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| Řeháčková L., Kalousek J.,Dobrovský L., Kursa M., Drápala J. |
| CONTRIBUTION TO MATHEMATICAL MODELLING OF MANGANESE DIFFUSION IN A WELDED JOINT OF TWO IRON-BASED MATERIALS |
Abstract
The work is based on the program of research works dealing with investigation of new materials. This investigation comprises attempts of use of numerical model of son of cast blanks. There are some differences between experimental results and results obtained from the model. Information about crystallization interval could contribute to higher precision of these results. It is assumed that within the interval of chemical composition of the available samples it is specifically the carbon contents that could have had the biggest influence of crystallization temperature.
From the viewpoint of the given stage of the project, which deals with transport phenomena in materials it is planned to make an experiment in the following manner: each sample will get its “counterpart” made form pure material and both parts will be welded by electric shock. After heat treatment an influence of carbon and manganese on chemical composition gradient will be studied in both parts of the sample. The presented work deals with manganese diffusion.
The paper is based on already previously developed and applied methodology of adaptation of Levenberg–Marquardt algorithm for the model of re-distribution of substitution elements in a welded joint of two iron-based materials. The procedure is illustrated numerically and graphically on the example of manganese.
Theoretical basis for evaluation is solution of the Fick’s second law of one-dimensional diffusion with the relevant boundary conditions. The boundary conditions assume the same values of the element diffusivities in both materials. They also presume that at great distance from the plane of the welded joint the concentrations are identical with initial chemical analysis. Parameters of diffusion equation were optimized by method of non-linear regression.
Program outputs comprise statistical results expressing the extent of usability of the model and structural and chemical heterogeneity. Final values of optimization parameters depend on the method of processing.
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| Keywords: welded joint|diffusion|manganese re-distribution| |
| No 4 (2007), p. 517-523 |
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