Estimation of Characteristic Parameters of a Grain-Bridging Model for Crack-Extension Resistance

An alternative method of analysis was developed to estimate characteristic parameters of a published grain‐bridging model for crack‐extension resistance (R‐curve) and to enable estimations of standard deviations of the parameters, which determine to a large extent the usefulness of the measurement results. The method is based upon fitting the model to both strength and crack‐length measurements, corresponding to a range of indentation loads. Indentation–strength data for an alumina ceramic that was hot‐pressed with a mean grain size of 10 μm were used to demonstrate the method of analysis. These data were taken from tests where the indentation cracks were much larger than the grain size of the alumina and where residual stresses due to the indentations were annealed out. The model in this situation can be reduced to an explicit expression of strength as a nonlinear function of crack length, which is easily amenable for analysis by a least‐squares method for nonlinear functions. The results indicate some limitations in the usefulness of estimating parameters of the grain‐bridging model. As many as three of the five major characteristic parameters of the model can be estimated from the selected indentation–strength data, but because the standard deviations of the three parameters are rather large, preferably not more than two parameters should be estimated, assuming the third is known.