Numerical Technique for Surface Opening Displacement of an External Crack in an Infinite Elastic Space

Abstract

This paper presents a numerical technique for determination of surface opening displacements of an external circular crack embedded in an infinite elastic space. Under the applied constant displacement at infinity, a Barenblatt – Dugdale crack whose crack tip plasticity governed by Tresca and von Mises yield criteria is numerically investigated. The proposed technique of a discretizing approach is qualitatively developed. It is then employed for the purpose of predicting the opening displacement of such crack with von Mises yielding criterion whose corresponding analytical expressions are not available. By superposition of Dugdale model's displacement functions, the influence function which is the essential basis of numerical implementation is obtained. The accuracy and convergence of the proposed technique has been judged by the comparison studies between Tresca analytic crack opening displacement and the one obtained from these numerical computations. Accordingly, this technique provides the sufficiently accurate results and shows a good agreement with the exact value and always converges to a stable solution. This leads to a conclusion that the problem can be estimated accurately by the simple numerical technique proposed within. Finally, the surface opening displacement of the cohesive external crack is compared for the three different yield conditions namely Dugdale, Tresca and von Mises.