This dissertation investigates problems that involve the cohesive response at a crack tip in a homogeneous material, at a crack tip in a bimaterial interface, and an investigation of the cohesive response of an interface. The first investigation outlines a methodology for computing the non-linear generalized load-displacement response of an edge-cracked beam shaped element with a softening crack-plane cohesive zone. The non-linear load-displacement response is intended for use in various possible techniques of nondestructive characterization of the cohesive material properties using the vibration properties of a cracked cohesive beam. The cracked beam shaped geometry is divided into two bodies which interact across the crack plane through appropriate boundary conditions and each body is loaded by a bending couple away from the crack plane. The mode I cohesive law used here is strictly softening and linear. The direct boundary element method (BEM) is applied to each body and the connecting boundary conditions and an iterative scheme is used to determine the extent of the cohesive zone. The J-integral associated with the single crack tip is then calculated from the BEM crack plane tractions and displacements and is used to numerically evaluate the generalized non-linear load-displacement relations. The second investigation outlines a novel approach to numerically model a Dugdale-Barenblatt cohesive zone at an interface crack between two dissimilar materials. The direct BEM approach is once again used here to appropriately apply the constraints in the cohesive zone and obtain a physically meaningful solution for tractions and displacements in the crack plane. The effect of material mismatch and the effect of varying bond strength on the interface fracture energy as expressed by the individual mode I and mode II contributions to the J-integral is also studied. This approach provides a heretofore unavailable convenient method for calculating the local crack tip mode mixity, the total energy release rate and its decomposition into the separate mode contributions as a function of the applied mode mixity and material mismatch. The third investigation concerns the dispersion relations for time-harmonic guided waves in a layer connected to a rigid substrate by a very thin interface layer of material with nonlinear and softening behavior. The interfacial spring stiffness which, is directly included in the dynamic layer boundary conditions, may be interpreted as the local slope of the cohesive law at the static pre-load level. The spring stiffnesses inferred from the dispersion relations of either SH or generalized Rayleigh-Lamb waves from a series of measurements taken at multiple pre-load levels could then be integrated to obtain the cohesive law.
展开▼
