Effects Of Inclusions On Magnetostriction Of High Temperature Superconductors

When the superconducting material is placed in an external magnetic field,the shape and properties of the inclusion will affect the effective magnetostriction of the superconductor.The effects of elastic modulus,volume fraction and permeability on effective magnetostriction can be obtained by using the continuous boundary condition in elastic mechanics.The specific work done in this paper is as follows:First,in this paper,the dependence of the effective magnetostriction of bulk superconductors on the elastic parameters including the volume fraction and elastic modulus ratio is studied by a three-dimensional model consisting of spherical inclusion-superconducting matrix system.The effect of the elastic modulus and volume fraction on the magnetostriction is also obtained through the magnetostriction loop.The results indicate that the elastic modulus and volume fraction have obvious effects on the effective magnetostriction of the superconducting composite,which gives an explanation about the differences between the experimental and the theoretical results.Furthermore,it is worth pointing out that the linear field dependence of magnetostriction is unique to the Bean model by comparing the curve shapes of the magnetostriction loop with and without inclusion.Second,in this paper,the effects of volume fraction,permeability and elastic modulus of embedded nonsuperconducting inclusions on the stress and magnetostriction of in thin superconductor are discussed.It is assumed that the circular inclusion is sparse and regular distributed in the inside of an equal thickness thin superconductor,and the external magnetic field Ba is perpendicular to the slab surface.In order to study the stress and the effective magnetostriction,the approximately two-dimensional model is established,and the model is effectively simplified.Using the continuity conditions and the plane strain approach,the corresponding equations are established.Based on the critical state Bean model,the corresponding stresses and displacements are derived,thus the dependence of stress and magnetostriction on a single parameter is obtained.The results show that the parameters of the inclusions have significant influence on the thin superconductors.This result may explain the small difference between the theoretical and experimental values.Last,a simple model is presented based on Kim-Anderson model to further investigate the dependence of the effective magnetostriction of magnetic inclusion-superconducting matrix system on both the elastic and magnetic parameters including the elastic modulus,permeability,and volume fraction.The effect of the permeability on the magnetostriction is also obtained by implementing the continuity conditions of displacement and strain at the interface between the inclusion and the matrix through the magnetostriction loop.The results indicate that a stiffer inclusion can decrease the effective magnetostriction no matter whether the inclusion is magnetic or not and a larger effective magnetostriction can be obtained by choosing the matrix with a higher permeability,which gives an explanation about why the composite made from a matrix with a high permeability but a negligibly small magnetostriction yields unexpectedly low magnetostriction.Of particular interest is that in a certain range the effective magnetostriction of composites can be enhanced until it is saturated by increasing the permeability of matrix.