Partial crack closure in a perforated body with heat release

Abstract

On the basis of the methods of the theory of thermoelasticity, we give a mathematical description of the effect of partial crack closure in an isotropic body with heat release weakened by a doubly periodic sys- tem of cooling cylindrical channels with circular cross sections. It is customary to believe that, as the in- tensity of heat release in the body increases, its elastic properties become temperature-dependent and the material is destroyed. It is assumed that the phenomenon of partial crack closure occurs under the action of thermal loading. At present, much attention is given to the investigation of doubly periodic problems of fracture mechanics, connected with the numerical analysis of fuel elements operating in nuclear reactors. These elements operate under extremely severe conditions caused by the presence of high temperatures and great powers of heat release. To guarantee the reliability of nuclear reactors, it is necessary to study the stress-strain state and fracture of fuel elements. The problems of strength of solid nuclear fuel remain urgent at present and, clearly, the interest to these problems will permanently grow in the future due to the existing trend of increase in the amount of energy released by this type of fuel. The problem of thermoelastic equilibrium of a plane weakened by a doubly periodic system of holes was studied in (1-3) under the assumption that the elastic characteristics of the body E (modulus of elasticity) and ν (Poisson's ratio) are independent of temperature. As the intensity of heat release q in the body increases, the zones of high stresses with doubly periodic location are formed around the holes. These stresses promote the formation and growth of cracks on the surfaces of the holes. The analysis of the stressed state of the body with hollows in the process of heat release shows (4) that the zones of compressive stresses are formed in the body in the course of its operation. We assume that the body with heat release contain zones in which the crack lips are in contact. We also assume that these zones adjoin the crack tips and their unknown sizes are comparable with the crack length. Further, it is assumed that the intensity of heat release is uniform over the entire volume of the body, that the heat is removed only through the surfaces of cylindrical channels, that the characteristics of the body E and ν depend on the drop of temperature, that the body is subjected to the action solely of internal thermal stresses but not to the action of external forces, that the stresses formed in the body do not go beyond the limits of elastic strains, that the properties of the material are isotropic in all directions, and that the body is in the stationary state.