STOCHASTIC-MODEL OF AN R-CURVE DUE TO CRACK BRIDGING IN FIBROUS AND TEXTURED CERAMICS

A stochastic model, previously formulated to analyze crack tip shieldi ng from an applied load in nontransforming polycrystalline ceramics wi th equiaxial grains, has been extended to include non-equiaxial and or iented grains. The aspect ratio of fibrous grains has been varied from one to 10, and the fraction of fibrous grains oriented normally to th e crack plane from 0.33 (representing random orientation) to 0.8 for t extured materials. The role of the distribution of grain size, aspect ratio, degree of texturing, and strength of grains and interfaces in t he development of the crack bridging is analyzed and numerically evalu ated. It is assumed that the crack closure stress arises predominantly due to the frictional pullout of grains, i.e. the contribution from e lastic bridges is neglected. The model parameters are chosen to repres ent ceramics such as aluminum oxide or silicon nitride, as extensive e xperimental data are available for various microstructural variants of these materials. The principal parameters resulting from the model in clude a maximum increment of the resistance to fracture Delta G due to the frictional bridging of long cracks, Delta G(m), and a slope of De lta C vs crack extension within the first 100 mu m of the crack growth , V-G = d(Delta G)/dx. As long cracks will almost never have a chance to develop in ceramic components under tensile or bending service stre sses, it is argued that the study of V-G = d(Delta G)/dx could be more informative as far as reliability of ceramics is concerned. Variation of both parameters is extensively mapped as a function of the microst ructural characteristics, such as grain aspect ratio, grains orientati on, grain and interfacial strength, and pullout stress due to grain su rface roughness. The model outcome confirms that long, strong, oriente d grains would result in the most effective toughening of R-curve exhi biting ceramics. However, an optimum grain aspect ratio that results i n the largest values of saturated toughness is predicted. In most case s the optimum aspect ratio is 4:8, but can be close to one for some mi crostructures. The general range of variation of the saturated toughne ss as a function of varying model parameters is similar to 100 J/m(2)- similar to 350 J/m(2). Weak interfacial shear strength is desirable i n most cases to achieve large final toughening. An optimum grain aspec t ratio of 4:8 is required to maximize the toughening gradient VG The highest toughening gradient V-G is expected for strong grains which ex perience large stresses due to resistance to pullout. These conditions would not simultaneously generate the largest saturated toughness. It is concluded, therefore, that the routes to achieve the large ultimat e toughening and the high reliability in ceramics are different. It is predicted that as long as the pullout stress due to interfacial rough ness is maintained high, high-reliability ceramics could be produced e ven with equiaxial grains. It appears that the grain aspect ratio of a bout four for strong, oriented grains with rough interfaces which are easy to separate is a necessary condition for achieving high reliabili ty of R-curve exhibiting ceramics. (C) 1997 Acta Metallurgica Inc.