Abstract

In this paper, the phase field crystal method is used to study the dislocation motion and reaction of the square phase symmetric tilt low-angle grain boundaries, and the dislocation configurations with different misorientation angles are analyzed under the action of applied strain. The geometric phase approach is used to characterize the strain field around the dislocations. The results show that after the solidification relaxation, the interfacial dislocations on both sides of the grain are distributed in parallel but opposite direction. With the increase of misorientation angle between grains, the number of dislocations increases, the spacing between them decreases, and the free energy of the system increases. Imposed by the applied strain, the grain boundary dislocations undergo climbing, launching, and reactive annihilation, with the free energy fluctuating. When the misorientation increases, the dislocation motion mode changes from climbing to climbing-sliping, resulting in more dislocation group configurations, and more reactions between dislocations and dislocation groups. For the dislocation reactions of different configurations, positive shear strain drives dislocations to approach, and negative shear strain drives dislocations to annihilate.

Highlights

  • the dislocation configurations with different misorientation angles was analyzed under the action of applied strain

  • the interfacial dislocations on both sides of the grain distributed in parallel

  • 4 期性边界条件。计算时,模拟区域的大小为 Lx Ly = 512 x 512 y ,初始区域分

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Summary

Introduction

基于密度泛函的晶体相场法[1,2,3](Phase-field-crystal,PFC)能够实现扩散时 间尺度与原子空间尺度的模拟,且自洽耦合了晶体点阵结构,从而被广泛用于相 结构转变[4,5,6]、晶界变形与位错机制[7, 8]、反霍尔佩奇效应[9, 10]、微观裂纹扩展[11, 12]、铁电磁复合材料的微结构[13, 14]、凝固的枝晶生长[15, 16]等的模拟,是探究原子 尺度微观组织演化的重要方法之一。 力、应变作用下,位错将发生运动、分解[17]、反应[18],导致晶界迁移,甚至湮灭 [19,20,21],从而影响材料的力学性能。近年来有许多关于实验方法研究晶界和位错的 报道[22, 23],但难以观察到其运动,而通过 PFC 方法能够从理论模拟上研究位错运 动。Hirouchi 等[24]通过引入等体积法假设,实现了在外加应变作用下 PFC 方法模 拟晶界与位错的运动,随后的研究者在此基础上进行了进一步研究[25,26,27]。但由于 其内在的规律及机理较为复杂,上述研究主要讨论了外在因素对晶界、位错运动 的影响。 同时,晶界、取向等特征以及缺陷引起的应变的表征对理解晶界和位错运动 有着重要意义。基于 Mumford-Shah 型泛函[28]和能量泛函最小化的变分方法[29]能 够实现对晶界的表征,并且上述方法还能表征缺陷周围的应变场。为了捕获多晶 变形中的晶粒取向,通过引入小波函数,利用小波变换的方法[30]可视化晶粒取向。 王 志 军 等 [31] 成功地将该方法由二维推向了三维 。 除此之外几何相位法 [32] (Geometric Phase Approach, GPA)和峰对法[33](Peak Pairs Algorithm, PPA)等也 能表征应变。PPA 方法是利用原子近邻峰之间的关系获得局部应变值,但对于原 子位置的精确程度较高,而 GPA 方法通过计算相位场获得应变,并兼顾两个实 虚空间的信息,不易受原子位置的干扰,从而常用于原子尺度下应变的表征[34, 35]。

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