Chapter 8 Elastic and plastic properties of quasicrystals

Takeuchi, Shin; Edagawa, Keiichi

doi:10.1016/s1570-002x(08)80023-7

Cited by 8 publications

(14 citation statements)

References 147 publications

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“…The values of K i are of the same order of magnitude as C ij obtained by resonant ultrasound spectroscopy (Chernikov et al 1998). There are no data available for R i which, based on the estimation of some experts (Edagawa 2007;Takeuchi & Edagawa 2007) working in the field of QCs, hold lower values than K i .…”

Section: (C) the Degenerated Form Of Infinite Quasi-crystal Solidsmentioning

confidence: 74%

Three-dimensional Green's functions for two-dimensional quasi-crystal bimaterials

Gao

Ricoeur

2011

Proc. R. Soc. A.

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Owing to their specific structure, which can neither be classified as crystalline nor amorphous, quasi-crystals (QCs) exhibit properties that are interesting to both material science and mathematical physics or continuum mechanics. Within the framework of a mathematical theory of elasticity, one major focus is on features evolving from the coupling of phonon and phason fields, which is not observed in classical crystalline or amorphous materials. This paper deals with the problems of combinations of point phonon forces and point phason forces, which are applied to the interior of infinite solids and bimaterial solids of two-dimensional hexagonal QCs. By using the general solution of QCs, a series of displacement functions is adopted to obtain the analytical results when the two half-spaces are supposed to be ideally bonded or to be in smooth contact. In the final expressions, we provide three-dimensional Green's functions for infinite bimaterial QC solids in the closed form, which are very convenient to be used in the study of dislocations, cracks and inhomogeneities of the new solid phase. Furthermore, the paper is concluded by a discussion of some special cases, in which Green's functions for infinite transversely isotropic solids and Green's functions for a half-space with free or fixed boundary are given.

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Section: (C) the Degenerated Form Of Infinite Quasi-crystal Solidsmentioning

confidence: 74%

Three-dimensional Green's functions for two-dimensional quasi-crystal bimaterials

Gao

Ricoeur

2011

Proc. R. Soc. A.

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“…Please see Table 1: Table 1. Mechanical properties of icosahedral quasicrystals [16,17,21,69,70]. This difference in Figure 10a can be summarized as: the change of wave is caused by the change of ν value, which can lead to the refraction and reflection of stress wave with different velocity in the solid.…”

Section: A Cracked Specimen Of Icosahedral Quasicrystals Of Plane Promentioning

confidence: 99%

“…Using the displacement formulas and the integration of the functions (70) and noting the Equation (71), we can get the displacement u y…”

Section: The Moving Dugdale Model For Plane Elasticity Of Dodecagonalmentioning

confidence: 99%

“…The related parameters are used, in which the density ρ = 5.1 g/cm 3 and the elastic constants λ = 75 (GPa), µ = 65 (GPa) for the phonon fields [69], meanwhile the elastic constants K 1 = 300 MPa, K 2 = −45 MPa for phason fields [70] and the relevant constant of diffusion coefficient Γ w = 1/κ = 4.8 × 10 −10 cm 3 ·µs/g for phason fields. The phonon-phason coupling constant has not been measured for icosahedral QCs so far.…”

Section: A Cracked Specimen Of Icosahedral Quasicrystals Of Plane Promentioning

confidence: 99%

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Elasto-Dynamics of Quasicrystals

Tang

2016

Crystals

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Abstract:A review on elasto-dynamics of quasicrystals (QCs) and their applications based on mathematical elasticity is given. In this study, recent studies on elasto-dynamics of QCs are reviewed, in which the focus of the problem lies in the role of phason variables and the coupling effect between phonons and phasons in the dynamic deformation process. On summarizing and describing the development of the elastic dynamics of QCs, this review mainly presents theelasto-dynamics of QCs and their application in a variety of research areas, ranging from problems with different QCs, including one-, two-, and three-dimensional QCs to various coupling problems. The plane elasticity and anti-plane elasticity of quasicrystals are included in this review.

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“…In a tiling picture, phasons are introduced by violations of the matching rules due to the missing periodicity in quasicrystals. The movement of their dislocations has to overcome this mismatch by the rearrangement of phasons [21], and the dislocation motion is difficult and the material is brittle.…”

Section: Introductionmentioning

confidence: 99%

Bridging room-temperature and high-temperature plasticity in decagonal Al–Ni–Co quasicrystals by micro-thermomechanical testing

Zou

Wheeler

Sologubenko

et al. 2016

Philosophical Magazine

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(2016) Bridging room-temperature and high-temperature plasticity in decagonal Al-Ni-Co quasicrystals by micro-thermomechanical testing, Philosophical Magazine, 96:32-34, 3356-3378, DOI: 10.1080/14786435.2016 Ever since quasicrystals were first discovered, they have been found to possess many unusual and useful properties. A long-standing problem, however, significantly impedes their practical usage: steadystate plastic deformation has only been found at high temperatures or under confining hydrostatic pressures. At low and intermediate temperatures, they are very brittle, suffer from low ductility and formability and, consequently, their deformation mechanisms are still not clear. Here, we systematically study the deformation behaviour of decagonal Al-Ni-Co quasicrystals using a micro-thermomechanical technique over a range of temperatures (25-500 °C), strain rates and sample sizes accompanying microstructural analysis. We demonstrate three temperature regimes for the quasicrystal plasticity: at room temperature, cracking controls deformation; at 100-300 °C, dislocation activities control the plastic deformation exhibiting serrated flows and a constant flow stress; at 400-500 °C, diffusion enhances the plasticity showing homogenous deformation. The micrometersized quasicrystals exhibit both high strengths of ~2.5-3.5 GPa and enhanced ductility of over 15% strains between 100 and 500 °C. This study improves understanding of quasicrystal plasticity in their lowand intermediate-temperature regimes, which was poorly understood before, and sheds light on their applications as small-sized structural materials.

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Chapter 8 Elastic and plastic properties of quasicrystals

Cited by 8 publications

References 147 publications

Three-dimensional Green's functions for two-dimensional quasi-crystal bimaterials

Three-dimensional Green's functions for two-dimensional quasi-crystal bimaterials

Elasto-Dynamics of Quasicrystals

Bridging room-temperature and high-temperature plasticity in decagonal Al–Ni–Co quasicrystals by micro-thermomechanical testing

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