Occurrence condition for steady crack propagation in quasi-brittle fracture and its application in determining initial fracture toughness

Abstract

Crack propagation is commonly assumed to be a parallel motion called the steady state in quasi-brittle materials. The steady crack propagation can be used to determine softening traction-separation relation because one-to-one correspondence exists between the crack growth resistance and the softening traction-separation relation. However, the steady-state crack propagation that all quantities like crack opening displacement and cohesive stress keep invariable may not occur due to the limitation of the fracture process zone (FPZ). For quasi-brittle fracture, it is essential to define when the steady crack propagation occurs for ensuring the applicability to determine the softening traction-separation relation based on steady crack propagation. In this study, numerical test results of three specimen geometries, seven specimen sizes and three softening traction-separation relations are employed to analyze the steady crack propagation. Through comparison between crack growth resistance based on steady-state assumption and equivalent LEFM R-curve, a pseudo-steady state regime that is very similar to the steady crack propagation is found. At the pseudo-steady state, the relationship between the softening traction-separation relation and the crack growth resistance under steady crack growth is still applicable. The occurrence condition for the pseudo-steady crack propagation is deduced. It is found that for most laboratory specimens, the critical situation (load reaches its maximum value) can be seen as a pseudo-steady state with an error of <20%. By choosing the softening traction-separation relation based on the pseudo-steady assumption, the initial fracture toughness can be determined. The errors of the initial fracture toughness determined by this method can be approximately estimated based on the range of lFPZ/(D-ac).