Evaluation of the T-stress and stress intensity factor for multi-crack problem using spline fictitious boundary element alternating method

Abstract

In this paper, the T-stress and stress intensity factor (SIF) of multiple cracks with arbitrary position in a finite plate is evaluated by the spline fictitious boundary element alternating method. The multi-crack problem is firstly divided into a simple model without crack which can be solved by the spline fictitious boundary element method and several infinite domains with one crack which can be solved by the fundamental solution of an infinite domain with a crack, namely Muskhelishvili's fundamental solutions. The technique is superior as no meshing is needed near crack face and the analytical solution for solving infinite domains with one crack is accurate and efficient. Then, instead of using the asymptotic expansion, the closed-form expression for calculating the T-stress in multi-crack problem is derived directly, which makes it convenient and accurate for calculating the T-stress. Besides, the SIF can be calculated using the analytical SIF expression in Muskhelishvili's fundamental solutions. Finally, T-stresses and SIFs in a numerical example with double cracks are computed to validate the accuracy of the presented method, And the other two examples with three cracks are further studied to investigate the influence of lengths and locations of multiple cracks on their T-stresses and SIFs.