东北大学学报:自然科学版  2016, Vol. 37 Issue (10): 1403-1406  
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关小军, 付杰. 三叉晶界优先形核模型及其动态再结晶仿真[J]. 东北大学学报:自然科学版, 2016, 37(10): 1403-1406.
[复制中文]
GUAN Xiao-jun , FU Jie . Preferential Nucleation Model at Triple Junction and Its Dynamic Recrystallization Simulation[J]. Journal Of Northeastern University Nature Science, 2016, 37(10): 1403-1406. DOI: 10.3969/j.issn.1005-3026.2016.10.008.
[复制英文]

基金项目

教育部高等学校博士学科点专项科研基金资助项目(200804220021)

作者简介

关小军(1952-), 男, 湖南湘阴人, 山东大学教授。

文章历史

收稿日期: 2015-06-16
三叉晶界优先形核模型及其动态再结晶仿真
关小军1,2, 付杰1,2    
1.山东大学 材料液固结构演变与加工教育部重点实验室, 山东 济南 250061;
2.山东大学 材料科学与工程学院, 山东 济南 250061
摘要: 为了实现三叉晶界处动态再结晶优先形核,基于元胞自动机的摩尔邻居,提出一个辨识三叉晶界处元胞的方法和三叉晶界优先形核模型,通过HPS485wf钢动态再结晶过程的元胞自动机仿真检验了该模型的合理性和应用效果.研究结果表明,所提方法和优先形核模型可有效用于动态再结晶过程仿真;与传统模型相比,其仿真结果不仅保持了由传统模型仿真得到的动态再结晶的多轮次演变过程、组织形貌特征、“S型”的动态再结晶面积分数-应变曲线和全程流变应力模拟精度(0.1%),而且能够在所辨识三叉晶界处实现优先形核,更真实地反映了动态再结晶的形核现象.
关键词动态再结晶    三叉晶界    优先形核    元胞自动机    仿真    
Preferential Nucleation Model at Triple Junction and Its Dynamic Recrystallization Simulation
GUAN Xiao-jun1,2, FU Jie1,2    
1.Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China;
2.School of Materials Science and Engineering, Shandong University, Jinan 250061, China
Corresponding author: GUAN Xiao-jun, E-mail: xjguan@sdu.edu.cn
Abstract: In order to perform preferential nucleation at triple junction during dynamic recrystallization (DRX), a method of identifying the cell existed at triple junction and a preferential nucleation model at triple junction were proposed on the basis of the Moore neighbor of cellular automata. The rationality and application of the model were proved by simulating the DRX process of HPS485wf steel. The results showed that the proposed method and model have the ability to simulate the DRX more effectively. Compared with those from the traditional models, the results from the present model don't only maintain the evolution of multiple rounds, microstructural feature, the "S-type" curve between area fraction and strain, the simulated flow stress with an accuracy of 0.1% in the process of DRX, and also reveal the preferential nucleation at triple junction, which would provide a more realistic DRX nucleation.
Key Words: dynamic recrystallization    triple junction    preferential nucleation    cellular automata    simulation    

材料热变形时,三叉晶界处比普通晶界处的应力集中程度更大、动态再结晶形核优势更强[1-3].但是,迄今为止,单相金属材料动态再结晶模拟研究中均采用晶界形核假设而忽略了三叉晶界优先形核现象[4-9].为了解决这一问题,本文提出了基于元胞自动机(CA)的二维四方形几何模型的摩尔邻居来辨识三叉晶界处元胞的方法及其相应的优先形核模型,以HPS485wf钢为研究对象,结合前期所建的瞬态形核率和回复阶段位错密度优化的动态再结晶CA模型[9-10],探讨了这一方法及其形核模型的合理性.

1 三叉晶界优先形核模型的建立 1.1 三叉晶界处元胞的识别

在CA模拟中,晶粒为取向数相同的元胞集合.若某一元胞与其邻居取向不同,则认为此元胞位于晶界处;若某一元胞中任意相邻的三个元胞中有两个取向不同且也与其取向不同,则认为此元胞位于三叉晶界处.

图 1为位于三叉晶界处的元胞识别图.可见,对于二维四方形CA空间的摩尔型邻居而言,若元胞C5的取向数SQ5与其邻居元胞i的取向数SQi满足下列16组布尔逻辑关系中任意一组时,即

图 1 位于三叉晶界处的元胞识别图 Fig.1 Identification of cells at triple junction

(a) SQ5SQ2SQ2SQ1SQ1SQ4SQ5=SQ4

(b) SQ5SQ4SQ5SQ2SQ4SQ1SQ1=SQ2

(c) SQ5SQ4SQ4SQ1SQ1SQ2SQ5=SQ2

(d) SQ5SQ4SQ5SQ2SQ1SQ2SQ1=SQ4

(e) SQ5SQ2SQ2SQ3SQ3SQ6SQ5=SQ6

(f) SQ5SQ6SQ5SQ2SQ3SQ6SQ2=SQ3

(g) SQ5SQ2SQ2SQ3SQ5SQ6SQ3=SQ6

(h) SQ5SQ6SQ2SQ3SQ3SQ6SQ5=SQ2

(i) SQ5SQ4SQ5SQ8SQ4SQ7SQ7=SQ8

(j) SQ5SQ8SQ7SQ8SQ4SQ7SQ5=SQ4

(k) SQ5SQ4SQ7SQ8SQ4SQ7SQ5=SQ8

(l) SQ5SQ8SQ5SQ4SQ7SQ8SQ4=SQ7

(m) SQ5SQ8SQ5SQ6SQ6SQ9SQ8=SQ9

(n) SQ5SQ8SQ8SQ9SQ6SQ9SQ5=SQ6

(o) SQ5SQ8SQ5SQ6SQ8SQ9SQ6=SQ9

(p) SQ5SQ6SQ8SQ9SQ6SQ9SQ5=SQ8.

则认为元胞C5位于三叉晶界处.

1.2 三叉晶界优先形核模型及其模拟流程

当满足形核条件时,位于三叉晶界处的元胞优先、随机形核;其次,若形核数量大于三叉晶界处的元胞数量,则位于普通晶界处的元胞随机形核.显然,与传统的动态再结晶形核模型相比,本文提出的动态再结晶形核模型在保持晶界随机形核的同时,又有在三叉晶界处优先形核的特点.

鉴于多轮次动态再结晶发生的情况[8-9],形核前后的元胞取向数Si, jSi, j的赋值范围分别为

(1)
(2)

式中:n为元胞当前所处的动态再结晶轮次;SQmax为元胞所在晶粒的最大取向数.

形核模拟流程如下:

1)  当应变量达到临界应变εc后,设置元胞选择次数m=0,动态再结晶轮次变量n=1,已形核元胞的统计数Nn=0(n=1, 2, …, nmax,为动态再结晶轮次;nmax为当前可发生动态再结晶的最高轮次).

2)  进行三叉晶界形核的判断和实施过程.令m=m+1,随机选择一个取向数为Si, j的元胞(i, j),判断其是否同时满足位于三叉晶界处(具有图 1的任意一组关系)和属于第n-1轮次动态再结晶.若满足,则该元胞(i, j)开始形核且被随机赋予新的取向Si, j,位错密度ρi, j降低至ρ0,所对应的动态再结晶轮次的形核元胞数Nn=Nn+1,进入下一步骤;若不满足,随机选择其他元胞,重复上述过程,直至m达到其总次数mmax为止.

3)  判断Nn=n, 若成立,执行步骤6);否则,进入下一步骤.

4)  判断m=mmax,若成立,进入下一步骤;反之,返回步骤2).

5)  进行普通晶界形核的判断和实施过程(与三叉晶界形核过程相似),直至Nn=n.

6)  判断当前的所有动态再结晶轮次的形核是否完成(n=nmax),若完成,形核模拟流程结束,进入后序的晶粒长大阶段模拟流程;反之,循环运行步骤2)~步骤6),直至n=nmax.

2 仿真检验

为了检验本文所提出的三叉晶界优先形核模型的可行性,在文献[9-10]的非恒形核率与动态回复位错密度优化的动态再结晶CA模型(模型A)中,引入三叉晶界优先形核模型而得到改进的动态再结晶CA模型(模型B),且分别采用两种模型对相同变形条件的HPS485wf钢动态再结晶过程进行了仿真.在模型B及其模拟流程中,除了三叉晶界优先形核取代了晶界形核之外,其余均与模型A相同.

鉴于CA模型的随机特点,两种模型均进行了5次模拟,且分别对它们的微观组织演变、应力相对误差平方δ、真应力-真应变曲线和动态再结晶面积分数进行了分析与比较.

2.1 模拟条件

模拟区域及其网格划分同文献[10],元胞选择总次数mmax为40 000,采用周期性边界条件.模拟的变形参数:T=1 373 K,=0.1 s-1εe=0.8.模拟的初始组织平均晶粒尺寸为50 μm,与热模拟实验值相似[11],由晶粒正常长大CA模型仿真得到[12].初始位错密度为109 m-2,最大晶粒取向数SQmax为180.相关模拟参数[9-10]:△CASm=80,CAS0=800,δ0=0.1%.材料参数见文献[13].

2.2 模拟结果与分析

图 2为两种模型模拟的热压缩HPS485wf钢动态再结晶过程不同时刻的微观组织演变.

图 2 两种模型所模拟的微观组织随应变的变化(T=1 373 K, =0.1 s-1) Fig.2 Microstructural evolution simulated by model A and B, respectively at T=1 373 K and =0.1 s-1 (a1, b1)-ε=0.12; (a2, b2)-ε=0.24; (a3, b3)-ε=0.8; (a1~a3)-模型A; (b1~b3)-模型B.

图 2a1~2a3可知,在模型A所模拟的动态再结晶过程中,再结晶晶核主要在晶界处生成,只有个别晶核生成于三叉晶界处;由图 2b1~2b3可知,在模型B所模拟的动态再结晶过程中,再结晶晶核优先生成于三叉晶界处,只在动态再结晶后期看到个别晶核生成于普通晶界.可见,本文所提出的三叉晶界处元胞识别方法及其优先形核模型行之有效.此外,除了形核位置不同,两种模型所模拟的组织演变过程相同,均呈现了动态再结晶组织形貌特征,变形结束时已发生9轮动态再结晶.这表明三叉晶界优先形核模型不影响动态再结晶演变及其组织形貌特征,只是致使随机形核局面发生一些有序改变.两种模型所得到的动态再结晶应力-应变曲线和面积分数-应变曲线近乎相同,两者的动态再结晶应力-应变曲线都均匀分布在热模拟实验曲线附近,而它们的动态再结晶面积分数-应变曲线都与热模拟实验曲线的变化趋势一致,呈典型的“S型”[10].

不论是各模拟次数的数值,还是5次模拟次数的平均数值,两种模型的系统平均流变应力值与热模拟实验应力值相对误差平方的最大值δmax及其平均值δ均未超过设定的模拟精度0.1%,且两者的模拟精度差别很小.

综上分析,模型B只是实现了动态再结晶在三叉晶界处优先形核,对于动态再结晶的演变过程、组织形貌特征、全程流变应力的模拟精度没有影响.

3 结论

1)  基于二维元胞自动机的摩尔邻居,提出了三叉晶界处元胞的识别方法及其优先形核原则,据此改进了传统的动态再结晶元胞自动机形核模型,并通过HPS485wf钢的动态再结晶仿真探讨了这一模型的实用效果.

2)  仿真结果证实了所改进的模型不仅呈现了更加符合实际的三叉晶界优先形核现象,而且不影响动态再结晶的演变过程、组织形貌特征和全程流变应力的模拟精度.

参考文献
[1] Chen C R, Li S X, Wen J L, et al. Finite element analysis about effects of stiffness distribution on stresses and elastic strain energy near the triple junction in a tricrystal[J]. Materials Science and Engineering A , 2000, 282 (1) : 170–176.
[2] Miura H, Andiarwanto S, Sato K, et al. Preferential dynamic nucleation at triple junction in copper tricrystal during high-temperature deformation[J]. Materials Transactions , 2002, 43 (3) : 494–500. DOI:10.2320/matertrans.43.494
[3] Hallberg H, Ristinmaa M. Microstructure evolution influenced by dislocation density gradients modeled in a reaction-diffusion system[J]. Computational Materials Science , 2013, 67 (2) : 373–383.
[4] Goetz R L, Seetharaman V. Modeling dynamic recrystallization using cellular automata[J]. Scripta Materialia , 1998, 38 (3) : 405–413. DOI:10.1016/S1359-6462(97)00500-9
[5] Qian M, Guo Z X. Cellular automata simulation of microstructural evolution during dynamic recrystallization of an HY-100 steel[J]. Materials Science and Engineering A , 2004, 365 (1/2) : 180–185.
[6] Yazdipour N, Hodgson P D, Davies C H J. Microstructure evolution modeling during and after deformation in 304 austenitic stainless steel through cellular automaton approach[J]. International Journal for Multiscale Computational Engineering , 2009, 7 (5) : 381–393. DOI:10.1615/IntJMultCompEng.v7.i5
[7] Chen F, Cui Z S, Liu J, et al. Modeling and simulation on dynamic recrystallization of 30Cr2Ni4MoV rotor steel using the cellular automaton method[J]. Modeling and Simulation in Materials Science and Engineering , 2009, 17 (7) : 5015–5022.
[8] Yu B J, Guan X J, Wang L J, et al. Mesoscale simulation of discontinuous dynamic recrystallization using the cellular automaton method[J]. ACTA Metallurgica Sinica (English Letters) , 2011, 24 (4) : 287–294.
[9] 关小军, 付杰, 禹宝军, 等. 一种确定动态再结晶瞬态形核率的模拟方法[J]. 材料热处理学报 , 2015, 36 (2) : 231–236.
( Guan Xiao-jun, Fu Jie, Yu Bao-jun, et al. A method for identifying transient nucleation rate of dynamic recrystallization by simulation[J]. Transactions of Materials and Heat Treatment , 2015, 36 (2) : 231–236. )
[10] 付杰.单相材料动态再结晶元胞自动机模型的改进[D].济南:山东大学, 2014.
( Fu Jie.Improvement of dynamic recrystallization model for single-phase materials using cellular automata method[D].Jinan:Shandong University, 2014. )
[11] 王丽君, 关小军, 赵健, 等. HPS485wf桥梁钢奥氏体动态再结晶规律及其本构关系模型[J]. 材料热处理学报 , 2010, 31 (10) : 154–158.
( Wang Li-jun, Guan Xiao-jun, Zhao Jian, et al. Dynamic recrystallization and mathematic model of HPS485wf steel[J]. Transactions of Materials and Heat Treatment , 2010, 31 (10) : 154–158. )
[12] 麻晓飞, 关小军, 刘运腾, 等. 基于改进转变规则的晶粒长大CA模型[J]. 中国有色金属学报 , 2008, 18 (1) : 38–44.
( Ma Xiao-fei, Guan Xiao-jun, Liu Yun-teng, et al. Cellular automaton model for grain growth based on a modified transition rule[J]. Transactions Nonferrous Metals Society China , 2008, 18 (1) : 38–44. )
[13] 王丽君.桥梁钢热压缩变形动态再结晶行为的双尺度模拟[D].济南:山东大学, 2011.
( Wang Li-jun.Simulation on dynamic recrystallization behavior of bridge steels in two scales[D].Jinan:Shandong University, 2011. )