A theoretical and numerical approach to the plastic behaviour of steels during phase transformations—II. Study of classical plasticity for ideal-plastic phases

Abstract The response of phase-transforming steels to variations of the applied stress (i.e. the ∑-term of the classical plastic strain rate Ė cp defined in Part I) is studied both theoretically and numerically for ideal-plastic individual phases. It is found theoretically that though the stress-strain curve contains no elastic portion, it is nevertheless initially tangent to the elastic line with slope equal to Young's modulus. Moreover an explicit formula for the beginning of the curve is derived for medium or high proportions of the harder phase, and a simple upper bound is given for the ultimate stress (maximum Von Mises stress). The finite element simulation confirms and completes these results, especially concerning the ultimate stress whose discrepancy with the theoretical upper bound is found to be maximum for low proportions of the harder phase. Based on these results, a complete model is proposed for the ∑-term of the classical plastic strain rate Ė cp in the case of ideal-plastic phases.