Estimation of C(t) and the creep crack tip stress field of functionally graded materials and verification via finite element analysis

Functionally graded materials (FGMs) are increasingly being used in high-temperature structural components. The time-dependent C-integral, C(t), is a significant parameter in characterizing the crack tip stress field from the small-scale to the extensive steady-state creep stages. In this paper, the creep crack behavior of FGMs with a crack parallel to the material property gradients was studied by using the finite element method. It was proven that C(t) remained valid for FGMs. An engineering method was proposed to estimate C(t) in the small scale and transition creep stages and estimate the crack tip stress field. Finite element results verified that the method could estimate C(t) in the small scale and transition creep stages and estimate the crack tip stress field. For cases with creep properties that increased in the crack growth direction, the effect of constraint on the estimated crack tip stress field had to be considered. The constraint parameter of Q was significantly affected by the creep property gradients. The method was independent of the gradient variation law of material properties.