In this work, a thermodynamically consistent constitutive framework is introduced that is capable of reproducing the significant time-dependent behaviour of austenite-to-bainite phase transformations. In particular, the aim is to incorporate the effect of these diffusion-controlled processes by plasticity-like evolution equations instead of incorporating related global diffusion equations. To this end, a variational principle for inelastic solids is adopted and enhanced by an additional term. This term essentially contributes to the evolution equations for the phase volume fractions of several crystallography-based bainite variants. Due to the specific modifications, special attention has to be paid with respect to the fulfilment of thermodynamical consistency, which can be shown to be unconditionally satisfied for the newly proposed modelling framework. The phase transformation model itself is based on the convexification of a multi-well energy density landscape in order to provide the effective material response for possible phase mixtures. Several material parameters are determined via parameter identification based on available experimental results for 51CrV4, which also allow the quantitative evaluation of the predicted results.
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