Thermal stresses in the plane problem of the theory of elasticity caused by phase transformations: PMM vol. 38, n≗5, 1974, pp. 847–850

Abstract

We study the state of stress in an elastic half-plane in the presence of phase transformations caused by temperature variations at the points of the half-plane. Separately we consider the states of stress caused by the lack of homogeneity in the temperature field and the consequent volume changes taking place in the regions of phase transformations. Under the term “phase transformation” we understand the structural change in the crystal lattice which occurs when the body is heated above a certain critical temperature [1, 2], Here the purely thermal stresses are accompanied by the stresses associated with the volume change in the region undergoing phase transformations. Similar problems arise during the investigation of the stress states in the case of elastic tension and in the problems on inclusions. Such problems were studied by D.I.Sherman, Iu.A. Amen-Zade, and others. However in all the problems studied the region occupied by an inclusion was always completely contained within some external region. The present paper deals with the case in which the boundary separating the media has common points with the outer boundary of the region containing the inclusion. The stresses and strains are assumed to satisfy the conditions of the linear theory of elasticity, with the external region and the inclusion possessing the same elastic properties.