Strength of nanostructured materials using a phase mixture model

A phase mixture model (PMM) was considered in which materials are treated as a mixture of grain interior phase, grain boundary phase and pores (if the material is porous) for the elasticity and plasticity of nanostructured materials (NSMs). In order to investigate the effects of grain size and porosity on the elastic modulus, a self-consistent method in conjunction with PMM was employed. The calculated results are compared with the experimental measurements in the literature. The elastic modulus of NSMs decreases with a decrease of the grain size and the decrement is relatively large at grain sizes below about 10 nm, The effect of porosity, however, is substantially greater than the grain size effect. For the plasticity of NSMs, grain size effects were introduced both via the dislocation glide mechanism and through the diffusion mechanisms providing mass transfer via grain boundaries. A good agreement between the calculated deformation behavior and experiment was found. The quality of the above predictions with regard to strength, strain hardening, strain sensitivity and ductility behavior testify the adequacy of the model. It is concluded that the model can be used as a convenient tool for simulating the deformation behavior of NSMs.