孪生诱发软化与强化效应的<strong>Cu</strong>晶体塑性行为模拟

doi:10.11900/0412.1961.2021.00230

金属学报

2022, Vol. 58

Issue (3): 375-384 DOI: 10.11900/0412.1961.2021.00230

研究论文

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孪生诱发软化与强化效应的Cu晶体塑性行为模拟

郭祥如¹^,², 申俊杰¹^,²(

)

^1.天津理工大学天津市先进机电系统设计与智能控制重点实验室天津 300384
^2.天津理工大学机电工程国家级实验教学示范中心天津 300384

Modelling of the Plastic Behavior of Cu Crystal with Twinning-Induced Softening and Strengthening Effects

GUO Xiangru¹^,², SHEN Junjie¹^,²(

)

^1.Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin 300384, China
^2.National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin 300384, China

引用本文:

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.
Xiangru GUO, Junjie SHEN. Modelling of the Plastic Behavior of Cu Crystal with Twinning-Induced Softening and Strengthening Effects[J]. Acta Metall Sin, 2022, 58(3): 375-384.

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摘要:

基于晶体塑性理论，考虑孪生软化效应建立了描述孪晶形核、增殖和长大的位错密度基晶体塑性有限元模型。应用该模型揭示了不同晶体取向Cu单晶拉伸变形过程中位错滑移、孪生激活及其交互作用下的宏观塑性行为演化规律，进一步分析了Cu多晶拉伸变形过程中晶粒间交互作用对孪生软化、应变硬化等宏观塑性行为的影响。结果表明：孪生具有明显的取向效应，在孪生主导塑性条件下，Cu单晶塑性变形过程中孪晶增殖导致应力-应变曲线存在明显的应力突降现象，其塑性变形分为滑移、孪生及位错与孪晶交互作用3个阶段；此外，随着饱和孪晶体积分数增加，Cu单晶塑性变形过程中第3阶段的应变硬化率也随之提升。进一步模拟Cu多晶拉伸变形的塑性行为可知，在晶粒间交互作用下孪晶形核、增殖和长大过程中不会出现应力突降现象，与Cu单晶相比整个塑性变形过程具有更高的应变硬化率；Cu多晶塑性变形过程中位错密度在晶界处出现集中现象，孪晶也容易在晶界处形成。

关键词 ：晶体塑性, 孪生软化, 取向效应, 应变硬化, 塑性变形

Abstract：

Dislocation slip and twinning are the main deformation mechanisms dominating plastic behavior of crystalline materials, such as twinning-induced plasticity steel, Cu, Mg, and their alloys. The influence of twinning and interaction between dislocations and twins on the plastic deformation of crystal materials is complex. On the one hand, a sudden stress drop in the stress-strain curve during twin nucleation, propagation, and growth (TNPG) of crystal materials, i.e., the twinning softening effect, is evident. On the other hand, the interaction between twins and dislocations demonstrates the strengthening effect of plastic deformation. Polycrystalline materials are used in engineering applications, and twin nucleation corresponds to different strains in each grain. Therefore, determining the influence of twin softening and strengthening effects on plastic deformation of polycrystalline materials is difficult. In this work, a crystal plastic finite element model of Cu, considering the twinning softening effect, was developed to describe the TNPG process based on the crystal plasticity theory. The method was used to reveal the influence of twins' activation and their interaction with dislocations on strain hardening during the tension of Cu single crystal and polycrystal. The results show that twinning has an evident orientation effect. Under twinning favorable orientation, a sudden stress drop in the stress-strain curve caused by twinning propagation during plastic deformation of Cu single crystal is evident, and the total plastic deformation can be divided into three stages: slip, twinning, and interaction between dislocations and twins. Compared with Cu single crystal, the stress-strain curve changes smoothly and the strain hardening rate is higher during the tension of Cu polycrystal. Meanwhile, the dislocation density is concentrated at the grain boundary, and twins are easy to form at the grain boundary during the plastic deformation of Cu polycrystal.

Key words： crystal plasticity twining softening orientation effect strain hardening plastic deformation

收稿日期: 2021-05-27

ZTFLH:

TG146.1

基金资助:国家自然科学基金项目(52105393);天津市自然科学基金项目(18JCYBJC88700)

作者简介: 郭祥如，男，1989年生，博士

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https://www.ams.org.cn/CN/10.11900/0412.1961.2021.00230 或 https://www.ams.org.cn/CN/Y2022/V58/I3/375

图1 Cu单晶拉伸过程的晶体塑性有限元模型示意图

Parameter	Value	Unit
C₁₁^[28]	168	GPa
C₁₂^[28]	121	GPa
C₄₄^[28]	75	GPa
$f t$ ^[2,31]	0.7
$γ ˙ 0$ ^[29,30]	0.001	s^-1
$m$ ^[29,30]	0.024
$s 0$ ^[29,30]	5	MPa
$μ$ ^[28]	48	GPa
b^[28]	0.025	nm
$ρ 0$ ^[29,30]	10¹²	m^-2
$k r$ ^[29,30]	6
$k f$ ^[29,30]	0.3
$e$ ^[2,31]	220	nm
D^[2,31]	3	mm
$s 0, β$	150	MPa
$s 1, β$	60	MPa
$s g, β$	110	MPa
$f g, β$ ^[23]	0.005
$h 0, β$ ^[23]	70
$h 1, β$ ^[23]	0

表1 CPFE模型中Cu单晶材料参数[2,23,28~31]

图2 Cu单晶沿[541]和[163]取向拉伸变形过程中真应力和孪晶体积分数随应变演化的模拟与实验[2,28]结果

图3 Cu单晶沿[541]取向拉伸变形过程中各滑移系和孪生系的激活演化结果

图4 [541]取向下不同饱和孪晶体积Cu单晶拉伸变形过程中真应力、应变硬化率和位错密度演化结果

图5 Cu多晶拉伸过程晶体塑性有限元模型示意图

图6 Cu多晶拉伸变形过程中真应力、位错密度和孪晶体积分数随应变的演化曲线

图7 不同取向Cu单晶和多晶变形过程中的应变硬化演化曲线

图8 多晶Cu拉伸变形后对应的位错密度和孪晶体积分布

图9 多晶Cu拉伸变形过程中不同应变对应的孪晶体积分布(a) ε = 0.32 (b) ε = 0.46 (c) ε = 0.67 (d) ε = 0.85

1	Guo X R, Sun C Y, Li R, et al. A dislocation density based model for twinning induced softening of TWIP steel [J]. Comput. Mater. Sci., 2017, 139: 8
2	Niewczas M, Basinski Z S, Basinski S J, et al. Deformation of copper single crystals to large strains at 4.2K—I. Mechanical response and electrical resistivity [J]. Philos. Mag., 2001, 81A: 1121
3	Seo J H, Park H S, Yoo Y, et al. Origin of size dependency in coherent-twin-propagation-mediated tensile deformation of noble metal nanowires [J]. Nano Lett., 2013, 13: 5112
4	Liang Z Y, Li Y Z, Huang M X. The respective hardening contributions of dislocations and twins to the flow stress of a twinning-induced plasticity steel [J]. Scr. Mater., 2016, 112: 28
5	Luo Z C, Huang M X. Revisit the role of deformation twins on the work-hardening behaviour of twinning-induced plasticity steels [J]. Scr. Mater., 2018, 142: 28
6	Paramatmuni C, Zheng Z B, Rainforth W M, et al. Twin nucleation and variant selection in Mg alloys: An integrated crystal plasticity modelling and experimental approach [J]. Int. J. Plast., 2020, 135: 102778
7	Zhi H H, Zhang C, Antonov S, et al. Investigations of dislocation-type evolution and strain hardening during mechanical twinning in Fe-22Mn-0.6C twinning-induced plasticity steel [J]. Acta Mater., 2020, 195: 371
8	Bertin N, Sills R B, Cai W. Frontiers in the simulation of dislocations [J]. Annu. Rev. Mater. Res., 2020, 50: 437
9	Zhang J, Li H W, Sun X X, et al. A multi-scale MCCPFEM framework: Modeling of thermal interface grooving and deformation anisotropy of titanium alloy with lamellar colony [J]. Int. J. Plast., 2020, 135: 102804
10	Agaram S, Kanjarla A K, Bhuvaraghan B, et al. Dislocation density based crystal plasticity model incorporating the effect of precipitates in IN718 under monotonic and cyclic deformation [J]. Int. J. Plast., 2021, 141: 102990
11	Sun C Y, Guo N, Fu M W, et al. Modeling of slip, twinning and transformation induced plastic deformation for TWIP steel based on crystal plasticity [J]. Int. J. Plast., 2016, 76: 186
12	Guo N, Tang B T, Liu J Y, et al. Characteristic stepwise strain hardening behaviour induced by slip and twinning of large-deformed copper single crystals: Crystal plasticity modelling and simulation [J]. Philos. Mag., 2021, 101: 1245
13	Li X X, Xu D S, Yang R. Crystal plasticity finite element method investigation of the high temperature deformation consistency in dual-phase titanium alloy [J]. Acta Metall. Sin., 2019, 55: 928
13	李学雄, 徐东生, 杨锐. 双相钛合金高温变形协调性的CPFEM研究 [J]. 金属学报, 2019, 55: 928
14	Chin G Y, Hosford W F, Mendorf D R. Accommodation of constrained deformation in f.c.c. metals by slip and twinning [J]. Proc. Roy. Soc., 1969, 309A: 433
15	Van Houtte P. Simulation of the rolling and shear texture of brass by the Taylor theory adapted for mechanical twinning [J]. Acta Metall., 1978, 26: 591
16	Choi S H, Shin E J, Seong B S. Simulation of deformation twins and deformation texture in an AZ31 Mg alloy under uniaxial compression [J]. Acta Mater., 2007, 55: 4181
17	Tomé C N, Lebensohn R A, Kocks U F. A model for texture development dominated by deformation twinning: Application to zirconium alloys [J]. Acta Metall. Mater., 1991, 39: 2667
18	Kalidindi S R. Modeling anisotropic strain hardening and deformation textures in low stacking fault energy fcc metals [J]. Int. J. Plast., 2001, 17: 837
19	Sun C Y, Guo X R, Huang J, et al. Modelling of plastic deformation on coupling twinning of single crystal TWIP steel [J]. Acta Metall. Sin., 2015, 51: 357
19	孙朝阳, 郭祥如, 黄杰等. 耦合孪生的TWIP钢单晶体塑性变形行为模拟研究 [J]. 金属学报, 2015, 51: 357
20	Sun C Y, Guo X R, Guo N, et al. Investigation of plastic deformation behavior on coupling twinning of polycrystal TWIP steel [J]. Acta Metall. Sin., 2015, 51: 1507
20	孙朝阳, 郭祥如, 郭宁等. 耦合孪生的TWIP钢多晶体塑性变形行为研究 [J]. 金属学报, 2015, 52: 1507
21	Beyerlein I J, Mara N A, Bhattacharyya D, et al. Texture evolution via combined slip and deformation twinning in rolled silver-copper cast eutectic nanocomposite [J]. Int. J. Plast., 2011, 27: 121
22	Wu P D, Guo X Q, Qiao H, et al. A constitutive model of twin nucleation, propagation and growth in magnesium crystals [J]. Mater. Sci. Eng., 2015, A625: 140
23	Qiao H, Barnett M R, Wu P D. Modeling of twin formation, propagation and growth in a Mg single crystal based on crystal plasticity finite element method [J]. Int. J. Plast., 2016, 86: 70
24	Wang H, Clausen B, Capolungo L, et al. Stress and strain relaxation in magnesium AZ31 rolled plate: In-situ neutron measurement and elastic viscoplastic polycrystal modeling [J]. Int. J. Plast., 2016, 79: 275
25	Kalidindi S R. Incorporation of deformation twinning in crystal plasticity models [J]. J. Mech. Phys. Solids, 1998, 46: 267
26	Allain S, Chateau J P, Bouaziz O. A physical model of the twinning-induced plasticity effect in a high manganese austenitic steel [J]. Mater. Sci. Eng., 2004, A387: 143
27	Arsenlis A, Parks D M. Modeling the evolution of crystallographic dislocation density in crystal plasticity [J]. J. Mech. Phys. Solids, 2002, 50: 1979
28	Sun Z K, Li F G, Zhu J M. Radial micro-cracks in pile-up region of single-crystal Cu in spherical indentation: Experimental observation and crystal plastic simulation [J]. J. Mater. Sci., 2019, 54: 9875
29	Khan A S, Liu J, Yoon J W, et al. Strain rate effect of high purity aluminum single crystals: Experiments and simulations [J]. Int. J. Plast., 2015, 67: 39
30	Dancette S, Delannay L, Renard K, et al. Crystal plasticity modeling of texture development and hardening in TWIP steels [J]. Acta Mater., 2012, 60: 2135
31	Blewitt T H, Coltman R R, Redman J K. Low-temperature deformation of copper single crystals [J]. J. Appl. Phys., 1957, 28: 651
32	Quey R, Dawson P R, Barbe F. Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing [J]. Comput. Methods Appl. Mech. Eng., 2011, 200: 1729

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