Stress/strain gradient plasticity model for size effects in heterogeneous nano-microstructures

Traditionally, modeling the effect of grain size on the mechanical behavior of crystalline materials is based on assuming an equivalent homogenous microstructure with strength being dependent on the average grain size, for example the well-known Hall-Petch relation. However, assuming an equivalent homogenized microstructure for a highly heterogeneous microstructure can lead to inaccurate prediction of strength and ductility, especially when the gradients in the spatial heterogeneity are severe. In this work, we employ a multiscale dislocation-based model combined with a strain/stress-gradient theory to investigate the effect of spatial heterogeneity of the microstructure on strength and ductility. We concentrate on understanding the effect of various grain size spatial distributions on the mechanical properties of interstitial free (IF)-steel. The results show that by controlling some parameters in the spatial distribution of the microstructure with regions composed of micro-grains and nano-grains one can achieve improved strength and ductility. Based on these results, it is suggested that the mechanical properties of gradient materials can be described by phenomenological relations that include two structural parameters, grain size and grain-size gradient, in contrast to Hall-Petch relation for homogenous materials where only grains size appears in the equation.