Numerical modelling of martensitic growth in an elastoplastic material

Abstract

Abstract A finite-strain-continuum thermomechanical approach is applied to the problem of temperature-induced martensitic transformation in elastoplastic materials. The key issue is to determine the transformation-induced stress and plastic strain fields and their effect on the thermodynamics and kinetics of transformation. The problems of appearance and growth of a temperature-induced rectangular martensitic unit in an austenitic matrix in both bulk and near-free-surface environments are formulated, solved and analysed. Very complex and heterogeneous stress-strain fields in the austenite and martensite phases and their non-monotonic time variation are predicted. Plastic shear strain at some points can reach 60∼ and, after an elastic growth stage, change sign and vary by 40∼. The interface velocity as a function of temperature and interface position is calculated. After the appearance of a martensitic particle, transformation work, which is the only variable part of the interface driving force, decreases by a factor of two during lengthening of the particle by 10∼. The component of the athermal interfacial friction due to dislocation forest hardening increases significantly as well, leading to interface deceleration and growth arrest. A free surface does not significantly affect the driving force until its distance from the moving interface falls below 0.75 times the particle thickness. Then the transformation work increases while the accumulated plastic strain and associated dislocation forest hardening decrease sharply. If the interface is not arrested at this point, it then accelerates to the free surface where an asymmetric plastic zone leaves ‘tent-shaped’ surface relief. The motion of a small step at the martensitic plate interface is studied as well. In contrast with elastic growth, the thermodynamic conditions for lengthening and thickening are almost equivalent for plastic growth. The results obtained allowed us to address the following fundamental problems: firstly, the morphological transition from plate to lath martensite; secondly, the relation of thermally activated kinetics at the interface level to athermal kinetics at the macrolevel; thirdly, the concentration of dislocations and plastic strain in martensite rather than in austenite despite the much higher yield stress of martensite in comparison with austenite.