Anti-Plane Elasticity Problem and Mode Ⅲ Crack Problem of Cubic Quasicrystal

The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.

AXISYMMETRIC CONTACT PROBLEM OF CUBIC QUASICRYSTALLINE MATERIALS

The axisymmetric elasticity theory of cubic quasicrystal was developed in Ref. [1]. The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function, based on which, the exact analytic solutions for the elastic field of an axisymmetric contact problem of cubic quasicrystalline materials are obtained for universal contact stress or contact displacement. The result shows that if the contact stress has order - 1/2 singularity on the edge of the contact domain, die contact displacement is a constant in the contact domain. Conversely, if the contact displacement is a constant, the contact stress must have order - 1/2 singularity on the edge of die contact domain.

MOVING SCREW DISLOCATION IN CUBIC QUASICRYSTAL

The elasticity theory of the dislocation of cubic quasicrystals is developed. The governing equations of anti-plane elasticity dynamics problem of the quasicrystals were reduced to a solution of wave equations by introducing displacement functions, and the analytical expressions of displacements, stresses and energies induced by a moving screw dislocation in the cubic quasicrystalline and the velocity limit of the dislocation were obtained. These provide important information for studying the plastic deformation of the new solid material.

Stress Intensity of Antiplane Conjugate Cracks in Cubic Quasicrystal

Based on the theory of Muskhelishvili, the general solutions for stress and strain of conjugate cracks in cubic quasicrystal are obtained, with which the stress intensity factors of cubic quasicrystal at crack tips and the stress distribution functions of phonon and phason fields are given. The results show that though phason field is coupled with phonon field by constitutive equations, the stress intensity factors are not coupled with any other factors.

Singularities of Three-Dimensional Cubic Piezoelectric Quasicrystal Composite Wedges and Spaces

In this paper,the planar problems of three-dimensional(3D)cubic piezoelectric quasicrystal composite wedges and spaces are investigated.The study focuses on the singular behaviors of interface corner and interface crack of composite wedges and spaces.To research the stress singularities,the stress function is assumed to have the exponential form.Based on the Stroh formalism and Barnett–Lothe matrices,we derive a crucial matrix concerned with material properties and wedge angle and obtain the transcendental equation determining the singular orders by simple multiplication of the crucial matrix.Numerical examples of the singular orders are given for some general cases including single,bi-material,and tri-material wedges and spaces under different boundary conditions.The correctness of numerical results is verified by comparison with the existing results of piezoelectric material.Numerical results show that the phonon field,phason field,electric field,material properties,and boundary conditions have great influences on singularities.