Stationary straight cracks in quasicrystals

Abstract

Stationary straight cracks in quasicrystals in linear elastic setting are under scrutiny. The analysis is developed by using Stroh formalism which is modified to account for a totally degenerate eigenvalue problem: in fact, the fundamental matrix of the governing equations of motion admits a repeated eigenvalue corresponding to a single eigenvector.\ud Cases of a semiinfinite rectilinear crack loaded along its margins and a crack of finite length under remote loading conditions are considered. \ud Standard and phason stresses display square-root singularities at crack tip. The latter stresses represent peculiar microstructural inner actions occurring\ud in quasicrystals and are determined by rearrangements\ud assuring quasi-periodicity of the atomic tiling modes described by a vector field, called phason field, collecting the local degrees of freedom exploited by the atoms within the material elements. \ud Energy release rate increases with the coupling parameter between displacement and phason fields

Interaction of a dislocation with an elliptical hole in icosahedral quasicrystals

“…the fracture toughness will be large for a large coupling parameter R. This conclusion is consistent with the results of Radi and Mariano [21] and Mikulla et al [25]. Note that the phonon-phason coupling effect on the stresses is not negligible.…”

“…For example, Gao et al [20] solved the elliptical hole and the rigid-line inclusion problems for 1D quasicrystals using a generalized Stroh formalism. Radi and Mariano [21] considered straight cracks in 2D quasicrystals using the same formalism. Closed-form expressions for the elastic displacement and stress fields induced by a dislocation in an icosahedral quasicrystal were obtained using the extended Stroh formalism [22].…”

Defects in Static Elasticity of Quasicrystals

“…More recently, the phonon-phason elasticity of quasicrystals attracted a lot of attention. For example, Radi and Mariano focused their attention on the straight cracks and dislocations in two-dimensional quasicrystals, and described linear elasticity of quasicrystals and obtained some profound results for [39][40][41]. Li and his workers induced fundamental solutions for thermo-elasticity of one-dimensional hexagonal quasicrystals with half infinite plane cracks and obtained some solutions [42][43][44].…”

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].…”