Probabilistic Prediction of Strength and Fracture Toughness Scatters for Ceramics Using Normal Distribution

Tensile strength f_t and fracture toughness K_IC of ceramic are not deterministic properties or fixed values, but fluctuate within certain ranges. A nonlinear elastic fracture mechanics model was developed in this study and combined with the common normal distribution to predict ceramic's f_t and K_IC with consideration of their scatters in a statistical sense. In the model, the relative characteristic crack size a*_ch/G (characteristic crack size a*_ch, average grain size G) was determined based on the fracture measurements on five types of ceramics with different G from 2 to 20 μm in the reference (Usami S, et al., Eng. Fract Mech. 1986, 23, 745). The combined application of the model and normal distribution has two functions: (i) probabilistic f_t and K_IC can be derived from seemingly randomly varied fracture tests on small ceramic specimens containing different initial defects/cracks, and (ii) with f_t or K_IC values (corresponding mean and standard deviation), fracture strength of heterogeneous samples with and without cracks can be predicted by considering scatter described by specified reliability. For the fine ceramics, the predicted results containing the mean and the upper and lower bounds with 96% reliability gained with the model, match very well with the experimental results (a, σ_N).