Method for calculating stress evolution in glass-metal composite taking into account structural and mechanical relaxation processes - Lyubimova, Ol’ga Nikolayevna; Barbotko, Maksim Andreyevich (Computational Continuum Mechanics, 2019)
Technological modes of annealing layered glass-metal composite material are investigated. A cylindrical glass-metal composite vessel with an internal glass cylinder is used as a model sample in the experimental studies of highly compressed fragile rocks mass. A mathematical model of the evolution of technological and residual stresses during its annealing is considered. The difficulty in modeling is due to the glass transition process and the elastic-plastic behavior of the metal. Structural and mechanical relaxation processes in glass are calculated using the Tula-Naariswami-Moynihan-Mazurin method, which is based on the concept of structural temperature, and the Boltzman-Volterra superposition principle. The dependence of viscosity and coefficient of linear temperature expansion on the structural temperature is taken into account. Elastic state in the stress space is limited by the surface of the Mises limit state for metal shell. In this paper, a finite-difference scheme for calculating structural changes and process stresses over the entire temperature treatment interval is proposed. To assess the accuracy of the developed calculation algorithm, we used an analytical solution of the problem with the Maxwell core in the absence of temperature-time analogy in glass and elastic deformation of the metal layer. Calculations of technological stresses in glass metal composite based on borosilicate glass and low carbon steel for various temperature regimes of annealing were carried out. The proposed mathematical model and calculation method can be used for evaluating residual stresses in the technology of applying glass coatings on metal pipes.