Fracture Analysis Of A Penny-shaped Crack In A Magnetoelectroelastic Cylinder

As a new intelligent material,magnetoelectroelastic(MEE)materials possessing unique magnetoelectro effects have found increasing applications for the manufactures of intelligent drivers,transducers,sensors and arresters.Because these materials often include cracks in the manufacturing and utilizing procedures,many mechanical researchers have focsed their attentions on the analyses of fracture problems about MEE materials.In recent years,although many achievements have been made in the fracture problem of MEE materials,these investigations have considered anti-plane or in-plane problems in two-dimensional dimensions.Only few achievements are reported for three-dimensional problems which are close to actual problems because the increase of the numbers of material constants and control equations increases the difficulties of mathematical solution.In this paper,we will consider some penny-shaped crack problems in a MEE cylinder as a specific case of three-dimensional fracture problems and reveal the fracture laws.These research results will provide theoretical references for designing and manufacturing cylindrical electromagnetic components.Firstly,the fracture problem of a magnetoelectrically permeable penny-shaped crack in a MEE cylinder of finite radius under magnetoelectromechanical loads is investigated.Two lateral boundary conditions of MEE cylinder are considered.The potential function theory and Hankel transform method are employed to reduce the mixed boundary-value problem to a system of dual integral equations,the solution of which is further given by solving a Fredholm integral equation of the second kind.The expressions of all kinds of field intensity factors at the crack edges are obtained by means of Gaussian integral.Numerical results show that the geometrical sizes of the structure and lateral boundary conditions have a significant effect on fracture characteristics.For a magnetoelectrically permeable model,whether or not the electromagnetic loads promote or inhibit the crack propagation depends on the mechanical loads applied in the far field are stress or strain.Secondly,the fracture problem of a magnetoelectrically semi-permeable penny-shaped crack in a MEE cylinder under magnetoelectromechanical loads is investigated.By means of introducing three auxiliary functions,the boundary-value problem is finally transformed to solve three coupled nonlinear Fredholm integral equations.Field intensity factors are obtained in terms of the solution of the equations.The effects of the geometrical sizes of the structure,applied electromagnetic loads and dielectric permittivity and magnetic permeability of the crack interior on the COD intensity factor are illustrated graphically.Numerical results show that electromagnetic boundary conditions on the crack surface play an important role in crack growth.The fracture toughness of a MEE material is affected by the direction of applied electromagnetic fields.The studies on magnetoelectrically impermeable and permeable cracks can be recovered from the present problem as two special cases.Thirdly,the fracture problem of a penny-shaped crack in a MEE cylinder is investigated under thermal shock load using semi-permeable electromagnetic boundary condition.The lateral surface of MEE cylinder is assumed to be free.Firstly,the temperature fields are obtained for MEE cylinder without crack under a thermal shock load.Using the superposition technique,the thermal stresses,electrical displacements and magnetic inductions caused by temperature fields are added to the surfaces of the penny-shaped crack in the MEE cylinder to form a magnetoelectromechanical coupling and mixed boundary-value problem.Through complex mathematical derivation,the expressions of all kinds of field intensity factors are given.The effects of thermal shock time,the geometrical sizes of the structure and magnetoelectrical crack surface conditions on COD intensity factors are evaluated.Numerical results show that for a given size of MEE cylinder,the larger the crack radius is,the easier the crack is to expand.At the most unstable time of the crack,considering the same ratio of the radius of crack to the radius of MEE cylinder,the model of magnetoelectrically permeable crack is the easiest to expand.Finally,the fracture problem of a penny-shaped crack including a Dugdale plastic zone in a MEE cylinder under magnetoelectromechanical loads is investigated.The crack surfaces are assumed to be magnetoelectrically permeable.The problem is translated into solve a sectionalized Fredholm integral equation of the second kind.Using the sequential method,the factors that influence the width of plastic zone are obtained.The effects of the mechanical,electric and magnetic loads and the size of the penny-shaped crack on the crack opening displacements are discussed graphically.Numerical results show that the magnetoelectromechanical loads in the far field and the geometrical sizes of the structure have a significant effect on the width of plastic zone.The negative electromagnetic loads are prone to promote the crack growth when the same mechanical loads are applied in the far field.