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考虑了晶粒取向随机的影响,分别建立了多晶铍的规则和非规则晶形二维多晶模型,对多晶铍的微观弹性失配行为进行了有限元(FEM)数值分析。规则模型晶粒形状取为正方形或正六边形;非规则模型利用Voronoi方法获得接近真实的非规则形状晶粒。考虑到单晶体力学性能的各向异性,对具有HCP结构单晶铍晶粒的含有5个参数的弹性刚度矩阵进行坐标变换,得到任意取向铍晶粒的弹性性能参数。将各组弹性性能参数随机地赋给各个晶粒,实现在晶粒取向随机化分布条件下对弹性性能差异性考虑的目的。基于以上工作对两类铍多晶模型进行了FEM应力分析,结果表明,两类不同模型的失配应力集中均发生在晶界处;相比规则多晶模型,不规则多晶模型的弹性失配效应更为显著;最大失配应力较平均应力(即不考虑弹性失配影响时的应力)高出10%左右。
Considering the random effects of grain orientation, two-dimensional polycrystalline model of polycrystal beryllium, both regular and irregular, was established respectively. The numerical analysis of the microscopic elastic mismatch of polycrystal beryllium by finite element method (FEM) was carried out. The regular model grain shape is taken as a square or a regular hexagon; the irregular model uses the Voronoi method to obtain near-real irregular shape grains. Considering the anisotropy of the mechanical properties of single crystal, the elastic stiffness matrix with five parameters of HCP monocrystal beryllium grains was transformed by coordinates to obtain the elastic performance parameters of randomly oriented beryllium grains. The elastic performance parameters of each group are randomly assigned to each grain to achieve the purpose of considering the difference of elastic properties under the random distribution of grain orientation. Based on the above work, FEM stress analysis of two types of beryllium polycrystalline model was carried out. The results show that the misfit stress concentration of the two types of model occurs at the grain boundary. Compared with the regular polycrystalline model, the elastic loss of the irregular polycrystalline model The effect is more significant; the maximum mismatch stress is about 10% higher than the average stress (that is, the stress when the elastic mismatch is not considered).