A thin circular disk is considered, the material of which exhibits elastic and plastic properties under thermal and force influences. In the central part of the disk, the temperature field is uniform. At the boundary of the disk, pressure and a constant temperature are set. Approximation of a plane stress state is adopted. The additive form of the connection of full, elastic, plastic deformations and deformations under free thermal expansion is considered. Elastic deformations are expressed in terms of stresses according to Hooke's law. A linear approximation of the dependence of the plasticity limit on temperature is proposed. The possibility of neutral loading of the central region of the disk and its external boundary is shown. Especially distinguished is the condition for the plasticity of Tresca.
Keywords: mathematical modeling, elastoplastic body, plane stress state, piecewise-linear plasticity conditions, plastic flow theory, thermoelastic plasticity
The steps of constructing an algorithm for calculating the stressed and strained state of a thin circular disk experiencing thermal and force effects are discussed. A homogeneous temperature field is created in the central part of the disk. Within the framework of the theory of the flow of an ideal elastoplastic body, conditions of general plasticity are considered. It is assumed that the plasticity limit for uniaxial tension is common for all plasticity conditions. Dependencies between the disk radius, the temperature of the central region of the disk and the external pressure, which determine the appearance of plastic regions, are established. For piecewise-linear plasticity conditions of general form, analogous dependences are defined, when singular plasticity regimes are realized at elastoplastic boundaries. For different values of the input parameters of the problem, the stresses, equivalent stresses and the hodograph of the stress vector are given.
Keywords: mathematical modeling, elastoplastic body, plane stress state, piecewise linear plasticity conditions, plastic flow theory, thermoelastic plasticity
Within the Tresca yield criterion and its associated flow rule, the stress-strain problem in an elastic-plastic thin circular solid disk is considered under a temperature field such as the yield stress of the material depends on the temperature. In the central part of the disk the temperature is homogeneous. On the outer boundary, the disk is subjected to uniformly distributed pressure and constant temperature. The objective of the paper is to determine the service conditions which allow to obtain the temperature in the central part of the disk and its radius such as the initiation of the plastic zone starts either from the center of the disk or from its outer contour. The elastic-plastic boundary is calculated, and the plots for stresses and strains are presented. To verify the solution, the equivalent stresses for permissible plastic regimes are investigated together with the stress vector hodograph . The algorithm of similar problems is developed. The validity of the usage of the Tresca yield criterion when the yield stress of the material depends on the temperature is discussed.
Keywords: mathematical modeling, elastoplastic body, plane stress state, piecewise linear plasticity conditions, plastic flow theory, thermoelastic plasticity