Micro-cracks damage constitutive model of quasi-brittle materials subjected to shock compression

Based on the nucleation criterion of wing tension crack of quasi-brittle material, the decrease of elastic moduli of material resulted from the crack damage are derived utilizing micro-mechanics theory. The influence of crack growth velocity on dynamic failure toughness is considered in dynamic growth criterion. The damage constitutive model for brittle materials subjected to compressive loading is developed. The influence of parameters of micro-cracks nucleation, initial crack size on dynamic failure strength are discussed. The stress-strain curves under high strain rate for alumina are compared to the experimental results and a good correlation is obtained.