Multiaxial Experiments and Constitutive Modeling of Superplasticity

Abstract

In the first part of the paper, multiaxial experiments of 5083Al alloy are carried out at 833K at constant strain-rates to elucidate the characteristic features of superplastic deformation under general forming conditions. Monotonic tension, compression and torsion tests were performed by using solid circular cylindrical specimens together with thin-walled tubular specimens. The values of the equivalent strain-rate of von Mises type are specified as 2 × 10 -3 , 1 × 10 -3 , 5 × 10 -4 and 2 × 10 -4 s -1 . The significant strain-rate dependence of flow stress and the material softening due to cavity growth are observed under the tension tests. The results of the tension and compression tests show that the material hardens under tension while it softens under compression. The comparison between tension and torsion tests shows that the equivalent flow stress of von Mises type under torsion is much smaller than that of the tension at the same equivalent strain-rate of von Mises type. Based on these observations, a constitutive model of superplasticity is then formulated based on the finite deformation theory. The rate of deformation tensor is divided into the sum of the elastic and inelastic parts, and the former part is represented by the isotropic linear elastic law. The inelastic part is modeled based on the invariant theory by employing the steady-state creep law of hyperbolic sine type and by taking account of the effects of yielding, grain and cavity growth. The rate of drag stress is assumed to be the sum of the terms due to the grain and cavity growth. The evolution equation of the grain growth is formulated by taking account of static growth and strain-induced growth. The evolution equation of the cavity volume fraction is represented by the sum of the two terms due to cavity diffusion and viscoplastic deformation. Comparison of the results of the proposed model with those of the experiments shows that the proposed model gives satisfactory predictions.