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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v7.i5.80
pages 475-485

Multiscale Modeling of Solute Bulk Diffusion at Dislocation Cores

D. Zhang
Chinese Academy of Sciences, Beijing, China
Catalin Picu
Department of Mechanical Engineering Rensselaer Polytechnic Institute Troy, NY, 12180, USA


A sequential multiscale modeling methodology is developed to study the diffusion of solute atoms in the vicinity of a dislocation core and the kinetics of the ensuing clustering process. The problem is set up in the continuum sense, taking into account the coupling between diffusion and deformation. Specifically, gradients of both strain and concentration drive diffusion, and the elastic constants are considered functions of the local solute concentration. These coupling parameters are calibrated from atomistic models. The problem is solved using a finite element formulation. Mg clustering at an edge dislocation in Al-5%Mg is studied, which is relevant for static and dynamic strain aging. The model is used to test the validity of the Cottrell-Bilby-Louat expression, broadly used to describe the kinetics of solute clustering at dislocation cores. It is concluded that the formula does not predict the variation in time of the concentration at every point within the cluster, the purpose for which it is customarily used. However, it properly describes the evolution of a global measure of the cluster size.


  1. Nowacki, W., Dynamic problem of diffusion in solids. DOI: 10.1016/0013-7944(76)90091-6

  2. Aifantis, E. C., On the problems of diffusion in solids. DOI: 10.1007/BF01202949

  3. Larche, F. C., and Cahn, W. J., Effect of self-stress on diffusion in solids. DOI: 10.1016/0001-6160(82)90023-2

  4. Girrens, S. P., and Smith, F. W., Finite element analysis of coupled constituent diffusion in thermoelastic solids. DOI: 10.1016/0045-7825(87)90024-7

  5. Sofronis, P., The influence of mobility of dissolved hydrogen on the elastic response of a metal. DOI: 10.1016/0022-5096(95)00037-J

  6. Thomas, J. P., and Chopin, C. E., Modeling of coupled deformation-diffusion in non-porous solids. DOI: 10.1016/S0020-7225(98)00029-9

  7. Weitsman, Y., Stress assisted diffusion in elastic and viscoelastic materials. DOI: 10.1016/0022-5096(87)90029-9

  8. Lufrano, J., Sofronis, P., and Birnbaum, H. K., Modeling of hydrogen transport and elastically accommodated hydride formation near a crack tip. DOI: 10.1016/0022-5096(95)00075-5

  9. Zhang, D., and Picu, R. C., Solute clustering in Al-Mg binary alloys. DOI: 10.1088/0965-0393/12/1/011

  10. Picu, R. C., and Zhang, D., Atomistic study of pipe diffusion in Al-Mg alloys. DOI: 10.1016/j.actamat.2003.09.002

  11. Picu, R. C., and Xu, Z., Vacancy concentration in Al-Mg solid solutions. DOI: 10.1016/j.scriptamat.2007.03.014

  12. Picu, R. C., Vincze, G., Ozturk, F., Gracio, J. J., Barlat, F., and Maniatty, A., Strain rate sensitivity of the commercial aluminum alloy AA5182-O. DOI: 10.1016/j.msea.2004.08.029

  13. Liu, X.-Y., Ohotnicky, P. P., Adams, J. B., Rohrer, C. L., and Hyland, R. W., Anisotropic surface segregation in Al-Mg alloys. DOI: 10.1016/S0039-6028(96)01154-5

  14. Liu, X.-Y., and Adams, J. B., Grain-boundary segregation in Al-10%Mg alloys at hot working temperatures. DOI: 10.1016/S1359-6454(98)00038-X

  15. Namilae, S., Chandra, N., and Nieh, T. G., Atomistic simulation of grain boundary sliding in pure and magnesium doped aluminum bicrystals. DOI: 10.1016/S1359-6462(01)01195-2

  16. Slabanja, M., and Wahnström, G., Kinetic Monte Carlo study of Al-Mg precipitation. DOI: 10.1016/j.actamat.2005.04.024

  17. Olmsted, D. L., Hector, L. G., and Curtin,W. A., Molecular dynamics study of solute strengthening in Al/Mg alloys. DOI: 10.1016/j.jmps.2005.12.008

  18. Abaqus Analysis User’s Manual.

  19. Abaqus User Subroutines Reference Manual.

  20. Zienkiewicz, O. C., and Zhu, J. Z., Superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. DOI: 10.1002/nme.1620330702

  21. Curtin, W. A., Olmsted, D. L., and Hector, L. G., A predictive mechanism for dynamic strain ageing in aluminium-magnesium alloys. DOI: 10.1038/nmat1765

  22. Xu, Z., and Picu, R. C., Dislocation-solute cluster interaction in Al-Mg binary alloys. DOI: 10.1088/0965-0393/14/2/005

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