Integral Equation Method For Crack Problems Of Functionally Graded Superconducting Materials

Superconductors are widely used in various fields such as medical imaging,transportation,and energy because of their unique electromagnetic properties.However,the magnetisation of superconductors under high magnetic fields can lead to stresses inside the superconductor,which can cause strain inside the superconductor and may lead to damage to the superconductor,resulting in a significant loss of material performance.In this paper,the fracture characteristics of homogeneous and functional graded superconductors under the influence of electromagnetic forces are investigated in terms of both temperature and magnetic field.The detailed work is as follows:Firstly,a model of superconductor with eccentric cracks is constructed,and the analytical solution of the internal temperature field function of the material is obtained from the heat conduction equation.The electromagnetic properties of the superconducting material are further considered,and the current distribution and magnetic field distribution inside the material are analyzed in conjunction with the superconducting critical state theory.The displacement and stress fields of the crack problem are then derived by means of the Fourier integral transform technique.By introducing auxiliary functions on the crack surface,the crack problem is transformed into a system of singular integral equations,which are converted into a linear algebraic system of equations using Chebyshev’s product formula to obtain an expression for the stress intensity factor at the crack tip.The numerical results discuss the influence of the geometrical properties of the superconductor and the applied magnetic field on the fracture properties of the superconductor when subjected to electromagnetic forces caused by flux pinning.Secondly,the fracture characteristics of exponential functional graded superconductors under the action of electromagnetic forces are investigated.Taking a high-temperature superconductor with a graded distribution as the object of study,the electromagnetic properties of the superconductor are treated by considering the unidirectional coupling of temperature to current and magnetic field,transforming the planar elastic control equation into a system of singular integral equations that can be solved for the dislocation function,and further using Chebyshev’s formula to obtain the expression for the stress intensity factor at the crack tip.The effect of material geometry,material gradient parameters and the temperature rise of the coolant on the stress intensity factor at the crack tip is analyzed by means of numerical examples.To conclude this thesis,we will continue to investigate the interrelationship between the mechanical properties of high-temperature superconducting materials in order to improve the performance of these materials for engineering applications in energy,transportation,medical and other fields.