假设在铸造镁合金材料中的微孔洞具有圆柱形的形状,然后隔离一个圆柱形微孔洞,建立圆柱形微孔洞体胞模型,在基体不可压条件下,得到圆柱形微孔洞的演化方程.根据圆柱形微孔洞体胞模型的速度场得到其应变场,进而基于材料内时本构理论,定义与材料孔洞弱化相关的内蕴时间,得到考虑变形强化和孔洞长大弱化的材料弹塑性本构方程.发展相应的有限元分析程序及数值算法,用其描述铸造镁合金试件在拉伸载荷作用下的应力与应变、塑性变形与材料孔隙率的关系以及试件缺口前缘孔隙率的变化,分析结果与实验结果有较好的一致性.
Supposing the microscopical voids in casting-magnesium alloy material are cylindrical, a cylindrical void-cell model was built. The void-evolution equation of the material was derived based on the void-cell model and the incompressible assumption of the matrix of the material. Through the analyses on the micro-velocity and strain fields of the model as well as the definition of an intrinsic-time measure which is related to void softening, an elastoplastic constitutive equation of the material was obtained, which can reflect the strengthening of deformation and the softening of void of the material. Corresponding finite element procedure was developed and applied to describe the relationships between the stress and the strain, and the plastic deformation and the porosity of the cylindrical specimens of the material, as well as the distribution of the porosity along the notch line of the specimens. Computed results show satisfactory agreement with experimental data.
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