Evolution of temperature stresses in the Gadolin problem of assembling a two-layer elastoplastic pipe
The work aims at solving the problem of the theory of unsteady thermal stresses simulating the assembling of the two-layer elastoplastic pipe using the shrink fit (Gadolin problem). The plastic flow condition is taken in the form of a piecewise linear condition of maximum reduced stresses (the Ishlinsky - Ivlev condition) with a parabolic yield point depending on temperature. It is shown that when solving the mechanical part of a disconnected problem of the theory of temperature stresses, the calculations of reversible and irreversible deformations and stresses can be carried out numerically, i.e. analytically without resorting to approximate calculation procedures and, therefore, without discretizing the computational domains. We present a diagram of the emergence and disappearance of plastic flow regions under the assembly conditions and its subsequent cooling. With a different choice of problem parameters, some plastic regions may not appear. However, it is impossible to obtain other areas of plastic flow by changing the geometry of the problem, properties of assembly materials, and the level of heating. This is the adequacy of the calculations. Only those plastic areas that are shown in the diagram appear and disappear. In contrast to the classical case of uniform heating of the outer pipe, this article deals with a widely used case of an uneven heating of the outer pipe from the inner surface. In this case, irreversible deformations are calculated, and then taken into account, which originated in the pipe material before the moment of landing. A comparison of the distribution of residual stresses obtained during the uniform and non-uniform heating of the outer pipe is given. As a result, the interference with the uniform heating exceeds the interference formed with the non-uniform heating of the pipe.