A Three-Dimensional Discrete Dislocation Dynamics Simulation on Micropillar Compression of Single Crystal Copper with Dislocation Density Gradient

doi:10.11900/0412.1961.2019.00025

Acta Metall Sin

2019, Vol. 55

Issue (11): 1477-1486 DOI: 10.11900/0412.1961.2019.00025

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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 Xu^1,²(

)

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

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.

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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)

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	Jian XIONG
	Dean WEI
	Songjiang LU
	Qianhua KAN
	Guozheng KANG
	Xu ZHANG

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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

Table 1 Number of sources, dislocation density and dislocation spacing in different layers for the model configurations

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 system	X direction [1 $1 ˉ$ 0]	Z direction [ $1 ˉ$ $1 ˉ$ 2]
(111)[ $1 ˉ$ 10]	0	0
(111)[ $1 ˉ$ 01]	0	0
(111)[0 $1 ˉ$ 1]	0	0
( $1 ˉ$ 11)[110]	0	0.272
( $1 ˉ$ 11)[101]	0.408	0.136
( $1 ˉ$ 11)[0 $1 ˉ$ 1]	0.408	0.408
(1 $1 ˉ$ 1)[110]	0	0.272
(1 $1 ˉ$ 1)[011]	0.408	0.136
(1 $1 ˉ$ 1)[ $1 ˉ$ 01]	0.408	0.408
(11 $1 ˉ$ )[ $1 ˉ$ 10]	0	0
(11 $1 ˉ$ )[011]	0	0.272
(11 $1 ˉ$ )[101]	0	0.272

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 (

1 ˉ

11)) and BCD (normal vector is (1

1 ˉ

1)) 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 [0

1 ˉ

1] and [101] in the slip plane ACD, respectively; BC and BD represent the slip directions of [

1 ˉ

01] 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

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