Abstract
The main types of the internal stresses are the thermal and residual ones and fields of structural defects as well. These stresses have an essential effect on the phase transformations in materials. The kinetics of the process is described by a parabolic equation under corresponding initial and boundary conditions. The aim of this paper is simulating the phase transformations in the field of the internal stresses with logarithmic coordinate dependence. Such dependence allows the exact solution of the diffusion kinetics task to be obtained. The triple grain boundaries are considered as structural defects. They serve as stress concentrators under external loadings. This is caused by the orientation dependence of elastic and thermophysical characteristics of the contiguous grain materials. The dilatation field of considered defects depends logarithmically on the radial coordinate. The hydride phases formation within the alloys on the base of zirconium is enough to be mentioned as an illustration. This material is used for claddings of fuel elements of nuclear reactors. Analytical relations for the field of atomic hydrogen concentration near the triple grain boundaries are given. If the concentration of hydrogen atoms exceeds the solubility limit at a given temperature, hydride phases are formed in zirconium. The further growth of hydrides is limited by the diffusion supply of hydrogen atoms. The exact analytical solution task of phase transformations in the area of the triple grain boundaries is the test example for a complex field of internal stresses.