考虑材料夹杂的接触问题数值分析  

Numerical Analysis of the Contact Problem Considering Inhomogeneous Inclusions

作　　者：张生光[1] 王文中[1] 赵自强[1] 孔凌嘉[1] 

机构地区：[1]北京理工大学机械与车辆学院,北京100081

出　　处：《机械工程学报》2015年第2期21-29,共9页Journal of Mechanical Engineering

基　　金：国家重点基础研究发展计划(973计划;2011CB706602);国家自然科学基金(51275045)资助项目

摘　　要：金属在冶炼过程中产生的非金属夹杂物以及裂纹等缺陷在交变载荷作用下产生应力集中,形成疲劳源,使部分材料与基体材料脱离产生裂纹,影响材料的疲劳寿命。基于半解析法(Semi-analytical method,SAM),将计算区域离散为若干个微立方体单元,每个夹杂可由不同数量的微立方体单元构成。根据等效夹杂方法(Equivalent inclusion method,EIM),每个单元夹杂均具有一个未知的等效特征应变,通过求解应力-应变本构方程组得到。接触压力通过共轭梯度法求解,进而得到表面残余变形和表层下应力分布等。采用二维和三维快速傅里叶变换(Fast Fourier transform,FFT)算法快速求解变形、特征应力等变量。结果表明,算法稳定,收敛性好;材料夹杂对接触压力和表层应力分布有显著影响;处于接触表面附近的大尺寸夹杂对材料性能影响最大。基于本模型可模拟任意形状和分布的夹杂的影响。Nonmetallic inclusions and cracks during the smelting generate stress concentration, which may be the fatigue source under an alternating load. The fatigue source may enable some materials to separate from the matrix material and the cracks occur. The cracks can greatly influence the fatigue life of material. Based on the semi-analytical method（SAM）, the computational domain is divided into many infinitesimal cuboids, thus each inclusion can be represented by a number of infinitesimal cuboids. According to equivalent inclusion method（EIM）, each cuboid has an unknown eigenstrains which are obtained by a set of simultaneous constitutive equations about stresses and strains relationship. The contact pressure is solved based on conjugate gradient method; furthermore, the subsurface stress distributions are obtained by the semi-analytical method. The two-dimensional and three-dimensional fast Fourier transform（DC-FFT） based approaches are used to speed up the computations related to deformation and eigenstress. The results show the excellent stability and convergence of the algorithm; the inclusions greatly affect the contact pressure and stress distribution; the inclusions with large size and small depth have significant effect on the contact performance.The inclusion with arbitrary shape can be modeled by this model.

关 键 词：特征应变 夹杂 接触压力 应力 

分 类 号：TG156[金属学及工艺—热处理]