Elaboration of an Inelastic Constitutive Model of Superplasticity and Extension to Multiaxial State of Stress

Elaboration of a uniaxial constitutive model of superplasticity taking account of grain and cavity growth proposed by the present authors and its extension to a multiaxial form are discussed. First the expression of an inelastic strain-rate is improved by adopting the hyperbolic sine law proposed by Garofalo to represent the stress dependence of inelastic strain-rate. The evolution equation of cavity volume fraction is also improved by incorporating the strain-rare dependence of cavity growth induced by inelastic deformation. A multiaxial constitutive equation at finite deformation is established by using the flow theory of von Mises type. Comparison of the predictions with the corresponding monotonic tension experiments in literature shows that the proposed model can give much better predictions of the typical deformation behavior of superplasticity ; e.g. the S-curve in the stress versus strain-rate relation on a log scale, the strain-rate dependence of the slope of hardening curve, the strain-rate history dependence of flow stress in the presence of static grain growth, and the softening of flow stress due to cavity growth.