Analysis solution method for 3D planar crack problems of two-dimensional hexagonal quasicrystals with thermal effects

Li, Yuan; Zhao, Minghao; Qin, Qing Hua; Fan, CuiYing

doi:10.1016/j.apm.2019.01.004

Cited by 27 publications

(6 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Zhang et al [16] proposed the Greens functions, the displacement and temperature discontinuity method to analyze interfacial cracks in a one-dimensional hexagonal quasicrystal coating under thermal-mechanical loading. Li et al [17] studied the problem of arbitrary shape plane crack in two-dimensional hexagonal quasicrystal media.…”

Section: Introductionmentioning

confidence: 99%

The plane elasticity problem of interface cracks between three-dimensional icosahedral quasicrystals and circular elastic inclusion under the thermal loading

Zhao

2023

Preprint

View full text Add to dashboard Cite

By using the complex variable method, the problem of interface cracks between three-dimensional icosahedral quasicrystals and circular elastic inclusion under the action of a point heat source was investigated. Combined with the Schwarz analysis continuation principle, the generalized Liouville theorem and the singularity analysis of complex functions, the problem is transformed into a Riemann boundary value problem, and the general solutions of temperature and stress functions are obtained. As a special case, the solutions of the interface with a single crack are derived, and the analytic expressions of intensity factors at the crack tips are obtained. Numerical examples are given to analyze the effects of inclusion radius, point hot source intensity and coupling coefficient on thermal stress and stress intensity factors of three common composites. The current research not only provides theoretical guidance for the reliability design and optimization of quasicrystal composites but also contributes to a deeper understanding of the thermomechanical behavior of quasicrystal composites.

show abstract

Section: Introductionmentioning

confidence: 99%

The plane elasticity problem of interface cracks between three-dimensional icosahedral quasicrystals and circular elastic inclusion under the thermal loading

Zhao

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…By employing Almansi's theorem, the thermoelastic plane problem of 2D decahedral QCs was systematically studied by introducing displacement function [11] and the plane cracks of arbitrary shape in 2D hexagonal QCs with thermal effect was analyzed by using the extended displacement discontinuous boundary element method [12]. The solutions of 3D planar cracks of 2D hexagonal QCs under various loads were established by using the analysis solution method [13]. The effect of T-stress on cross crack tip of unequal arm cracks in 2D decagonal QCs was studied [14].…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of a one‐dimensional hexagonal quasicrystal rod in the framework of fractional‐order thermoelasticity

Zhou

2023

Z Angew Math Mech

View full text Add to dashboard Cite

Based on the fractional-order thermoelastic theory, the dynamic response of a finite quasicrystal (QC) rod fixed at both ends and subjected to a moving heat source is analyzed. The governing equations of one-dimensional (1D) hexagonal QC rod are derived. And then the numerical solution is obtained by using the Laplace transform and its numerical inversion. The effects of time; the velocity of heat source; and fractional-order parameter on displacement, stress, and temperature of the QCs are discussed and compared with classical materials in this paper.

show abstract

“…Therefore, crack analyses are very important to understand the effect of cracks on the mechanical behavior of a quasicrystal material. Up to now cracks are analyzed by classical elasticity theory [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Path-independent J-integral for cracks in decagonal quasicrystals

Sládek

Repka

2020

MATEC Web Conf.

View full text Add to dashboard Cite

The path-independent J-integral is derived for fracture mechanics analysis of decagonal quasicrystals (QCs). The gradient theory of quasicrystals is developed here to consider large strain gradients at the crack tip vicinity. The constitutive equations contain phonon and phason stresses, and the higher-order stress tensor. The higher-order elastic material parameters are proportional to the internal length material parameter and the conventional elastic coefficients. The FEM equations are derived to solve general boundary value problems for the strain gradient theory of the QCs.

show abstract

Analysis solution method for 3D planar crack problems of two-dimensional hexagonal quasicrystals with thermal effects

Cited by 27 publications

References 48 publications

The plane elasticity problem of interface cracks between three-dimensional icosahedral quasicrystals and circular elastic inclusion under the thermal loading

The plane elasticity problem of interface cracks between three-dimensional icosahedral quasicrystals and circular elastic inclusion under the thermal loading

Dynamic response of a one‐dimensional hexagonal quasicrystal rod in the framework of fractional‐order thermoelasticity

Path-independent J-integral for cracks in decagonal quasicrystals

Contact Info

Product

Resources

About