Thermoelastic Equilibrium of a Three-Layer Circular Hollow Cylinder Weakened by a Crack
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THERMOELASTIC EQUILIBRIUM OF A THREE-LAYER CIRCULAR HOLLOW CYLINDER WEAKENED BY A CRACK В. М. Zelenyak
UDC 539.3
We solve plane problems of stationary heat conduction and thermoelasticity for a hollow three-layer cylinder weakened by a crack by the method of singular integral equations. The cross section of the cylinder is a circular concentric ring with similar rings of a different material inserted into this ring. The inner ring contains an edge radial crack. The surfaces of the cylinder are free of loads and temperature conditions of the first kind are satisfied on these surfaces. On the interface of the media, we impose the conditions of perfect thermal and mechanical contact. The numerical solution is obtained for the case where unequal constant temperatures are given on the inner and outer surfaces of the cylinder. The stress intensity factors at the tip of an edge crack are found for different values of thermal and mechanical parameters of the components of the cylinder. Keywords: crack, temperature field, method of singular integral equations, stress intensity factor, piecewise homogeneous bodies.
The method of singular integral equations (SIE) was used for the solution of two-dimensional problems of thermoelasticity [1–4] and the theory of elasticity [5–8] for piecewise homogeneous bodies with cracks, as well as for the solution of force problems for three-component composites with cracks [9–12]. The stress intensity factors (SIF) were found for three-layer composites [13–15]. In the process of operation, various structures (pipelines, high-pressure apparatuses, shafts of turbines, etc.) are often subjected to the action of loads, including thermal loads under which the conditions of plane problem are satisfied. As a computational scheme used for the investigation of fracture processes in these structures, it is customary to use a composite circular ring weakened by a crack. The proposed model of a three-layer ring containing a crack is of great practical importance for the numerical analysis of the thermoelastic state of composite materials with regard for the presence of various stress concentrators. We analyze the action of an axisymmetric temperature field in a three-layer composite concentric ring weakened by a radial edge crack. The solution of the problem of thermoelasticity in the analyzed domain is represented (by the method of superposition) as the sum of the solutions of two separate problems: the problem of thermoelasticity for a three-layer composite ring (without cracks) under given temperature conditions within the boundaries of the ring and the problem of thermoelasticity for a composite ring containing a crack whose lips are subjected to the action of stresses equal in modulus to the stresses determined in the first problem on the crack line but with the opposite sign. Stationary Axisymmetric Temperature Field of a Long Hollow Composite Three-Layer Cylinder Consider a three-layer hollow circular cylinder whose cross section has the form of three circular concentric nested rings made of di
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