R-curve effect on statistical fracture behaviour of ceramics

The increase of fracture resistance with crack extension has been well documented for many high performance ceramics, e.g. ZrO₂-containing ceramics and aluminas. This pronounced R-curve effect is believed to have increased the mechanical reliability of the ceramics, i.e. to improve the Weibull strength distribution of the material. The improvement is reflected by an increased Weibull modulus though the Lnσ_f-LnLn[1/(1 - P_f)] relationship is still essentially linear. However, the strength distribution curves of sintered Al₃O₂/ZrO₂ composite and PSZ/β-Al₃O₂ are non-linear. In this paper, a theoretical explanation is given for the non-linear Lnσ_f-LnLn [1/(1 - P_f)] relationship for ceramic materials with R-curve characteristics. Predictions of lifetimes of these ceramics subjected to constant static stress, constant stressing rate and constant amplitude cyclic fatigue are given.