Size dependent thermoelasticity for interface crack problems with a quasicrystal layer.

A thin quasicrystal layer is lying on an isotropic base matrix with rather large thickness. The interface crack between these dissimilar materials is considered and the bilayered structure is under a heat flux load. Due to the very thin quasicrystal layer, size effects cannot be ignored and utilization of the gradient theory is a challenge for proper description. Decagonal quasicrystal material properties are considered for this layer. The uncoupled thermoelasticity is considered here, where the thermal transport is analyzed independently on mechanical fields. Classical heat conduction seems to be inadequate for thermal transport in nano-sized structures. A novel gradient theory is applied here, where in contrast to the Fourier law, the heat flux is affected not only by a temperature gradient but also by the 2nd order derivative of temperature. In the gradient elasticity of quasicrystals the constitutive equations for phonon and phason stresses contain both phonon and phason strains, however, only the phonon strain gradients and the conjugated higher-order stresses are taken into account. The finite element method (FEM) is developed for boundary-value problems where governing equations have higher-order derivatives than in classical theories. Therefore, the standard C° continuous finite elements are insufficient. A mixed FEM is developed for boundary value problems of both the gradient theory of heat conduction and elasticity. In numerical examples various microstructural length-scale parameters and the thickness of the quasicrystal layer are considered. The influence of these parameters on the crack opening displacement is investigated in the paper. [ABSTRACT FROM AUTHOR]