Application the mechanism-based strain gradient plasticity theory to model the hot deformation behavior of functionally graded steels

Functionally graded steels (FGSs) are a family of functionally graded materials (FGMs) consisting of ferrite (a), austenite (v), bainite (B) and martensite (M) phases placed on each other in different configurations and produced via electroslag remelting (ESR). In this research, the flow stress of dual layer austenitic-martensitic functionally graded steels under hot deformation loading has been modeled considering the constitutive equations which describe the continuous effect of temperature and strain rate on the flow stress. The mechanism-based strain gradient plasticity theory is used here to determine the position of each layer considering the relationship between the hardness of the layer and the composite dislocation density profile. Then, the released energy of each layer under a specified loading condition (temperature and strain rate) is related to the dislocation density utilizing the mechanism-based strain gradient plasticity theory. The flow stress of the considered FGS is obtained by using the appropriate coefficients in the constitutive equations of each layer. Finally, the theoretical model is compared with the experimental results measured in the temperature range 1000-1200\'C and strain rate 0.01-1 s-1 and a sound agreement is found.