On the energetics of tensile and shear void coalescences

Abstract

This paper investigates the mechanisms of tensile and shear void coalescences in ductile materials from energetics perspective. By examining and comparing the elastic and plastic energies of a voided cell throughout its deformation history, the onset of and final coalescence can be distinctly established. This energy-based approach offers a single unified method and criterion for determining the occurrences of both mechanisms. This paper also reports a novel micromechanics model that considers general stress states described by three macroscopic normal stresses and one macroscopic shear stress. Detailed formulation of the model is presented that includes the homogenization-based derivation and implementation of a 4×4 orthogonal transformation matrix, which relates the macroscopic deformation rate of the cell to displacement rates of non-physical degrees-of-freedom (DOFs), and the polar decomposition of the macroscopic deformation gradient tensor which admits the explicit determination of the logarithmic strain measures and rotation angle.In terms of stress ratios, ρ1(=Σ11/Σ22),ρ2(=Σ12/Σ22),ρ3(=Σ33/Σ22), it is analytically shown that multiple macroscopic stress states {ρ1,ρ2,ρ3} can exist that result in the same stress triaxiality T and Lode parameter L. Specifically, it is shown that for a prescribed pair of T and L and in the absence of shear stress, at most six stress states {ρ1,0,ρ3} are possible. On the other extreme in the presence of shear stress, an infinite number of stress states is possible, due to the existence of Mohr's circle for this stress state. This model, together with the proposed energy-based criteria, is used to examine void coalescence under multiple stress-state conditions for any given T and L. Numerical results have shown that the presence of shear stress has a significant effect of reducing the effective strains for the onset of and final void coalescences. In addition, a relationship has also been established between shear angle and effective strain at the onset of shear void coalescence.