A non-linear model for internal stress superplasticity

Abstract

Most models of internal stress superplasticity predict a linear relationship between the applied stress and the plastic strain per cycle, and are only valid at low applied stresses. In the present paper, we extend the original linear theory of phase transformation superplasticity by Greenwood and Johnson [1] and derive a non-linear closed-form solution valid over the whole range of stresses, from the low-stress regime (where a linear relationship between strain and stress is predicted in agreement with the model by Greenwood and Johnson ( Proc. R. Soc. Lond., 1965, 283, 403), to the high-stress regime (where the strain increases non-linearly as the applied stress approaches the yield stress of the weaker phase). The model is found to be in agreement with literature data on transformation superplasticity of iron spanning both stress regimes. Furthermore, the model is adapted to the case where internal stresses are produced by thermal expansion mismatch: it is compared to experimental literature data for metals with anisotropic thermal expansion (Zn and U) and for metal matrix composites with inhomogeneous thermal expansion (Al SiC).