Role of interfacial grain-bridging sliding friction in the crack-resistance and strength properties of nontransforming ceramics

A grain-bridging model of crack-resistance or toughness (R-curve, or T-curve) properties of nontransforming ceramics is developed. A key new feature of the fracture mechanics treatment is the inclusion of internal residual (thermal expansion mismatch) stresses in the constitutive stress-separation relation for pullout of interlocking grains from an embedding matrix. These internal stresses play a controlling role in the toughness properties by determining the scale of frictional tractions at the sliding grain-matrix interface. By providing a physical account of the underlying micromechanics of the bridging process the analysis allows for predetermination of the material factors in the constitutive relation, thereby reducing parametric adjustments necessary in fitting the theoretical toughness curve to experimental data. The applicability of the model is illustrated in a case study on indentation-strength data for a “reference” polycrystalline alumina with particularly strong T-curve characteristics. From theoretical fits to these data the constitutive relation, and thence the entire T-curve, can be deconvolved. This “parametric calibration”, apart from demonstrating the plausibility of the model, allows for quantitative predictions as to how the toughness and strength characteristics of ceramics depend on such microstructural variables as grain size and shape, grain boundary energy, level of internal stress and sliding friction coefficient. An indication of this predictive capacity is provided by a preliminary calculation of the grain-size dependence of strength, using some existing data for other aluminas as a basis for comparison.