The asymptotic expansion of elastic fields in the vicinity of the contour of a plane crack at the interface of two materials

✍ Scribed by E.I. Shifrin

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 600 KB
• Volume: 65
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(01)00107-1

✦ Synopsis

The stress-strain state in the neighbourhood of the front of a plane crack at the interface of two dissimilar half-spaces of ideally elastic isotropic materials is investigated. The form of the asymptotic expansions of the projections of the displacement vector onto the axis, d~rected along the tangent, the principal normal and the binormal to the crack contour is obtained. It is shown that asymptotic expansions of the projections of the displacement vector onto directions corresponding to the tangent and principal normal, beginning with the second-order term of the expansion, include both terms with half-integer and complex powers of the distances to the crack contour. This indicates that these projections of the solutions of the three-dimensional problem have singularities, defined by the solutions of both the annplane and plane strain problems of cracks at the interface of materials. The singularities of the projection of the displacement vector on to the binormal correspond to the singularities of the solution of the plane strain problem.