539.3 Mathematical modeling of thermal stresses in a solid with an internal crack

Valishin A. A. (Bauman Moscow State Technical University), Kartashov E. M. (MIREA - Russian Technological University/Moscow Technological University)

THERMOELASTICITY, DYNAMIC VOLTAGE, INERTIAL EFFECTS


doi: 10.18698/2309-3684-2018-3-321


The purpose of this study was to evaluate the influence of the inertial effects and their deviation from the same quasi-static results. The role of inertial effects in the problem of thermal shock is studied on the example of a massive body with an internal spherical crack. We study the thermal reaction of an elastic space with an internal spherical crack whose surface, initially stress-free and at a temperature of T0, is instantly heated to a temperature of TC > T0 and then maintained at that temperature. Thermal stress state occurs under different modes of heat exposure, creating heat stroke. The most common in practice, three cases: temperature heating, thermal heating and heating medium. The generalized dynamic thermoelasticity equation for all three cases in rectangular and curvilinear coordinates is obtained. Considered the thermal response of a massive rigid body with internal spiroborate crack. The exact analytical solution of the problem is obtained. Earlier in the works of one of the authors the solution of the dynamic problem in the form of bulky functional structures was obtained, which greatly complicated their practical use. In this paper, we propose a solution to the problem in new classes of functions, which makes the solution more convenient for numerical experiments. A generalized differential relation for dynamic thermoelasticity is proposed, which has an extensive field of practical applications in the study of thermal response to heat stroke of solids of different shapes. It is shown that the component of the radial stress is a spherical elastic wave propagating from the cavity surface into the material. Numerical calculations of dynamic effects are performed and it is shown that the quasi-static interpretation of time problems in the theory of heat stroke does not allow to take into account the basic laws of transient thermoelasticity and inertial effects.


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