Scattering Of SH-Waves By Interacting Holes And Cracks In Functionally Graded Piezoelectric/Piezomagnetic Media

Piezoelectric/piezomagnetic composite materials are widely used in the production of various smart components due to their good mechanical-electrical,mechanical-magnetic and electric-magnetic coupling effects.The components are prone to impurity,cracks,microholes and other defects during the preparation process,and due to the brittle nature of the material,its safety performance has attracted much attentions.With the rapid development of materials science,people have found that the gradient characteristics of materials can effectively reduce stress concentration,which makes more and more scholars turn to research on functionally graded materials.In engineering practice,there is a type of dynamic problems of great significance,that is,the dynamic stress concentration caused by elastic wave at the defects(holes,cracks,notches,interfaces,grooves,inclusions,corners,etc.)in solids,which will lead to material failure or even destruction.In this paper,the emphasis will be focused on the interaction of elastic waves with holes,cracks and composite defects in piezoelectric solids and functionally graded piezoelectric-piezomagnetic solids.A lot of valuable results were obtained.The main content of this research includes the following three parts:Firstly,the piezoelectric bi-material with eccentric elliptical hole and cracks is taken as the research object,and then the mechanical model of this structure under the action of SH waves is established.By using Green's function method and conformal mapping method,combined with crack cutting and interface fitting technology,the boundary value problem is transformed into the first kind of Fredholm type integral equation,and the dynamic stress intensity factor(DSIF)at the crack tip is expressed theoretically.Numerical results reveal the relations of parameters such as the eccentric distance of the hole,the wave number,the angle of incidence,the size and distance of the hole and crack on the mechanical properties of the inner and the outer crack tips.Secondly,based on the research foundation of homogeneous piezoelectric materials,the effect of inhomogeneity of the material on the DSIF of the crack tip field is considered.The basic methods(Green's function method,crack cutting and interface fitting technology)in the first part used to solve the crack problem in homogeneous material are introduced into the fracture analysis of functionally graded piezoelectric materials.Taking the bonding structure of two semi-infinite functionally graded piezoelectric materials with hole and cracks as the research object.Two cases are considered:one is the interaction between a circular hole and cracks,and the other is the cracks emanating from the edge of a circular hole.The dependence of the DSIF at crack tip on the gradient parameters of the piezoelectric material,the incident wave number,the incident angle,the size and distance of the cracks and the hole,and other parameters are discussed.Finally,the interaction between composite defect and cracks in functionally graded piezoelectric/piezomagnetic media is analyzed.The external load is still anti-plane shear wave.The above two parts belong to the mechanical-electric coupling problem,but this part belongs to the magnetic-electric-elastic coupling problem,which is still solved by the Green's function method,crack"cutting"and interface"conjuction"technology.Finally,the expression of the DSIF at the crack tip is derived,and the numerical results are given by taking the piezoelectric/piezomagnetic material Ba Ti O₃-Co Fe₂O₄ as an example.The effects of gradient parameters of the material,geometric parameters of defects and physical parameters of the material on the stress field at the crack tip are analyzed.The results show that the eccentric distance of the defect,the inhomogeneous parameters of the materials and the frequency of the incident wave all have a significant effect on the stress field at the crack tips.The methods and results in this paper may provide theoretical basis for mechanics analysis of piezoelectric media and functionally graded magneto-electro-elastic media with complex defects,and security analysis of piezoelectric/piezomagnetic components.