A multiscale constitutive model coupled with martensitic transformation kinetics for micro-scaled plastic deformation of metastable metal foils

The mechanical behavior of metastable austenitic foils at the size scale from micron to submillimeter is strongly affected by the coupling between size effect and strain-induced martensitic transformation (SIMT), which remains to be a pressing issue to be explored. In this research, the focus is on developing a multiscale constitutive model to reveal the mechanical behavior of metastable foils and more accurately predict the size effect on SIMT. In tandem with this, the martensitic transformation and hardening behavior of SUS304 foils with different thicknesses and grain sizes were explored. The results figured out that the SIMT is promoted by the increase in grain size and foil thickness. Furthermore, the onset and end of stages II of work-hardening behavior are advanced and the work-hardening rate in stage II increases faster with increasing grain size and foil thickness. The SIMT kinetic model was coupled with the intermediate mixture law and the iso-work hypothesis to identify the stress-strain relationship of individual austenite and martensite at the surface and interior layers, which was used to construct the multiscale constitutive model. The multiscale model was developed based on the framework of the surface layer model and the intermediate mixture law to represent the coupling between the size effect and the SIMT. Through finite element simulation by using the proposed multiscale constitutive model, the dispersion hardening mechanism in micro-scaled deformation of metastable austenitic foils caused by the non-homogeneous plastic deformation at the interface between austenite and martensite was revealed. The multiscale model was validated via the corroboration of finite element simulation with experiments and therefore can provide a robust analysis of the micro-scaled deformation behavior of metastable austenitic foils.