Analytical model of thermal-stress induced cracking in two-component material with anisotropic components

This paper deals with an analytical model of cracking in an anisotropic matrix and anisotropic spherical particles with the radius R which are periodically distributed in the infinite matrix. This model multi-particle–matrix system with the particle volume fraction v ∈ 〈0, π/6〉 is applicable to a two-component material of the precipitate-matrix type with anisotropic components. The cracking which is induced by thermal stresses is investigated within a cubic cell with a central spherical particle. This cubic cell represents such infinite matrix part which is related to one particle. The analytical model of cracking in the spherical particle (q = p) and cell matrix (q = m) includes (1) an analytical determination of the critical particle radius Rqc = Rqc(v) which is a reason of a crack initiation; and (2) an analytical determination of the function fq = fq(x, v, R) with the variable x and the parameters v, R > Rqc. This function of the position x in the components describes a crack shape in such plane which is perpendicular to the cracking plane. The analytical determination is based on a curve integral of elastic energy density induced by the thermal stresses. As an illustrative application example, these analytical results are applied to the YBaCuO superconductor which represents a two-component material with the Y2BaCuO5 precipitates and the YBa2Cu3O7 matrix.