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 a nd internal cavity evolution, which are controlled by the rheological parameters (i.e., the strain-rate sensitivity index m, the strain-hard ening exponent n, and the visco-plastic anisotropy parameter) and the cavity growth rate of the materials. Based on Gurson's constitutive re lationship for porous ductile materials, with some modifications, and Hill's normal anisotropic (plane isotropy) yield criterion begin quadr atic in the stress components, a thermo-viscoplastic anisotropic damag e-instability model is proposed. It includes strain hardening, strain- rate hardening, the anisotropy parameter nd the internal cavity volume fraction. The superplastic sheet metal are modelled using this thermo -viscoplastic damage-instability constitutive relationship that accoun ts for strength degradation resulting from the growth of cavities. The current stress components and their ratio (alpha = sigma(2)/sigma(1)) , the stress triaxiality ratio (sigma(m)/<(sigma$)over bar>), and the cavity volume fraction (f) during superplastic deformation of sheet me tals for any strain path between uniaxial tension and biaxial equitens ion, are studied numerically. Finally, taking the occurence of localiz ed instability (<d(epsilon)over bar (2)> = 0) or the cavity volume fra ction reaching the critical value (fc) as a fracture criterion, the li mit strain and the maximum uniform strain are predicated. The rheologi cal parameters (m, n, r), the initial cavity volume fraction and other material constants used in the calculations are determined experiment ly. Comparisons of the calculations with experimental results indicate that the thermo-viscoplastic damage-instability model can provide goo d estimations of the cavity volume fraction, the strength reduction in duced by cavity growth, the deformation and instability behaviour, and the limit strain under various strain histories.