Computation of Trajectories and Displacement Fields in a Three-Dimensional Ternary Diffusion Couple: Parabolic Transform MethodReportar como inadecuado




Computation of Trajectories and Displacement Fields in a Three-Dimensional Ternary Diffusion Couple: Parabolic Transform Method - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Mathematical Problems in Engineering - Volume 2015 2015, Article ID 650452, 11 pages -

Research Article

AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland

Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Received 27 February 2015; Accepted 18 May 2015

Academic Editor: Hang Xu

Copyright © 2015 Marek Danielewski and Henryk Leszczyński. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The problem of Kirkendall’s trajectories in finite, three- and one-dimensional ternary diffusion couples is studied. By means of the parabolic transformation method, we calculate the solute field, the Kirkendall marker velocity, and displacement fields. The velocity field is generally continuous and can be integrated to obtain a displacement field that is continuous everywhere. Special features observed experimentally and reported in the literature are also studied: i multiple Kirkendall’s planes where markers placed on an initial compositional discontinuity of the diffusion couple evolve into two locations as a result of the initial distribution, ii multiple Kirkendall’s planes where markers placed on an initial compositional discontinuity of the diffusion couple move into two locations due to composition dependent mobilities, and iii a Kirkendall plane that coincides with the interphase interface. The details of the deformation material trajectories in these special situations are given using both methods and are discussed in terms of the stress-free strain rate associated with the Kirkendall effect. Our nonlinear transform generalizes the diagonalization method by Krishtal, Mokrov, Akimov, and Zakharov, whose transform of diffusivities was linear.





Autor: Marek Danielewski and Henryk Leszczyński

Fuente: https://www.hindawi.com/



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