材料微结构三维建模及其晶体塑性有限元模拟

3D modeling of material microstructure and crystal plasticity finite element simulation

采用Voronoi图,生成具有随机晶粒形状的三维多晶集合体模型,并赋予每个晶粒相应的取向。基于率相关晶体塑性理论,开发了用户材料子程序,并将其嵌入有限元软件中模拟面心立方多晶集合体在单轴单向拉伸过程中的应力-应变响应,分析了网格细化及晶粒取向对模拟结果的影响。研究表明,随网格细化应力值有所降低,但变化不大,为保证结果的可靠度,平均每个晶粒离散的单元数目在5个以上;随多晶集合体中晶粒数目的增加,由于取向的随机性产生的应力-应变的差异逐渐减小,模拟时多晶集合体中晶粒的数目大于50个;模型较好的反映了材料的真应力随应变速率增加而增大的规律,且模拟结果和实验结果吻合良好,说明该模型具有较高的可靠性。

Three dimensional polycrystalline aggregate models with random grain shapes are generated by Voronoi diagram method and the crystal orientation is assigned for each grain. A user defined material subroutine （UMAT） developed based on rate-de- pendent crystal plasticity theory is embedded into the finite element software to simulate the stress-strain response of FCC material during uniaxial tension, and the effects of the mesh refinement and the crystal orientation on simulation results are investigated. The results indicate that the magnitude of stress reduces slightly with the mesh refinement and no less than five elements should be used to averagely disperse per grain to ensure the reliability. The differences between stress-strain response caused by the random orientations become smaller with the increase of grain number in the polycrystalline aggregate, and it is reasonable that the aggre- gate is composed of more than 50 grains. The simulation result agrees well with the experimental data and the true stress becomes higher with greater strain rate which indicates a high reliability of the model.