摘要
从单晶滑移变形分析的角度探讨多晶体塑性变形和应力的不均匀性及宏观力学响应:建议了一种当前构形下以应力为基本变量的单晶黏塑性增量迭代计算方法;用Voronoi晶粒集合体模型研究多晶体由于晶粒几何及取向的随机性造成的变形和应力的不均匀性,进行了多晶集合体的宏观响应和晶粒位向演化数值分析.结果表明:(1)多晶体内等效塑性应变和应力分量在统计上呈现高斯分布,在应变硬化过程中,随着塑性变形增加多晶体微观应力的统计变异系数会越来越大;(2)用Voronoi模型计算可得到沿最大剪应力方向的滑移变形带;(3)多晶体内最高三轴拉应力一般出现在晶界特别是三晶交界处;(4)Voronoi模型能用于织构分析.
The micromechanical heterogeneous states of plastic deformation and stress of polycrystalline materials are analyzed on the basis of a microscopic model of crystal plasticity, taking into account the randomness of the crystal grain geometry and the anisotropy of crystal slip. The major aspects of the work are: (1) an iterative algorithm is developed for single-crystal plasticity incremental constitutive relations under the current configuration, in which the basic variable for iteration is the Cauchy stress tensor, (2) the polycrystal is modeled by Voronoi tessellation with randomly oriented crystallographic orientations, the heterogeneous local stress and strain distributions and their statistical characteristics are analyzed in detail, and (3) the macroscopic response with its texture evolution of the polycrystal under respectively uniaxial tension and plane strain compression are simulated. The simulation results show that: (1) the stress components and effective plastic strain in the Voronoi polycrystal aggregate have the statistical feature of Gaussian like distribution, and the ratio of the standard deviation a to the mean μ of the microscopic longitudinal stresses in the polycrystalline aggregate increases with the plastic strain; (2) the simulated plastic zones in the polycrystal aggregate appear in the direction of maximum macroscopic shear stress; (3) the microscopic stresses are highly heterogeneous, and very large triaxial stress generally appear at the grain boundaries and the triple junctions; (4) Voronoi model can be used to texture analysis.
出处
《力学学报》
EI
CSCD
北大核心
2004年第6期714-723,共10页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(19972055
10472092)
航空科学基金(04C53027)资助项目~~
关键词
多晶体
应力分量
变形带
微观应力
单晶
等效
增量
塑性变形
织构
晶界
anisotropy, crystal viscoplasticity, Voronoi polycrystal tessellation, random orientation, stress inhomogeneous
