Shape of dislocation line in stochastic shear stress field


I. M. Frantsevich Institute for Problems of Materials Science of the NAS of Ukraine, Kyiv
Usp. materialozn. 2021, 2:19-34


The shape of the dislocation line in the stochastic shear stress field in the glide plane was studied using the method of discrete dislocation dynamics. Stochastic shear stresses can occur due to the distortion of the crystal lattice. Such distortion may exist, for example, in a solid solution. Different atoms in a solid solution induce atomic size misfit and elastic modulus misfit into crystal lattice. These misfits result in crystal lattice distortions which varies spatially. The distortions are the origin of internal stresses in the lattice. Such internal stress in certain location has stochastic value normally distributed. The particular case of such stresses is shear stress distribution in the glide plane. The special method was developed to model such stress distribution. The stochastic shear stress field results in movement of different segments of dislocation line to form its equilibrium shape. The important characteristic parameters of the equilibrium shape can be measured by numerical methods. This shape also includes a "long-wavelength" component that has a non-zero amplitude and was formed without thermal activation. The shape of the dislocation line determines to some extent the yield strength of the material. Thus, the study of dislocation line shape and modeling its formation in the field of stochastic shear stresses can help to determine the yield strength of multicomponent alloys, especially multi-principal element alloys.

Download full text



1. Nabarro F.R.N., Hirsch P.B. Solution and precipitation hardening. The Physics of Metals. Cambridge: Cambridge University Press, 1976. P. 152—188. doi:

2. Miracle D.B., Senkov O.N. A critical review of high entropy alloys and related concepts. Acta Mater. 2017. Vol. 122. P. 448—511. doi:

3. George E.P., Curtin W.A., Tasan C.C. High entropy alloys: A focused review of mechanical properties and deformation mechanisms. Acta Mater. 2020. Vol. 188. P. 435—474. doi:

4. Labusch R. Physical aspects of precipitation- and solid solution-hardening. Czech J Phys. 1981. Vol. 31. P. 165—176. doi: 32 ISSN 2709-510X. УСПІХИ МАТЕРІАЛОЗНАВСТВА, 2021, № 2

5. Leyson G., Curtin W., Hector L., Woodward C.F. Quantitative prediction of solute strengthening in aluminium alloys. Nature Mater. 2010. Vol. 9. P. 750—755. doi:

6. Leyson G.P.M., Hector L.G., Curtin W.A. Solute strengthening from first principles and application to aluminum alloys. Acta Mater. 2012. Vol. 60, No. 9. P. 3873—3884. doi:

7. Leyson G.P.M., Curtin W.A. Friedel vs. Labusch: the strong/weak pinning transition in solute strengthened metals. Philos Mag. 2013. Vol. 93, No. 19. P. 2428— 2444. doi:

8. Leyson G.P.M., Curtin W.A. Solute strengthening at high temperatures, Modelling Simul. Mater. Sci. Eng. 2016. Vol. 24. P. 065005. doi:

9. Varvenne C., Luque A., Curtin W.A. Theory of strengthening in fcc high entropy alloys. Acta Mater. 2016. Vol. 118. P. 164—176. doi:

10. Varvenne C., Leyson G.P.M., Ghazisaeidi M., Curtin W.A. Solute strengthening in random alloys. Acta Mater. 2017. Vol. 124. P. 660—683. doi:

11. Nöhring W.G., Curtin W.A. Correlation of microdistortions with misfit volumes in high entropy alloys. Scripta Mater. 2019. Vol. 168. P. 119—123. doi:

12. Bracq G., Laurent-Brocq M., Varvenne C., Perrière L., Curtin W.A., Joubert J.-M., Guillot I. Combining experiments and modeling to explore the solid solution streng-thening of high and medium entropy alloys. Acta Mater. 2019. Vol. 177. P. 266—279. doi:

13. Hu Y., Szajewski B.A., Rodney D., Curtin W.A. Atomistic dislocation core energies and calibration of non-singular discrete dislocation dynamics. Modelling Simul. Mater. Sci. Eng. 2020. Vol. 28. P. 015005. doi:

14. Zaiser M. Dislocation motion in a random solid solution. Philos. Mag. A. 2002. Vol. 82, No. 15. P. 2869—2883. doi:

15. Zhai J.-H., Zaiser M. Properties of dislocation lines in crystals with strong atomicscale disorder. Mater. Sci. Engineering: A. 2019. Vol. 740–741. P. 285—294. doi:

16. Péterffy G., Ispánovity P.D., Foster M.E., Zhou X., Sills R.B. Length scales and scale-free dynamics of dislocations in dense solid solutions. Mater Theory. 2020. Vol. 4, Article No. 6. doi:

17. Pasianot R., Farkas D. Atomistic modeling of dislocations in a random quinary high-entropy alloy. Comp. Mater. Sci. 2020. Vol. 173. P. 109366. doi:

18. Lugovy M., Slyunyayev V., Brodnikovskyy M. Solid solution strengthening in multicomponent fcc and bcc alloys: Analytical approach. Progress in Natural Science: Mater. Internat. 2021. Vol. 31. P. 95—104. doi:

19. Lugovy, M., Slyunyayev, V., Brodnikovskyy, M., Firstov, S. O. (2017). Calculation of solid solution strengthening in multicomponent high temperature alloys. Elektronnaya mikroskopiya i prochnost materialov. Kyiv: IPM NAN Ukrainy, Vol. 23, pp. 3—9 [in Ukrainian].

20. Lugovy, M., Slyunyayev, V., Brodnikovskyy, M. (2019). Additivity principle for thermal and athermal components of solid solution strengthening in multicomponent alloys. Elektronnaya mikroskopiya i prochnost materialov. Kyiv: IPM NAN Ukrainy, Vol. 25, pp. 26—34 [in Russian].

21. Rönnpagel D., Streit T., Pretorius T. Including thermal activation in simulation calculations of dislocation glide. Phys. Stat. Sol. (a). 1993. Vol. 135. P. 445—454. doi:

22. Podrezov, Yu., Lugovy, M., Verbylo, D. (1997). Effect of crack tip shielding by dislocations on quasibrittle fracture energy. Elektronnaya mikroskopiya i prochnost materialov. Kyiv: IPM NAN Ukrainy, Vol. 3, pp. 14—23 [in Russian].