Numerical simulation of dislocation motion in three-dimensional icosahedral quasicrystals

Schaaf, Gunther; Roth, Johannes; Trebin, Hans‐Rainer; Mikulla, R.

doi:10.1080/01418610008212142

Cited by 17 publications

(4 citation statements)

References 16 publications

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“…For crack propagation in QCs, some investigations have been conducted based on the atomistic model [ 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ]. However, it is inconvenient to apply atomistic simulation to engineering.…”

Section: Introductionmentioning

confidence: 99%

“…From the above literature review, it is found that increasing attention has been paid to the fracture of QCs. However, most of them were concentrated on the derivation of exact solutions and determination of fracture parameters of cracked QCs, and the investigations on crack propagation were mainly based on the atomistic model [ 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ]. The work on crack growth in QCs based on continuum mechanics is still insufficient.…”

Section: Introductionmentioning

confidence: 99%

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A Phase Field Approach to Two-Dimensional Quasicrystals with Mixed Mode Cracks

Yang

et al. 2023

Materials

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Quasicrystals (QCs) are representatives of a novel kind of material exhibiting a large number of remarkable specific properties. However, QCs are usually brittle, and crack propagation inevitably occurs in such materials. Therefore, it is of great significance to study the crack growth behaviors in QCs. In this work, the crack propagation of two-dimensional (2D) decagonal QCs is investigated by a fracture phase field method. In this method, a phase field variable is introduced to evaluate the damage of QCs near the crack. Thus, the crack topology is described by the phase field variable and its gradient. In this manner, it is unnecessary to track the crack tip, and therefore remeshing is avoided during the crack propagation. In the numerical examples, the crack propagation paths of 2D QCs are simulated by the proposed method, and the effects of the phason field on the crack growth behaviors of QCs are studied in detail. Furthermore, the interaction of the double cracks in QCs is also discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Phase Field Approach to Two-Dimensional Quasicrystals with Mixed Mode Cracks

Yang

et al. 2023

Materials

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“…Numerical methods, such as the molecular dynamic method, the finite difference method, and the mesh-free method, the finite element method, have in general been used to solve complex boundary value problems. The molecular dynamic method [24] has been used to simulate the 3D mechanical behaviors of icosahedral QCs. The finite difference method [25] has also been adopted to solve the plane dynamic problems of icosahedral QCs.…”

Section: Introductionmentioning

confidence: 99%

Finite size specimens with cracks of icosahedral Al—Pd—Mn quasicrystals

et al. 2014

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Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral Al-Pd-Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon-phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral Al-Pd-Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon-phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of phonon-phason coupling effect on the icosahedral Al-Pd-Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.

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“…Yang et al 1995;Ricker et al 2001). The investigation has been extended to moving dislocation in Zhu et al (2007) by using a displacement function and in Schaaf et al (2000) by a numerical approach.…”

Section: Introductionmentioning

confidence: 99%

Steady-state propagation of dislocations in quasi-crystals

Radi

Mariano

2011

Proc. R. Soc. A.

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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.

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Numerical simulation of dislocation motion in three-dimensional icosahedral quasicrystals

Cited by 17 publications

References 16 publications

A Phase Field Approach to Two-Dimensional Quasicrystals with Mixed Mode Cracks

A Phase Field Approach to Two-Dimensional Quasicrystals with Mixed Mode Cracks

Finite size specimens with cracks of icosahedral Al—Pd—Mn quasicrystals

Steady-state propagation of dislocations in quasi-crystals

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