Asymptotic analysis of crack interaction with free boundary
type: Item
instance of: scholarly article
title: Asymptotic analysis of crack interaction with free boundary
zbMATH Open document ID: 1015.74050
DOI: 10.1016/S0020-7683(99)00063-3
author: K. B. Ustinov
author: A. V. Dyskin
author: Leonid N. Germanovich
published in: International Journal of Solids and Structures
publication date: 2003-07-17T00:00:00Z
review text: This paper employs the beam and dipole asymptotic techniques for modelling interaction of a crack with parallel free boundaries. Two configurations are considered: a crack in a half-plane, and a crack in the centre of an infinite strip. Simple approximation formulae for the stress intensity factors (SIFs) and the areas of crack openings are obtained for all considered cases by interpolation between two asymptotic solutions: for crack close to and far from the boundary. For the crack situated close to the boundary, the part of the material between the crack and the boundary is represented by a beam (plate in plane strain). It is shown that this asymptotic method allows obtaining two leading terms for the SIFs and the crack opening area. When the distance between the crack and the free surface is large, the problem is treated in the far field approximation. Thus, dipole asymptotic method allows to find the leading asymptotic terms responsible for crack-boundary interaction. Examples of cracks loaded by pair of concentrated forces and of crack under uniform loading are considered. It is interesting that the values of the parameters of interpolating formulae obtained by fitting to numerical data are consistent for different geometries and loads.
reviewed by: Anatoliy S. Semenov
Mathematics Subject Classification ID: 74R10
Mathematics Subject Classification ID: 74G10
zbMATH DE Number: 1444155
zbMATH Keywords: beam asymptotic approximation
zbMATH Keywords: dipole asymptotic method
zbMATH Keywords: half-plane
zbMATH Keywords: infinite strip
zbMATH Keywords: stress intensity factors
zbMATH Keywords: interpolation
zbMATH Keywords: free boundary
zbMATH Keywords: crack opening area
zbMATH Keywords: far field approximation
zbMATH Keywords: crack-boundary interaction
zbMATH Keywords: concentrated forces
zbMATH Keywords: uniform loading
MaRDI profile type: Publication
full work available at URL: s0020-7683(99)00063-3
OpenAlex ID: W2009653725
description: scientific article; zbMATH DE number 1444155