A strain-gradient plasticity theory of bimodal nanocrystalline materials with composite structure

For the purpose of evaluating the mechanical property of bimodal nanocrystalline (nc) materials, a new composite constitutive model comprised of coarse grains evenly distributed in the nc matrix with respect to strain gradient has been developed. Due to their dissimilar properties and mismatch between the two phases, dislocation-controlling mechanism based on the statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) was analyzed and extended to consider the different influences of two parts in the composite model. We firstly built a stress-strain relation for strain gradient plasticity to predict the effect of grain size distribution on the flow stress. To describe the strain strength quantitatively, a strain-hardened law determined from strain gradient and a nanostructure characteristic length parameter were developed. The strain-hardened law and nanostructure characteristic length parameter were not the same as described in classical strain gradient theory.