Calibration of a phase mixture model for hardening and softening regimes in tempered martensitic steel over wide stress and temperature ranges

Abstract

Tempered martensitic steels are used for turbine components in power plants under high temperatures $(T\approx 873\mathrm{K})$ . In addition, the components are subjected to temperature changes during start-up and shutdown procedures. In order to model the mechanical behavior of tempered martensitic steels in the high-temperature range, this article presents a phase mixture model accounting for hardening and softening effects. The alloy is described as an iso-strain mixture of a hard phase and a soft phase. Thereby, the hard phase is related to the subgrain boundaries, that is, regions with high dislocation density, while the soft phase is related to the subgrain interior, that is, regions with low dislocation density. The volume fraction of the hard phase is assumed to decrease toward a saturation value, such that softening effects due to the coarsening of subgrains are taken into account. The introduction of two internal variables, a backstress and a softening variable, allows for the calibration based on macroscopic material tests, that is, creep and high-temperature tensile tests. Special emphasis is placed on the detailed description of this non-trivial calibration procedure. The calibration is based on the distinction of stresses and strain rates in initial and steady states. Starting from three differential equations with respect to the inelastic overall strain rate, the backstress, and the softening variable, all required functions and parameters are determined. The calibrated model is verified by the simulation of additional material tests at high temperature, highlighting the wide application range with respect to stresses $(100-700\mathrm{MPa})$ and temperature $(673-923\mathrm{K})$ .