Three-dimensional surface singularity of an interface crack

Abstract

The three-dimensional singularity field near the terminal point of an interface crack at the free surface of an elastic bimaterial is investigated. The Finite Element Iterative Method (FEIM) is used for evaluating the asymptotic field. A spherical coordinate system r, θ, φ is used and the singular displacement field is assumed to be of a product form r ^λ g(θ, φ), where λ and g(.) are in general complex. To validate the model, the method is first applied to the three dimensional surface crack in a homogeneous elastic material. The results for this case show excellent agreement with previously published analytical and numerical results. For an extreme effect of bimaterial property mismatch, on the surface crack singularity, an elastic material bonded to a rigid substrate is investigated (E1/E2=∞). The results show that the complex power singularity depends strongly on Poisson's ratio ν. The real part of the stress singularity is greater than 0.5 of the plane strain case and the imaginary part becomes almost zero at ν ≥ 0·25 instead of at ν=0.5. The second term in the expansion of the asymptotic field was shown to have a singularity of 0.5.