Please wait a minute...
金属学报  2023, Vol. 59 Issue (8): 1042-1050    DOI: 10.11900/0412.1961.2023.00083
  研究论文 本期目录 | 过刊浏览 |
铁素体晶间变形协调与硬化行为模拟研究
徐永生, 张卫刚(), 徐凌超, 但文蛟
上海交通大学 船舶海洋与建筑工程学院 上海 200240
Simulation of Deformation Coordination and Hardening Behavior in Ferrite-Ferrite Grain Boundary
XU Yongsheng, ZHANG Weigang(), XU Lingchao, DAN Wenjiao
School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
引用本文:

徐永生, 张卫刚, 徐凌超, 但文蛟. 铁素体晶间变形协调与硬化行为模拟研究[J]. 金属学报, 2023, 59(8): 1042-1050.
Yongsheng XU, Weigang ZHANG, Lingchao XU, Wenjiao DAN. Simulation of Deformation Coordination and Hardening Behavior in Ferrite-Ferrite Grain Boundary[J]. Acta Metall Sin, 2023, 59(8): 1042-1050.

全文: PDF(2662 KB)   HTML
摘要: 

鉴于晶体塑性有限元法(CPFEM)在晶粒模型构造、取向设置和边界条件施加上的自由,对典型的铁素体-铁素体对称倾斜和扭转双晶模型实施不同应力状态下的变形模拟,分析应力状态和晶粒相对取向对晶界区应变分布和硬化行为的影响。结果表明,晶界区应变均匀程度由晶间滑移传递因子和滑移分切应力因子共同决定,晶粒的晶界区变形均匀程度与滑移传递因子正相关,主要由滑移传递因子控制晶间变形协调行为。然而,软取向晶粒(由应力状态和取向决定)的晶界区变形均匀,滑移传递因子对晶界区的应变协调不造成影响。此外,当滑移传递因子和滑移分切应力因子都很小时,易造成晶界区应变集中,使得晶间变形协调困难。因此,将滑移传递因子和滑移分切应力因子结合的晶间变形协调预测结果更为合理。双晶模型的流动应力与滑移分切应力因子负相关,晶界区非均匀变形易引发几何必需位错增殖,促进晶界处强化。

关键词 晶界晶体塑性变形协调硬化双晶模型    
Abstract

The deformation coordination of grain boundaries determines the nucleation and evolution of microvoids and affects the damage and fracture behavior of materials. However, grain boundary deformation is extremely complex and difficult to predict owing to the difference in intergranular orientation and grain stress state. Among them, two important ways of coordinating deformations are the accumulation of dislocations at grain boundaries and intergranular transfer. The geometric relationship of the activated intergranular slip systems determines the difficulty of slip transfer and the uniformity of deformation at grain boundaries. Moreover, owing to the complex grain boundary conditions of polycrystalline materials, it is difficult to accurately measure the actual stress state and deformation of grain boundaries, so there is a substantial discreteness between the experimentally observed slip transfer behavior and theoretical prediction results. Herein, based on the advantages of the crystal plasticity finite element method (CPFEM) in polycrystalline model construction, grain orientation, and mechanical boundary condition setting, the ferrite-ferrite symmetrical tilt and twist bicrystal models under different stress states was used to analyze the impact of stress state and relative grain orientation on grain boundary strain coordination and hardening behavior. The results show that the intergranular slip transfer factor and the resolve shear stress factor determine the strain uniformity at the grain boundary. The deformation uniformity at the grain boundary is positively correlated with the slip transfer factor, which mainly controls the intergranular deformation coordination behavior. However, the deformation at the grain boundaries of soft-oriented grains (determined by stress state and orientation) is uniform, and the slip transfer factor has little effect on strain coordination. When the slip transfer factor and the resolve shear stress factor are very small, strain concentration at the grain boundary easily occurs, making intergranular deformation coordination difficult. Therefore, the prediction results of intergranular deformation coordination combined with the slip transfer factor and resolving the shear stress factor are reasonable. In addition, the flow stress of the bicrystal model is negatively correlated with the slip shear stress factor, and the uneven deformation at the grain boundary easily causes geometrically necessary dislocations to proliferate and promote grain boundary hardening.

Key wordsgrain boundary    crystal plasticity    deformation coordination    hardening    bicrystal model
收稿日期: 2023-03-02     
ZTFLH:  TG142  
通讯作者: 张卫刚,wgzhang@sjtu.edu.cn,主要从事高强钢强韧化机理研究
Corresponding author: ZHANG Weigang, professor, Tel:13801875720, E-mail: wgzhang@sjtu.edu.cn
作者简介: 徐永生,男,1990年生,博士
图1  双晶模型:对称倾斜晶界的双晶模型及扭转晶界的双晶模型
AngleΣEuler angle / (o)
(axis: <100>)Right grainLeft grain
0.001(0 0 0)(0 0 0)
16.2625(180 8.13 180)(0 8.13 0)
22.6213(180 11.31 180)(0 11.31 0)
28.0717(180 14.04 180)(0 14.04 0)
36.875(180 18.44 180)(0 18.44 0)
53.135(180 26.57 180)(0 26.57 0)
61.9317(180 30.97 180)(0 30.97 0)
67.3813(180 33.69 180)(0 33.69 0)
73.7425(180 36.87 180)(0 36.87 0)
90.001(180 45 180)(0 45 0)
表1  <100>对称倾斜/扭转晶界双晶模型晶粒取向[27]
AngleΣEuler angle / (o)
(axis: <110>)Right grainLeft grain
0.001(0 0 0)(0 0 0)
26.5319(-135 13.26 135)(45 13.26 -45)
31.5927(-135 15.79 135)(45 15.79 -45)
38.949(-135 19.47 135)(45 19.47 -45)
50.4811(-135 25.24 135)(45 25.24 -45)
70.533(-135 35.26 135)(45 35.26 -45)
109.473(-135 54.74 135)(45 54.74 -45)
129.5211(-135 64.76 135)(45 64.76 -45)
141.069(-45 70.53 135)(45 70.53 -45)
148.4127(-135 74.21 135)(45 74.21 -45)
180.001(-135 90 135)(45 90 -45)
表2  <110>对称倾斜/扭转晶界双晶模型取向[27]
AngleΣEuler angle / (o)
(axis: <111>)Right grainLeft grain
0.001(0 0 0)(0 0 0)
13.1719(-136.9 5.37 133.1)(46.9 5.37 -43.1)
21.797(-138.1 8.89 131.8)(48.1 8.89 -41.8)
27.8013(-139.0 11.34 131.0)(49.0 11.34 -41.0)
32.2013(-139.7 13.13 130.3)(49.7 13.1 -40.3)
38.217(-140.5 15.6 129.5)(50.5 15.6 -39.5)
46.8219(-141.8 19.1 128.2)(51.8 19.1 -38.2)
60.001(-143.8 24.4 126.2)(53.8 24.4 -36.2)
表3  <111>对称倾斜/扭转晶界双晶模型取向[27]
图2  双晶模型不同应力状态加载示意图
图3  不同应力状态下晶界区变形及其控制因素随倾转角度演化曲线
图4  <110>对称倾斜晶界(70.53°,(111)<110>Σ3)单轴拉伸时晶界区应变云图
图5  晶界区几何必需位错(GND)密度随距离和倾转角演化曲线
图6  晶界区应变比与滑移传递因子m、m*以及滑移分切应力因子散点图
图7  晶界区流动应力与滑移分切应力因子关系
1 Roters F, Eisenlohr P, Hantcherli L, et al. Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications [J]. Acta Mater., 2010, 58: 1152
doi: 10.1016/j.actamat.2009.10.058
2 Soer W A, Aifantis K E, De Hosson J T M. Incipient plasticity during nanoindentation at grain boundaries in body-centered cubic metals [J]. Acta Mater., 2005, 53: 4665
doi: 10.1016/j.actamat.2005.07.001
3 Soer W A, De Hosson J T M. Detection of grain-boundary resistance to slip transfer using nanoindentation [J]. Mater. Lett., 2005, 59: 3192
doi: 10.1016/j.matlet.2005.03.075
4 Aifantis K E, Konstantinidis A A. Yielding and tensile behavior of nanocrystalline copper [J]. Mater. Sci. Eng., 2009, A503: 198
5 Gurtin M E. A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations [J]. J. Mech. Phys. Solids, 2002, 50: 5
doi: 10.1016/S0022-5096(01)00104-1
6 Okumura D, Higashi Y, Sumida K, et al. A homogenization theory of strain gradient single crystal plasticity and its finite element discretization [J]. Int. J. Plast., 2007, 23: 1148
doi: 10.1016/j.ijplas.2006.11.001
7 Ohno N, Okumura D, Shibata T. Grain-size dependent yield behavior under loading, unloading and reverse loading [J]. Int. J. Mod. Phys., 2008, 22B: 5937
8 Ma A, Roters F, Raabe D. A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations [J]. Acta Mater., 2006, 54: 2169
doi: 10.1016/j.actamat.2006.01.005
9 Ma A, Roters F, Raabe D. On the consideration of interactions between dislocations and grain boundaries in crystal plasticity finite element modeling—Theory, experiments, and simulations [J]. Acta Mater., 2006, 54: 2181
doi: 10.1016/j.actamat.2006.01.004
10 Schiotz J. Mechanical deformation of nanocrystalline materials [J]. Philos. Mag. Lett., 1996, 74: 339
doi: 10.1080/095008396180065
11 Guo Y, Collins D M, Tarleton E, et al. Dislocation density distribution at slip band-grain boundary intersections [J]. Acta Mater., 2020, 182: 172
doi: 10.1016/j.actamat.2019.10.031
12 Livingston J D, Chalmers B. Multiple slip in bicrystal deformation [J]. Acta Metall. 1957, 5: 322
doi: 10.1016/0001-6160(57)90044-5
13 Clark W A T, Wagoner R H, Shen Z Y, et al. On the criteria for slip transmission across interfaces in polycrystals [J]. Scr. Metall. Mater., 1992, 26: 203
doi: 10.1016/0956-716X(92)90173-C
14 Luster J, Morris M A. Compatibility of deformation in two-phase Ti-Al alloys: Dependence on microstructure and orientation relationships [J]. Metall. Mater. Trans., 1995, 26A: 1745
15 Sun J, Jin L, Dong J, et al. Towards high ductility in magnesium alloys—The role of intergranular deformation [J]. Int. J. Plast., 2019, 123: 121
doi: 10.1016/j.ijplas.2019.07.014
16 Haouala S, Alizadeh R, Bieler T R, et al. Effect of slip transmission at grain boundaries in Al bicrystals [J]. Int. J. Plast., 2020, 126: 102600
doi: 10.1016/j.ijplas.2019.09.006
17 Bieler T R, Eisenlohr P, Zhang C, et al. Grain boundaries and interfaces in slip transfer [J]. Curr. Opin. Solid State Mater. Sci., 2014, 18: 212
doi: 10.1016/j.cossms.2014.05.003
18 Hutchinson J W. Bounds and self-consistent estimates for creep of polycrystalline materials [J]. Proc. R. Soc. London, 1976, 348A:101
19 Harder J. A crystallographic model for the study of local deformation processes in polycrystals [J]. Int. J. Plast., 1999, 15: 605
doi: 10.1016/S0749-6419(99)00002-9
20 Ohashi T. Numerical modelling of plastic multislip in metal crystals of f.c.c. type [J]. Philos. Mag., 1994, 70A: 793
21 Paquin A, Berbenni S, Favier V, et al. Micromechanical modeling of the elastic-viscoplastic behavior of polycrystalline steels [J]. Int. J. Plast., 2001, 17: 1267
doi: 10.1016/S0749-6419(00)00047-4
22 Ohashi T. Crystal plasticity analysis of dislocation emission from micro voids [J]. Int. J. Plast., 2005, 21: 2071
doi: 10.1016/j.ijplas.2005.03.018
23 Lee W B, Chen Y P. Simulation of micro-indentation hardness of FCC single crystals by mechanism-based strain gradient crystal plasticity [J]. Int. J. Plast., 2010, 26: 1527
doi: 10.1016/j.ijplas.2010.01.011
24 Han C S, Gao H J, Huang Y G, et al. Mechanism-based strain gradient crystal plasticity—I. Theory [J]. J. Mech. Phys. Solids, 2005, 53: 1188
doi: 10.1016/j.jmps.2004.08.008
25 Siddiq A, Schmauder S, Huang Y. Fracture of bicrystal metal/ceramic interfaces: A study via the mechanism-based strain gradient crystal plasticity theory [J]. Int. J. Plast., 2007, 23: 665
doi: 10.1016/j.ijplas.2006.08.007
26 Kronberg M L, Wilson F H. Secondary recrystallization in copper [J]. JOM, 1949, 1(8): 501
doi: 10.1007/BF03398387
27 Shibuta Y, Takamoto S, Suzuki T. A molecular dynamics study of the energy and structure of the symmetric tilt boundary of iron [J]. ISIJ Int., 2008, 48: 1582
doi: 10.2355/isijinternational.48.1582
28 Xu Y S, Dan W J, Ren C, et al. Study of the mechanical behavior of dual-phase steel based on crystal plasticity modeling considering strain partitioning [J]. Metals, 2018, 8: 782
doi: 10.3390/met8100782
29 Gou R B, Dan W J, Zhang W G, et al. Research on flow behaviors of the constituent grains in ferrite-martensite dual phase steels based on nanoindentation measurements [J]. Mater. Res. Express, 2017, 4: 076510
[1] 王磊, 刘梦雅, 刘杨, 宋秀, 孟凡强. 镍基高温合金表面冲击强化机制及应用研究进展[J]. 金属学报, 2023, 59(9): 1173-1189.
[2] 陈礼清, 李兴, 赵阳, 王帅, 冯阳. 结构功能一体化高锰减振钢研究发展概况[J]. 金属学报, 2023, 59(8): 1015-1026.
[3] 常松涛, 张芳, 沙玉辉, 左良. 偏析干预下体心立方金属再结晶织构竞争[J]. 金属学报, 2023, 59(8): 1065-1074.
[4] 张海峰, 闫海乐, 方烽, 贾楠. FeMnCoCrNi高熵合金双晶微柱变形机制的分子动力学模拟[J]. 金属学报, 2023, 59(8): 1051-1064.
[5] 王宗谱, 王卫国, Rohrer Gregory S, 陈松, 洪丽华, 林燕, 冯小铮, 任帅, 周邦新. 不同温度轧制Al-Zn-Mg-Cu合金再结晶后的{111}/{111}近奇异晶界[J]. 金属学报, 2023, 59(7): 947-960.
[6] 李福林, 付锐, 白云瑞, 孟令超, 谭海兵, 钟燕, 田伟, 杜金辉, 田志凌. 初始晶粒尺寸和强化相对GH4096高温合金热变形行为和再结晶的影响[J]. 金属学报, 2023, 59(7): 855-870.
[7] 李昕, 江河, 姚志浩, 董建新. O原子对高温合金基体NiCoNiCr晶界作用的理论计算分析[J]. 金属学报, 2023, 59(2): 309-318.
[8] 杨杜, 白琴, 胡悦, 张勇, 李志军, 蒋力, 夏爽, 周邦新. GH3535合金中晶界特征对碲致脆性开裂影响的分形分析[J]. 金属学报, 2023, 59(2): 248-256.
[9] 刘路军, 刘政, 刘仁辉, 刘永. Nd90Al10 晶界调控对晶界扩散磁体磁性能和微观结构的影响[J]. 金属学报, 2023, 59(11): 1457-1465.
[10] 王楠, 陈永楠, 赵秦阳, 武刚, 张震, 罗金恒. 应变速率对X80管线钢铁素体/贝氏体应变分配行为的影响[J]. 金属学报, 2023, 59(10): 1299-1310.
[11] 任平, 陈兴品, 王存宇, 俞峰, 曹文全. 预变形和双级时效对Fe-30Mn-11Al-1.2C奥氏体低密度钢显微组织和力学性能的影响[J]. 金属学报, 2022, 58(6): 771-780.
[12] 王江伟, 陈映彬, 祝祺, 洪哲, 张泽. 金属材料的晶界塑性变形机制[J]. 金属学报, 2022, 58(6): 726-745.
[13] 郭祥如, 申俊杰. 孪生诱发软化与强化效应的Cu晶体塑性行为模拟[J]. 金属学报, 2022, 58(3): 375-384.
[14] 李海勇, 李赛毅. Al <111>对称倾斜晶界迁移行为温度相关性的分子动力学研究[J]. 金属学报, 2022, 58(2): 250-256.
[15] 沈国慧, 胡斌, 杨占兵, 罗海文. 回火温度对含 δ 铁素体高铝中锰钢力学性能和显微组织的影响[J]. 金属学报, 2022, 58(2): 165-174.