The grain size and porosity dependent elastic moduli and yield strength of nanocrystalline ceramics

For the purpose of investigating the effects of grain size and porosity on the elastic modulus and strength of porous and possible multi-phase nanocrystalline ceramics, a mixtures-based model is firstly developed to describe the mechanical behavior of an individual phase in multi-phase nanocrystalline ceramics, then Budianskyʹs self-consistent method is used to calculate the elastic modulus of porous, multi-phase, nanocrystalline ceramic, the predictions are in good agreement with the results in literature. Further, the established method is extended to describe the constitutive relations with small plastic deformation and yield strength of porous and possible multi-phase nanocrystalline ceramics in conjunction with the secant-moduli approach and iso-strain assumption. Overall, the developed method appears to be capable of reflecting the effects of grain size and porosity on the elastic moduli and yield strength of porous, multi-phase, nanocrystalline ceramics.