A theory of compressive yield strength of nano-grained ceramics

While most coarse-grained ceramics are brittle, nano-grained ceramics can exhibit significant ductility before failure. Such ductility is primarily contributed by the grain-boundary phase, but in grains of certain ceramic phase some plastic deformation has been found to occur and contribute to the overall plastic strain. In this paper a micromechanics-based composite model is developed to elucidate and predict the compressive yield strength of nano-grained ceramics as the grain size decreases from the coarse-grained to the nano-meter scale. The effects of porosity and second elastic phases are also considered. In such a multi-phase, porous, nano-grained ceramic, the collective behavior of all grains of a phase is represented by an elastoplastic constitutive equation, while the relative atomic sliding inside the grain boundary as observed in recent molecular dynamic simulations is represented by Druckerʹs [Q. Appl. Math. 7 (1950) 411] pressure-dependent plasticity theory. The average stress and strain state of the collective grains of each phase and the grain boundary, as well as the strain of the pores, are determined by the generalized self-consistent scheme and the direct self-consistent scheme, respectively, in conjunction with the secant-moduli approach. Applications of the developed theory to a TiO2 indicated that the Hall–Petch plot, i.e., the compressive yield strength vs. d−1/2 relation, showed a positive slope, but the slope continued to decrease, and eventually turned negative. Porosity can significantly lower the compressive yield stress, but it does not alter the fundament characteristics of its grain-size dependence. Second elastic phase can also have a significant effect on the yield strength of a nano-ceramic composite even at 10% of volume concentration.