Singularities, Interfaces and Cracks in Dissimilar Anisotropic Media

• Published in: Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1990-02, Vol.427 (1873), p.331-358
• Main Author: Suo, Zhigang
• Format: Article
• Language: English
• Subjects: Composite materials; Condensed matter: structure, mechanical and thermal properties; Deformation; Eigenvalues; Exact sciences and technology; Fatigue, brittleness, fracture, and cracks; Fracture mechanics; Geometric lines; Half planes; Mathematical vectors; Mechanical and acoustical properties of condensed matter; Mechanical properties of solids; Physics; Stress intensity factors; Tensors; Toughness
• ISSN: 1364-5021; 0080-4630; 1471-2946; 2053-9169
• DOI: 10.1098/rspa.1990.0016

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.