Crack velocity- and strain rate- dependent dynamic compressive responses in brittle solids

Crack velocity and strain rate have an important influence on the dynamic fracture in brittle solids. However, the correspondence between crack velocity- and strain rate- dependent dynamic compressive responses is hardly established. In this study, a dynamic compression-based model triggered by microcrack growth of brittle solids is proposed. This dynamic model consists of the improved model of wing crack extension containing crack inclination effect, the correlation of crack velocity and strain rate, and the crack velocity-related dynamic fracture toughness. This correlation of crack velocity and strain rate is obtained by the time derivative of crack extension relating to axial strain. Crack extension relating to axial strain is obtained by use of correlation of damage relating to crack and strain. The whole variations of strain rate- (or crack velocity-) dependent stress-strain constitutive relationships from low strain rate (or crack velocity) to high strain rate (or crack velocity) are studied. The micro-mechanisms corresponding to the dynamic stress-strain curves also are explained. Moreover, a unified conclusion revealing the sensitivities of strain rate on peak axial strain epsilon(1peak) appearing at peak strength and initial tangent modulus E-ini of stress-strain curves is proposed. Influences of crack velocity and strain rate on crack initiation stress and dynamic strength are analyzed in compression. Effects of the size, inclination and friction of microcracks on dynamic strength also are illustrated. The reasonability of these proposed theoretical results is verified via the published experimental results.