Stressed state of bodies with thermal cylindrical inclusions and cracks (plane deformation)
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STRESSED STATE OF BODIES WITH THERMAL CYLINDRICAL INCLUSIONS AND CRACKS (PLANE DEFORMATION) H. S. Kit1, 2 and . S. Chernyak1
UDC 539.3
The thermoelastic potential of displacements and Airy stress function are used to determine stresses in infinite and semiinfinite planes with circular thermal inclusions (whose coefficients of linear thermal expansion differ from the corresponding coefficients of the matrix) subjected to uniform heating. The stress concentration is investigated in the case where inclusions are located near the boundary of the half plane. Analytic expressions are deduced for the stress intensity factors in the vicinity of a rectilinear crack located between two identical inclusions. Keywords: semiinfinite body, cylindrical inclusions, temperature stresses, rectilinear crack, stress intensity factor.
The strength and fracture of heated brittle bodies strongly depend on the presence of inclusions and cracks in the vicinity of which temperature stresses increase. Actual composite bodies contain systems of inclusions introduced to form new properties of materials or get certain their combinations not characteristic of each of the constituent materials. The fracture of these bodies (composites) is determined by the concentration interactions of the inclusions with the matrix and between the inclusions complicated by the presence of initial technological stresses caused by temperature tension. The distributions of temperature and stresses in bodies with inclusions depend on numerous factors, including the mechanical and thermal characteristics of the materials of the inclusions and the matrix. If the inclusions are located close to each other, then the corresponding temperature fields and stresses interact as a result of which the analysis of the stressed state becomes much more complicated. The situation is additionally complicated by the presence of a large number of parameters that should be taken into account in the numerical analyses. These are the elasticity moduli, Poisson’s ratios, the coefficients of linear thermal expansion of the materials, and the geometric characteristics of the inclusions. The analysis of the influence all these factors makes the solution of the problems of thermoelasticity much more difficult. However, in the case where the mechanical characteristics of the materials of the inclusions and the matrix are identical and only the coefficients of linear thermal expansion (CLTE) are different, it is possible to obtain the exact solution of the problem and make certain conclusions concerning the distribution of stresses in the body. According to the terminology proposed in [7], the inclusions whose elastic properties are identical to the elastic properties of the body but their CLTE are different are called thermal inclusions. Numerous works are devoted to the investigation of the stationary thermoelastic state of piecewise homogeneous bodies with cracks. In these works, the integral representations of functions of complex variable are used to reduce the analyzed problems to si
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