Finite element simulations of crack propagation in laminar ceramic composites

Laminar ceramic materials composed of alternate layers of two different ceramics, in which residual stresses are generated, exhibit a threshold strength. Strength limiting cracks are trapped by the compressive layers and require a minimum (threshold) applied stress to cause them to fail the laminate ceramic. These cracks are observed to propagate straight through the compressive layers in some laminates. Other laminates, however, undergo crack bifurcation; that is, the crack after penetrating some small distance into the compressive layers branches into two symmetrical cracks. Each branch makes an angle of around 60 degrees with the original crack path.; A theoretical analysis is developed to optimize the threshold strength. In this analysis the compressive and tensile layers were assumed to have the same elastic properties. The best result is shown to be associated with the toughest material and the highest residual stress. For each material system, the threshold strength is further optimized by making the layers as thin as possible. Given a laminar ceramic system with a specific compressive layer thickness, the threshold strength is optimized by selecting a ratio of tensile to compressive layer thickness.; Furthermore, finite element calculations were carried out to study the influence of the elastic modulus mismatch between the alternate tensile and compressive layers. Results were obtained for a variety of combinations of different ceramics and suggest that threshold strength is further optimized by making the tensile layer material as stiff as possible and the compressive layer material as compliant as possible.; Finite element analysis is also carried out to explore the cause of crack bifurcation. In this analysis calculations of energy release rate for both straight crack and cracks bifurcated at 60 degrees are performed. If the crack is considered to propagate through an infinite body, the finite element model predicts bifurcation for only one material combination, whereas in experiments bifurcation is observed in three material combinations. When the effect of thermal stress induced edge cracks is incorporated to the model, it is shown that the simulation results are in good agreement with the experimental observations. Crack bifurcation is predicted in all three materials combinations.