Critical Dynamics of Damage to Composites and Two-Parameter Fracture Criteria

The dualism of the regularities of transition from the dispersion accumulation of damages to macroscopic failure, which is presented in two-parameter criteria of fracture, is tied to two types of singular solutions in solid bodies with defects: self-similar intermediate-asymptotic distribution of stresses in the vicinity of the crack tip and self-similar kinetics of localization of the damage. In addition to the value of the coefficient of stress intensity, two extra parameters (cohesive strength and cohesion length) are determined by kinetic conditions for the formation of fracture zones on the characteristic spatial scale when the critical values are attained by the stresses in the zones of local damage. These parameters are associated with the nonlinear self-similar kinetics of damage localization, and the existence of two self-similar solutions determines different stages of fracture, including the initiation and propagation of cracks and the fracture of specimens in the presence of concentrators. The stages of development of fracture in the presence of two types of self-similar solutions is investigated experimentally from the data on the kinetics of crack extension in PMMA and DIC data during the deformation of a composite specimen with a circular concentrator, and also demonstrates the analogous dynamics of stages of fracture, which confirms the possibility of using two-parameter criteria to describe the stages of fracture.