TOUGHENING BY CRACK BRIDGING IN HETEROGENEOUS CERAMICS

The toughening of a ceramic by crack bridging is considered, including the heterogeneity caused simply by spatial randomness in the bridge l ocations, The growth of a single planar crack is investigated numerica lly by representing the microstructure as an array of discrete springs with heterogeneity in the mechanical properties of each spring, The s tresses on each microstructural element are determined, for arbitrary configurations of spring properties and heterogeneity, using a lattice Green function technique. For toughening by (heterogeneous) crack bri dging for both elastic and Dugdale bridging mechanisms, the following key physical results are found: (i) growing cracks avoid regions which are efficiently bridged, and do not propagate as selfsimilar penny cr acks; (ii) crack growth thus proceeds at lower applied stresses in a h eterogeneous material than in an ordered material; (iii) very little t oughening is evident for moderate amounts of crack growth in many case s; and (iv) a different R-curve is found for every particular spatial distribution of bridging elements. These results show that material re liability is determined by both the flaw distribution and the ''toughn ess'' distribution, or local environment, around each flaw. These resu lts also demonstrate that the ''microstructural'' parameters derived f rom fitting an R-curve to a continuum model may not have an immediate relationship to the actual microstructure; the parameters are ''effect ive'' parameters that absorb the effects of the heterogeneity. The con ceptual issues illuminated by these conclusions must be fully understo od and appreciated to further develop microstructure-property relation ships in ceramic materials.