Steady-state propagation of dislocations in quasi-crystals

Abstract

We analyse the steady propagation at constant speed, lower than the shear wave-speed, of a straight dislocation in an unbounded elastic quasi-crystal with five-fold symmetry. We discuss only the ideal elastic behaviour, neglecting the dissipation associated with the atomic rearrangements. Under these conditions, we provide the expressions of phonon and phason fields in closed form. Both phonon and phason stresses appear to be singular near to the dislocation core. We also find the explicit expression of the energy per unit length around a moving dislocation.

Fundamental solutions of penny-shaped and half-infinite plane cracks embedded in an infinite space of one-dimensional hexagonal quasi-crystal under thermal loading

“…On the other hand, the values of the materials can be approximately estimated by referring to the results associated with isotropic QCs. Such a purpose can be fulfilled in view of the results available in the literature [32,[41][42][43][44][45][46]. It has been reported that the Lamé constants of AlPdMn, a special kind of icosahedral QC, are reported to be λ 0 = 85 GPa and μ 0 = 65 GPa [42], and that the ratio between the phonon-phason coupling coefficient and the shear modulus R i /μ 0 is approximately 0.03 [44].…”

“…As a consequence, numerical analysis can be readily performed, once the values of the material constants are available. However, owing to the absence of the experimental data, especially those characterizing interactions between phonon and phason fields [2,32], such a goal seems not to be achieved. On the other hand, the values of the materials can be approximately estimated by referring to the results associated with isotropic QCs.…”

“…Furthermore, Richer et al [42] also showed that the phason constants K 1 = 0.084 GPa and K 2 = 0.036 GPa. In addition, the coefficient of thermal conductivity is lower than those of conventional crystals [2,32]. In this paper, the material constants, tabulated in table 1, are adopted in the present analyses, by referring to the aforementioned works.…”

“…According to Mariano [29] and Colli & Mariano [30], the absence of a conservative self-action in the standard theory of quasi-crystal may lead to non-physical results. However, the topic is not discussed further here and the common assumptions are accepted, as in the recent studies for static problems [24,31] and dynamic problems [24,32].…”

Elasto-Dynamics of Quasicrystals

“…More recently, the phonon-phason elasticity of QCs has attracted a lot of attention too. For example, Radi and Mariano have described linear elasticity of QCs, and obtained some meaningful results for the straight cracks and dislocations in two-dimensional quasicrytals [36][37][38]. An important reference concerning fundamental aspects of generalized elasticity and dislocation theory deriving the generalized three-dimensional elastic Green tensor and all the dislocation key-formulas including an application to dislocation loops for arbitrary quasicrytals is presented by Lazar and Agiasofitou [39].…”