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A format of f(ik,jk ) = Es (ide )2(1-(jre )2) to express cold deformed stored energy is suggested in a phase-field model for simulating recrystallization in alloys. Using AZ31 magnesium alloy as an example, the recrystallization process is simulated by the new model, and the simulation results are in good agreement with experimental measurements. The nucleation process of recrystallization is realized for the first time by the model based on the physical background. The simulation results show that the grain growth of a cold deformed alloy in the annealing process indicates automatically two stages: recrystallization driven by the restored energy and thermal growth driven by boundary energy. A theoretical time spent in finishing recrystallization, obtained by simulation, is found to be 2/3 of that obtained by industrial practice. The mechanism and the experimental results about the influence of cold deformation on subgrain size and stored energy are examined, and the experimental results are introduced into the simulation. The common experimental phenomenon shows that there is a peak at the critical strain on the curve of recrystallized grain size versus cold strain. A theoretical explaination to the mechanism of the peak occurrence is also discussed.
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Keywords:
- phase field method /
- nucleation /
- stored energy /
- recrystallization
[1] Liss K D, Garbe U, Li H, Schambron T, Almer J D, Yan K 2009 Adv. Eng. Mater. 11 637
[2] Radhakrishnan B, Sarma B, Zacharia T 1998 Acta Mater. 46 4415
[3] Kugler G, Turk R 2006 Comput. Mater. Sci. 37 284
[4] Raabe D, Becker R C 2000 Simul. Mater. Sci. Eng. 8 445
[5] Wang M T, Zong B Y, Wang G 2008 J. Mater. Sci. Technol. 24 829
[6] Zong Y P, Wang M T, Guo W 2009 Acta Phys. Sin. 58 S161 (in Chinese) [宗亚平, 王明涛, 郭巍 2009 58 S161]
[7] Zhang X G, Zong Y P, Wang M T, Wu Y 2011 Acta Phys. Sin. 60 068201 (in Chinese) [张宪刚, 宗亚平, 王明涛, 吴艳 2011 60 068201]
[8] Gao Y J, Luo Z R, Hu X Y, Huang C G 2010 Acta Metall. Sin. 46 1161 (in Chinese) [高英俊, 罗志荣, 胡项英, 黄创高 2010 金属学报 46 1161]
[9] Wang G, Xu D S, Yang R 2009 Acta Phys. Sin. 58 S343 (in Chinese) [王刚, 徐东升, 杨锐 2009 58 S343]
[10] Takaki T, Tomita I Y 2010 Int. J. Mech. Sci. 52 320
[11] Cahn J W 1961 Acta Metall. 9 795
[12] Gunton J D, Miguel M S, Sahni P S 1983 Phase Transitions and Critical Phenomena (London: Academic Press) pp267---466
[13] Moreau G, Cornet J A, Calais D 1971 J. Nucl. Mater. 38 197
[14] Watari H, Haga T, Koga N, Davey K 2007 J. Mater. Process. Technol. 192 300
[15] Miyashita Y, Borrisutthekul R, Chen J, Mutoh Y 2007 Key Eng. Mater. 353 1956
[16] Verdier M, Groma I, Flandin L, Lendvai J, Brechet Y, Guyot P 1997 Scripta Mater. 37 449
[17] Liu R C, Wang L Y, Gu L G, Huang G S 2004 Light Alloy Fabr. Technol. 32 22 (in Chinese) [刘饶川, 汪凌云, 辜蕾钢,黄光胜 2004 轻合金加工技术 32 22]
[18] Langford G, Cohen M 1969 ASM Trans. Quart. 62 623
[19] Doherty R D, Hughes D A, Humphreys F J, Jonas J J, Juul J D, Kassner M E, King W E, McNelley T R, McQueen H J, Rollett A D 1997 Mater. Sci. Eng. A 238 219
[20] Hansen N, Ralph B 1982 Acta Metall. 30 411
[21] Belyakov A, Sakai T, Miura H, Tsuzakit K 2001 Philos. Mag. A 81 2629
[22] Barnett M R, Keshavarz Z, Beer A G, Atwell D 2004 Acta Mater. 52 5093
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[1] Liss K D, Garbe U, Li H, Schambron T, Almer J D, Yan K 2009 Adv. Eng. Mater. 11 637
[2] Radhakrishnan B, Sarma B, Zacharia T 1998 Acta Mater. 46 4415
[3] Kugler G, Turk R 2006 Comput. Mater. Sci. 37 284
[4] Raabe D, Becker R C 2000 Simul. Mater. Sci. Eng. 8 445
[5] Wang M T, Zong B Y, Wang G 2008 J. Mater. Sci. Technol. 24 829
[6] Zong Y P, Wang M T, Guo W 2009 Acta Phys. Sin. 58 S161 (in Chinese) [宗亚平, 王明涛, 郭巍 2009 58 S161]
[7] Zhang X G, Zong Y P, Wang M T, Wu Y 2011 Acta Phys. Sin. 60 068201 (in Chinese) [张宪刚, 宗亚平, 王明涛, 吴艳 2011 60 068201]
[8] Gao Y J, Luo Z R, Hu X Y, Huang C G 2010 Acta Metall. Sin. 46 1161 (in Chinese) [高英俊, 罗志荣, 胡项英, 黄创高 2010 金属学报 46 1161]
[9] Wang G, Xu D S, Yang R 2009 Acta Phys. Sin. 58 S343 (in Chinese) [王刚, 徐东升, 杨锐 2009 58 S343]
[10] Takaki T, Tomita I Y 2010 Int. J. Mech. Sci. 52 320
[11] Cahn J W 1961 Acta Metall. 9 795
[12] Gunton J D, Miguel M S, Sahni P S 1983 Phase Transitions and Critical Phenomena (London: Academic Press) pp267---466
[13] Moreau G, Cornet J A, Calais D 1971 J. Nucl. Mater. 38 197
[14] Watari H, Haga T, Koga N, Davey K 2007 J. Mater. Process. Technol. 192 300
[15] Miyashita Y, Borrisutthekul R, Chen J, Mutoh Y 2007 Key Eng. Mater. 353 1956
[16] Verdier M, Groma I, Flandin L, Lendvai J, Brechet Y, Guyot P 1997 Scripta Mater. 37 449
[17] Liu R C, Wang L Y, Gu L G, Huang G S 2004 Light Alloy Fabr. Technol. 32 22 (in Chinese) [刘饶川, 汪凌云, 辜蕾钢,黄光胜 2004 轻合金加工技术 32 22]
[18] Langford G, Cohen M 1969 ASM Trans. Quart. 62 623
[19] Doherty R D, Hughes D A, Humphreys F J, Jonas J J, Juul J D, Kassner M E, King W E, McNelley T R, McQueen H J, Rollett A D 1997 Mater. Sci. Eng. A 238 219
[20] Hansen N, Ralph B 1982 Acta Metall. 30 411
[21] Belyakov A, Sakai T, Miura H, Tsuzakit K 2001 Philos. Mag. A 81 2629
[22] Barnett M R, Keshavarz Z, Beer A G, Atwell D 2004 Acta Mater. 52 5093
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