N‐Phase decagonal quasicrystalline circular inclusions under thermomechanical loadings

Abstract

AbstractIn 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.