A statistical Ritchie-Knott-Rice (RKR)  model for brittle fracture is considered for an FGM containing a slender notch. The FMG is modeled as linear elastic, with its strength described by two-parameter Weibull statistics. The Young’s modulus is assumed to vary either linearly or sigmoidally. A compact tension (C(T)) fracture mechanics specimen is analyzed via the finite element method, considering the effect of modulus variation on the near-tip stress state. Results can be characterized by the stress intensity, K. For spatially constant Weibull parameters, the RKR model is used to predict the expected fracture toughness, KΦ, i.e., the K at which the first flaw failure occurs with probability Φ. For sufficiently high Weibull modulus, the failure occurs essentially at the notch tip. For sufficiently low Weibull modulus (m < 4), KΦ for an FGM is found to vary up to 25% from that of a homogeneous body.
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