N‐Phase decagonal quasicrystalline circular inclusions under thermomechanical loadings

Abstract

In this work a simple and effective method is proposed to solve the problem corresponding to plane strain deformations of an N‐phase decagonal quasicrystalline circular inclusion‐matrix system in which the circular inclusion is bonded to the surrounding matrix through (N‐2) co‐axial interphase layers. We consider three kinds of thermomechanical loadings: (i) the matrix is subjected to a remote uniform stress field; (ii) the composite undergoes a uniform temperature change; (iii) the matrix is subjected to a uniform heat flux at infinity. We find that it is sufficient to manipulate three 8 × 8 real matrices, a 5 × 5 real matrix, and another 4 × 4 real matrix to arrive at the complete temperature and thermoelastic fields within the circular inclusion and the surrounding matrix, irrespective of the number of interphase layers existing within the composite system. Our results clearly indicate that the existence of the intermediate interphase layer(s) mean that the internal stresses within the circular inclusion are: (i) sextic functions of the two coordinates x1 and x2 under the loading of a remote uniform stress field; (ii) quadratic functions of the two coordinates under the loading of a uniform temperature change; (iii) cubic functions of the two coordinates under the loading of a remote uniform heat flux. The design of neutral and harmonic coated circular inclusions is also discussed as an application of the derived solution. Our analysis suggests that a coated inclusion can be made neutral only to a remote isotropic phonon stress field; whereas it can be made harmonic to any remote uniform phonon stress field.

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

“…Utilizing Equation 14, the unknown constant column matrix for layer j with its lower surface at 3 = ( ) 3 can be derived as […”

“…Guo et al [13] derived a general solution for the 2D thermoelastic QCs with a conductive elliptic hole in terms of the Stroh-type formalism. Wang and Schiavone [14] utilized the complex variable formulation and the transfer matrix method to analyze the plane strain deformations of N-Phase decagonal quasicrystalline circular inclusions under F I G U R E 1 A FGM 2D QC plate made of N-layers thermomechanical loadings. The general solution of three-dimensional thermoelasticity of 2D hexagonal QCs was obtained on the basis of the operator method and the introduction of displacement function.…”

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

“…Considering that elastic materials contain inclusions, the performance difference between matrix and inclusions may interfere with the stress field around and inside inclusions [7][8]. For quasicrystal composites, various inclusion problems are studied, such as a spheroidal inclusion [9], a thin inclusion [10], circular inclusion [11], elliptical inclusion [12,13] and cylindrical inclusions [14]. Under thermal load, the crack problems have also attracted the attention of scholars.…”

Circular inclusion problem of two‐dimensional decagonal quasicrystals with interfacial rigid lines under concentrated force

“…For quasicrystal materials, the defects such as holes and inclusions have been studied by many scholars [7][8][9][10][11][12][13][14][15][16]. However, there are few studies on quasicrystal materials with rigid line inclusions.…”