Resolved shear stress analytical modelling: application to the determination of CRSS in olivine thanks to dislocation electron tomography

ABSTRACT

Critical resolved shear stresses (CRSS) are generally obtained from uniaxial mechanical tests on oriented single crystals. However, slip systems are sometimes difficult to isolate with these mechanical tests. The dislocation radii of curvature (observed with transmission electron microscopy) let us estimate the resolved shear stresses but far from high lattice friction conditions, i.e. far from initial deformation conditions. A new analytical model has been developed to evaluate the resolved shear stresses with high lattice friction conditions. This model uses the parallel between beams flexure and dislocation physics in elastic anisotropy conditions, i.e. for most crystalline materials. Moreover with the dislocation transmission electron tomography technique, it is possible to orientate dislocations perfectly in order to obtain their precise geometry. Thanks to this tool, one can also access a sufficient amount of dislocation configurations and so of resolved shear stresses in order to get closer to CRSS. This model has been implemented to estimate the CRSS of the $\left[001\right]\left\{110\right\}$ and $\left[001\right]\left(100\right)$ slip systems in olivine.

KEYWORDS:

• Dislocation
• CRSS
• tomography
• transmission electron microscopy
• olivine

Acknowledgements

I would like to thank V. Brugidou for interesting discussions about differential equations and the two anonymous referees for precious comments on the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Alexandre Mussi http://orcid.org/0000-0003-2093-0144

Additional information

Funding

The TEM facility in Lille (France) is supported by the Conseil Regional du Nord-Pas de Calais, and the European Regional Development Fund (ERDF).