On the energetics of tensile and shear void coalescences

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.