Three-dimensional Analyses Of Elliptical Crack Problems For Multiferroic Composite Media

With the development of science and technology,a growing list of nontraditional materials with multifield coupling effects,such as magneto-electro-elastic(MEE)or multiferroic composite media,are used in numerous industrial fields,to cater for the requirements of the era of intelligent materials.Multiferroic composite materials,which have piezoelectric and piezomagnetic effects simultaneously,usually serve as actuators,sensors and energy storage in a variety of engineering fields,such as space plane,supersonic aircraft,rockets,spacecraft,nuclear reactors,nuclear submarines,electronic packaging,and so forth.Owing to their brittleness,the multiferroic composite materials are susceptible to fracture when subjected to electric,magnetic and mechanical loads in service.Consequently,the analyses on crack problems of multiferroic composite materials are of engineering significance and academic value.The elliptical crack problems of multiferroic composite materials are investigated systemically in this dissertation,by virtue of the static general solution and the generalized method of potential theory.The mechanical mechanism of fracture in the context of magneto-electro-elasticity is clarified.Moreover,some conclusions which are of important practical value are drawn.3D analytical solutions for an elliptical crack under normal and shear loads have been carried out in a systematic way.For the mode I problem of an elliptical or penny-shaped crack subjected to uniform combined loads,boundary integro-differential equations,corresponding to the crack with different magneto-electric properties,are established using the generalized method of potential theory in conjunction with the static general solution.For four physical cases,closed-form coupling magneto-electro-elastic field variables in the space are explicitly obtained.The crack surface displacement,generalized stress intensity factor and crack compliance matrix generalized from the rock mechanics all turn out to be an intrinsic combination of a material factor and a geometrical factor.For an elliptical problem under shear mode,exact and complete field variables are obtained in terms of elliptical functions.Important parameters in fracture mechanics,e.g.,the crack slip displacement,the shear stress at the crack front,and the corresponding stress intensity factor,are explicitly derived.The corresponding solutions,in the context of piezoelectricity,piezomagnetism and pure elasticity are also presented,as byproducts of the present work.It is found that the directions of the shear stress and the induced crack slip displacement are generally not coincident for an elliptical crack,in contrast to the case of a penny-shaped crack.The present closed-form analytical solutions may serve as benchmarks for future simplified and numerical studies.Analytical and numerical analyses for an elliptical or penny-shaped crack embed-ded in an infinite transversely isotropic multiferroic composite medium on the semipermeable electro-magnetic boundary condition are presented.The perfectly permeable and impermeable models may lead to unreliable results in the prediction of the coupling field,because they totally ignore the influence of the medium in the crack gap.However,the crack problems are of non-linear nature,when the crack is electromagnetically semipermeable.Due to the complexity in mathematics,such problems are generally resorted to approximation method of iteration.By virtue of the generalized method of potential theory and the general solutions,the boundary integro-differential equations governing the mode I crack problem,which are of non-linear nature,are established and solved analytically.Exact and complete coupling magneto-electro-elastic field is obtained in terms of elementary functions.Important parameters in fracture mechanics on the crack plane are explicitly presented.To validate the analytical solutions,a numerical code by virtue of finite element method is established for 3D crack problems in the framework of magneto-electro-elasticity.Furthermore,the effects of various electro-magnetic boundary conditions on the important quantities in fracture mechanics are discussed in detail.Unlike the conventional crack problems in the context of magneto-electro-elasticity,in which the cracks are usually assumed to be located on a horizontal plane parallel to the isotropic plane of a transversely isotropic medium,this dissertation studies a vertical crack with its surface normal to the isotropic plane.The boundary integrodifferential equations corresponding to different types of external loads are established,by introducing the proper potential functions.The complete and closed-form magnetoelectro-elastic field in the infinite space is obtained in the integral form,for the first time.Furthermore,some important parameters in fracture mechanics are obtained explicitly,in terms of elementary functions.The effects of the orientation of the elliptical crack on the important parameters,such as the crack surface/slip displacement and the stress intensity factors,are discussed.The analytical solutions obtained in this dissertation are of significance to fracture mechanics of multiferroic composite materials.