Modelling cracks in finite bodies by distributed dislocation dipoles

• Published in: Fatigue & fracture of engineering materials & structures Vol. 25; no. 1; pp. 27 - 39
• Main Author: Dai, D. N.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Science Ltd 01.01.2002; Blackwell Science
• Subjects: Applied sciences; dislocation dipoles; distributed dislocations; Exact sciences and technology; Fractures; Mechanical properties and methods of testing. Rheology. Fracture mechanics. Tribology; Metals. Metallurgy; singular integral equations; T-stress; Cracking; Mechanical properties; Dislocation dipole; Modeling
• ISSN: 8756-758X; 1460-2695
• DOI: 10.1046/j.1460-2695.2002.00440.x

The method of continuous distribution of dislocations is extended here to model cracks in finite geometries. The cracks themselves are still modelled by distributed dislocations, whereas the finite boundaries are represented by a continuous distribution of dislocation dipoles. The use of dislocation dipoles, instead of dislocations, provides a unified formulation to treat both simple and arbitrary boundaries in a numerical solution. The method gives a set of singular integral equations with Cauchy kernels, which can be readily solved using Gauss–Chebyshev quadratures for finite bodies of simple shapes. When applied to arbitrary geometries, the continuous distribution of infinitesimal dislocation dipoles is approximated by a discrete distribution of finite dislocation dipoles. Both the stress intensity factor and the T‐stress are evaluated for some well‐known crack problems, in an attempt to assess the performance of the methods and to provide some new engineering data.