Treatment of singularities in cracked bodies

Abstract

Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements with collapsed, non-singular elements at the crack front. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields. The near-field singular stress has the form σ =C ₀(θ,z)r ^-/12' +D ₀ (0,ϕ)R ^λ _σ The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 percent (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second singularity is dominant at the free surface and becomes nearly zero away from the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer was about 0%, 2%, 4%, and 5% of the total specimen thickness for Poisson's ratio of 0.0, 0.3, 0.4, and 0.45, respectively.

Because there are two singular fields near the free surface, the strain-energy-release rate (G) is an appropriate parameter to measure the severity of the crack front. The G-distribution for M-T and bend specimens were different.