Finite crack kinking and T-stresses in functionally graded materials

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.