Exact and approximate solutions of the system of interrelated equations of the theory of creep and long-term strength

Abstract

The problem of creep and long-term strength of metallic materials and alloys is considered. Under the long action of high temperatures and relatively small stresses, many metallic alloys and pure metals loose plasticity and undergo brittle fracture. This problem in mechanics of materials is known as the phenomenon of thermal brittleness. To solve this problem Kachanov and Rabotnov introduced the concept of damage into the mechanics of materials. Also, they suggested a system of interrelated kinetic equations for creep deformation and damage parameter. In this work, a modified system of interrelated kinetic equations for creep deformation and damage parameter are formulated. In these equations, the mass conservation law is taking into account and the relative changes of material density are considered as a damage parameter. The results of numerous studies on the changes of porosity and density of various metals and alloys due to the formation and development of micropores and microcracks under conditions of high-temperature creep make it possible to consider density as an integral measure of the accumulation of structural microdefects. Different analytical and numerical solutions of the considered system of kinetic equations are obtained. It is shown, that the character of the curves according to different solutions is identical and agrees with the corresponding experimental results. It was shown, that the numerical solution completely coincides with the case of purely brittle fracture and small deformations. The long-term strength criterion is formulated. Comparison of theoretical creep and long-term strength curves with experimental results for 2.25Cr-1Mo steel is given. A good agreement between the corresponding theoretical and experimental results is observed.