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A Self-Organization Model of Collective Dislocations Based on Geometry of Crystal Defects and Thermodynamics of Complexity

基于晶体缺陷几何和复杂热力学的集体位错自组织模型

基本信息

批准号：
12650095
负责人：
SHIZAWA Kazuyuki
金额：
$ 1.92万
依托单位：
Keio University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

项目摘要

A mathematical model of persistent slip bands (PSBs) generated in fatigued f.c.c. crystals is rigorously developed, and a numerical simulation for spatial patterning of dislocations is carried out by use of this model Mobile and immobile dislocation density tensors with particulate image are proposed so that these densities have a precise correspondence to geometrical crystal defects and have both components of edge and screw dislocations.Simultaneous reaction-diffusion equations for self-organization of collect dislocations are derived on the basis of thermodynamics for complexity. New reaction terms are introduced into the equation system, which represent an immobilization of mobile edge component caused by dipole formation and a mobilization of immobile screw component by cross slip. Production terms concerning pair annihilation of screw dislocations after cross slip and pair annihilation of a dipole based on thermal activations are added to the equations.The obtained reaction -diff … More usion equations are applied to a two-dimensional problem and then a size effect parameter is defined as a spontaneous intrinsic length scale of dislocation structure such as vein or ladder one. Generation conditions of the structures are given and theoretical wavelengths of the structures are predicted through the linear stability analysis. A computational analysis using the finite difference method is performed and it leads to the following results. The wavelengths of vein and ladder structures can be fixed in 1 μm size, since the similarity law does not hold m this theory because of existence of the size effect parameter. The present model of PSBs can qualitatively express the dislocation patterns observed experimentally and can simulate the formation process of anisotropic ladder structure generated from the isotropic vein-like structure by the Turing bifurcation. The screw dislocations monotonously annihilate by the cross slip and their mobile components slightly remain in the channels of PSBs. Less

建立了疲劳f.c.c. c中持续滑移带的数学模型。晶体是严格开发的，利用该模型对位错的空间分布进行了数值模拟，提出了具有颗粒像的移动的和非移动的位错密度张量，使其与晶体几何缺陷有精确的对应关系，并同时含有刃型位错和螺型位错分量。收集位错的组织是基于热力学复杂性。在方程组中引入了新的反应项，它代表了由偶极形成引起的移动的边缘组分的固定和由交叉滑移引起的不移动的螺旋组分的移动。在方程中加入了关于交叉滑移后螺位错对湮灭和基于热激活的偶极子对湮灭的产生项，得到了反应微分方程。 ...更多信息将位错运动方程应用于二维问题，定义了脉状或阶梯状位错结构的自发内禀长度尺度作为尺寸效应参数。给出了该结构的产生条件，并通过线性稳定性分析预测了该结构的理论波长。使用有限差分法进行计算分析，并得出以下结果。脉状和阶梯状结构的波长可以固定在1 μm尺度上，因为尺寸效应参数的存在，使得相似律在该理论中不成立。该模型能定性地描述实验观察到的位错斑图，并能模拟各向同性脉状结构经图灵分叉产生各向异性梯形结构的过程。螺位错在交叉滑移作用下单调湮灭，其移动的分量在PSB通道中略有残留。少