Determining the stresses near crack tips in composite plates based on the Williams series and singular integral equations

Abstract

The paper presents a numerical-analytical method developed to determine the stresses formed in composite plates near the tips of curved cracks by means of the Williams series. The coefficients of the terms of the Williams series and T-stresses have been calculated based on the derivatives of the displacement discontinuity of the crack edges. It has been shown that the calculations can be simplified implementing the Green's solutions by the Lekhnitskii method. The numerical algorithms based on Lobatto quadrature formulas have been used to solve the singular equations and determine both the coefficients the Williams power series and T-stresses. The proposed approach has been used to analyze rectilinear and curvilinear cracks in composite plates. In addition, the Green's solutions have been implemented to investigate the cracks located in a half-plane, near an elliptical hole, in rectangular plates, and in strip. One- and two-period problems have been considered for plates with cracks in the present calculations. The high accuracy of the performed calculations of the stresses near the crack tips in composite plates using elementary formulas contained by the Williams series has been confirmed on the test examples.