Model for Fatigue Crack Growth in Grain-Bridging Ceramics

Abstract

A model for fatigue crack propagation based on sliding wear of bridging grains is analyzed for polycrystalline ceramics. Taking into account damage development and crack tip energy balance, we have obtained rigorous solutions for equilibrium and compatibility equations in the crack wake under monotonic and cyclic loading/unloading conditions. Fatigue mechanics in ceramics is found to be formally similar to elastic-plastic mechanics of a path-dependent hardening material, due to the frictional resistance to reverse sliding. It features a load-displacement hysteresis causing energy dissipation and wear, and a longer cohesive zone required for supporting the same peak load with the wear-reduced bridging stresses. The unloading crack opening displacement is more strongly dependent on Kmax than on DeltaK; such displacement causes wear on the bridging grains. Meanwhile, incremental crack growth brings in new bridging grains that has a shielding effect on the crack tip stress field; such an effect is strongly dependent on Kmax but independent of DeltaK. At steady state, when shielding accumulation and shielding degradation are balanced, the fatigue crack growth rate has a form da/dN=A(Kmax)b(DeltaK)c, where A, b, and c are material-dependent parameters. Fatigue is predicted to have a very high b, a modest c, a higher fatigue resistance for tougher ceramics, and a stronger Kmax dependence for less tough ceramics. These predictions are in agreement with experimental observations.