On Micromechanical Evolutionary Damage Models for Polycrystalline Ceramics

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Abstract
Evolutionary micromechanical constitutive models for polycrystalline MgO ceramics with distributed dislocations and integranular microcracks are presented. Based on the description of dominant modes of microstructural changes in polycrystals, the kinetics of microcrack evolution in a typical grain is studied. Four basic deformation modes are considered within the micromechanics framework—the elastic deformation, slip band, microcrack nucleation, and microcrack kinking mechanisms. In particular, a slip band is assumed to be caused by the Frank-Read dislocation source, and a microcrack is assumed to be nucleated by the Zener-Stroh mechanism. At the onset, the stress-strain relation of the polycrystalline MgO ceramics is taken as linearly elastic. As the loading stress increases, slips will occur first in those crystals having the "easiest" slip planes at an angle of 45 degree. At some point, the stress in front of a dislocation pileup will exceed the cohesive strength of an intergranular plane. Therefore, a microcrack will nucleate on the grain boundary ("Cleavage 2" process). By computing the strain and compliance contributions due to many probabilistically distributed and evolutionary dislocations, microcracks and kinked microcracks, effective moduli and stress-strain relations can be derived based on micromechanics and approximate effective medium methods. Effects of different grain size distributions are investigated in detail by considering five cases (the fixed grain size, uniform distribution, normal distribution, square-root normal distribution, and linear decreasing distribution functions). The proposed models are subsequently applied to uniaxial tensile loadings, biaxial loadings, and residual stresses. Several interesting evolutionary examples are also presented to illustrate the capability and behavior of the proposed micromechanical damage models.