Crack resistance by interfacial bridging: Its role in determining strength characteristics

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Abstract
An indentation-strength formulation is presented for nontransforming ceramic materials that show an increasing toughness with crack length (T curve, or R curve) due to the restraining action of interfacial bridges behind the crack tip. By assuming a stress-separation function for the bridges a microstructure-associated stress intensity factor is determined for the penny-like indentation cracks. This stress intensity factor opposes that associated with the applied loading, thereby contributing to an apparent toughening of the material, i.e., the measured toughness in excess of that associated with the intrinsic cohesion of the grain boundaries (intergranular fracture). The incorporation of this additional factor into conventional indentation fracture mechanics allows the strengths of specimens with Vickers flaws to be calculated as a function of indentation load. The resulting formulation is used to analyze earlier indentation-strength data on a range of alumina, glass-ceramic, and barium titanate materials. Numerical deconvolution of these data determines the appropriate T curves. A feature of the analysis is that materials with pronounced T curves have the qualities of flaw tolerance and enhanced crack stability. It is suggested that the indentation-strength methodology, in combination with the bridging model, can be a powerful tool for the development and characterization of structural ceramics, particularly with regard to grain boundary structure.