Study On Fracture Problems Of Magneto-electro-elastic Coupling Materials

The megnetoelectroelastic composite material, as a kind of intelligent materials, which has been used in aeronautics/astronautics, precision manufacturing, electric packaging, nuclear equipment, and so on, attracts extensive attention of many researchers due to its properties of piezoelectric effect, piezomagnetic effect and coupled effect of magneto-electric. The fracture problem of megnetoelectroelastic materials was investigated in this article using the classical theory or the non-local theory. Some useful conclusions were achieved in analyzing the fracture mechanism of megnetoelectroelastic materials.In chapter one, the research and problem about the fracture of megnetoelectroelastic composite materials are reviewed, the main research contents of this article were confirmed according to these comments.In chapter two, the anti-plane static fracture problems of non-symmetrical multi-cracks and the anti-plane dynamic fracture problems of collinear cracks were solved in functionally graded megnetoelectroelastic composite materials. The problems were formulated through Fourier transform into dual integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the Schmidt method was used. Then the expressions of the full field stress, electric displacement, magnetic induction, the stress intensity factor, the electric displacement intensity factor and the magnetic induction intensity factor were obtained. The numerical results reveal the effects of the number, length and distributing of cracks, the changing of material properties and the loading of kind on the fracture characteristics of magnetoelectroelastic material. And it can be concluded that the material gradient parameter has obvious effects on the fracture characteristics of magnetoelectroelastic material.In chapter three, the multiple mode-I cracks fracture problems were studied with the electromagnetic limited-permeable boundary conditions. The basic solution of multiple mode-I crack problem was formulated by using general Almansi theory. Then this problem was translated into the dual integral equations which could be solved using the Schmidt method. Finally, the stress intensity factors, electric displacement intensity factors and magnetic induction intensity factors at the crack tips were achieved. The effects of the dielectric permittivities and magnetic permeabilities of the medium inside cracks on fracture characteristics of cracks were drawn. It can be found that the dielectric permittivities and magnetic permeabilities of the medium inside cracks have clear impact on electric and magnetic fields near the crack tips.In chapter four, considering the dielectric permittivities and magnetic permeabilities of the medium inside cracks, the basic solutions of the rectangular cracks in megnetoelectroelastic composite material were derived in three-dimension using general Almansi theory. As a result, the effects of the dielectric permittivities and magnetic permeabilities of the medium inside cracks, the distance between two rectangular cracks and the rectangular geometry of cracks were summarized on fracture characteristics of rectangular cracks in magnetoelectroelastic composite material. And the weak parts of the rectangular crack were given.In chapter five, the non-local theory was firstly employed to study the fracture problem of megnetoelectroelastic material or functionally graded material. The mathematical difficult encountered in similar problems in previous literature were conquered by transforming the fracture problems into the dual integral equations. Different from the classical solutions, that the present non-local theory solution exhibits no stress, electric displacement and magnetic flux singularities at the crack tips in a magnetoelectroelastic media. The finite value of the stress fields at the crack tips exhibits the clear physical meaning, which make it possible using maximum stress criterion to predict the destroy condition of crack. At the same time, the rules of the effects of the dielectric permittivities and magnetic permeabilities of the medium inside cracks on fracture characteristics of cracks were given.In this article, the investigation on fracture characteristics of megnetoelectroelastic composite material is very important to designing, manufacture and application of megnetoelectroelastic composite material.