A quantitative model for the plastic deformation of icosahedral quasicrystals was described. This was based upon shear which occurred, in planes of high atomic density, via dislocation activity. A single-slip dislocation friction stress was first derived on a microscopic basis, and was then introduced into a viscoplastic Kocks-type constitutive law where the dislocation density was the single microstructural internal variable. Dislocations were assumed to be stored and annihilated dynamically during deformation; as in simple crystals. The difference for quasicrystals, with long-range but non-periodic atomic order, was the introduction of a friction stress which limited dislocation mobility and which decreased with increasing strain; as suggested by molecular dynamics simulations. Such a constitutive plastic law led to shear localization and to strain softening. The mean-field single-slip behaviour was then introduced into a multiple-slip state, where quasi-lattice rotation and activation of the various slip systems were modelled. The role of the quasicrystal symmetry which related the available slip systems was examined as a function of the quasi-lattice orientation. The results of the model were compared with experimental data for single icosahedral Al-Mn-Pd quasicrystals which had been deformed at high temperatures using a constant strain rate, or using a constant stress in uniaxial compression.

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