Finite crack kinking and T-stresses in functionally graded materials

Abstract The optimum direction of in-plane continuous crack advance in functionally graded materials (FGMs) is discussed. The FGM is modeled using finite element analysis as a linear elastic material with spatially varying Young’s modulus. The kink direction was determined as the angle at which either the energy release is maximized ( G max ) or at which the kink tip is deformed without shear ( K II =0). Results are found to asymptote toward that from the infinitesimal short kink analyses for homogeneous materials, based on the local gradient-adjusted phase angle but only for very short kinks. The systematic discrepancy between the finite and infinitesimal results can be accounted for by including the effect of the apparent parallel T -stress. This T -stress is affected by both the far-field parallel loading and, unlike in homogeneous materials, the far-field phase angle. The magnitude of the T -stress is, on average, greater than that for the identical geometry comprised of a homogeneous material. For kink lengths of the same order of the gradient dimension and greater, there is a divergence between the kink angles for the two criteria. In addition, there is a bifurcation in the G max results for negative far-field phase angles. This is caused by the competition between the near-tip K -dominant field and the nonsingular gradient-induced terms, which, in turn, reflects differing effects of the far-field loading and the tendency of the crack to move toward the more compliant region within the modulus gradient.