Fe2C 合金中形变诱导动态相变的蒙特卡罗模拟3 - 沈阳材料科学国家 ...

58 2009 6 

100023290Π2009Π58 ()ΠS169208 

 

ACTA PHYSICA SINICA 

Vol. 58 ,Special ,June ,2009 

ν 2009 Chin. Phys. Soc. 

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PACC: 6470 , 8110 , 8140 

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g E2mail : nmxiao @imr. ac. cn 

© 1994-2009 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net

S 170 

58 

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31 

,Fe20111wt %C 1300 K 

10 min. MC , 

800 400 , 

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S 172 

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S 174 

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[1] Weng Y Q 2003 Ultrafine Grained Steel ( Beijing : Metallurgical 

Industry Press) p9 (in Chinese) [ 2003 (: 

) 9 ] 

[2] Yada H , Matsumura Y, Nakajima K 1984 United State Patent 

4466842 

[3] Hodgson P D , Hickson M R , Gibbs R K 2000 United State Patent 

6027587 

[4] Ferreira J L , de Melo T M F , Bott I S , Santos D B , Rios P R 2007 

ISIJ Int. 47 1638 

[5] Srolovitz D J , Anderson M P , Sahni P S , Grest G S 1984 Acta 

Metall . 32 1429 

[6] Rollett A D , Luton M J , Srolovitz D J 1992 Acta Mater. 40 43 

[7] Xiao N M , Tong M M , Lan YJ , Li D Z , Li Y Y2006 Acta Mater. 

54 1265 

[8 ] Kaufman L , Clougherty E V , Weiss R J 1963 Acta Metall . 11 323 

[9 ] Read W , Shockley W 1950 Phys. Rev. 78 275 

[10] Mecking H , Kocks U F 1981 Acta Metall . 29 1865 

[11] Hatta N , Kokado J , Kikuchi S , Takuda H 1985 Steel Res. 56 575 

[12] Singh S B , Bhadeshia H K D H 1998 Mater. Sci. Tech. 14 832 

[13] Offerman S E , van Dijk N H , Sietsma J , Grigull S , Lauridesn E M , 

Margulies L , Poulsen H F , Rekveldt M T , van der Zwaag S 2002 

Science 298 1003 

[14] Son Y I , Lee Y K, Park K T 2006 Metall . Mater. Trans. A 37 

3161 

[15] Sun Z Q , Yang W Y, Qi J J , Hu A M 2002 Mater. Sci. Eng. A 

334 201 


S 176 

58 

Numerical inve stigation of deformation2induced dynamic 

transformation in Fe2C alloy by using a 

Q2state potts Monte Carlo model 3 

Xiao Na2Min g Li Dian2Zhong Li Yi2Yi 

( Shenyang National Laboratory for Materials Science , Institute of Metal Research , Chinese Academy of Sciences , Shenyang 110016 , China) 

(Received 16 December 2008 ; revised manuscript received 8 January 2009) 

Abstract 

The deformation induced dynamic transformation ( DIDT) of a Fe2C alloy above austenite transformation equilibrium 

temperature is simulated by using a Q2state potts Monte Carlo (MC) model. The austenite2to2ferrite transformation , dynamic 

recrystallization ( DRX) of austenite and ferrite , and the ferrite2to2austenite reverse transformation can be simulated 

simultaneously in the same MC model by building suitable MC transition rules. Meanwhile , an affine transformation model based 

on vector operation is also coupled with the MC model for the first time for tracking the changes in grain shape during dynamic 

transformation. The formation of ferrite during DIDT and the influence of austenite DRX on DIDT are simulated based on this MC 

model. The simulation results show that the competition between the DRX of austenite and the austenite2to2ferrite transformation 

causes the oscillation behaviour of ferrite kinetics. 

Keywords : deformation induced dynamic transformation , Monte Carlo model , dynamic recrystallization , mesoscopic simulation 

PACC: 6470 , 8110 , 8140 

3 Project supported by the National Natural Science Foundation of China ( Grant No. 50871109) . 

g E2mail : nmxiao @imr. ac. cn

Fe2C 合金中形变诱导动态相变的蒙特卡罗模拟3 - 沈阳材料科学国家 ...

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