On temperature rate terms for viscoplastic constitutive models with applications to high temperature materials

The material parameters of viscoplastic constitutive models are often determined from isothermal test data at different temperatures. Applications of these models to non-isothermal load conditions require temperature rate terms to be considered in addition to the temperature interpolation of the material model parameters. Temperature rate terms are of particular importance for the simulation of fast transient loadings of materials with pronounced temperature dependence. The paper presents temperature rate terms for the kinematic hardening parameters of the Robinson viscoplastic model. The development is first shown for uniaxial conditions and later extended to general multiaxial load cases. The proposed formulation is applied to an out-of-phase thermomechanical fatigue (TMF) cycle to compare the numerical predictions of the constitutive models with and without temperature rate terms with measured data. Finally, simulations of three engineering examples with fast thermal transients are presented to show the influence of temperature rate terms on predicting the size and the position of the material stress–strain response.