Martensitic transformations in isotropic inhomogeneous elastic-plastic solids: continuum theory and analysis of nucleation, kinetics and size effect

A thermodynamically consistent phenomenological theory of interactions between strain-gradient plasticity (SGP) and martensitic transformations (MTs) is developed for isotropic solids with incoherent phase boundaries (PBs) at the microscale, including a heterogeneous nucleation criterion for the phases, nucleation and PB kinetic laws and plasticity rules for the phases and PBs, which are all coupled. This work is a generalization of Basak (Basak. 2025 Proc. R. Soc. A 481, 20240564. (doi:10.1098/rspa.2024.0564)), introducing a rigorous thermodynamic nucleation theory in a non-local elastic-plastic solid for the first time. Within the von Mises-type second-order plasticity theory for the phases and PBs, the yield strengths are considered functions of plastic incompatibilities, which measure the material inhomogeneities, in the respective regions and depend on the intrinsic length scales. No higher-order stresses are considered. The principle of maximum transformation rate, equivalent to the principle of minimum transformation time, is derived and used to obtain a scale-dependent thermally activated nucleation criterion assuming no stable intermediate state exists between the phases. An athermal threshold to the driving force for nucleation, dependent on plastic inhomogeneity, is considered. A semi-analytical solution for the thermomechanical response of a thin, semi-infinite austenitic slab nucleating a plate-like martensite and subsequent transformations, coupled to SGP, is presented.