Matrix crack formation in Y-Ba-Cu-O superconductor

The paper deals with an approximate model of thermal-induced stresses in an anisotropic particle-matrix system of one spherical particle embedded in the infinite matrix. Radial and tangential stresses originate during a cooling process as a consequence of different thermal expansion coefficients of the matrix and the particle, shear stresses are not considered. In case of the matrix tensile radial stress, a crack forms in the matrix around the particle of a radius greater than a critical value obtained by an energy balance criterion of the matrix crack formation. Due to the fact that a shape of the crack in the anisotropic matrix around the anisotropic particle cannot be easily mathematically described, a model of the circular crack in an isotropic plane of the particle-matrix system of matrix and particle tetragonal lattices, forming in the brittle matrix, and consequently the formula of the particle critical radius, are presented. Material constants of the Y2BaCuO5 (211)-YBa2Cu3O7 (123) particle-matrix system are applicated for the calculation of the radial and tangential stresses acting in the 123 matrix and in the 211 particle and for the calculation of the 211 particle critical radius representing the matrix crack formation condition as illustrated by the observed matrix crack pattern. (C) 2002 Elsevier Science B.V. All rights reserved.