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 eleme nt analysis as a linear elastic material with spatially varying Young's mod ulus. The kink direction was determined as the angle at which either the en ergy release is maximized (G(max)) or at which the kink tip is deformed wit hout shear (K-II = 0). Results are found to asymptote toward that from the infinitesimal short kink analyses for homogeneous materials, based on the l ocal gradient-adjusted phase angle but only for very short kinks. The syste matic discrepancy between the finite and infinitesimal results can be accou nted forby including the effect of the apparent parallel T-stress. This T-s tress is affected by both the far-field parallel loading and, unlike in hom ogeneous materials, the far-held 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 th e two criteria. In addition, there is a bifurcation in the G(max) results f or negative far-field phase angles. This is caused by the competition betwe en the near-tip K-dominant field and the nonsingular gradient-induced terms , which, in turn, reflects differing effects of the far-field loading and t he tendency of the crack to move toward the more compliant region within th e modulus gradient. (C) 2001 Published by Elsevier Science Ltd.