STRESS STATE OF MATRIX AND CYLINDRICAL INCLUSION MADE OF A HARD SUPERCONDUCTOR UNDER ITS MAGNETIZATION IN A TRANSVERSE FIELD

In supercondlictors with strong pinning (hard superconductors, HSCs), under the action of Lorentz forces, significant stresses can occur. In [1], the limit stress state of a long round wire of an HSC at the initial stage of its transverse magnetization under the conditions of quasistatic plane strain state was considered. In particular, it was shown that, in a wire of a high-temperature superconductor, as the induction of the initial magnetic field B0 = 25T decreases by \deltaB\ = 3T, tensile stresses ~ 10^8 N/m^2 occur (these stresses coincide in order of magnitude with the tensile strength of many materials), and the stress stale of the wire can be assumed to be uniform. In widely used wires of composite superconductors (CSCs), the filaments and fibers of an HSC are arranged in the matrix of a normal metal. To estimate the local stresses in composites with weak elastic interaction between the inclusions, the solution of the problem of the pondermotive influence on an isolated superconducting inclusion in a matrix which is free of stresses far away from this inclusion is of interest. Since t he twist pitch of the wire made of a multifilamentary CSC is usually much larger than its diameter, and the ratio of the typical longitudinal size of an HSC to the transverse size in the fibered composites ranges from 10 to 10^6 [2], we restrict ourselves to the investigation of the plane case. In a nontwisted CSC. the macroscopic electric and magnetic fields are distributed as in a homogeneous superconductor; we must only replace jc by js = Ksjc, where jc is the density of the critical current in the superconductor, js is the density of the current in the nontwisted CSC, and Ks is the concentration of the superconductor. The macroscopic approach is valid if the typical time of change of the magnetic field, tm, exceeds the time of diffusion of the magnetic flux in the superconductor and in the normal metal, and (he electric and magnetic fields only slightly change at dislances of the same order of magnitude as transverse dimensions of the sinictural elements of the CSC [2]. Thus, the approximation under consideration corresponds to the magnetization of both a long wire of nontwisted composite arranged in a nonfen-omagnetic matrix (for instance, in an epoxy matrix, which is widely used in superconducting systems) and an HSC filament outside the saturated region in a twisted composite. For the case in which the matrix is a ferromagnetic, we assume that the external magnetic field significantly exceeds its saturation induction. For brevity, in the present paper we mostly speak of an inclusion of an HSC. In what follows we present a solution of the problem of linear elasticity for a long cylindrical inclusion of circular cross-section of an HSC that is embedded in an infinite matrix under its magnetization, so that the quasistatic stress state holds and the saturated region is small. The objective of the present paper is to investigate the influence of the matrix on the stress state of the wire and to determine zones of maximal stresses.