A statistical model for brittle fracture of functionally graded materials

A model has been developed to assess the structural assessment of functionally graded materials in which yield strength and toughness vary spatially. The yield strength of the material at any point is deterministic, but varies spatially. The local cleavage toughness also varies spatially, but is statistically distributed following a two parameter Weibull model. The Weibull moduli quantify reliability and the second Weibull parameter is interpreted in terms of the mean toughness of the local material. The model intended to determine the crack propagation direction and failure probabilities of a stationary pre-crack. The effect of simple yield strength and toughness gradients are discussed, before the model is applied to experimental data on laser welded joints.