Numerical crack path prediction under mixed-mode loading in 1D quasicrystals

Abstract

Quasicrystals are being implemented in industry since this new class of materials appears to have some peculiar properties. However, the fracture behaviour of quasicrystals is not yet clear, which could be a hindrance to its wide usage. This work adopts the generalized linear elastic framework of fracture theory in quasicrystals and develops numerical tools in a finite element environment to compute the fracture quantities. Crack growth is simulated in diverse specimens undergoing an intrinsic mixed-mode loading and the influence of the phonon-phason coupling effect on crack paths is investigated.

Simulation of crack growth under mixed‐mode loading in 1D piezoelectric quasicrystals

“…where Y P Q , the so called Irwin matrix, and S P J are characteristic matrices which only depend on material constants and the geometric relationship between the crack and the symmetric direction of the transversal isotropic material [4]. The Jintegral criterion is adopted to determinate the direction of the crack growth for problems without piezoelectricity, where θ c = arctan(J 2 /J 1 ).…”

“…The use of isoparametric finite elements shows great advantage, where the same shape functions are employed for all field quantities. The total stiffness matrix k is assembled by different parts [4]…”

Thermo‐elastic analysis of functionally graded multilayered two‐dimensional decagonal quasicrystal plates

“…A new elementary excitation phason, which is different from the well‐known phonon, is introduced to describe the rearrangements of atomic configurations in the elastic energy theory of QCs . QCs can be seen as a projection with respect to a higher‐dimensional analogue of a periodic lattice, and one‐, two‐, three‐dimensional QCs are considered in the real three‐dimensional physical space . A two‐dimensional (2D) QCs refers to a three‐dimensional body with atomic arrangement being quasiperiodic in one plane and periodic in the direction perpendicular to that plane …”

“…[3,4] QCs can be seen as a projection with respect to a higher-dimensional analogue of a periodic lattice, and one-, two-, three-dimensional QCs are considered in the real three-dimensional physical space. [5,6] A two-dimensional (2D) QCs refers to a three-dimensional body with atomic arrangement being quasiperiodic in one plane and periodic in the direction perpendicular to that plane. [7] The quasiperiodic structure of QCs leads to many attractive physical properties, such as high hardness, high wear resistance, low thermal conductivity and low friction coefficient.…”

Cylindrical bending analysis of a layered two-dimensional piezoelectric quasicrystal nanoplate

“…According to the quasi-periodic dimension in physical space, QCs can be divided into one-, two-, and three-dimensional QCs. The two-dimensional (2D) QCs studied in this article refer to a three-dimensional solid with atomic arrangement that is quasi-periodic in a plane and periodic along the direction normal to the plane (Fan, 2011; Li et al, 2014; Wang and Ricoeur, 2017; Wang and Zhong, 2004). Owing to the quasi-periodic atomic arrangement, QCs process many attractive properties, such as low friction coefficient, low adhesion, high wear resistance, high hardness, and piezoelectricity (Dubois et al, 1991; Louzguine-Luzgin and Inoue, 2008; Wu et al, 2017).…”