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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]

In this paper the strain gradients in constitutive equation of stresses are considered as coupled to the thermos-electric-mechanical problem with cracks. The principle of virtual work is applied to derive the finite element equation for a general 2d boundary value problem. Due to the higher order of derivatives in gradient theory it is needed to use C¹- continuous elements to guarantee the continuity of the derivates at the element boundaries. It is not an easy task to develop C¹ continuous elements. Therefore, the mixed FEM formulation is developed here. The C0 continuous interpolation is independently applied for both the displacements and displacement gradients. The kinematic constraints between strains and displacements are satisfied at some cleverly chosen internal points inside elements. [ABSTRACT FROM AUTHOR]

The fracture toughness characteristics of ZrO2ceramics were determined experimentally using an original technique of wedging small-sized chevron notch specimens developed at the Institute of Strength Physics and Materials Science SB RAS (Russia) in the laboratory of physical mesomechanics of materials and non-destructive testing. Measurements have shown that inelastic displacements can be more than 22% of the total displacement of the consoles by the time of the specimen failure. The effect of the Y2O3 stabilizer on the critical stress intensity factor KIc was verified. It was shown that an increase in the Y2O3 stabilizer content from 3 to 8% significantly decreases the fracture toughness. The stress intensity factor KIc falls within the range from 5.7 to 2.35 MPa m1/2. [ABSTRACT FROM AUTHOR]

This study offers a model of crack surrounded by a layer of plastically deformed material. The stress-strain state of continuous medium with this crack is considered. The distribution of plastic deformation in the layer satisfies the material continuity condition, at which a gradual stress reduction occurs from the values in the bulk to a zero value on the crack surface. The calculations are based on the relaxation element method developed by the author. It is shown that the maximum stress gradient is observed at the free surface of crack and the maximum stress concentration in the plastic deformation zone. At high plastic deformation gradients, the stress concentration in the zone of plastic deformation can exists an order of magnitude greater than the external applied stress. [ABSTRACT FROM AUTHOR]