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On the mesoscopic length scale, dual-phase steel (DP) consists of hard and brittle martensitic inclusions, which are embedded in a soft and ductile ferritic matrix. On the macroscopic scale, this composite-like structure is responsible for the attractive combination of good formability and high tensile strength. In order to improve the properties of DP, computer models can be used to investigate the effects of various influencing factors during the production chain. As an extension to our previous work (Schoof et al 2018 Int. J. Solids Struct. 134 181-94), we include a J 2 -viscoplasticity formulation into a multiphase-field framework to study plastic effects in an EBSD-based DP microstructure during the martensitic phase transformation. The hardening behavior of each phase is modeled using a nonlinear function. The effect of the plastic relaxation rate on the microstructure formation and the residual strains is investigated. Two different models for introducing a yield criterion into a diffuse interface framework are discussed, and the results are compared. In this context, a plastic driving force is formulated, and its influence on the microstructure evolution is evaluated. The model not only predicts high values of accumulated plastic strain in ferritic regions, close to ferrite-martensite grain boundaries, but also within martensitic islands.

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