THE STRESSED STATE NEAR A MICROFLAW CLUSTER POINT

The stressed state near cluster point z = 0 for microflaws (MiFs) in t he form of cracks or thin linear sharply-angled inclusions in an elast ic plane located along a line on one side or other of the cluster poin t and satisfy certain conditions is investigated. This is preceded by the analytic solution of the first and second fundamental problems of the theory of elasticity for a plane with an infinite set of collinear linear singularities clustering at a finite point. Cases are consider ed in which the flaws are such that their images under the mapping zet a = 1/z are situated periodically along an entire line or only along a ray. Stability to fracture, both in the neighbourhood of an MiF clust er point and globally for an MiF system, are investigated using force and energy fracture criteria. Examples describing the fracture mechani sm are given. An analytic solution of the problem of the interaction o f a macroflaw (MaF) with an infinite series of MiFs collinear with it and clustering at the vertex of the MaF is obtained. The investigation is based on a conformal mapping and the results of [1-4], in which so lutions are obtained in closed form of the first and second fundamenta l problems of the theory of elasticity for a plane with a denumerable set of cuts with a cluster point at infinity.