Investigation of fracture characterizations of functionally graded materials

In this paper, the mode I crack problem of functionally gradient materials (FGMs) with the gradient direction parallel to the crack is discussed, and the differences of stress distribution between the gradient materials and the homogeneous materials are analyzed. It is shown that a mode I crack problem of FGMs with the gradient direction parallel to the crack direction can become a mixed‐mode crack problem. In FGMs, the crack initiation angles are determined by the fracture toughness gradient, elastic modulus and crack mode. If the gradient coefficients are small, the crack initiation angles in FGMs are the same as those in homogeneous materials. If the elastic modulus gradient is large, the principal stress terms without the gradient coefficients can be ignored in obtaining the crack initiation angle. In this study, all the above results are generalized to the mixed‐mode crack problems with arbitrary angle between the gradient direction and the crack direction.