Saturday, February 18, 2006

4. Singularities, interfaces and cracks in dissimilar anisotropic media

Z. Suo, Singularities, interfaces and cracks in dissimilar anisotropic media. Proceedings of Royal Society of London A427, 331-358 (1990).

For a non-pathological bimaterial in which an interface crack displays no oscillatory behaviour, it is observed that, apart possibly from the stress intensity factors, the structure of the near-tip field in each of the two blocks is independent of the elastic moduli of the other block. Collinear interface cracks are analysed under this non-oscillatory condition, and a simple rule is formulated that allows one to construct the complete solutions from mode III solutions in an isotropic, homogeneous medium. The general interfacial crack-tip field is found to consist of a two-dimensional oscillatory singularity and a one-dimensional square root singularity. A complex and a real stress intensity factors are proposed to scale the two singularities respectively. Owing to anisotropy, a peculiar fact is that the complex stress intensity factor scaling the oscillatory fields, however defined, does not recover the classical stress intensity factors as the bimaterial degenerates to be non-pathological. Collinear crack problems are also formulated in this context, and a strikingly simple mathematical structure is identified. Interactive solutions for singularity-interface and singularity-interface-crack are obtained. The general results are specialized to decoupled antiplane and in-plane deformations. For this important case, it is found that if a material pair is non-pathological for one set of relative orientations of the interface and the two solids, it is non-pathological for any set of orientations. For bonded orthotropic materials, an intuitive choice of the principal measures of elastic anisotropy and dissimilarity is rationalized. A complex-variable representation is presented for a class of degenerate orthotropic materials. Throughout the paper, the equivalence of the Lekhnitskii and Stroh formalisms is emphasized. The article concludes with a formal statement of interfacial fracture mechanics for anisotropic solids.

3. Steady-state cracking in brittle substrates beneath adherent films

Z. Suo and J. W. Hutchinson, Steady-state cracking in brittle substrates beneath adherent films. International Journal of Solids and Structures, 25, 1337-1353, (1989).

A crack in a brittle substrate parallel to the film/substrate interface is considered. Stress intensity factors are obtained as a function of film/substrate thickness, elastic properties and edge loads at arbitary crack depth. These results, combined with the criterion K sub II = 0, are used to predict the steady-state cracking depth. The critical combination of residual stress and film thickness below which steady-state substrate cracking is avoided can be inferred provided the substrate toughness is known.

2. Singularities interacting with interfaces and cracks

Z. Suo, Singularities interacting with interfaces and cracks. International Journal of Solids and Structures, 25, 1133-1142 (1989).

Solutions to singularities such as point force, point moment, edge dislocation and transformation strain spot embedded in bonded elastic blocks of dissimilar materials are found to relate to the solutions to the same singularities in an infinite homogeneous plane by a formula independent of the nature of the singularities. This universal result is then used to analyze the interactions between singularities and interface cracks. The complete solutions and stress intensity factors are presented for two important interface crack configurations.

1. Sandwich specimens for measuring interface crack toughness.

Z. Suo and J. W. Hutchinson, Sandwich specimens for measuring interface crack toughness. Materials Science and Engineering, A107, 135-143 (1989).

The present analysis of a crack lying along one interface on an elastic sandwich structure notes the existence, for cases where middle-layer thickness is small by comparison with other structure length scales, of a universal relation between actual interface stress intensity factors at the crack tip, on the one hand, and the apparent modes I and II stress intensity factors associated with the corresponding problem for a homogeneous material crack, on the other. This discovery serves as a theoretical basis for the development of sandwich specimens on which interface crack toughness can be measured; the universal relation reveals the degree to which the intrinsic asymmetry of a bimaterial interface induces asymmetry near the crack field.