Numerical computation of cavity damage and failure during the superplastic deformation of sheet metals

Superplastic deformation is considered as a thermo-viscoplastic flow. The deformation and failure of superplastic sheet metals are a result of a combination and interaction process between tensile instability and internal cavity evolution, which are controlled by the rheological parameters (i.e., the strain-rate sensitivity index m, the strain-hardening exponent n, and the visco-plastic anisotropy parameter) and the cavity growth rate of the materials. Based on Gurson's constitutive relationship for porous ductile materials, with some modifications, and Hill's normal anisotropic (plane isotropy) yield criterion being quadratic in the stress components, a thermo-viscoplastic anisotropic damage-instability model is proposed. It includes strain hardening, strain-rate hardening, the anisotropy parameter and the internal cavity volume fraction. The superplastic sheet metals are modelled using this thermo-viscoplastic damage-instability constitutive relationship that accounts for strength degradation resulting from the growth of cavities. The current stress components and their ratio (α = σ₂/σ₁), the stress triaxiality ratio (σ_m/σ̄), and the cavity volume fraction (f) during superplastic deformation of sheet metals for any strain path between uniaxial tension and biaxial equitension, are studied numerically. Finally, taking the occurence of localized instability (dε̄₂ = 0) or the cavity volume fraction reaching the critical value (f_c) as a fracture criterion, the limit strain and the maximum uniform strain are predicted. The rheological parameters (m, n, r), the initial cavity volume fraction and other material constants used in the calculations are determined experimently. Comparisons of the calculations with experimental results indicate that the thermo-viscoplastic damage-instability model can provide good estimations of the cavity volume fraction, the strength reduction induced by cavity growth, the deformation and instability behaviour, and the limit strain under various strain histories.