Please wait a minute...
Acta Metall Sin  2019, Vol. 55 Issue (11): 1477-1486    DOI: 10.11900/0412.1961.2019.00025
Current Issue | Archive | Adv Search |
A Three-Dimensional Discrete Dislocation Dynamics Simulation on Micropillar Compression of Single Crystal Copper with Dislocation Density Gradient
XIONG Jian1,WEI Dean1,LU Songjiang1,KAN Qianhua1,KANG Guozheng1,ZHANG Xu1,2()
1. Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China
2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China
Download:  HTML  PDF(7681KB) 
Export:  BibTeX | EndNote (RIS)      
Abstract  

In recent years, many gradient materials have been studied. The metal materials with gradient microstructure mainly include: grain size distribution gradient, twin density gradient, dislocation density gradient, solute or precipitate density gradient, or combinations thereof. There are many studies of gradient nanograined material, but few studies of the dislocation density gradient. In fact, the dislocation density gradient structure is ubiquitous. The Taylor relation is only applicable to reveal the relationship between dislocation density and plastic flow stress, without the description of its dependence on dislocation density gradient. Discrete dislocation dynamics (DDD) has its advantage in describing plastic deformation in terms of dislocation motion and dislocation interactions. In this work, Three-dimensional discrete dislocation dynamics (3D-DDD) simulation was performed to investigate the compression behavior of single crystal copper micropillar with dislocation density gradient structure. The effects of loading direction perpendicular and parallel to the direction of dislocation density gradient on the anisotropic responses of micropillar compression were analyzed. The compressional stress-strain response shows that, when the loading direction is parallel to the gradient direction, the critical stress of elastic-plastic transition is higher. However, the plastic flow stress is not affected by the loading direction when the strain is relative larger. Further analysis of spatial-temporal evolution of plastic strain and dislocation density indicate that: when the loading direction is perpendicular to the dislocation density gradient direction, the dislocation sources are firstly activated in the region with the lowest dislocation density, then the dislocations in the region with higher dislocation density are activated subsequently; and the whole deformation process is accompanied with multiple slip bands, then the deformation of the whole model is relatively more uniform. When the loading direction is parallel to the dislocation density gradient direction, the dislocation sources start to activate in the middle layer of the model, then expand to the two adjacent ends; and the plastic deformation of the whole model mainly concentrates in only one slip band.

Key words:  micropillar compression      discrete dislocation dynamics      dislocation density gradient      plastic deformation      loading direction     
Received:  28 January 2019     
ZTFLH:  TG146.1  
Fund: National Natural Science Foundation of China Nos(11672251);National Natural Science Foundation of China Nos(11872321);and Opening Fund of State Key Laboratory for Strength and Vibration of Mechanical Structures(SV2018-KF-10)
Corresponding Authors:  Xu ZHANG     E-mail:  xzhang@swjtu.edu.cn

Cite this article: 

XIONG Jian,WEI Dean,LU Songjiang,KAN Qianhua,KANG Guozheng,ZHANG Xu. A Three-Dimensional Discrete Dislocation Dynamics Simulation on Micropillar Compression of Single Crystal Copper with Dislocation Density Gradient. Acta Metall Sin, 2019, 55(11): 1477-1486.

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2019.00025     OR     https://www.ams.org.cn/EN/Y2019/V55/I11/1477

Fig.1  Dislocation discretization in the discrete dislocation dynamics simulation (The red node is the physical node, representing the real dislocation node; the blue nodes are the discretization nodes, which are generated according to certain rules; the green point is the surface node, which connects a dislocation segment; the black line is the dislocation segment)Color online

Layer

Number of source

Dislocation density

1012 m-2

Dislocation spacing

nm

Bottom layer10038.0162
Middle layer20076.5114
Top layer300114.093
Table 1  Number of sources, dislocation density and dislocation spacing in different layers for the model configurations
ParameterValueUnit
Burgers vector (b)0.256nm
Mean dislocation density (ρ)76.51012 m-2
Mean dislocation source length (lFRS)400nm
Poisson's ratio (ν)0.324-
Shear modulus (μ)54.6GPa
Drag coefficient (B)1×10-4Pa·s
Table 2  Material parameters used in the discrete dislocation dynamics simulation
Fig.2  Initial dislocation configurations of dislocation density gradient structure model under different loading directions (The colors of dislocation lines in the graph represents different types of Burgers vectors of dislocations)Color online(a) the loading direction is perpendicular to the direction of dislocation density gradient, the arrows indicate loading direction(b) the loading direction is parallel with the direction of dislocation density gradient, the arrows indicate loading direction
Fig.3  Equivalent stress-strain curves and dislocation density evolution curves of single crystal copper micropillar with dislocation density gradient structure under different loading directions
Slip systemX direction [11ˉ0]Z direction [1ˉ1ˉ2]
(111)[1ˉ10]00
(111)[1ˉ01]00
(111)[01ˉ1]00
(1ˉ11)[110]00.272
(1ˉ11)[101]0.4080.136
(1ˉ11)[01ˉ1]0.4080.408
(11ˉ1)[110]00.272
(11ˉ1)[011]0.4080.136
(11ˉ1)[1ˉ01]0.4080.408
(111ˉ)[1ˉ10]00
(111ˉ)[011]00.272
(111ˉ)[101]00.272
Table 3  Schmid factors of 12 slip systems in single crystalline copper under different loading directions
Fig.4  Primary slip systems under two different loading directions (The planes ACD (normal vector is (1ˉ11)) and BCD (normal vector is (11ˉ1)) are the primary slip planes, and the red edges of the Thompson tetrahedron are the primary slip directions, AC and AD represent the slip directions of [01ˉ1] and [101] in the slip plane ACD, respectively; BC and BD represent the slip directions of [1ˉ01] and [011] in the slip plane BCD, respectively)Color online(a) along X axis (b) along Z axis
Fig.5  The snapshots of evolved dislocation structures corresponding to strains of 0.05% (a), 0.10% (b), 0.15% (c), 0.20% (d) and 0.25% (e) in the compression process along the X-axis direction which is perpendicular to the dislocation density gradient directionColor online
Fig.6  Distributions of plastic strain on the surface corresponding to strains of 0.05% (a), 0.10% (b), 0.15% (c), 0.20% (d) and 0.25% (e) in the compression process along the X-axis direction which is perpendicular to the dislocation density gradient directionColor online
Fig.7  The evolutions of plastic strain (a) and the dislocation density (b) in bottom, middle and top layer, which have different dislocation densities, when loading direction is along X-axis which is perpendicular to the dislocation density gradient direction
Fig.8  The snapshots of evolved dislocation structure corresponding to strains of 0.05% (a), 0.10% (b), 0.15% (c), 0.20% (d) and 0.25% (e) in the compression process along the Z-axis direction which is parallel with the dislocation density gradient directionColor online
Fig.9  Distributions of plastic strain on the surface corresponding to strains of 0.05% (a), 0.10% (b), 0.15% (c), 0.20% (d) and 0.25% (e) in the compression process along the Z-axis direction which is parallel with the dislocation density gradient directionColor online
Fig.10  The evolutions of plastic strain (a) and the dislocation density (b) in bottom, middle and top layer, which have different dislocation densities, when loading direction is along Z-axis which is parallel with the dislocation density gradient direction
[1] LiuZ Q, MeyersM A, ZhangZ F, et al. Functional gradients and heterogeneities in biological materials: Design principles, functions, and bioinspired applications [J]. Prog. Mater. Sci., 2017, 88: 467
[2] LiY. Research progress on gradient metallic materials [J]. Mater. China, 2016, 35: 658
[2] 李 毅. 梯度结构金属材料研究进展 [J]. 中国材料进展, 2016, 35: 658
[3] LuK. Gradient nanostructured materials [J]. Acta Metall. Sin., 2015, 51: 1
[3] 卢 柯. 梯度纳米结构材料 [J]. 金属学报, 2015, 51: 1
[4] LuK. Making strong nanomaterials ductile with gradients [J]. Science, 2014, 345: 1455
[5] WuX L, JiangP, ChenL, et al. Extraordinary strain hardening by gradient structure [J]. Proc. Natl. Acad. Sci. USA, 2014, 111: 7197
[6] ZhaoJ F, KanQ H, ZhouL C, et al. Deformation mechanisms based constitutive modelling and strength-ductility mapping of gradient nano-grained materials [J]. Mater. Sci. Eng., 2019, A742: 400
[7] LuX C, ZhangX, ShiM X, et al. Dislocation mechanism based size-dependent crystal plasticity modeling and simulation of gradient nano-grained copper [J]. Int. J. Plast., 2019, 113: 52
[8] ChengZ, ZhouH F, LuQ H, et al. Extra strengthening and work hardening in gradient nanotwinned metals [J]. Science, 2018, 362: eaau1925
[9] ZhouH F, QuS X. Investigation of atomistic deformation mechanism of gradient nanotwinned copper using molecular dynamics simulation method [J]. Acta Metall. Sin., 2014, 50: 226
[9] 周昊飞, 曲绍兴. 利用分子动力学研究梯度纳米孪晶Cu的微观变形机理 [J]. 金属学报, 2014, 50: 226
[10] SakaiT, OhashiM, ChibaK, et al. Recovery and recrystallization of polycrystalline nickel after hot working [J]. Acta Metall., 1988, 36: 1781
[11] SakaiT, OhashiM. Dislocation substructures developed during dynamic recrystallisation in polycrystalline nickel [J]. Mater. Sci. Technol., 1990, 6: 1251
[12] HeD, HuanY, LiQ. Effect of dislocation density gradient on deformation behavior of pure nickel subjected to torsion [A]. DEStech Transactions on Materials Science and Engineering [C]. Nanjing: DEStech Publications, 2017
[13] ArsenlisA, CaiW, TangM, et al. Enabling strain hardening simulations with dislocation dynamics [J]. Model. Simul. Mater. Sci. Eng., 2007, 15: 553
[14] TangH, SchwarzK W, EspinosaH D. Dislocation escape-related size effects in single-crystal micropillars under uniaxial compression [J]. Acta Mater., 2007, 55: 1607
[15] SengerJ, WeygandD, GumbschP, et al. Discrete dislocation simulations of the plasticity of micro-pillars under uniaxial loading [J]. Scr. Mater., 2008, 58: 587
[16] MotzC, WeygandD, SengerJ, et al. Initial dislocation structures in 3-D discrete dislocation dynamics and their influence on microscale plasticity [J]. Acta Mater., 2009, 57: 1744
[17] LuS J, ZhangB, LiX Y, et al. Grain boundary effect on nanoindentation: A multiscale discrete dislocation dynamics model [J]. J. Mech. Phys. Solids, 2019, 126: 117
[18] WeiD A, FanH D, TangJ, et al. Effect of a vertical twin boundary on the mechanical property of bicrystalline copper micropillars [A]. TMS 148th Annual Meeting & Exhibition Supplemental Proceedings [C]. Cham: Springer, 2019: 1305
[19] WeinbergerC R, CaiW. Surface-controlled dislocation multiplication in metal micropillars [J]. Proc. Natl. Acad. Sci. USA, 2008, 105: 14304
[20] SengerJ, WeygandD, MotzC, et al. Aspect ratio and stochastic effects in the plasticity of uniformly loaded micrometer-sized specimens [J]. Acta Mater., 2011, 59: 2937
[21] El-awadyJ A. Unravelling the physics of size-dependent dislocation-mediated plasticity [J]. Nat. Commun., 2015, 6: 5926
[22] LiZ H, HouC T, HuangM S, et al. Strengthening mechanism in micro-polycrystals with penetrable grain boundaries by discrete dislocation dynamics simulation and Hall-Petch effect [J]. Comput. Mater. Sci., 2009, 46: 1124
[23] HuangM S, LiangS, LiZ H. An extended 3D discrete-continuous model and its application on single- and bi-crystal micropillars [J]. Model. Simul. Mater. Sci. Eng., 2017, 25: 035001
[24] HuangM S, LiZ H. Coupled DDD-FEM modeling on the mechanical behavior of microlayered metallic multilayer film at elevated temperature [J]. J. Mech. Phys. Solids, 2015, 85: 74
[25] HuangS, HuangM S, LiZ H. Effect of interfacial dislocation networks on the evolution of matrix dislocations in nickel-based superalloy [J]. Int. J. Plast., 2018, 110: 1
[26] LiuZ L, LiuX M, ZhuangZ, et al. A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales [J]. Int. J. Plast., 2009, 25: 1436
[27] CuiY N, LiuZ L, ZhuangZ. Quantitative investigations on dislocation based discrete-continuous model of crystal plasticity at submicron scale [J]. Int. J. Plast., 2015, 69: 54
[28] FanH D, AubryS, ArsenlisA, et al. Discrete dislocation dynamics simulations of twin size-effects in magnesium [A]. MRS Online Proceedings Library [C]. Cambridge: Cambridge University Press, 2015: 1741
[29] GuoX R, SunC Y, WangC H, et al. Investigation of strain rate effect by three-dimensional discrete dislocation dynamics for fcc single crystal during compression process [J]. Acta Metall. Sin., 2018, 54: 1322
[29] 郭祥如, 孙朝阳, 王春晖等. 基于三维离散位错动力学的fcc结构单晶压缩应变率效应研究 [J]. 金属学报, 2018, 54: 1322
30 BulatovV, CaiW, FierJ, et al. Scalable line dynamics in ParaDiS [A]. Proceedings of 2004 ACM/IEEE Conference on Supercomputing [C]. Pittsburgh: IEEE, 2004
[31] WeygandD, FriedmanL H, Van der GiessenE, et al. Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics [J]. Model. Simul. Mater. Sci. Eng., 2002, 10: 437
[32] VattréA, DevincreB, FeyelF, et al. Modelling crystal plasticity by 3D dislocation dynamics and the finite element method: The discrete-continuous model revisited [J]. J. Mech. Phys. Solids, 2014, 63: 491
[33] SengerJ, WeygD, MotzC. Aspect ratio and stochastic effects in the plasticity of uniformly loaded micrometer-sized specimens [J]. Acta Mater., 2011, 59: 2937
[34] ZhangX, AifantisK E, SengerJ, et al. Internal length scale and grain boundary yield strength in gradient models of polycrystal plasticity: How do they relate to the dislocation microstructure? [J]. J. Mater. Res., 2014, 29: 2116
[35] WuZ J, ZhaoE J, XiangH P, et al. Crystal structures and elastic properties of superhard IrN2 and IrN3 from first principles [J]. Phys. Rev., 2007, 76B: 054115
[1] CHEN Yongjun, BAI Yan, DONG Chuang, XIE Zhiwen, YAN Feng, WU Di. Passivation Behavior on the Surface of Stainless Steel Reinforced by Quasicrystal-Abrasive via Finite Element Simulation[J]. 金属学报, 2020, 56(6): 909-918.
[2] CHEN Xiang,CHEN Wei,ZHAO Yang,LU Sheng,JIN Xiaoqing,PENG Xianghe. Assembly Performance Simulation of NiTiNb Shape Memory Alloy Pipe Joint Considering Coupling Effect of Phase Transformation and Plastic Deformation[J]. 金属学报, 2020, 56(3): 361-373.
[3] WANG Lei, AN Jinlan, LIU Yang, SONG Xiu. Deformation Behavior and Strengthening-Toughening Mechanism of GH4169 Alloy with Multi-Field Coupling[J]. 金属学报, 2019, 55(9): 1185-1194.
[4] Jian PENG,Yi GAO,Qiao DAI,Ying WANG,Kaishang LI. Fatigue and Cycle Plastic Behavior of 316L Austenitic Stainless Steel Under Asymmetric Load[J]. 金属学报, 2019, 55(6): 773-782.
[5] Zongwei JI,Song LU,Hui YU,Qingmiao HU,Levente Vitos,Rui YANG. First-Principles Study on the Impact of Antisite Defects on the Mechanical Properties of TiAl-Based Alloys[J]. 金属学报, 2019, 55(5): 673-682.
[6] Aidong TU, Chunyu TENG, Hao WANG, Dongsheng XU, Yun FU, Zhanyong REN, Rui YANG. Molecular Dynamics Simulation of the Structure and Deformation Behavior of γ/α2 Interface in TiAl Alloys[J]. 金属学报, 2019, 55(2): 291-298.
[7] Xiangru GUO, Chaoyang SUN, Chunhui WANG, Lingyun QIAN, Fengxian LIU. Investigation of Strain Rate Effect by Three-Dimensional Discrete Dislocation Dynamics for fcc Single Crystal During Compression Process[J]. 金属学报, 2018, 54(9): 1322-1332.
[8] Haifeng ZHANG, Haile YAN, Nan JIA, Jianfeng JIN, Xiang ZHAO. Exploring Plastic Deformation Mechanism of MultilayeredCu/Ti Composites by Using Molecular Dynamics Modeling[J]. 金属学报, 2018, 54(9): 1333-1342.
[9] Jun SUN, Suzhi LI, Xiangdong DING, Ju LI. Hydrogenated Vacancy: Basic Properties and Its Influence on Mechanical Behaviors of Metals[J]. 金属学报, 2018, 54(11): 1683-1692.
[10] Xiaosong ZHANG,Yong XU,Shihong ZHANG,Ming CHENG,Yonghao ZHAO,Qiaosheng TANG,Yuexia DING. Research on the Collaborative Effect of Plastic Deformation and Solution Treatment in the Intergranular Corrosion Property of Austenite Stainless Steel[J]. 金属学报, 2017, 53(3): 335-344.
[11] Jinrui ZHANG, Yanwei ZHANG, Yulin HAO, Shujun LI, Rui YANG. Plastic Deformation Behavior of Biomedical Ti-24Nb-4Zr-8Sn Single Crystal Alloy[J]. 金属学报, 2017, 53(10): 1385-1392.
[12] Jun SUN, Jinyu ZHANG, Kai WU, Gang LIU. SIZE EFFECTS ON THE DEFORMATION AND DAMAGEOF Cu-BASED METALLIC NANOLAYEREDMICRO-PILLARS[J]. 金属学报, 2016, 52(10): 1249-1258.
[13] Jie DENG,Jiawei MA,Yiyang XU,Yao SHEN. EFFECT OF MARTENSITE DISTRIBUTION ON MICROSCOPIC DEFORMATION BEHAVIOR AND MECHANICAL PROPERTIES OF DUAL PHASE STEELS[J]. 金属学报, 2015, 51(9): 1092-1100.
[14] Lichu ZHOU,Xianjun HU,Chi MA,Xuefeng ZHOU,Jianqing JIANG,Feng FANG. EFFECT OF PEARLITIC LAMELLA ORIENTATION ON DEFORMATION OF PEARLITE STEEL WIRE DURING COLD DRAWING[J]. 金属学报, 2015, 51(8): 897-903.
[15] Xiaogang WANG,Chao JIANG,Xu HAN. PLASTIC STRAIN HETEROGENEITY AND WORK HARDENING OF Ni SINGLE CRYSTALS[J]. 金属学报, 2015, 51(12): 1457-1464.
No Suggested Reading articles found!