Some Mechanical Problems Of Superconducting Materials

Recently, as a new sort of smart materials, superconducting materials have been extensively researched, and a set of theoretical systems have been established. Due to the unique properties, high-temperature superconductors(HTS) have been widely applied in electric power technology, communication technology, mechanical manufacturing technology and other advanced smart science and technology. However, HTS are fragile materials, and the HTS with high critical current density subjected to the strong electromagnetic body force when they are applied in the magnetic filed or transport current. Therefore, it is very significant to the investigations of the mechanical property and fracture behaviors of HTS. This dissertation mainly research some mechanical problems from the views of principal theorems, relations of electromagnetic and mechanical property, and fracture behaviors. The specific content as follows:A reciprocity relation which involves two processes at different instants is established to form the basis of a uniqueness result and a reciprocal theorem. Then the continuous dependence theorem is discussed upon two external data systems. Finally, the variational principle of Hamilton type which fully characterizes the solution of the mixed boundary-initial-value problem(mixed problem) is obtained.Based on the hypothesis of planar section and elastic linear strengthening constitutive theory, the relation between torque and shear strain is firstly obtained. Then a linear weakening relation between critical current density and shear strain is put forward. Finally the effects of the applied torque together with the mechanical properties of superconducting core on the degradation behavior of critical current are calculated and discussed.The multiple isoparametric finite element method(MIFEM) is used to investigate external circumferential crack problem of a functionally graded superconducting cylinder subjected to electromagnetic forces. A crack reference region is defined to reflect the effects of crack on the flux and current densities, and the magnetically impermeable crack surface condition and the generalized Irie-Yamafuji critical state model outside the crack region are adopted. The distributions of magnetic flux density in the superconducting cylinder are obtained analytically for both the zero-field cooling(ZFC) and the field cooling(FC) activation processes. Based on the MIFEM, the stress intensity factors(SIFs) at crack fronts in the process of field ascent and/or descent are then numerically calculated.A double exponential model is proposed to investigate the cylindrical crack problem for a functionally graded superconducting cylinder(FGSC), where the Young’s modulus is assumed to vary in an exponential form in the radial direction, and the critical current density is assumed to depend on the magnetic flux density in an exponential form. The stress intensity factors(SIFs) are analytically obtained by transforming the corresponding crack problem into two pairs of dual integral equations, which are further solved by the Schmidt method. The effects of applied magnetic field, model parameters, and crack configuration on the SIFs are numerically calculated and analyzed.The arc-shaped crack between a homogeneous superconducting cylinder and its functionally graded coating is investigated subjected to transport currents. The extended generalized Irie-Yamafuji critical state model in the coating is put forward. The distributions of both current and flux densities in the superconducting composite are presented for the processes of both transport current ascent and descent. The stress intensity factors and energy release rates at crack tips are given in concise forms and numerically calculated by solving a system of linear algebra equations. This study will be beneficial to the design and application of superconducting composites.