Study On The Influence Of Inclusions And Cracks On The Mechanical Behavior Of Functionally Graded Superconductors

Superconducting materials have been around for more than 100 years and are regarded as "one of the greatest scientific discoveries of the 20 th century".Superconducting materials are widely used in medical,scientific and technological,military and other fields,but superconducting materials prepared under the existing technical conditions inevitably have cracks,inclusions and other defects;and the functional gradient superconducting materials developed on the basis of superconducting materials have the advantages of higher mechanical strength,thermal shock resistance,effective reduction of residual stress and high temperature resistance.In order to solve the limitations of superconducting materials,the preparation of energy gradient superconducting materials can optimize the material properties and expand its application scope.There are relatively few studies on the mechanical problems of functional gradient superconducting materials,especially the problems of inclusions and cracks have received little attention,this paper focuses on the effects of inclusions and cracks on the mechanical properties of functional gradient superconductors.Firstly,a columnar functional gradient superconductor model containing cracks and inclusions is built and placed in a liquid nitrogen environment for cooling,and its functional gradient properties are related to the elastic properties of the superconductor.The mechanical properties of functional gradient superconducting cylinders are studied under thermal loading while considering the effects of cracks and inclusions,and the exact distribution of the temperature field is obtained by solving the heat conduction equation using the analytical method,and it is found that the temperature drops rapidly in a very short period of time.The non-uniform thermal stress distribution of the columnar functional gradient superconductor is obtained from the thermoelastic equation,and this non-uniform distribution is defined by the ABAQUS subroutine UTRACLOAD module.The results show that: the low temperature makes the inhibition of crack expansion by inclusions ineffective;the radial thermal stress tends to increase and then decrease with increasing radius,and the circumferential thermal stress is in the opposite direction inside the cylinder and at the edges;the change in the functional gradient parameter not only affects the value of the thermal stress but also its trend;the stress intensity factor is significantly lower on the side near the inclusions than on the other side.Secondly,based on the above model,the effect of cracks on functional gradient superconductors is neglected,the thermal stress is equated to the physical force,and the concept of volume fraction is introduced to further investigate the effect of inclusions on the mechanical properties of functional gradient superconductors.Numerical results show that:increasing temperature increases radial displacement,radial strain and circumferential strain in functional gradient superconductors;the rate of decrease of radial stress in the elastic intercalation phase is greater than that in the rigid intercalation phase;increasing volume fraction promotes the increase of radial displacement in the intercalation but suppresses the increase of radial displacement in the matrix;at the connection between the intercalation and the superconducting matrix,radial strain changes abruptly while circumferential strain changes continuously.Finally,a functional gradient superconducting flat plate model containing inclusions and co-linear cracks is developed to study the mechanical behavior of functional gradient superconductors under the action of an applied magnetic field while considering the effects of co-linear cracks and inclusions.The Bean model is used to describe the electromagnetic behavior of superconductors,and the expressions for the magnetic flux density of superconductors during the drop of the magnetic field are obtained for magnetoelastic analysis,and the stress intensity factors(SIF)at the crack tips are determined using the software ABAQUS.The results show that the stress intensity factor at the crack tip increases as the flux viscous flow rate increases;the inclusions have a stronger inhibitory effect on the stress intensity factor at the crack tip near the end;the stress intensity factor shows a trend of increasing and then decreasing during the downfield process;the crack length,the inclusions size and the distance between the inclusions and the crack all have a significant effect on the stress intensity factor at the crack tip.