STOCHASTIC-MODEL OF AN R-CURVE DUE TO CRACK BRIDGING

A stochastic model is formulated to analyse crack tip shielding from t he applied load, as a function of microstructural parameters and loadi ng conditions, in nontransforming polycrystalline ceramics. The model recognizes the random nature of the microstructural elements, such as grains, inclusions or fibres, which are traversed by the propagating c rack. The role of distribution of grain size, and strength of grains a nd interfaces in the development of the crack interface bridging is em phasized, and numerically evaluated. The standard model parameters are chosen to represent aluminium oxide, as an extensive experimental dat a base is available for this material. Quantitative predictions of tou ghening and closure stresses within the bridging process zone are in a greement with experimental data quoted in the literature. It is found that a typical coarse-grained alumina with geometric average grain siz e of 10 mu m and geometric standard deviation of 1.3 exhibits a 5 mm l ong bridging zone, with the maximum closure stress of 86 MPa, and the maximum toughening due to crack bridging of 90 J/m(2). The R-curve has been confirmed to depend both on the average grain size and on the gr ain size distribution, as well as on the level of residual stresses, s ingle grain strength, interfacial roughness and the grain boundary str ength. The validity of the relatively simple Monte Carlo model propose d in this work opens up a possibility for optimization of microstructu res of monolithic and composite ceramics for maximum resistance to fra cture.