单晶体塑性滑移有限变形下的应力计算

为了探讨和发展单晶金属材料的非弹性有限变形分析方法,提出一种单晶体各向异性弹塑性分析的计算格式.该方法是一种以初始构形为变形计算参考构形的描述方法,它对单晶体塑性构形的演化用增量计算以跟随加载路径,而在应力计算时在卸载构形的基础上用Hencky对数弹性应变来计算总量的应力以保证计算的稳定和收敛;通过求解满足瞬时屈服条件和应力与弹性应变关系的广义胡克定律的非线性方程组来搜索激活滑移系.

STRESS CALCULATION OF SINGLE CRYSTAL UNDER FINITE SLIP PLASTIC DEFORMATION

In the present paper, a calculation scheme of anisotropic finite elastic-plastic defor-mation for a single crystal is proposed. This scheme applies the initial configuration as reference configuration. By using this scheme the incremental calculation is adopted to follow the loading path to describe the evolution of single crystal's plastic configuration and the Hencky's logarithm elastic strain is used to calculate the stress under the unloading configuration in order to keep the stability and convergence of calculation. And in this scheme, the crystal's active slip systems are searched through solving the equations, which satisfying the instantaneous active conditions of slip systems and satisfying the relation between stress and elastic strain.The computational procedure in fact consists of following steps: compute the intermediate configuration; apply the elastic stretching; rotate to the current principle material axis to compute the total stress; then exert the rotation to rotate back to current global axis to calculate the total stress under the global axes.The computation results represent the phenomena observed in experiment by foregone re-searchers:(1)The yield, hardening abilities, number and order of activated slips for different orientations are evident different.(2)When tensioning a crystal in some orientation maybe a greater yield stress than that in other orientation can be obtained but this not always means that in this orientation the crystal will have a stronger hardening ability.(3)The crystal latent hardening has great influence on the hardening properties of single crystal materials.The calculations in the present paper preliminarily proved that the proposed calculation scheme could describe reasonably the mechanical behaviors of plastic slip of single crystals at finite strains.