A 3D mechanistic model for brittle materials containing evolving flaw distributions under dynamic multiaxial loading

We present a validated fully 3D mechanism-based micromechanical constitutive model for brittle solids under dynamic multiaxial loading conditions. Flaw statistics are explicitly incorporated through a defect density, and evolving flaw distributions in both orientation and size. Interactions among cracks are modeled by means of a crack-matrix-effective-medium approach. A tensorial damage parameter is defined based upon the crack length and orientation development under local effective stress fields. At low confining stresses, the wing-cracking mechanism dominates, leading to the degradation of the modulus and peak strength of the material, whereas at high enough confining stresses, the cracking mechanism is completely shut-down and dislocation mechanisms become dominant. The model handles general multiaxial stress states, accounts for evolving internal variables in the form of evolving flaw size and orientation distributions, includes evolving anisotropic damage and irreversible damage strains in a thermodynamically consistent fashion, incorporates rate-dependence through the micromechanics, and includes dynamic bulking based on independent experimental data. Simulation results are discussed and compared with experimental results on one specific structural ceramic, aluminum nitride. We demonstrate that this 3D constitutive model is capable of capturing the general constitutive response of structural ceramics.