On Thermomechanical Effects in Elastic Media with Reinforcing Rods (Fibers)

Within the framework of the theory of thermoelasticity, the problem of investigating the influence of thermomechanical compatibility and incompatibility of parameters (thermal linear expansion coefficients, elastic moduli and Poisson’s ratios) of materials of a non-uniform system of an elastic medium and a reinforcing rod on the distribution of thermal stress fields in it is set. The system of solvable differential equations is constructed as a result of including the thermal influence factors into the Lame–Gadolin equation. For the cases of plane deformed and plane stressed states of an elastic rod of circular cross section in an elastic medium their analytical solutions have been found; expressions for thermoelastic displacements and stresses in the system have been obtained in finite form. The thermoelastic incompatibility condition for the materials of the medium and the reinforcement is formulated. The analysis of obtained relations shows that in the case of incompatible values of thermomechanical parameters of medium and reinforcement, under the action on the system of temperature disturbances, its reinforcement leads to the negative effect associated with an additional increase in thermal stresses. They are concentrated in a narrow zone of the medium, which is close to the surface of the body contact, and decrease inversely proportional to the square of the distance from the axis of the reinforcement to the isolated point. Examples of the thermomechanical joint combination of the material properties of cement concrete reinforced with steel bars and the incompatible properties of polyester-reinforced road pavements are presented. It is shown that in the road structure, the applied thermal stresses can reach high values, which may additionally contribute to the formation of imperceptible defects and cracks. More generally, the results obtained can be used to evaluate the thermomechanical properties of composite materials.