A quantitative model was developed for the plastic deformation of icosahedral quasicrystals. It was based upon the concept that shear occurred in planes of high atomic density, via dislocation activity. A single-slip dislocation friction-stress was first derived at the microscopic scale, and was incorporated into a viscoplastic Kocks-type constitutive law in which the dislocation density was the only microstructural internal variable. The dislocations were assumed to be stored and annihilated dynamically during deformation; as in simple crystals. The key characteristic of quasicrystals, with their long-range but non-periodic atomic order, was the introduction of a friction stress that limited the dislocation mobility. This decreased with increasing strain, as indicated by molecular dynamics simulations. Such a constitutive plastic law led to shear localization and strain-softening. Mean-field single-slip behaviour was then introduced into a multiple-slip state, for which quasi-lattice rotation and activation of the various slip systems were calculated. The role which was played by the quasicrystal symmetry, with regard to available slip systems, was considered as a function of the quasi-lattice orientation.

The Plasticity of Icosahedral Quasicrystals. P.Guyot, G.Canova: Philosophical Magazine A, 1999, 79[11], 2815-32