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A Coupled Model of Controlled Synthesis, of a Composite on a Substrate

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Abstract

A mathematical model of the process of composite synthesis from a mixture of powders is formulated. It is assumed that the synthesis is performed on a substrate and is controlled by a scanning laser beam. The stress-strain state is described in quasi-static approximation. The model takes into account two phenomena that are neglected in traditional surface treatment and 3D models: the mutual influence of the heat transfer process and deformation and the heat sources and sinks that result from chemical reactions. The formation of the composition is described by a total reaction scheme that includes a strengthening particle formation stage and a matrix formation stage. The nonlinear model is reduced to a dimensionless form and investigated numerically using an implicit difference scheme for the thermal conductivity equation, the semi-implicit Euler method for the kinetic equations, and the iteration procedure for the mechanical equilibrium problem. As a result of the calculations, we have the fields of temperature, concentrations, stresses, and strains at an arbitrary moment of time, as well as the final composition of the composite. It is shown that the coupling of processes of different physical nature is important both for determining the composition of the composite and for estimating the residual stresses and strains.

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Funding

This work was supported by the Russian Foundation for Basic Research, grant no. 20-03-00303.

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Authors and Affiliations

  1. Institute of Strength Physics and Materials Science of Siberian Branch of Russian Academy of Sciences, 634055, Tomsk, Russia

    A. G. Knyazeva & O. N. Kryukova

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  1. A. G. Knyazeva
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  2. O. N. Kryukova
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Correspondence to A. G. Knyazeva or O. N. Kryukova.

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(Submitted by A. M. Elizarov)

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Knyazeva, A.G., Kryukova, O.N. A Coupled Model of Controlled Synthesis, of a Composite on a Substrate. Lobachevskii J Math 43, 1878–1893 (2022). https://doi.org/10.1134/S1995080222100183

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  • DOI: https://doi.org/10.1134/S1995080222100183

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