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Below is a brief description of a method to calculate singuariltes that exists at an interface seperating two dissimilar anisotropic materials where a ply crack terminates normal to this interface. A more complete description is give in Section 7. "Cracks Near Interfaces Between Dissimilar Anisotropic Materials"

Figure 1. Coordinates defined for stress free edge singularity Ref.[25]

It is important to note that singularities coincide with the coordinate system origin. Hence each interface singularity has a unique coordinate system. Since the objective here is to reproduce published results the same coordinate system established by Ting et al. will be used. For this module we have expanded on the solution introduced by Ting et al. and developed the numerical approach to solve for these singularities. The solution is organized into three parts: 1) transformation of fourth order stiffness tensor, C_ijkl, for arbitrary rotation in the 1-3 plane, see eqn 35 Ref.[25], 2) calcuate eigenvalues, p_k, and eigen vectors, ν_i and τ_ij, from equations (9) and (10) Ref.[25], and 3) calcuate exponent, k (singularity) on radius, r, from the determinate of equations (21) and (22) of Ref.[26] using appropriate boundary conditions equation (36) of Ref.[26]. From these boundary conditions 18 homogeneous equations are generated. Equation coefficients are functions of elastic properties and exponent, k, on the radius vector whose origin is located at the crack tip where the singularity exists. With the elastic properties prescribed inthe NPIB form the determinate of the coefficient matrix is only a function of the exponent, k. For comparison results from Ting et al. Ref.[26] are listed below in Table 1 using the Pipes-Pagano approximation which are the default elastic properties in the NPIB form.

E₁=E₂=+2.100E+06,    E₁=+2.000E+07
G₁₂=G₁₃=G₂₃=+0.850E+06
ν₂₁= ν₃₁= ν₃₂=+0.210E+00