A statistical RKR fracture model for the brittle fracture of functionally graded materials

摘要

A statistical Ritchie-Knott-Rice (RKR) [1] model forbrittle fracture is considered for an FGM containing a slender notch.The FMG is modeled as linear elastic, with its strength describedby two-parameter Weibull statistics. The Young's modulus is assumedto vary either linearly or sigmoidally. A compact tension (C(T))fracture mechanics specimen is analyzed via the finite elementmethod, considering the effect of modulus variation on the near-tipstress state. Results can be characterized by the stress intensity,K. For spatially constant Weibull parameters, the RKR model is usedto predict the expected fracture toughness, K_#PHI#, i.e., the Kat which the first flaw failure occurs with probability #PHI#. Forsufficiently high Weibull modulus, the failure occurs essentiallyat the notch tip. For sufficiently low Weibull modulus (m <4),K_#PHI# for an FGM is found to vary up to 25 percent from that ofa homogeneous body.