Modelling of R-curve behaviour in ceramic–metal laminates

In materials that display R-curve behaviour, the magnitude of the bridging stress is dependent on the local crack opening. Therefore, the bridging stress distribution and consequently, the toughness can be quite different for different crack geometries and crack lengths, even if the same bridging law is applied. In the present study, using the exact stress–displacement function (σ(u)) of the constrained metal layer and a weight-function-based approach, it was possible to obtain the crack opening profile (u(x)), and hence the bridging stress distribution along the bridging zone. The calculated displacement profiles using the weight function were checked by comparison with that obtained using the Finite Element Method at different crack sizes. Predicted fracture toughness resistance curves were compared to experimental results for different ceramic–metal combinations. The effect of different properties of the bridging layer (thickness, ductility, strength and debonding) on the predicted R-curve has been studied by their effect on the bridging traction-displacement relationship.