Evaluation of residual stresses in additively produced thermoelastic cylinder. Part I. Thermal fields

Abstract

The study is aimed at mathematical modeling of non-stationary temperature and stress-strain fields in growing thermoelastic cylinder, which growth is due to the layer-by-layer sintering over its lateral surface. This modeling makes it possible to estimate the reciprocal impact of non-stationary temperature fields, stress-strain state and the scenario of the additive process even in manufacturing of more complicated shapes. The problem is considered in the framework of the theory of thermal stresses with non-linear radiative boundary condition. A distinctive feature of modeling is that the material composition of the body changes over time. Therefore, the mathematical model is represented by the recurrent sequence of initial boundary value problems, formulated for each step of the additive process in different domains with respect to the increments of thermal and stress fields. The domains constitute nested sequence of regions and, together with the sequence of the moments of layer sintering, define the scenario of additive process. Initial values for a step are taken to be equal to the corresponding values at the final moment of previous step. The solution for each step is represented in the form of decomposition over eigenfunctions of differential operator, generated by boundary value problem on this step. Computational modeling of various sintering modes has been carried out. A classification of thermomechanical additive processes, based on the relationship between the characteristic time of the process and the time of thermal relaxation of the attached layer is given. Special attention is paid to non-uniform volume heating, which can be obtained by skin effect during high-frequency induction. Computational simulations based on obtained analytical solution show that auxiliary inductive heating makes it possible to substantially reduce the non-uniformity of the temperature field and thus to reduce the temperature stresses caused by it.