Evaluation of Strain, Strain Rate and Temperature Dependent Flow Stress Model for Magnesium Alloy Sheets

DOI : 10.5228/KSTP.2011.20.3.229

͑

穢剳暒昷儆击穟箒滆V洢YW劒G 洢Z笾SGYWXX噊V

YY`G

G

廎勾嘪枞 穯匎 砖沲汞 懆笛幦, 懆笛幦 暓壊 愕 欮壊 筞凃汊 処崪穢 氦壟汗崫

微塾櫖 堆穢 櫶割

G

暧殶滊 ¹ · 竎昷焲 ² · 割痢歊 ¹ · 儛憚朞 ² · 卆 洛 ^# G

Evaluation of Strain, Strain Rate and Temperature Dependent Flow Stress Model for Magnesium Alloy Sheets

G

W. J. Song, S. C. Heo, T. W. Ku, B. S. Kang, J. Kim

(Received February 22, 2011 / Revised April 20, 2011 / Accepted April 22, 2011) G

Abstract

The formability of magnesium alloy sheets at room temperature is generally low because of the inherently limited number of slip systems, but higher at temperatures over 150ºC. Therefore, prior to the practical application of these materials, the forming limits should be evaluated as a function of the temperature and strain rate. This can be achieved experimentally by performing a series of tests or analytically by deriving the corresponding modeling approaches.

However, before the formability analysis can be conducted, a model of flow stress, which includes the effects of strain, strain rate and temperature, should be carefully identified. In this paper, such procedure is carried out for Mg alloy AZ31 and the concept of flow stress surface is proposed. Experimental flow stresses at four temperature levels (150ºC, 200ºC, 250ºC, 300ºC) each with the pre-assigned strain rate levels of 0.01

s ^-1

s ^-1

s ^-1

This study shows that the proposed concept of flow stress surface is practically relevant for the evaluation of temperature and strain dependent formability.

G G

Key Words : Flow Stress Surface, Magnesium Alloy, Strain Rate, Temperature-Compensated Strain Rate, Elevated

41# ⇆# ᤊG G

䕦㨂㎇䡫Ὃ㩫㠦㍲㦮 ㎇䡫㎇ 䘟Ṗ⓪ ṖὋὋ㩫 㭧 䢏㦖 㾲㫛 ㎇䡫㩲䛞㠦 䕦㨂㦮 㹸㠊㰦(fracture) 㧊⋮ ῃ⿖㩗㧎 ⍻䌏(necking) 䡚㌗㧊 ⹲㌳䞮⓪⌦

㡂⿖㠦 ➆⧒ 䕦┾♲┺. Ⱎ⁎⍺㓮 䞿⁞㦖 㨂⬢ ⌊

⿖㦮 㔂ⰓⳊ(slip plane)㦮 㩲䞲㎇㦒⪲ 㧎䟊, 㧒⹮㩗

㦒⪲ ㌗㡾㠦㍲㦮 ㎇䡫䞲ἚṖ 㩲䞲♲┺[1, 2]. 䞮㰖 Ⱒ, Ⱎ⁎⍺㓮 䞿⁞䕦㨂⓪ ㎇䡫㡾☚Ṗ 150 C 㧊㌗

㧎 ἓ㤆, 䋆 㡆㎇ὒ ⏨㦖 ✲⪲㧟 䞲Ἒ㡗㡃㦚 ⽊㡂 㭒ἶ 㧞┺[1]. ➆⧒㍲, 㡾☚ ⹥ ⼖䡫㏣☚㠦 ➆⧒

⼖䡫Ệ☯㧊 ㌗㧊䞲 䕦㨂⁞㏣㠦 ╖䞲 ἶ㡾㎇䡫 Ὃ 㩫㍺Ἒ ⹥ 㩗㣿㠦 㧞㠊 ㎇䡫䞲Ἒ 㡗㡃 ′ⳛ㧊 㣪 ῂ♲┺.

G

XUG ⿖㌆╖䞯ᾦG ⿖䛞㏢㨂㌆䞯䡧⩻㡆ῂ㏢G G

YUG ⿖㌆╖䞯ᾦG 䟃Ὃ㤆㭒Ὃ䞯ὒG

JG ᾦ㔶㩖㧦aG ⿖㌆╖䞯ᾦG 䟃Ὃ㤆㭒Ὃ䞯ὒSG G lT”ˆ“aGŽ™Œˆ›’‘g—œšˆ•UˆŠU’™G

YZW

䕦㨂㎇䡫Ὃ㩫㦮 ㎇䡫㎇㦖 㩗㣿 䕦㨂㨂⬢㠦 ╖ 䞲 㧒⩾㦮 ㎇䡫㎇ 㔲䠮ὒ 㧊⪶㩗㧎 ὒ㩫㦚 䐋䞮 㡂 䕦┾ Ṗ⓻䞮┺[3]. 㧊⩂䞲 㧊⪶㩗㧎 䕦㨂㎇䡫㎇

㡞䁷㦖 ㎇䡫㎇ 㡞䁷 ╖㌗ 䕦㨂㨂⬢㦮 㥶☯㦧⩻

(flow stress) ⳾◎㦚 㩫㦮䞮⓪ ộ㧊 ⰺ㤆 㭧㣪䞮┺.

䔏䧞, Ⱎ⁎⍺㓮 䞿⁞ὒ ṯ㧊, 㨂⬢㦮 㥶☯䔏㎇㧊 㡾☚ ⹥ ṖὋ㏣☚㠦 㡗䟻㦚 ⹱⓪ 㨂⬢⓪ ㎇䡫♮

⓪ 㡾☚ ⹥ ṖὋ㏣☚㠦 ➆⯎ ⼖䡫䔏㎇㦚 ⳾㌂ Ṗ

⓻䞲 㥶☯㦧⩻㦒⪲ 㩫㦮 ♮㠊㟒Ⱒ 㔺㰞㩗㧎 ㎇䡫

㎇ 䕦┾㧊 Ṗ⓻䞮┺.

㎇䡫Ὃ㩫 ㍺Ἒὖ⩾ 㧊⪶㩗 㡆ῂ ⹥ 㑮䂮㩗 䟊

㍳㠦 䞚㑮㩗㧎 㡾☚ ⹥ ⼖䡫㏣☚ 㦮㫊䡫 ⁞㏣㨂

⬢㦮 㥶☯㦧⩻ 㩫㦮㠦 ὖ䞲 ┺㑮㦮 㡆ῂṖ 䡚㨂 㰚䟟♮ἶ 㧞┺[4~9]. 䞮㰖Ⱒ, ╖⿖⿚㦮 㨂⬢ 㥶☯

㦧⩻ ′ⳛ㧊 㞫㿫䞮㭧 ㌗䌲㠦㍲㦮 ⼖䡫Ệ☯㦚 ἶ

⩺䞲 㡆ῂṖ 㭒⯒ 㧊⬾ἶ 㧞⓪ 㔺㩫㧊┺[4~6]. 䕦 㨂㎇䡫Ὃ㩫㦖 㼊㩗㎇䡫ὒ⓪ ╂Ⰲ 䕦㨂䘟Ⳋ㌗㦮 㧎㧻䞮㭧㧊 ⼖䡫Ệ☯ 㥶⹲㠦 㰖⺆㩗㧎 㡗䟻㦚 ⹎ 䂲┺. 㧊㢖 ὖ⩾♲ 㧎㧻䞮㭧 ㌗䌲㠦㍲ Ⱎ⁎⍺㓮 䞿⁞䕦㨂㦮 㥶☯㦧⩻ ⳾◎㦚 㩫㦮䞲 㡆ῂ☚ 㰚䟟

♮㠞㦒⋮[7~9], ☚㿲♲ 㥶☯㦧⩻ ⳾◎㧊 ㎇䡫Ὃ㩫

㍺Ἒ ὖ⩾ 㧊⪶㩗 㡆ῂ ⹥ 㑮䂮㩗 䟊㍳㠦 㩗㣿♮

₆㠦⓪ ┺㏢ ⽋㧷䞲 䡫䌲⯒ 䀾䞮ἶ 㧞┺. ⽎ ⏒ⶎ 㠦㍲⓪, 㡾☚ ⹥ ⼖䡫㏣☚ 㦮㫊䡫 ⁞㏣㨂⬢㧎 Ⱎ

⁎⍺㓮 䞿⁞ AZ31㠦 ╖䞲 㥶☯㦧⩻ ⳾◎ ☚㿲㠦

╖䞲 㡆ῂṖ 㑮䟟♮㠞┺. 㧊⩂䞲 㥶☯㦧⩻ ⳾◎㦖 㡾☚㢖 ⼖䡫⮶ ㏣☚⯒ ἶ⩺䞮ἶ, 㥶☯㦧⩻ ⳾◎㦚 㧊㣿䞲 䤚㏣ 㡆ῂ 㩗㣿㧊 㣿㧊䞲 䡫䌲⪲ ☚㿲䞮₆ 㥚䞮㡂 㡾☚⽊㌗䡫 ⼖䡫⮶ ㏣☚ 㧎㧦(temperature- compensated strain rate)⯒ ἶ⩺䞮ἶ 㧞┺. Ⱎ⁎⍺㓮 䞿⁞ AZ31 䕦㨂㏢㨂㠦 ╖䞲 150 C , 200 C , 250 C , 300 C ⍺ Ṗ㰖 㡾☚ 䢮ἓὒ 0.2mm/s, 2.0mm/s, 20.0

mm/s ㎎ Ṗ㰖 ⼖䡫㏣☚ 㡗㡃㠦㍲ 㑮䟟♲ 㺎ἶⶎ

⼖䡫⮶ ㏣☚㠦 ➆⯎ 㥶☯㦧⩻ 䘟Ⳋ㦚 㩲㔲䞮㡖┺.

#

#

51# ᩲຢᇎ⍂# 㘓າ# ㎺⡖# ⟊ᒃ⟻ᣏ# ⇊ᑮ#

514# ⟻ᣏ0ᵪ㚿ᨊ# ⇊ᑮ#

㌗㣿 Ⱎ⁎⍺㓮 䞿⁞ AZ31 (Mg - 3% Al - 1% Zn) 䕦㨂㦮 ┾㑲㧎㧻 㔲䠮ἆὒ⓪ Fig. 1㠦 ⋮䌖⌊㠞┺

[1]. ┾㑲㧎㧻㔲䠮㦖 150 C , 200 C , 250 C , 300

C ⍺ Ṗ㰖 㡾☚ 䢮ἓὒ 0.2mm/s, 2.0mm/s, 20.0 mm/s

0.0 0.2 0.4 0.6 0.8 1.0

0 50 100 150 200 250 300

Eff ecti ve S tress

Effective Strain

%

%

%

%

(a) Stres-strain curve at crosshead speed 0.2 mm/s

0.0 0.2 0.4 0.6 0.8 1.0

0 50 100 150 200 250 300

Effe c tiv e Str e s s

Effective Strain

%

%

%

%

(b) Stres-strain curve at crosshead speed 2.0 mm/s

0.0 0.2 0.4 0.6 0.8 1.0

0 50 100 150 200 250 300

E ffecti ve S tr e ss

Effective Strain

%

%

%

%

(c) Stress-strain curve at crosshead speed 20.0 mm/s

Fig. 1 Stress-strain curves from the tensile test of

magnesium based alloy AZ31 sheet material

[1]

穢剳暒昷儆击穟箒滆V洢YW劒G 洢Z笾SGYWXX噊V

YZXG

G

Extract

Extract K K _{IJ IJ}

y n n _{IJ IJ} for each stress- for each stress -strain curve strain curve

V K

H

I : Temperature Level

•

J : Effective Strain Level

Analysis of the relationship Analysis of the relationship

Ä T y Z y

H

H ^

_IJ

_IJ

Determination of flow stress model Determination of flow stress model

Ä

V f T

H H

Extract

Extract K K _{IJ IJ}

y n n _{IJ IJ} for each stress- for each stress -strain curve strain curve

V K

H

I : Temperature Level

•

J : Effective Strain Level

Analysis of the relationship Analysis of the relationship

Ä T y Z y

H

H ^

_IJ

_IJ

Determination of flow stress model Determination of flow stress model

Ä

V f T

H H

Fig. 2 Procedure to determine flow stress model of magnesium based alloy AZ31 sheet material with strain, strain rate and temperature

㎎ Ṗ㰖 ⼖䡫㏣☚ 㡗㡃(⼖䡫⮶ ㏣☚: 0.01 s

^-1

s ^-1

s ^-1

⯒ ㌊䘊⽊Ⳋ, ⏨㦖 㡾☚㢖 ⌄㦖 ⼖䡫⮶ ㏣☚ 㡗㡃 㠦㍲ 䋆 㡆㔶㥾㦚 䢫⽊䞶 㑮 㧞㦢㦚 㞢 㑮 㧞┺.

515# ⟊ᒃ⟻ᣏ# ⇊ᑮ# ᭒ᐢᩫ#

㧒⹮㩗㦒⪲ ṫ㏢㎇ 㨂⬢ Ṗ㩫㦚 䐋䞲 㨂⬢㦮 㥶☯㦧⩻㦖 ┺㦢㦮 㔳㦒⪲ 䚲䡚 Ṗ⓻䞮┺.

K

V H

㡂₆㍲,

K⓪ ṫ☚Ἒ㑮(strength coefficient)㧊Ⳇ, n

☚ ⹥ ⼖䡫㏣☚㠦 ➆⧒ ⼖䡫Ệ☯㧊 ╂⧒㰖⓪ Ⱎ

⁎⍺㓮 䞿⁞䕦㨂㦮 㥶☯㦧⩻㦖 Fig. 2㦮 㩞㹾⯒ 䐋 䞮㡂 㩫㦮䞮㡖┺. Ⲓ㩖, Fig. 3ὒ ṯ㧊 ㍶䡫 ἷ㍶㩧 䞿(curve fitting) ⹿⻫㦚 㧊㣿䞮㡂 ṗṗ㦮 㡾☚ ⹥

⼖䡫㏣☚ 㡗㡃㠦㍲㦮 ṫ☚Ἒ㑮㢖 ṖὋἓ䢪㰖㑮⯒

㿪㿲䞮ἶ, 㧊⩝Ợ ☚㿲♲ ṗṗ㦮 ṫ☚Ἒ㑮 ⹥ Ṗ Ὃἓ䢪㰖㑮㠦 ╖䞮㡂 㡾☚, ⼖䡫⮶ ⹥ ⼖䡫⮶ ㏣

☚㢖㦮 㡆ὖὖἚ⯒ ⿚㍳䞾㦒⪲㖾 㾲㫛㩗㧎 㥶☯

㦧⩻ ⳾◎㦚 ἆ㩫䞮㡖┺. ㌂㩚 㩫㦮♲ 㡾☚ ⹥ ⼖ 䡫⮶ ㏣☚ 㡗㡃㠦㍲ ☚㿲♲ ṫ☚Ἒ㑮 ⹥ ṖὋἓ 䢪㰖㑮⓪ Table 1㠦 㩫Ⰲ䞮㡖┺.

Ṗ䟊㰖⓪ 㣎⩻㠦 㦮䟊 ⼖䡫㧊 ⹲㌳♮⓪ ὒ㩫㠦

㍲, ṫ☚Ἒ㑮 ⹥ ṖὋἓ䢪㰖㑮⓪ ṖὋ㡾☚㢖 ⼖䡫

⮶ ㏣☚㦮 㡗䟻㦚 ⹱㞚 㡆㔶㥾㧊 㯳Ṗ䞮⓪ 㡗㡃

0.01 0.1 1

10 100 1000

E ff e ct iv e S tr e ss [ log scal e]

Effective Strain [log scale]

% %

% %

(a) Crosshead speed 0.2 mm/s

0.01 0.1 1

10 100 1000

Effecti v e Stress [l og s c al e]

Effective Strain [log scale]

p

% %

% %

(b) Crosshead speed 2.0 mm/s

0.01 0.1 1

10 100 1000

E ff e cti ve S tre ss [ log scal e]

Effective Strain [log scale]

% %

% %

(c) Crosshead speed 20.0 mm/s

Fig. 3 Relationships between effective stress and strain

under various temperatures and crosshead

speed levels

YZY

Table 1 Strength coefficients and work hardening exponents under various temperatures and crosshead speed levels

Crosshead Speed [mm/s]

Temperature [

^o

Strength Coefficient,

K

[MPa]

Work Hardening Exponent,

n

300 156.1 0.1632 150 311.7 0.1886 200 239.3 0.1816 250 174.3 0.1634 2

300 117.7 0.1528 150 273.6 0.1876 200 208.2 0.1937 250 134.8 0.1468 0.2

300 79.1 0.0488

㦒⪲ ⼖䢪♮ἶ 㧞㦢㦚 㞢 㑮 㧞㦒Ⳇ, ┺㦢㦮 㔳ὒ ṯ㧊 䚲䡚 Ṗ⓻䞮┺.

  ^{, ,   ,}

K K H ^ T n n H ^ T

㥶☯㦧⩻ὒ ⼖䡫⮶, ⼖䡫⮶ ㏣☚ ⹥ 㡾☚ ㌂㧊 㦮 㡆ὖ㎇㦚 ′ⳛ䞮₆ 㥚䞮㡂, ⽎ ⏒ⶎ㠦㍲⓪ 㡾

☚㢖 ⼖䡫⮶ ㏣☚㠦 㦮䞲 㡗䟻㎇㦚 ☯㔲㠦 ἶ⩺

Ṗ⓻䞲 㡾☚ ⽊㌗䡫 ⼖䡫⮶ ㏣☚ 㧎㧦(temperature- compensated strain rate,

Z)⯒ ☚㧛䞮㡖┺. 㡾☚ ⽊㌗

䡫 ⼖䡫⮶ ㏣☚ 㧎㧦⓪ ┺㦢㧊 㔳㦒⪲ 㩫㦮 ♲┺

[10].

exp Q Z H § RT ·

¨ ¸

© ¹



㡂₆㍲,

R㦖 㧒⹮₆㼊㌗㑮(universial gas constant,

J mol ^-1 K ^-1

Q⓪ Ⱎ⁎⍺㓮 䞿⁞㦮 ⼖䡫㠦

^-1

[11]. Fig. 4 (a)㢖 ṯ㧊, 㥶䣾㦧⩻ὒ 㥶䣾⼖䡫⮶ ㏣

☚㢖㦮 ὖἚ⯒ ṗṗ㦮 㡾☚ ⹥ 㥶䣾 ⼖䡫⮶㠦 ➆

⧒ ゚ᾦ䟊 ⽎ ἆὒ, 㥶䣾⼖䡫⮶ ㏣☚Ṗ 㯳Ṗ䞾㠦

➆⧒ 㥶䣾㦧⩻ 㑮㭖㧊 ㍶䡫㩗㦒⪲ 㯳Ṗ䞾㦚 㞢 㑮 㧞㦒 Ⳇ, 䔏䧞 㡾☚Ṗ 300 C 㑮㭖㠦㍲⓪ 㥶䣾

0.01832 0.13534 1

50 100 150 200 250 300 350 400 450

Effe c tiv e Stre s s [MPa ]

Effective Strain Rate [ln scale]

%

H 0.1

% % %

H 0.2 H 0.3 H 0.4 H 0.5 H 0.7 0.6 H

(a) Relationship between stress and strain rate under various temperatures and strain levels

1.44626E12 2.14644E14 3.18559E16 50

100 150 200 250 300 350

Ef fe c tiv e St re s s [M Pa ]

Z (Temperature-Compensated Strain Rate) [ln scale]

%

H 0.1

% % %

H 0.2 H 0.3 H 0.4 H 0.5 H 0.7 0.6 H

(b) Relationship between stress and temperature- compensated strain rate (Z) under various temperatures and strain levels

Fig. 4 Relationships among stress, strain, strain rate and temperature

⼖䡫⮶ ㏣☚Ṗ 㧧㦚 ἓ㤆 ⼖䡫⮶㠦 ㌗ὖ㠜㧊 ㌗

╖㩗㦒⪲ ☯㧒䞲 㑮㭖㦮 㥶䣾㦧⩻㧊 ⋮䌖⋾㦚 㞢 㑮 㧞┺. 㧊⯒ ₆⹮㦒⪲, Fig. 4(b)㢖 ṯ㧊 ☯㧒䞲 㫆Ị㠦㍲ 㥶䣾㦧⩻ὒ 㡾☚ ⽊㌗䡫 ⼖䡫⮶ ㏣☚

㧎㧦㢖㦮 ㌗ὖὖἚ⯒ Ỗ䏶䟊 ⽊Ⳋ, ṗṗ㦮 ⼖䡫⮶

㑮㭖㠦㍲ 㡾☚Ṗ 㯳Ṗ䞾㠦 ➆⧒ 㡾☚ ⽊㌗䡫 ⼖ 䡫⮶ 㧎㧦㢖 㥶䣾㦧⩻㧊 ⳾⚦ ㍶䡫㩗 ὖἚ⯒ Ṗ 㰦㦚 㞢 㑮 㧞┺. 㧊ộ㦖 㥶䣾㦧⩻ 㑮㭖㦚 ⋮䌖⌊

⓪ ṫ☚Ἒ㑮 ⡦䞲 㡾☚ ⽊㌗䡫 ⼖䡫⮶ ㏣☚㧎㧦 㢖 ㍶䡫㩗 ὖἚ⯒ Ṗ㰦㦚 䕦┾ Ṗ⓻䞮Ợ 䞲┺.

穢剳暒昷儆击穟箒滆V洢YW劒G 洢Z笾SGYWXX噊V

YZZG

G

3.58491E9 7.8963E13

50 100 150 200 250 300 350

S trength Co effi ci ent [MP a]

Z (Temperature-Compensated Strain Rate) [ln scale]

(a) Relationship between strength coefficient and temperature-compensated strain rate (Z)

3.58491E9 7.8963E13

0.04979 0.13534

Work H a rd eni ng E x pon ent

Z (Temperature-Compensated Strain Rate) [ln scale]

(b) Relationship between work hardening exponent and temperature-compensated strain rate (Z) Fig. 5 Relationships among strength coefficient, work

hardening exponent and temperature- compensated strain rate (Z)

Table 2 Curve-fitted parameters in flow stress model

K 1

K 2

n 1

n 2

n 3

0.0 0.2 0.4 0.6 0.8 1.0

0 50 100 150 200 250 300

Effe c tive Stre ss

Effective Strain

%

%

%

%

(a) Crosshead speed 0.2 mm/s

0.0 0.2 0.4 0.6 0.8 1.0

0 50 100 150 200 250 300

Effecti v e St ress

Effective Strain

%

%

%

%

(b) Crosshead speed 2.0 mm/s

0.0 0.2 0.4 0.6 0.8 1.0

0 50 100 150 200 250 300

Effecti v e St ress

Effective Strain

% %

%

%

(c) Crosshead speed 20.0 mm/s

Fig. 6 Comparison between the measured stress-strain

curves and the modeled flow stress curves

YZ[

(a) Flow stress surfaces with respect to the crosshead speed

(b) Flow stress surfaces with respect to the temperature Fig. 7 Comparisons of flow stress surfaces under

various temperatures and crosshead speed levels

㧊⩂䞲 䕦┾⁒Ệ⯒ ⹪䌫㦒⪲, Fig. 5 (a)㠦 ṗṗ㦮 㫆Ị㠦㍲㦮 ṫ☚Ἒ㑮㢖 㡾☚ ⽊㌗䡫 ⼖䡫⮶ 㧎㧦

⯒ ☚㔲䞮㡖㦒Ⳇ, 㞴㍲ ⿚㍳䞲 ἆὒ㢖 ṯ㧊 㡾☚

⽊㌗䡫 ⼖䡫⮶ ㏣☚ 㧎㧦㢖 ṫ☚Ἒ㑮Ṗ ㍶䡫㩗 ὖἚ⯒ Ṗ㰦㦚 㞢 㑮 㧞┺. 㞚㤎⩂, ṖὋἓ䢪㰖㑮 㢖 㡾☚ ⽊㌗䡫 ⼖䡫⮶ ㏣☚ 㧎㧦☚ Fig. 5 (b)㠦

☚㔲䞮㡖┺. ṫ☚Ἒ㑮 ⹥ ṖὋἓ䢪㰖㑮㢖 㡾☚ ⽊

㌗䡫 ⼖䡫⮶ ㏣☚ 㧎㧦㢖㦮 ㌗ὖὖἚ⯒ ㍶䡫 ⽊ Ṛ₆⻫㦚 䐋䞮㡂 ἷ㍶㩧䞿䞮Ⳋ ┺㦢ὒ ṯ㦖 㔳㦒

⪲ 䚲䡚 Ṗ⓻䞮┺.

  ^{1 2   ln}

K Z K K  Z

  ^{1 2}  

n Z  n n Z

㔳 (4)㢖 (5)㠦㍲㦮 ἷ㍶㩧䞿 㧎㧦(K

1 , K 2 , n 1 , n 2 , n 3

⽎ ⏒ⶎ㠦㍲ 㩲㞞♲ 㡾☚ ⽊㌗䡫 ⼖䡫⮶ ㏣☚

㧎㧦 ₆⹮㦮 㥶☯㦧⩻ ⳾◎ ἆὒ㢖 Fig. 1㠦㍲ ☚ 㔲䞲 㧎㧻㔲䠮 ἆὒ⯒ Fig. 6㠦㍲ ゚ᾦ䞮㡖┺. ⏨ 㦖 㡾☚㡗㡃ὒ 䋆 ⼖䡫⮶ ㏣☚㡗㡃㠦㍲ ⹲㌳䞮⓪ 㨂⬢㦮 ṖὋ㡆䢪(work softening) 䡚㌗㦖 㩲㞞♲ 㥶

☯㦧⩻ ⳾◎㠦 ἶ⩺䞮㰖 㞠㞮₆ ➢ⶎ㠦, ┺㏢ 㹾 㧊⯒ ⽊㧊ἶ 㧞㦒⋮, ṗṗ㦮 㡾☚ ⹥ ⼖䡫⮶ ㏣☚

㡗㡃㠦㍲ ╖㼊㩗㧎 㨂⬢ ⼖䡫Ệ☯㦖 㤦䢲䞮Ợ ⳾

㌂䞮ἶ 㧞┺. 㔳 (4)㢖 (5)⯒ ₆⹮㦒⪲, 㔳 (1)㠦 㩲㔲䞲 㥶☯㦧⩻ ⳾◎㦚 㩫Ⰲ䞮Ⳋ ┺㦢ὒ ṯ┺.

V K Z H

㧊⩂䞲 㦧⩻ ⼖䡫⮶ ㍶☚⯒ ₆⹮㦒⪲, Ⱎ⁎⍺㓮 䞿⁞ 䕦㨂㨂⬢㦮 㡾☚ ⹥ ⼖䡫⮶ ㏣☚㠦 ➆⯎ ⼖ 䡫Ệ☯㦖 Fig. 7ὒ ṯ㧊 ⼖䡫⮶, 㡾☚ ⹥ ⼖䡫⮶

㏣☚⯒ 3㿫㦒⪲ 䞮⓪ 3㹾㤦 㫢䚲Ἒ㠦 㥶☯㦧⩻

䘟Ⳋ㦒⪲ ☚㔲䞶 㑮 㧞┺.

61# ൚# ᤊ#

⽎ ⏒ⶎ㦖 㡾☚ ⹥ ⼖䡫㏣☚ 㦮㫊䡫 ⁞㏣㨂⬢

㧎 Ⱎ⁎⍺㓮 䞿⁞ 䕦㨂㨂㰞 AZ31㠦 ╖䞲 㥶☯㦧

⩻㦚 㡾☚ ⹥ ⼖䡫⮶ ㏣☚⯒ ἶ⩺䞮㡂 ☚㿲䞮㡖

┺. 㥶☯㦧⩻ ⳾◎㦚 㧊㣿䞲 䤚㏣ 㡆ῂ 㑮䟟㠦 㣿 㧊䞲 䡫䌲⪲ ☚㿲䞮₆ 㥚䞮㡂, ⽎ ⏒ⶎ㠦㍲⓪ 㥶

☯㦧⩻ ⳾◎㠦 㡾☚ ⽊㌗䡫 ⼖䡫⮶ ㏣☚ 㧎㧦⯒

ἶ⩺䞮ἶ 㧞┺.

㥶☯㦧⩻ ⳾◎ ☚㿲ὒ㩫㠦㍲, 㡾☚ ⹥ ⼖䡫⮶

㏣☚㠦 ➆⯎ 䕦㨂㦮 㥶䣾㦧⩻㦖 㡾☚ ⽊㌗䡫 ⼖ 䡫⮶ ㏣☚㢖 ㍶䡫㩗㧎 ὖἚ⯒ Ṗ㰦㦚 㞢 㑮 㧞㠞

┺. ⡦䞲, 㧊⩝Ợ 㩫㦮♲ 㥶☯㦧⩻ ⳾◎㦚 ₆⹮㦒

⪲ ㌗㣿 Ⱎ⁎⍺㓮 䞿⁞ 䕦㨂㨂㰞 AZ31㦮 㡾☚,

⼖䡫⮶ ⹥ ⼖䡫⮶ ㏣☚㠦 ➆⯎ 㥶☯㦧⩻ 䘟Ⳋ㦚 㩲㔲䞮㡖┺.

㞚㤎⩂, 㡾☚㢖 ⼖䡫⮶ ㏣☚㠦 ➆⯎ 㥶☯㦧⩻

⳾◎ ☚㿲₆⻫㦖 䟻䤚 㡾☚ ⹥ ⼖䡫㏣☚㠦 ⹒Ṧ

穢剳暒昷儆击穟箒滆V洢YW劒G 洢Z笾SGYWXX噊V

YZ\G

G

㣿♮Ⰲ⧒ 䕦┾♲┺.

㝮 ໚ G

㧊 ⏒ⶎ㦖 ⿖㌆╖䞯ᾦ 㧦㥶ὒ㩲 䞯㑶㡆ῂ゚(2

⎚)㠦 㦮䞮㡂 㡆ῂ♮㠞㦒Ⳇ, 㭒㩖㧦⓪ 㧊㠦 Ṧ㌂

✲Ⱃ┞┺.

Ⳣ ඊ ᯢ 㙶

[1] H. Takuda, T. Morishita, T. Kinoshita, N.

Shirakawa, 2005, Modelling of formula for flow stress of a magnesium alloy AZ31 sheet at elevated temperatures, J. Mater. Process. Technol., Vol. 164- 165, pp. 1258~1262.

[2] J. H. Lee, S. H. Kang, Forming technologies of magnesium alloy sheet and automobile applications, 2007, Auto J., pp. 24~31.

[3] M. H. Lee, K. K. Kim, H. Y. Kim, S. I. Oh, 2008, Evaluation of the formability of warm forming simulation of magnesium alloy sheet using FLD, Trans. Mater. Process., Vol. 17, pp. 501~506.

[4] Y. C. Lin, M. S. Chen, J. Zhong, 2008, Constitutive modelling for elevated temperature flow behavior of 42CrMo steel, Comp. Mater. Sci., Vol. 42, pp.

470~477.

[5] Y. C. Lin, M. S. Chen, J. Zhong, 2008, Prediction of 42CrMo steel flow stress at high temeprature and strain rate, Mech. Res. Commun., Vol. 35, pp.

142~150.

[6] Y. J. Qin, Q. L. Pan, Y. B. He, W. B. Li, X. Y. Liu, X. Fan, 2010, Modellng of flow stress for magnesium alloy during hot deformation, Mat. Sci.

Eng. A-Struct., Vol. 527, pp. 2790~2797.

[7] K. Mathis, Z. Trojanova, P. Lukac, C. H. Caceres, J.

Lendvai, 2004, Modelling of hardening and softening processes in Mg alloys, J. Alloy. Compd., Vol. 378, pp. 176~179.

[8] X. Huang, K. Suzuki, A. Watazu, I. Shigematsu, N.

Saito, 2008, Mechanical properties of Mg-Al-Zn alloy with a titled basal texture obtained by differential speed rolling, Mat. Sci. Eng. A-Struct., Vol. 488, pp. 2790~2797.

[9] Z. Zeng, S. Jonsson, H. J. Roven, Y. Zhang, 2009, Modelling the flow stress for single peak dynamic recrystallization, Mater. Design, Vol. 30, pp. 1939~

1943.

[10] C. Zener, H. Hollomon, 1944, Effect of strain rate upon plastic flow of steel, J. Appl. Phys., Vol. 15, pp. 22~32.

[11] Z. Q. Sheng, R. Shivpuri, 2006, Modelling flow stress of magnesium alloys at elevated temperature, Mat. Sci. Eng. A-Struct., Vol. 419, pp. 202~208.