Delamination and deflection at interfaces

Cohesive-zone models have been used to study the effects of strength and toughness on the delamination and crack deflection/penetration behavior in beam-like geometries. It has been determined that the LEFM phase angle provides an excellent description of the partitioning of mode-I and mode-II energy-release rates. In particular, the nominal phase angle can be a useful parameter, even when the fracture-length scale is so large that the interface stresses do not exhibit the expected inverse-square-root dependence. The analysis has also shown that nominal phase angles greater than 90° can have physical significance, provided the interface layer is thick enough to accommodate compression without crack-surface contact. The role of modulus mismatch has been studied. A length scale introduced by the cohesive strength allows a crack-tip phase angle to be established, when LEFM predicts oscillating stress fields at the crack tip. This crack-tip phase angle is shifted from the nominal phase angle based on a characteristic geometrical length by an amount that depends on the cohesive parameters of the interface and the modulus mismatch. It has been shown that both modulus mismatch parameters can influence the interface strength.; The cohesive-zone model used here reveals a number of interesting results when applied to crack deflection/penetration behavior. Of particular note is the apparent absence of any lower bound for the ratio of the substrate to interface toughness to guarantee crack penetration. It appears that, no matter how tough an interface is, crack deflection can be induced if the interface strength is low enough compared to the substrate strength. Conversely, it appears that there is a lower bound for the ratio of the substrate strength to interfacial strength, below which penetration is guaranteed no matter how brittle the interface. The effect of modulus mismatch on crack deflection is very sensitive to the mixed-mode failure criterion for the interface, particularly if the cracked layer is much stiffer than the substrate. Finally, it was determined that the relative length of the kinks required in energy-based solutions corresponds to the relative size cohesive zones existing in cohesive-zone solutions.