Modification of Gauss-Chebyshev quadrature for modelling of crack growth in the field of residual stresses

摘要

A modification of the Gauss-Chebyshev quadrature for solving singular integral equations appearing in plane fracture problems is proposed. This modification is aimed at accurate modelling of the crack growth in non-homogeneous stress fields, which is the case that presents certain difficulties because the positions of collocation points on the crack vary with the crack length. In the proposed modification they are fixed, which extends the application of the well-established technique for oscillating or piecewise loads acting on the crack surfaces. In the latter case, despite lowering the degree of approximation, the proposed method provides better accuracy in calculations as confirmed by comparisons of numerical and analytic results for some examples.