲ٻ190^oC 㦮ٻ㡾☚⪲ٻ2 㔲Ṛ☯㞞ٻ㠊┦Ⱇ(Annealingڄ䞲ٻ䤚ٻ┾Ⳋ㦚ٻ㡆Ⱎ䞮㡂ٻ 1.58 mm(1/16inchڄٻṫῂ㧛㧦⪲ٻ15 kg 㭧㦮ٻ䞮㭧㦚ٻ 30㽞ṚٻṖ䞮㡂ٻṗٻ㔲䘎Ⱎ┺ٻ20 Ṳ㦮ٻἓ☚ٻṨ㦚ٻ䁷 2

Fig. 1 Finite element meshes and boundary conditions for single action pressing of Al6061 powder under die pressing

㩫䞮㡖┺ډٻ ٻ 䁷㩫♲ٻ ἓ☚Ṩ✺㦚ٻ 䘟‶䞮㡂ٻ Al6061

⿚Ⱖٻ㎇䡫㼊㦮ٻ㌗╖⹖☚㢖ٻ⪲䋂㥆ٻἓ☚ٻṨ㦮ٻ㌗ὖٻ ὖἚ⯒ٻῂ䞮㡖┺ډٻٻ㡾Ṛٻ❇Ṗ㞫ٻ㎇䡫ὒٻ㡾Ṛٻ⁞䡫 㞫㿫䞲ٻ ㎇䡫㼊㦮ٻ ㌗╖⹖☚ٻ ⿚䙂⯒ٻ㫆㌂䞮₆ٻ㥚䞮 㡂ٻ ṗṗ㦮ٻ㎇䡫㼊⌊⿖㠦ٻ 㧒㩫䞲ٻ Ṛỿ㦒⪲ٻ ⪲䋂㥆ٻ ἓ☚⯒ٻ 䁷㩫䞮ἶٻ ἓ☚㢖ٻ ㌗╖⹖☚㦮ٻ ㌗ὖὖἚ⯒ٻ 㧊㣿䞮㡂ٻ㔲䘎ٻ⌊⿖㦮ٻ㌗╖⹖☚ٻ⿚䙂⯒ٻῂ䞮㡖┺ډٻٻ

3. 決 嵦

3.1 ἶⶊ㦮 ῂ㎇ ⹿㩫㔳

ἶⶊ㦮 ⼖䡫㦖 ❇⹿㎇㦮 ㎇㰞㦚 Ṭἶ 㧞┺ἶ Ṗ㩫䞾㦒⪲㖾 㽞䌚㎇㼊㦮 ⼖䡫⮶ 㠦⍞㰖 䞾㑮⪲

⋮䌖⌒ 㑮 㧞┺. Ogden^(12~14)㦖ٻἶⶊ㦮ٻỆ☯㦚ٻ⋮

䌖⌊₆ٻ 㥚䟊ٻ ⼖䡫⮶ٻ 㠦⍞㰖ٻ 䞾㑮⯒ٻ ┺㦢ὒٻ ṯ㧊ٻ 㩫㦮䞮㡖┺ډٻٻٻ

( ) ^N ( ^el )²ⁱ

1

i i

3 2 1 N

1

i 2

i i

o J 1 R

D 3 1

U 2 λⁱ+λⁱ+λ ⁱ− + − − α

=¦ µ ¦

= α

α α

=

(1)

㡂₆㍲ λ_i ^, ὒ N 㦖 ṗṗ 䘎㹾 㭒 㡆㔶㥾 (

Jel i 13

i =J λ

λ ⁻

i

), 䌚㎇ 㼊㩗゚㢖 㨂⬢㌗㑮⯒ ⋮䌖⌎┺.

⡦䞲, µ ^, 㢖 ⓪ 㡾☚㠦 㦮㫊䞮⓪ 㨂⬢㌗㑮 㧊┺. 㔳 (1)㠦㍲ ⓪ 㨂⬢㦮 㞫㿫㎇㦚 ⋮䌖⌊

Ⳇ, 㦖 㨂⬢Ṗ 㢚㩚 ゚㞫㿫㎇㧚㦚 㦮⹎䞲┺.

αi Di

D_i 0

D_i =

3.2 把廖 昷笛熺汞 割昷 愯洛柣

⁞㏣ٻ ⿚Ⱖ㦮ٻ ㏢㎇ ⼖䡫⮶ ㏣☚ 䎦㍲⓪ ┺㦢ὒ ṯ㧊 㩫㦮♲┺.

ij p

ij ∂σ

Φ λ ∂

=

ε  (2)

㡂₆㍲ 㢖 ⓪ ṗṗ ⿚Ⱖ 㨂⬢㦮 䟃⽋ 䞾㑮 㢖 㟧㦮 㓺䃒⧒ 㟧㧊┺.

Φ λ

㌗╖⹖☚㦮ٻ ⼖䢪㥾㦖ٻ 㰞⨟ٻ ⿞⼖㦮ٻ ὖἚ⪲⿖䎆ٻ

┺㦢ὒٻṯ㧊ٻ㝎ٻ㑮ٻ㧞┺ډٻٻٻ

p

D kk

D =− ε (3)

⡦䞲ٻ ⿚Ⱖٻ㎇䡫㼊㦮ٻ⼖䡫㠦⍞㰖Ṗٻ⳾㨂㦮ٻ ⼖䡫㠦

⍞㰖㢖ٻ ṯ┺ἶٻ Ṗ㩫䞮Ⳋٻ ┺㦢ὒٻ ṯ㧊ٻ ⋮䌖⌒ٻ 㑮ٻ 㧞┺ډٻ

p ij ij p m

Dσmε =σ ε (4) 㡂₆㍲ σ_m㦖ٻ⳾㨂㦮ٻ㥶☯㦧⩻ڇٻε_m^{p㦖ٻ⳾㨂㦮ٻ❇}

Ṗٻ㏢㎇ٻ⼖䡫⮶ٻ㏣☚⯒ٻ⋮䌖⌎┺ډٻٻٻ

Shima ❇⁽⁹⁾㦖 ⿚Ⱖ㦮 ㏢㎇ 䟃⽋ Ệ☯㦚 ⋮䌖⌊

⓪ 㫆Ị㔳㦚 ┺㦢ὒ ṯ㧊 㩲㞞䞮㡖┺.

0 D

) p D 1 ( 49 . q 2 ) D , , (

5

2

m 028 . 1 2 2

m p

m

=

−

¸¸¹

·

¨¨©

§

− σ

¸¸ +

¹

·

¨¨©

§

= σ ε σ Φ

(5)

⁞㏣ ⿚Ⱖ㦮 䂮⹖䢪 Ệ☯㦖 Shima ❇⁽¹⁵⁾ 㦮 ῂ㎇

⹿㩫㔳㦚 ABAQUS⁽¹⁴⁾㦮 ㌂㣿㧦 㩫㦮 ㍲ぢ⬾䕊㧎 UMAT㠦 㩗㣿䞮㡂 䟊㍳䞮㡖┺.

4. 冶刂 愕 処然

4.1 㥶䞲㣪㏢䟊㍳

4.1.1 㡾Ṛ ⁞䡫㞫㿫

Fig. 1 㦖ٻ㥶䞲㣪㏢䟊㍳㠦㍲ٻ㌂㣿♲ٻ㡾Ṛٻ⁞䡫㞫 㿫㦮ٻ 㥶䞲㣪㏢ٻ ỿ㧦㢖ٻ ⁎ٻ ἓἚ㫆Ị㦚ٻ ⋮䌖⌎┺ډٻٻٻٻٻ

۔ٻ㿫㦮ٻ㿫╖䃃ٻ㫆Ị㦒⪲ٻ⿖䎆ٻ㩚㼊ٻ┾Ⳋ㦮ٻ1/2 Ⱒ 㦚ٻ䟊㍳䞮㡖┺ډٻٻ㔲䘎㦮ٻ㽞₆ٻ㌗╖⹖☚ٻDo= 0.5⪲ٻ

㌂㣿䞮㡖㦒Ⳇڇٻỿ㧦⓪ٻ145 Ṳ㦮ٻ8 㩞㩦ٻ2 㹾ٻ㿫ٻ╖

䃃ٻ㣪㏢㧎ٻCAX8(8-node Axisymmetric Quadrilateral, Biquadratic Displacement)ٻ㣪㏢㢖ٻ53 Ṳ㦮ٻ㿫╖䃃ٻṫٻ 㣪㏢㧎ٻ RAX2(2-node Linear Axisymmetric Rigid Rinkڄٻ 㣪㏢⯒ٻ ㌂㣿䞮㡖┺.⁽¹⁴⁾ ⿚Ⱖὒ ⁞䡫 ⌊⿖

⹥ 䗖䂮 ㌂㧊㦮 Ⱎ㺆 Ἒ㑮 ജ =0.17 ⪲ Ṗ㩫䞮㡖

┺.⁽¹⁶⁾

4.1.2 㡾Ṛ ἶⶊ ❇Ṗ㞫 ㎇䡫

Fig. 2 ⓪ٻ㡾Ṛٻἶⶊٻ❇Ṗ㞫ٻ㎇䡫㠦ٻ㌂㣿♲ٻ㥶䞲 㣪㏢ٻỿ㧦㢖ٻἓἚ㫆Ị㦚ٻ⋮䌖⌎┺ډٻٻ۔ٻ㿫㦮ٻ㿫ٻ╖

䃃ٻ㫆Ị㦒⪲ٻ⿖䎆ٻ㩚㼊ٻ┾Ⳋ㦮ٻ1/2 Ⱒ㦚ٻ䟊㍳䞮㡖 㦒Ⳇڇٻ⿚Ⱖٻ㎇䡫㼊㦮ٻ㣪㏢⓪ٻ㡾Ṛٻ⁞䡫㞫㿫ὒٻ☯

3

CL

upper punch

die powder

rubber mold

X Y

Fig. 2 Finite element meshes and boundary conditions for an Al6061 powder compact in a silicone rubber mold under rubber isostatic pressing

-12 -10 -8 -6 -4 -2 0

-0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 10^-2/s strain rate 10^-3/s strain rate 10^-4/s strain rate Ogden, N=3

Nominal Stress

Nominal Strain Uniaxial Compression

300^oC

Fig. 4 Variation of nominal stress with nominal strain for silicone rubber under uniaxial compression at 300^oC

0 100 200 300 400 500 600

0.5 0.6 0.7 0.8 0.9 1

10^-2/s strain rate 10^-3/s strain rate 10^-4/s strain rate Ogden, N=3

Pressure, MPa

Contraction

Volumetric Compression 300^oC

Fig. 5 Variation of pressure with contraction for silicone rubber under volumetric compression at 300^oC

㧒䞲ٻ㣪㏢㧎ٻ210 Ṳ㦮ٻCAX8ٻ㣪㏢⯒ٻ㌂㣿䞮㡖┺ډٻٻ ἶⶊٻⴆ✲⯒ٻ㥚䟊㍲⓪ٻ230 Ṳ㦮ٻ8 㩞㩦ٻ2 㹾ٻ㿫ٻ╖

䃃ٻ䞮㧊ぢⰂ✲ٻ㣪㏢㧎ٻCAX8H(8-node Axisymmetric Quadrilateral, Biquadratic Displacement, Hybrid with Linear Pressureڄ⯒ٻ㌂㣿䞮㡖┺.⁽¹⁴⁾ٻٻ⿚Ⱖὒٻἶⶊٻ㌂

㧊⓪ٻ 㢚㩚ٻ 㩧䞿㦒⪲ٻ Ṗ㩫䞮㡖㦒Ⳇڇٻ 㔺Ⰲ䆮ٻ ἶⶊٻ ⴆ✲㢖ٻ⁞䡫ٻ㌂㧊㦮ٻⰞ㺆Ἒ㑮 ജژٻ0.18 㦚ٻ㌂㣿䞮 㡖┺.^ٻٻ

4.2 ἆὒ㦮 ἶ㺆

4.2.1 ἶⶊ㦮 ₆Ἒ㩗 ㎇㰞

Fig. 3 㦖ٻ┺㟧䞲ٻ⼖䡫⮶ٻ㏣☚⯒ٻ㧊㣿䞮㡂ٻ㧒㿫ٻ 㧎㧻㔲ٻ 㔺Ⰲ䆮ٻ ἶⶊ㠦ٻ ╖䟊ٻ Ὃ䃃ٻ ⼖䡫⮶㠦ٻ ➆⯎ٻ Ὃ䃃㦧⩻ὒ㦮ٻ ὖἚ⯒ٻ ⋮䌖⌊⓪ٻ 㔺䠮䂮㢖ٻ Ogden^(12~14)⳾◎㦚ٻ㌂㣿䞲ٻ㥶䞲㣪㏢䟊㍳ٻἆὒ㦮ٻ゚

ᾦ⯒ٻ⋮䌖⌎┺ډٻٻOgden ⳾◎㦚ٻ㌂㣿䞲ٻ㥶䞲㣪㏢䟊

㍳ٻ ἆὒ⓪ٻ 㔺䠮䂮⯒ٻ ゚ᾦ㩗ٻ 㧮ٻ ⋮䌖⌊ἶٻ 㧞㰖Ⱒٻ

⼖䡫⮶㧊ٻ㯳Ṗ䞾㠦ٻ ➆⧒ٻ 㔺䠮䂮㢖㦮ٻ 㹾㧊Ṗٻ 㯳Ṗ 䞮Ⳇڇٻ⼖䡫⮶ٻ㏣☚㠦ٻ➆⧒ٻ㧎㧻ٻṫ☚☚ٻ㟓Ṛٻ⼖䞮 㡖┺ډٻٻٻ

0 0.05 0.1 0.15 0.2 0.25

0 0.05 0.1 0.15 0.2 0.25 0.3

10^-2/s strain rate 10^-3/s strain rate 10^-4/s strain rate Ogden, N=3

Nominal Stress, MPa

Nominal Strain Uniaxial Tension

300^oC

Fig. 3 Variation of nominal stress with nominal strain for silicone rubber under uniaxial tension at 300^oC

Fig. 4 ⓪ٻ 㧒㿫ٻ 㞫㿫ٻ 䞮㠦㍲ٻ Ὃ䃃ٻ 㦧⩻ὒٻ Ὃ䃃ٻ

⼖䡫⮶㠦ٻ╖䞲ٻ㥶䞲㣪㏢䟊㍳䂮㢖ٻ㔺䠮ἆὒ㦮ٻ゚ᾦ

⯒ٻ⋮䌖⌎┺ډٻٻ㧒㿫ٻ㞫㿫㦖ٻ㧎㧻ٻ㔺䠮ἆὒ㢖ٻⰞ㺂 Ṗ㰖⪲ٻ⼖䡫⮶㧊ٻ㯳Ṗ䞮Ⳋ㍲ٻ㔺䠮䂮㢖ٻ䟊㍳䂮㢖㦮ٻ 㹾㧊Ṗٻ㯳Ṗ䞮Ⳇڇٻ⼖䡫⮶ٻ㏣☚㠦ٻ➆⯎ٻ㡗䟻㧊ٻ゚

ᾦ㩗ٻ䋂Ợٻ⋮䌖⌂┺ډٻٻٻ

Fig. 5 ⓪ٻ㔺Ⰲ䆮ٻἶⶊ⯒ٻ㼊㩗ٻ㞫㿫ٻ㔺䠮䞮㡂ٻ㠑 㦖ٻ⿖䞒ٻ㑮㿫⨟ὒٻ㿫ٻ㦧⩻ὒ㦮ٻ㔺䠮䂮㢖ٻ㥶䞲㣪㏢

䟊㍳ٻἆὒ㢖㦮ٻ゚ᾦ⯒ٻ⋮䌖⌎┺ډٻٻ㼊㩗ٻ㞫㿫ٻ㔺䠮 㦖ٻ㧒㿫ٻ㧎㧻ٻ⹥ٻ㞫㿫ٻ㔺䠮㠦ٻ゚䟊ٻ㌗╖㩗㦒⪲ٻ⼖

䡫⮶ٻ㏣☚㠦ٻ╖䞲ٻ㡗䟻㧊ٻ㧧㦒ⳆڇٻOgden^(12~14)⳾◎

㦚ٻ ㌂㣿䞲ٻ㥶䞲㣪㏢䟊㍳ٻ ἆὒ⓪ٻ ゚ᾦ㩗ٻ 㔺䠮䂮⯒ٻ 㧮ٻ㡞䁷䞮㡖┺ډٻٻ

4.2.2 ⳾㨂㦮 㡾Ṛ 㞫㿫 4

㡊Ṛٻ ❇Ṗ㞫ٻ ㏢ἆ⪲ٻ 㩲㫆䞲ٻ 㞢⬾⹎ⓚٻ 䞿⁞ٻ ⿚ Ⱖٻ⳾㨂ٻ㔲䘎㦖ٻ300^oC 㦮ٻ㡾☚㠦㍲ٻ㧒㩫䞲ٻ䞮㭧㏣

☚㧎ٻ0.1 MPa/s ⯒ٻṖ䞮㡂ٻ㞫㿫ٻ㦧⩻ὒٻ㏢㎇⼖䡫⮶

㦮ٻὖἚ⯒ٻ┺㦢ὒٻṯ㧊ٻῂ䞮㡖┺. ٻ MPa )

( 98 . 55 244 .

94 _m^{p 0.99397}

m = + ε

σ (6)

㡾Ṛٻ⁞䡫㞫㿫ٻ⹥ٻ㡾Ṛٻἶⶊٻ❇Ṗ㞫ٻ㎇䡫㠦ٻ╖

䞲ٻ䟊㍳㔲ٻ㔳ٻ(6)㦚ٻShima-Oyane⁽²³⁾ 㦮ٻ㏢㎇䟃⽋㔳 㠦ٻ 㩗㣿䞮㡂ٻ 㞢⬾⹎ⓚٻ 䞿⁞ٻ ⿚Ⱖ㦮ٻ 䂮⹖䢪ٻ Ệ☯ٻ

⹥ٻ䡫㌗⼖䢪⯒ٻ㡞䁷䞮㡖┺ډٻٻ䞲䘎ٻ⳾㨂㦮ٻ㞫㿫ἆ ὒ⪲⿖䎆ٻ㠑㦖ٻ䌚㎇Ἒ㑮ٻE=ٻ2.35 GPa 㧊Ⳇڇٻٻ䙂㞚

㏷ٻ゚ٻ౜ژٻ0.33⁽¹⁷⁾㧊㠞┺ډٻٻٻ 4.2.3ٻ⼖䡫 䡫㌗㦮 㡞䁷

Yang ❇⁽¹¹⁾ٻ㦖ٻ㡾Ṛٻἶⶊٻ❇Ṗ㞫ٻ㎇䡫㔲ٻ㤦㭒䡫ٻ 䡫㌗㦮ٻ 㞢⬾⹎ⓚٻ ⿚Ⱖٻ㎇䡫㼊㠦ٻ╖䞲ٻ 㥶䞲㣪㏢䟊

㍳㦚ٻ㑮䟟䞲ٻ⹪ٻ㧞┺ډٻٻ㧒⹮㩗㦒⪲ٻἶⶊٻⴆ✲ٻ⌊

⿖⯒ٻ㔺Ⰶ▪ٻ䡫㌗㦒⪲ٻ㩲㫆䞶ٻἓ㤆ٻ㞫㿫♲ٻ㎇䡫㼊

⓪ٻ㟧ٻ⊳┾ٻ⳾㍲Ⰲٻ⿖⁒㠦㍲ٻ㕂䞲ٻ⼖䡫㧊ٻ⹲㌳䞮 Ợٻ♲┺ډٻٻ➆⧒㍲ٻ㧊⩂䞲ٻ⼖䡫㦚ٻ⹿㰖䞮₆ٻ㥚䟊㍲

⓪ٻἶⶊٻⴆ✲ٻ⹥ٻ⿚Ⱖٻ㎇䡫㼊㦮ٻỆ☯㦚ٻ㩫䢫䧞ٻ㡞 䁷䞶ٻ㑮ٻ㧞⓪ٻ㥶䞲㣪㏢䟊㍳㦚ٻ㑮䟟䞮㡂ٻἶⶊٻⴆ✲

㦮ٻ䡫㌗㦚ٻ㾲㩗䢪䞶ٻ䞚㣪Ṗٻ㧞┺ډ^(9)ٻ

⽎ٻ⏒ⶎ㠦㍲⓪ٻ⻶⻾₆㠊ٻ䡫䌲㦮ٻ㽞₆⿖䛞㦚ٻ㥶 䞲㣪㏢䟊㍳㠦ٻ 㦮䟊ٻ 㾲㩗䢪♲ٻ ἶⶊٻⴆ✲⯒ٻ ㌂㣿䞮 㡂ٻ㡾Ṛٻἶⶊٻ❇Ṗ㞫ٻ㎇䡫㦚ٻ䞮㡖┺ډٻٻ⡦䞲ٻ㡾Ṛٻ

⁞䡫㞫㿫ٻ㎇䡫㦚ٻ㑮䟟䞮㡂ٻἶⶊٻ❇Ṗ㞫ٻ㎇䡫䞲ٻộ ὒٻ゚ᾦٻ⿚㍳䞮㡖┺ډٻٻٻ

Fig. 6 㦖ٻ㡾Ṛٻἶⶊٻ❇Ṗ㞫ٻ㎇䡫ٻ⹥ٻ㡾Ṛٻ⁞䡫

㞫㿫ٻ ㎇䡫㔲ٻ 㥶䞲㣪㏢䟊㍳ὒٻ 㔺䠮ἆὒ㠦ٻ ╖䞲ٻ⼖

䡫ٻ䡫㌗㦚ٻ⋮䌖⌎┺ډٻٻ⼖䡫♲ٻ䡫㌗㦮ٻ㌗⿖ٻ⿖⁒㠦

㍲⓪ٻ 㥶䞲㣪㏢䟊㍳ὒٻ㔺䠮ἆὒ㦮ٻ㹾㧊⓪ٻ Ệ㦮ٻ㠜 㦒⋮ٻ㥶䞲㣪㏢䟊㍳㠦ٻ㦮䞲ٻ䞮⿖ٻ⿖⁒㦮ٻ⊳┾ٻ⳾㍲

Ⰲٻ⿖⁒㠦㍲⓪ٻ┺㏢ٻ䋆ٻ⼖䢪Ṗٻ⹲㌳䞮㡖┺ډٻٻ㧊ộ 㦖ٻ㔺㩲ٻἶⶊٻⴆ✲㦮ٻ㌗⿖㢖ٻ䞮⿖Ṗٻ⿚Ⰲ♮₆ٻ➢

ⶎ㧎◆ٻ㥶䞲㣪㏢䟊㍳㠦㍲ٻ㧊㩦㦚ٻ┾㑲䢪䞮㡂ٻ䞮⋮

㦮ٻἶⶊⴆ✲⪲ٻἶ⩺䞮㡂ٻ㹾㧊Ṗٻ⹲㌳䞲ٻộ㧊┺ډٻٻٻ

CL

(EXP.)

(FEM.) (EXP.) Initial shape warm die pressing

rubber isostatic pressing

Fig. 6 Comparison between experimental data and FEM results for deformation of an Al6061 powder compact pressed under 170 MPa by rubber isostatic pressing and die pressing at 300^oC

1 2 1

2 2

3 3

3

4 4

4

5 5 5

6

6 6

7

7 7 7

8 8

CL

2 1 2

2

3 3

3

4 4

4

5 5

5

6 6

6

7 7

7 7

7 7

8 8

8

5

CL

1: 0.845 2: 0.866 3: 0.888 4: 0.909 5: 0.931 6: 0.952 7: 0.974 8: 0.995 Relative Density

(a) (b)

Fig. 7 Distributions of relative density of an Al6061 powder compact by die pressing under 170 MPa at 300^oC by (a) experiment and (b) FEM

4.2.4 ⿚Ⱖ ㎇䡫㼊㦮 ⹖☚ ⿚䙂

⿚Ⱖٻ㎇䡫㼊㦮ٻ㌗╖⹖☚ٻ⿚䙂⓪ٻἓ☚㢖ٻ㌗╖⹖

☚㦮ٻὖἚ⯒ٻ㧊㣿䞮㡂ٻṚ㩧㩗㦒⪲ٻ䁷㩫䞶ٻ㑮ٻ㧞┺ډٻٻ

2 5 (HR15T) 10

41 . 1 T 15 HR 00275 . 0 8365 . 0

D= + ⋅ + × ⁻ ⋅ (7)ٻ

Fig. 7 㦖 㡾Ṛ ⁞䡫㞫㿫㔲 ⿚Ⱖ ㎇䡫㼊 ⌊⿖㦮

㌗╖⹖☚ ⿚䙂㠦 ╖䞲 㔺䠮ἆὒ㢖 㥶䞲㣪㏢䟊㍳

ἆὒ⯒ ⋮䌖⌎┺. ⁞䡫㞫㿫㠦 㦮䞲 ㎇䡫㼊⌊⿖㠦

⓪ ㌗╖⹖☚ ⿚䙂Ṗ 0.85~0.995 ₢㰖 䋂Ợ ⼖䢪䞮

⓪ ộ㦚 㞢 㑮Ṗ 㧞┺. ➆⧒㍲ ⁞䡫㞫㿫㠦 㦮䞲

㎇䡫㼊㦮 ⹖☚Ṗ ⌄㦖 䞮⿖ ⿖⁒㠦㍲⓪ ₆ἚṖὋ 㧊 ⰺ㤆 㠊⪋₆ ➢ⶎ㠦 㰗㩧 㩲䛞㦒⪲ ㌂㣿䞮₆㠦

⓪ ⿖㩗㩞䞶 ộ㧊┺. 䞲䘎 㥶䞲㣪㏢䟊㍳ ἆὒ⓪ 㧊⩂䞲 ⿞‶㧒䞲 ⹖☚ ⿚䙂⯒ ゚ᾦ㩗 㧮 㡞䁷䞮㡖

┺.

Fig. 8㦖 300^oC 㦮 㡾☚㠦㍲ 170 MPa 㦮 㞫⩻㦒

⪲ ἶⶊ ❇Ṗ㞫 ㎇䡫䞲 ἓ㤆 㞢⬾⹎ⓚ 䞿⁞ ⿚Ⱖ

㎇䡫㼊 ⌊⿖㦮 ㌗╖⹖☚㠦 ╖䞲 㔺䠮ἆὒ㢖 㥶䞲 㣪㏢䟊㍳ ἆὒ⯒ ⋮䌖⌎┺. 㡾Ṛ ἶⶊ ❇Ṗ㞫 ㎇ 䡫㠦 㦮䟊 ㎇䡫♲ ἓ㤆⓪ 㩚㼊㩗㦒⪲ 0.95 㧊㌗㦮

゚ᾦ㩗 ⏨ἶ ‶㧒䞲 ㌗╖⹖☚ ⿚䙂⯒ ⽊㧊Ⳇ, 㡾 Ṛ ⁞䡫㞫㿫 ㎇䡫㠦 ゚䟊 ₆Ἒ㩗 ㎇㰞㧊 ㌗╏䧞 䟻㌗♶ ộ㧊⧒ἶ 㡞䁷䞶 㑮 㧞┺. 䞲䘎 㔺䠮ἆὒ 㢖 㥶䞲㣪㏢䟊㍳ ἆὒ㦮 㹾㧊Ṗ ┺㏢ ⹲㌳䞮⓪ ộ 㦚 㞢 㑮 㧞⓪◆ 㧊⓪ 㔺䠮䂮㦮 ㌗╖⹖☚ ⿚䙂Ṗ 5

ἓ☚㢖 ㌗╖⹖☚ ὖἚ㦮 㠦⩂ ⻪㥚㠦 䙂䞾♮₆ ➢ ⶎ㠦 㔲䘎⌊㦮 ⹖☚ ⿚䙂⯒ 㩫䢫䧞 ῂ䞮⓪ ◆⓪ 䞲ἚṖ 㧞₆ ➢ⶎ㧊┺. ⡦䞲 㥶䞲㣪㏢䟊㍳㔲 ἶ

⩺䞮㰖 㞠㞮▮ ἶⶊ ⴆ✲㢖 ⿚Ⱖ㦮 Ⱎ㺆☚ 㔺䠮䂮

⯒ 㡞䁷䞮⓪◆ 㭧㣪䞲 㣪㧎㦒⪲ 㧧㣿䟞㦚 ộ㧊⧒

ἶ 䕦┾♲┺.

5. 冶 嵦

⽎ ⏒ⶎ㠦㍲⓪ ⁞㏣ ⿚Ⱖ㠦 ╖䞲 Shima- Oyane⁽¹⁵⁾㦮 ῂ㎇⹿㩫㔳ὒ ἶⶊ㠦 ╖䞲 Ogden^(12~14) 㦮 ⼖䡫⮶ 㠦⍞㰖 䙂䎦㎲㦚 㥶䞲㣪㏢䟊㍳㠦 㩗㣿 䞮㡂 㽞₆ ἶⶊ ⴆ✲㦮 䡫㌗㦚 㾲㩗䢪 䞮㡖㦒Ⳇ,

㌗╖⹖☚ ⿚䙂 ⹥ 䡫㌗ ⼖䢪㠦 ╖䞮㡂 㔺䠮ἆὒ㢖

゚ᾦ ⿚㍳䞮㡂 ┺㦢ὒ ṯ㦖 ἆ⪶㦚 㠑㠞┺.

(1) 㡾Ṛ ἶⶊ ❇Ṗ㞫 ㎇䡫㠦 㦮䞲 㥶䞲㣪㏢䟊

㍳ ἆὒ⓪ 㔺䠮䂮㦮 䡫㌗⼖䢪⯒ ゚ᾦ㩗 㧮 㡞䁷䞮 㡖㰖Ⱒ ⿚Ⱖ ㎇䡫㼊 ⌊⿖㦮 ⹖☚ ⿚䙂⓪ 㫆⁞ ⏨ Ợ 㡞䁷䞮㡖┺.

(2) 㡾Ṛ ἶⶊ ❇Ṗ㞫 ㎇䡫㠦 㦮䞲 㔲䘎㦖 㩚 㼊㩗㦒⪲ 0.95 㧊㌗㦮 ‶㧒䞲 ㌗╖⹖☚ ⿚䙂⯒ ⽊ 㡂 㾲㫛 㩲䛞㦒⪲㦮 ṖὋ㧊 㣿㧊䞮㡖㦒⋮, 㡾Ṛ

⁞䡫㞫㿫 ㎇䡫㠦 㦮䞲 㔲䘎㦖 䞮⿖ ⿖⁒㠦㍲㦮 ⌄ 㦖 ⹖☚ ⹥ ⿞‶㧒䞲 ⹖☚ῂ⺆⯒ ⽊㡖┺.

焾処怾竒

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(2) Ariffin, A. K., Mujibur Rahman, Md. and Muhamad, N., Sahari, J., “Thermal-Mechanical Model of Warm Powder Compaction Process,” J. Mater. Pro. Tech.,

Vol. 116, 2001, pp. 67~71.

5

5

4 4

4 4

3 3 CL

1 1

1

2 2

3 3

3 4

4 4

4 4

4

5

5

3 3

3 3

CL

1: 0.945 2: 0.948 3: 0.952 4: 0.955 5: 0.959 Relative Density

(a) (b)

Fig. 8 Distributions of relative density of an Al6061 powder compact by rubber isostatic pressing under 170 MPa at 300^oC by (a) experiment and (b) FEM

(3) Lin, T. et al., “Warm Compaction Behavior of Metal Powders,” PM Tech., Vol. 18, 2000, pp. 261~264.

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Int. J. Powder Metall., Vol.31, 1995, pp. 9~17.

(5) Gagne, M., “Behavior of Powder Mix Constituents During Cold and Warm Compaction,” International Conference on Powder Metallurgy and Particulate Materials, 29 June to 2 July 1997, Chicago, IL.

(6) Chemlar, J., Nelson, B., Rutz, H., Lutz, M. and Porter, J., “An Evaluations of the ANCORDENSE Single Compaction Process and HPP Processing Technique on Fine Pitched Spur and Helical Gears,”

Advances in Powder Metallurgy and Particulate Materials, Vol. 5, 1994, pp. 73~89.

(7) Miller, T. and Hanejko, F., “Development of a Warm Compacted Automatic Transmission Torque Converter Hub,” Paper 970428, Society of Automotive Engineers.

(8) Sagawa, M., Nagata, H., Watanabe, T. and Itatani, O.,

“Rubber Isostatic Pressing (RIP) of Powder for Magnets and other Materials,” Materials & Design, Vol. 21, 2000, pp. 243~249.

(9) Shima, S., Sakamoto, Y. and Kotera, H., “Simulation of Rubber Isostatic Pressing and Shape Optimization of Rubber Mold,” Int. J. Mech. Sci., Vol. 44, 2002, pp. 1603~1623.

(10)Kim, H. G., Lee, J. W. and Kim, K. T., “The Effect of Rubber Mold on Densification and Deformation of a Metal Powder Compact During Cold Isostatic Pressing,” Mat. Sci. Eng. A318, 2001, pp. 174~182.

(11) Yang, H. C., Lee, J. W. and Kim, K. T., “The Effect of a Rubber Mold on Densification and Deformation of Metal Powder during Warm Isostatic Pressing,”

EURO PM2001, Vol. 3, pp. 172~177.

(12) Yeoh, O. H., “Some Forms of the Strain Energy Function for Rubber,” Rubber Chem. Tech., Vol. 66, 1993, pp. 754~771.

(13) Ogden, R. W., “Non-linear Elastic Deformation, Wiley, New York. 1984, pp. 73~520.

(14) ABAQUS User’s ช, ซ and ฌ Manual, Ver. 6.2, H. D. Hibbitt, I. Karlsson and E. P. Sorenson, U. S.

A.

(15) Shima, S. and Oyane, M., “Plasticity Theory for Porous Metals,” Int. J. Mech. Sci., Vol. 18, 1976, pp.

285~291.

(16) Han, H. N., Lee, Y. G., Oh, K. H. and Lee, D, N.,

“Analysis of Hot Forging of Porous Metals,” Mat.

Sci. Eng. A206, 1996, pp. 81~89.

(17) Hatch, J. E., Aluminum Properties and Physical Metallurgy, ASM, Metals Park, Ohio, 1995, pp.

684~687.

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