Determination of the effective mode-I toughness of a sinusoidal interface between two elastic solids

A finite element model of crack propagation along a sinusoidal interface with amplitude A and wavelength a between identical elastic materials is presented. Interface decohesion is modeled with the Xu and Needleman (J Mech Phys Solid 42(9):1397,1994) cohesive traction-separation law. Ancillary calculations using linear elastic fracture mechanics theory were used to explain some aspects of stable and unstable crack growth that could not be directly attained from the cohesive model. For small aspect ratios of the sinusoidal interface (A/lambda <= 0.25), we have used the analytical Cotterell-Rice (Intl J Fract 16:155-169,1980) approximation leading to a closed-form expression of the effective toughness, K-1c, given by K-1c root(1 - v(2))/E Phi n = 2/ (1 + [1 + 4 pi(2) (A/lambda(2)]-(1/2)), where Phi n is the work of separation, E is Young's modulus, and v is Poisson's ratio. For A/lambda > 0.25, both the cohesive zone model and numerical J-integral estimates of crack tip stress intensity factors suggest the following linear relationship: K1c root(1- v(2)) / E Phi n = 0.81+1.89(A/lambda). Parametric studies show that the length of the cohesive zone does not significantly influence K-1c, although it strongly influences the behavior of the crack between the initiation of stable crack growth and the onset of unstable fracture.