Edge singularities in anisotropic composites

Abstract The stress singularity at the vertex of an anistropic wedge has the form r − ϵ F ( r , θ ) as r → 0 where 0 F is a real function of the polar coordinates ( r , θ). In many cases, F is independent of r . The explicit form of F ( r , θ ) depends on the eigenvalues of the elasticity constants, called p here and on the order of singularity k . When k is real, ξ = k If k is complex, ξ is the real part of k . The p 's are all complex and consist of 3 pairs of complex conjugates which reduce to ± i when the material is isotropic. The function F depends not only on p and k , it also depends on whether p and k are distinct roots of the corresponding determinants. In this paper we present the function F ( r , θ ) in terms of p and k for the cases when p and k are single roots as well as when they are multiple roots. The relationship between the complex variable Z introduced in the analysis and the polar coordinates ( r , θ ) is interpreted geometrically. After presenting the form of F for individual cases, a general form of F is given in eqn (74). We also show that the stress singularity at the crack tip of general anisotropic materials has the order of singularity ξ=1/2 which is at least a multiple root of order 3. The implication of this on the form F ( r , θ ) is discussed.