Abstract
The concept of stochastic fiber process is used in conjunction with the method of dislocation dynamics simulation to compute the pair correlations in three-dimensional dislocation systems. The results show that the pair correlations exhibit oscillatory behavior as a function of the radial distance and that the correlations are highly anisotropic in the crystal and dislocation line orientation spaces. The correlation oscillations are found to have smaller magnitude at higher strain levels and to decay as a function of distance to unity or to asymptotic values slightly below unity in some cases, which indicates that dislocations can be uncorrelated or anti-correlated at long range. The results suggest that incorporating the dislocation pair correlations in density-based kinetic dislocation models is not an easy task because of the need to represent the correlations as functions of three spatial coordinates and two line-orientation coordinates.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Groma, I.: Link between the microscopic and mesoscopic lenght-scale description of the collective behaviour of dislocations. Phys. Rev. B 56, 5807–5813 (1997)
Zaiser, M., Miguel, M.-C., Groma, I.: Statistical dynamics of dislocation systems: the influence of dislocation-dislocation correlations. Phys. Rev. B 64, 224102–224111 (2001)
Groma, I., Csikor, F., Zaiser, M.: Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics. Acta Mater. 51, 1271–1281 (2003)
Zaiser, M., Hochrainer, T.: Some steps towards a continuum representation of 3D dislocation systems. Scr. Mater. 54, 717–721 (2006)
Zaiser, M., Nikitas, N., Hochrainer, T., Aifantis, E.: Modeling size effects using 3D density-based dislocation dynamics. Phil. Mag. 87, 1283–1306 (2007)
El-Azab, A.: Statistical mechanics treatment of the evolution of dislocation distributions in single crystals. Phys. Rev. B 61, 11956–11966 (2000)
El-Azab, A.: Statistical mechanics of dislocation systems. Scr. Mater. 56, 723–727 (2006)
El-Azab, A., Deng, J., Tang, M.: Statistical characterization of dislocation ensembles. Phil. Mag. 87, 1201–1223 (2007)
Liboff, R.L.: Kinetic Theory: Classical, Quantum and Relativistic Descriptions. Printice-Hall, Inc., Englewood Cliffs (1990)
El-Azab, A., Zaiser, M., Busso, E. (eds.): Density-based modelling of dislocations. Phil. Mag. 87(8–9), 1159–1446 (2007)
Ghoniem, N., Tong, S., Sun, L.: Parametric dislocation dynamics: a thermodynamics-based approach to investigation of mesoscopic plastic deformation. Phys. Rev. B 61, 913–927 (2000)
Devincre, B., Kubin, L.: The modeling of dislocation dynamics: elastic behavior versus core effects. Phil. Trans. Math. Phys. Eng. Sci. 355, 2003–2012 (1997)
Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and its Applications. Wiley, New York (1995)
Cai, W., Bulatov, V.V., Pierce, T.G., Hiratani, M., Rhee, M., Bartelt, M., Tang, M.: Massively- parallel dislocation dynamics simulations. In: Kitagawa, H., Shibutani, Y. (eds.) Solid Mechanics and its Applications, vol. 115, pp. 1–12. Kluwer Academic Publisher (2004)
Deng, J., El-Azab, A.: Mathematical and computational modelling of correlations in dislocation dynamics, under preparation
Hanisch, K.-H., Klimanek, P., Stoyan, D.: Stereological analysis of dislocation arrangements in crystals from TEM images. Cryst. Res. Technol. 20, 921–930 (1985)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Deng, J., El-Azab, A. Dislocation pair correlations from dislocation dynamics simulations. J Computer-Aided Mater Des 14 (Suppl 1), 295–307 (2007). https://doi.org/10.1007/s10820-008-9090-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10820-008-9090-4