Effect of Strain Rate on the Anisotropic Deformation Behavior of Advanced High Strength Steel Sheets

http://dx.doi.org/10.5228/KSTP.2011.20.8.595G G

穢剳暒昷儆击穟箒滆V洢YW劒G 洢_笾SGYWXX噊V\`\G G

懆笛幦暓壊櫖 娶幾 処儛壊 儛砖汞 決愯昷 懆筚櫖 分穢 櫶割

G

竎滆窫¹· 竎 篎^#· 決煃朞² G

Effect of Strain Rate on the Anisotropic Deformation Behavior of Advanced High Strength Steel Sheets

G

J. Huh, H. Huh, C. S. Lee

(Received September 2, 2011 / Revised September 9, 2011 / Accepted September 28, 2011) G

Abstract

This paper investigates the effect of strain rate on the anisotropic deformation behavior of advanced high strength steel sheets. Uniaxial tensile tests were carried out on TRIP590 and DP780 steel sheets at strain rates ranging from 0.001/sec to 100/sec to determine yield stresses and r-values at various loading angles from the reference rolling direction. R-values were determined by the digital image correlation technique. Hill48 and Yld2000-2d yield functions were tested for their capability to describe the plastic deformation anisotropy of the materials. Initial yield loci were constructed using the Yld2000-2d yield function, which adequately described the anisotropic behavior of the materials. The shape of the initial yield loci was found to change with different strain rate, and the anisotropic behavior decreased with increasing strain rate.

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Key Words : Anisotropy, Strain-rate, Yield Function, AHSS

41# ⇆# ᤊG G

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⏨₆ ➢ⶎ㠦 ㌆㠛㦮 㡂⩂ ⿚㟒㠦㍲ ⍦Ⰲ ㌂㣿♲

┺. ⹫䕦 ㎇䡫Ὃ㩫㠦㍲ ㎇䡫㎇㦚 䘟Ṗ䞮ἶ ⁎㠦 ⰴ⓪ Ὃ㩫 ⼖㑮⯒ ㍺Ἒ䞮₆ 㥚䞮㡂 㑮䂮䟊㍳ ₆

⻫㧊 ⍦Ⰲ 㧊㣿♮ἶ 㧞┺. 㞫㡆Ὃ㩫㦒⪲ ㌳㌆♮⓪

⹫䕦㨂⬢⓪ 䕦㨂㦮 ⚦℮⹿䟻 ⹥ 䘟Ⳋ ⌊㦮 㧊⹿

㎇㦚 㰖┞⸖⪲ 㑮䂮䟊㍳㦮 㩫䢫☚⯒ 䟻㌗㔲䋺₆ 㥚䞮㡂 㨂⬢㦮 㧊⹿㎇㦚 㩫䢫䧞 䘟Ṗ䞮⓪ ộ㧊 䞚㑮㩗㧊┺. 䔏䧞 䘟Ⳋ ⌊㦮 䟃⽋ṫ☚㢖 r-Ṩ㦮 ⼖ 䢪⓪ 㨂⬢㦮 㧊⹿㎇㦚 ἆ㩫䞮⓪ 㭧㣪䞲 㧎㧦㧊┺.

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┺ἶ ⚦ἶ 䟃⽋ἷⳊ㦮 䋂₆Ⱒ ⼖䡫⮶㏣☚㦮 㡗䟻 㦚 ⹱⓪┺ἶ Ṗ㩫䞲┺. 䞮㰖Ⱒ Lee[1]㢖 Huh[2-3]

❇㧊 ὖ㺆䞲 ⹪ 㧞❅㧊 㨂⬢㦮 r-Ṩ㦖 ⼖䡫⮶㏣☚

㠦 ➆⧒ ⼖䢪䞮Ⳇ 㧊⓪ 㨂⬢㦮 㧊⹿㎇㧊 ⼖䡫⮶

㏣☚㠦 ➆⧒ ╂⧒㰦㦚 㦮⹎䞲┺. ➆⧒㍲ 㑮䂮䟊㍳

㦮 㩫䢫☚⯒ 䟻㌗㔲䋺₆ 㥚䞮㡂 ⼖䡫⮶㏣☚⯒ ἶ

⩺䞲 㧊⹿㎇㦮 ⼖䢪⯒ 㡆ῂ䞮ἶ 㧊⯒ 㹾㼊ṫ䕦㦮 䟊㍳㠦 㩗㣿䞮㡂㟒 䞲┺.

⽎ ⏒ⶎ㠦㍲⓪ 㧦☯㹾 㣎䕦㠦 Ⱔ㧊 㝆㧊⓪ ἶ ṫ☚ ṫ䕦㧎 TRIP590(1.2t)㢖 DP780(1.0t)㠦 ╖䞮㡂

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\`]GV穢剳暒昷儆击穟箒滆V洢YW劒G 洢_笾SGYWXX噊G (a) 0^o(RD)

(b) 45^o(DD)

(c) 90^o(TD)

Fig. 1 Engineering stressstrain curves of TRIP590 at various strain rates

㩫㩗 ⹥ 㭧ἶ㏣ ⼖䡫⮶㏣☚(0.001/sec~100/sec)㠦㍲

┾㿫㧎㧻㔲䠮㦚 㑮䟟䞮ἶ ❪㰖䎎 㧊⹎㰖 䝚⪲㎎

㕇 ₆⻫㦚 㧊㣿䞲 ⼖䡫⮶ 䁷㩫 ₆⻫[2]㦚 ㌂㣿 䞮 㡂 r-Ṩ㦚 䁷㩫䞮㡖┺. 䁷㩫♲ 䟃⽋ṫ☚ ⹥ r-Ṩ㦚

⹪䌫㦒⪲ Hill1984[4]㢖 Yld2000-2d[5] 䟃⽋䞾㑮⯒

ῂ㎇䞮ἶ 㩗㩞䞲 䟃⽋䞾㑮⯒ ㍶㩫䞮㡖┺. ㍶㩫♲

䟃⽋䞾㑮㠦 ╖䞮㡂 ⼖䡫⮶㏣☚㠦 ➆⯎ 䟃⽋ἷⳊ 㦮 ⼖䢪⯒ ὖ㺆䞮㡖┺.

ٻ

51# ᵪ㚿ᨊ∷ᑮᨦ# ඊᣎ㘆# ᎒⸿⠢⡏⎆㚂#

514# ᒃ⢫# ᎒⸿⠢⡏⎆㚂#

㩫㩗㧎㧻㔲䠮₆(INSTRON5583) ⹥ ἶ㏣㨂⬢㔲 䠮₆(HSMTM)[6,7]⯒ 㧊㣿䞮㡂, 㹾㼊㣿 ἶṫ☚ ṫ

(a) 0^o(RD)

(b) 45^o(DD)

(c) 90^o(TD)

Fig. 2 Engineering stressstrain curves of DP780 at various strain rates

䕦㧎 TRIP590(1.2t)㢖 DP780(1.0t)㠦 ╖䞮㡂 㞫㡆⹿

䟻㦒⪲⿖䎆 0☚(RD), 45☚(DD), 90☚(TD)⹿䟻㠦 ╖ 䞮㡂 ┾㿫㧎㧻㔲䠮㦚 㔺㔲䞮㡖┺. ⼖䡫⮶ ㏣☚㠦

➆⯎ 㦧⩻⼖䡫⮶ ㍶☚ ⹥ 䟃⽋㦧⩻㦖 ṗṗ Fig.

1~2㢖 Table 1~2㢖 ṯ┺.

515# ∶⇛ᵪ㚿ᨊỮ#

㏢㎇⼖䡫⮶゚(r-Ṩ)㦖 ⚦℮⹿䟻㦮 ㏢㎇ 㰚⼖䡫⮶

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w l

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d

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穢穢剳暒昷儆击穟箒滆V洢YW劒G 洢_笾SGYWXX噊V\`^G G Table 1 Yield stress of TRIP590 with respect to

the strain rates[MPa]

Loading Direction

Strain rate [/sec]

0.001 0.01 0.1 1 10 100 RD 360 392 413 433 460 491 DD 405 418 438 451 468 485 TD 392 413 424 441 464 493

Table 2 Yield stress of DP780 with respect to the strain rates [MPa]

Loading Direction

Strain rate [/sec]

0.001 0.01 0.1 1 10 100 RD 457 488 530 548 550 566 DD 444 472 518 535 545 573 TD 460 492 517 537 559 580

Table 3 r-value of TRIP590 with respect to the strain rates

Loading Direction

Strain rate [/sec]

0.001 0.01 0.1 1 10 100 RD 1.02 0.97 0.94 1.02 1.06 1.10 DD 0.76 0.72 0.70 0.79 0.81 0.87 TD 1.06 1.03 0.98 1.06 1.10 1.15

Table 4 r-value of DP780 with respect to the strain rates

Loading Direction

Strain rate [/sec]

0.001 0.01 0.1 1 10 100 RD 0.79 0.73 0.66 0.81 0.82 0.86 DD 0.99 0.93 0.86 1.02 1.05 1.09 TD 0.80 0.78 0.70 0.84 0.86 0.89

㡂₆㍲ l㦖 ₎㧊⹿䟻, w⓪ 䙃⹿䟻, t⓪ ⚦℮⹿

䟻 ㏢㎇ 㰚⼖䡫⮶㧊Ⳇ Ⱎ㰖Ⱏ 䟃㦖 㼊㩗㧒㩫 㫆 Ị㠦 㦮䞮㡂 㥶☚♮㠞┺. r-Ṩ㦖 㨂⬢㦮 ㎇䡫㎇㦮 㻯☚㧊Ⳇ r-Ṩ㧊 䋆 㨂⬢⓪ ❪䝚✲⪲㧟㎇㧊 㤆㑮 䞮┺.

㧎㧻⹿䟻 ⹥ ⼖䡫⮶㏣☚㠦 ➆⯎ ㏢㎇⼖䡫⮶゚

⯒ 䁷㩫䞮₆ 㥚䞮㡂 ❪㰖䎎 㧊⹎㰖 䝚⪲㎎㕇 ₆

⻫㦚 㧊㣿䞮㡖┺[2]. 䁷㩫䞲 ㏢㎇⼖䡫⮶゚⓪ Table 3~4㠦 ⋮䌖⌊㠞┺.

61# ⠞᳓⇛# 㘗ᶟ⎇#

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䘟Ⳋ㦧⩻㌗䌲㠦㍲ Hill48 㧊㹾 䟃⽋㔳㦖 ┺㦢ὒ ṯ┺[4].

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) 1 ( 2

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㎇ 䟃⽋㔳㦚 㩲㞞䞮㡖┺[5].

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⓪ 㔳 (5)㢖 ṯ㧊 㩫㦮♮⓪ ⚦ Ṳ㦮 ㍶䡫⼖䢮㦧⩻

䎦㍲㦮 㭒䂮㧊┺.

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7 2 1

66 22 21 12 11

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0 2 2 8 2

0 1 4 4 4

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0 3 / 2 0

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L L L L L L L L L L 㡂₆㍲

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\

\`_GV穢剳暒昷儆击穟箒滆V洢YW劒G 洢_笾SGYWXX噊G

0 15 30 45 60 75 90

0.0 0.8 0.9 1.0 1.1

1.2 TRIP590 1.2t, 0.001/sec

Normalized Yield Surface

Loading angle from RD[^o] Experimental data Hill48

Yld2000-2d

0 15 30 45 60 75 90

0.0 0.8 0.9 1.0 1.1

1.2 TRIP590 1.2t, 1/sec

Normalized Yield Surface

Loading angle from RD[^o] Experimental data Hill48

Yld2000-2d

0 15 30 45 60 75 90

0.0 0.8 0.9 1.0 1.1

1.2 TRIP590 1.2t, 100/sec

Normalized Yield Surface

Loading angle from RD[^o] Experimental data Hill48

Yld2000-2d

(a) 0.001/sec (b)1/sec (c) 100/sec Fig. 3 Normalized yield stress with the variation of loading angle from RD (TRIP590)

0 15 30 45 60 75 90

0.0 0.8 0.9 1.0 1.1 1.2

DP780 1.0t, 0.001/sec

Normalized Yield Surface

Loading angle from RD[^o] Experimental data Hill48

Yld2000-2d

0 15 30 45 60 75 90

0.0 0.8 0.9 1.0 1.1 1.2

DP780 1.0t, 1/sec

Normalized Yield Surface

Loading angle from RD[^o] Experimental data Hill48

Yld2000-2d

0 15 30 45 60 75 90

0.0 0.8 0.9 1.0 1.1 1.2

DP780 1.0t,100/sec

Normalized Yield Surface

Loading angle from RD[^o] Experimental data Hill48

Yld2000-2d

(a) 0.001/sec (b)1/sec (c) 100/sec Fig. 4 Normalized yield stress with the variation of loading angle from RD (DP780)

0 15 30 45 60 75 90

0.00 0.6 0.9 1.2 1.5

TRIP590 1.2t, 0.001/sec

r-value

Loading angle from RD[^o] Experimental data Hill48

Yld2000-2d

0 15 30 45 60 75 90

0.00 0.6 0.9 1.2 1.5

TRIP590 1.2t, 1/sec

r-value

Loading angle from RD[^o] Experimental data Hill48 Yld2000-2d

0 15 30 45 60 75 90

0.00 0.6 0.9 1.2 1.5

TRIP590 1.2t, 100/sec

r-value

Loading angle from RD[^o] Experimental data Hill48

Yld2000-2d

(a) 0.001/sec (b)1/sec (c) 100/sec Fig. 5 r-value with the variation of loading angle from RD (TRIP590)

0 15 30 45 60 75 90

0.00 0.6 0.9 1.2 1.5

DP780 1.0t, 0.001/sec

r-value

Loading angle from RD[^o] Experimental data Hill48

Yld2000-2d

0 15 30 45 60 75 90

0.00 0.6 0.9 1.2 1.5

DP780 1.0t, 1/sec

r-value

Loading angle from RD[^o] Experimental data Hill48

Yld2000-2d

0 15 30 45 60 75 90

0.00 0.6 0.9 1.2 1.5

DP780 1.0t, 100/sec

r-value

Loading angle from RD[^o] Experimental data Hill48

Yld2000-2d

G (a) 0.001/sec (b)1/sec (c) 100/sec

Fig. 6 r-value with the variation of loading angle from RD (DP780)

穢穢剳暒昷儆击穟箒滆V洢YW劒G 洢_笾SGYWXX噊V\``G G Table 5 Anisotropy coefficients of Yld2000-2d yield function for TRIP590

Strain rate [/sec] 1 2 3 4 5 6 7 8

0.001 1.1386 0.8042 1.0545 0.9543 0.9901 1.0545 0.8873 0.7810 0.01 1.0771 0.8809 1.0311 0.9698 0.9985 1.0311 0.9183 0.9048 0.1 1.0310 0.9414 1.0115 0.9863 1.0020 1.0115 0.9204 0.9245 1 1.0273 0.9668 1.0148 0.9869 0.9982 1.0148 0.9452 0.9463 10 1.0158 0.9918 1.0131 0.9897 0.9972 1.0131 0.9660 0.9984 100 1.0087 1.0103 1.0142 0.9895 0.9963 1.0142 0.9942 1.0573

Table 6 Anisotropy coefficients of Yld2000-2d yield function for DP780

Strain rate [/sec] 1 2 3 4 5 6 7 8

0.001 0.9810 0.9650 0.9815 1.0068 1.0116 0.9815 1.0232 1.0768 0.01 0.9659 0.9666 0.9781 1.0056 1.0162 0.9781 1.0180 1.0941 0.1 0.8981 1.0336 0.9493 1.0302 1.0204 0.9493 1.0008 1.0839 1 0.9374 1.0375 0.9695 1.0190 1.0115 0.9695 1.0202 1.0533 10 0.9968 0.9556 0.9921 0.9980 1.0098 0.9921 1.0139 1.0166 100 1.0216 0.9327 1.0020 0.9915 1.0063 1.0020 0.9990 0.9572

0☚, 45☚, 90☚ ⹿䟻㠦 ╖䞲 䟃⽋㦧⩻ὒ r-Ṩ, 㧊㿫䟃⽋㦧⩻㧊 㭒㠊㰖ἶ C₁₂cc C₂₁cc㦮 㫆Ị㦚 㧊 㣿䞮Ⳋ Yld2000-2d 䟃⽋ἷⳊ㦚 ῂ㎇䞶 㑮 㧞┺[8].

⽎ ⏒ⶎ㠦㍲⓪ 㧊㿫䟃⽋㦧⩻㦚 㔺䠮㦒⪲⿖䎆 㠑 㦚 㑮 㠜₆ ➢ⶎ㠦 㧊㿫䟃⽋㦧⩻ὒ 㞫㡆⹿䟻㦮䟃

⽋㦧⩻㧊 ṯ┺ἶ Ṗ㩫䞮㡖┺.

616# 㘗ᶟ⎇⠂# 㑳ಪ#

Table 1~4㦮 㔺䠮◆㧊䎆⯒ 㧊㣿䞮㡂 TRIP590ὒ DP780㠦 ╖䞮㡂 ┺㟧䞲 ⼖䡫⮶㏣☚㠦㍲ Hill48ὒ Yld2000-2d 䟃⽋㔳㦚 ῂ㎇䞮ἶ ⹿䟻㠦 ➆⯎ r-Ṩ

⹥ 䟃⽋㦧⩻㦚 㡞䁷䞮㡖┺. Fig. 3~4⓪ 䞮㭧⹿䟻㠦

➆⯎ 䟃⽋㦧⩻㦮 ⼖䢪⯒ ⋮䌖⌎ ộ㧊┺. 䟃⽋㦧⩻

㦖 㞫㡆⹿䟻㦮 䟃⽋㦧⩻㦒⪲ 㩫′䢪䞮㡂 ⋮䌖⌊

㠞┺. Hill48 䟃⽋䞾㑮⓪ ⚦ 㨂⬢㦮 㧊⹿㎇㦚 㩲╖

⪲ ⁒㌂䞮㰖 ⴑ䞮ἶ 45☚, 90☚ ⹿䟻㦮 䟃⽋㦧⩻

㡞䁷㠦 䋆 㡺㹾⯒ ⽊㧎┺. 䞮㰖Ⱒ Yld2000-2d 䟃

⽋䞾㑮⓪ 㭒㠊㰚 㔺䠮Ṩ㦚 㧮 ⁒㌂䞲┺. 㧊⓪ Yld2000-2d 䟃⽋䞾㑮㦮 Ἒ㑮⯒ ἆ㩫䞶 ➢ 45☚㢖 90☚㠦㍲㦮 䟃⽋㦧⩻㧊 ἶ⩺♮㠞₆ ➢ⶎ㧊┺.

Fig. 5~6⓪ 䞮㭧⹿䟻㠦 ➆⯎ r-Ṩ㦮 ⼖䢪⯒ ⋮䌖

⌎ ộ㧊┺. ⚦ 䟃⽋䞾㑮 ⳾⚦ 㔺䠮Ṩ㦚 㧮 㡞䁷䞲

┺. 㥚㦮 䘟Ṗ⪲⿖䎆 ⚦ 㨂⬢㦮 㧊⹿㎇㦚 Yld2000- 2d 䟃⽋䞾㑮⪲ ⁒㌂䞮⓪ ộ㧊 Ṗ㧻 㩗㩞䞮┺ἶ 䕦

┾䞮㡖┺.

71# ᵪ㚿ᨊ∷ᑮ♺# ᗚᨢ# ⠞᳓⇛⠂# ᵪ㛾#

Table 5~6㦖 TRIP590ὒ DP780㠦 ╖䞮㡂 Yld2000- 2d 䟃⽋䞾㑮㦮 Ἒ㑮⯒ ⋮䌖⌎ ộ㧊┺. Yld2000-2d 䟃⽋䞾㑮㦮 Ἒ㑮Ṗ ⳾⚦ 1㧊Ⳋ ❇⹿㎇ 㨂⬢⯒ 㦮

⹎䞲┺. ⚦ 㨂⬢ ⳾⚦ ⼖䡫⮶㏣☚Ṗ 㯳Ṗ䞶㑮⪳

㧊⹿㎇ Ἒ㑮Ṗ 1㠦 Ṗ₢㤢㰖⓪ ộ㦚 䢫㧎䞶 㑮 㧞┺. 㧊⓪ ⼖䡫⮶㏣☚Ṗ 㯳Ṗ䞮Ⳋ 㨂⬢㦮 㧊⹿㎇

㧊 Ṧ㏢䞮⓪ ộ㦚 㦮⹎䞲┺. Fig. 7~8㦖TRIP590ὒ DP780㦮 ⼖䡫⮶㏣☚㠦 ➆⯎ 㽞₆ 䟃⽋ἷⳊ㦚 ⋮ 䌖⌎ ộ㧊┺. ⼖䡫⮶㏣☚㦮 㯳Ṗ㠦 ➆⧒ 䟃⽋㦧⩻

㧊 㯳Ṗ䞮ἶ ㏢㎇⼖䡫⮶゚Ṗ ⼖䢪䞮⸖⪲ ⼖䡫⮶

㏣☚Ṗ 㯳Ṗ䞾㠦 ➆⧒ 䟃⽋ἷⳊ㧊 䢫㧻♾ὒ ▪⿞

㠊 䟃⽋ἷⳊ㦮 䡫㌗㧊 ⼖䢪䞮⓪ ộ㦚 ὖ㺆䞶 㑮 㧞┺.

81# ൚# ᤊ#

#

⽎ ⏒ⶎ㠦㍲⓪ 㹾㼊㣿 ṫ䕦㦒⪲ 㝆㧊ἶ 㧞⓪ TRIP590ὒ DP780㦮 㩫㩗 ⹥ ☯㩗 ┾㿫㧎㧻㔲䠮㦚 䐋䞮㡂 ⼖䡫⮶㏣☚㢖 㧎㧻⹿䟻㠦 ➆⯎ 䟃⽋㦧⩻ ⹥

㏢㎇⼖䡫⮶゚⯒ 㠑㠞┺. 㧊⯒ ⹪䌫㦒⪲ Hill48ὒ Yld2000-2d 䟃⽋䞾㑮⯒ 䘟Ṗ䞮ἶ Yld2000-2d 䟃⽋

䞾㑮Ṗ ⚦ 㨂⬢㦮 㧊⹿㎇㦚 㧮 ⁒㌂䞶 㑮 㧞㦢㦚 䢫㧎䞮㡖┺. ⼖䡫⮶㏣☚㠦 ➆⯎ 㨂⬢㦮 㧊⹿㎇ ⼖

]

]WWGV穢剳暒昷儆击穟箒滆V洢YW劒G 洢_笾SGYWXX噊G Fig. 7 Yld2000-2d Loci of TRIP590 at various strain

rates

Fig. 8 Yld2000-2d Loci of DP780 at various strain rates

䢪⯒ ὖ㺆䞲 ἆὒ ⼖䡫⮶㏣☚Ṗ 㯳Ṗ䞮Ⳋ 㨂⬢㦮 㧊⹿㎇㧊 Ṧ㏢䞮⓪ ộ㦚 ὖ㺆䞮㡖㦒Ⳇ ⼖䡫⮶㏣

☚Ṗ 㯳Ṗ䞾㠦 ➆⧒ 䟃⽋ἷⳊ㧊 䢫㧻♾ὒ ☯㔲㠦 䡫㌗㧊 ⼖䢪䞮⓪ ộ㦚 䢫㧎䞮㡖┺. 㧊㢖 ṯ㧊 ⼖ 䡫⮶㏣☚㠦 ➆⧒ 㨂⬢㦮 㧊⹿㎇㧊 ⼖䢪䞮⸖⪲ 䟊

㍳ὒ㩫㠦㍲ ⼖䡫⮶㏣☚㠦 ➆⯎ 㧊⹿㎇㦮 ⼖䢪⯒

ἶ⩺䞮㡂㟒 䟊㍳㦮 㩫䢫☚⯒ 䟻㌗㔲䌂 㑮 㧞┺.G Ⳣ ඊ ᯢ 㙶

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