Constitutive model for casting magnesium alloy involving spherical void evolution

Casting magnesium alloys are highly heterogeneous materials inevitably containing numerous voids. These voids will evolve during material deformation and markedly affect material behaviors, so it is important to investigate the equation of the void evolution and the constitutive relation involving the void evolution. By assuming the voids in casting magnesium alloys were spherical, the growth equation of the voids was obtained from the incompressibility and continuity conditions of material matrix. Through combining the obtained void-growth equation with the void-nucleation equation relative to the increment of intrinsic-time measure, the evolution equation of the voids was presented. By introducing the presented void-evolution equation to a nonclassical elastoplastic constitutive equation, a constitutive model involving the void evolution was put forward. The corresponding numerical algorithm and finite element procedure of the model were developed and applied to the analysis of the elastoplastic response and the porosity change of casting magnesium alloy ZL305. Computed results show satisfactory agreement with those of the corresponding experiments.