Graded finite element simulation of thermal stress in inhomogeneous high-Tc superconductor

YBa2Cu3Oy is an orthotropic material with different material properties in a, b and c directions, such as Young’s modulus, coefficient of thermal expansion (CTE), and thermal conductivity. It is assumed that the material properties of inhomogeneous high temperature superconductor (HTS) vary with different height coordinate and temperature. A model is presented in this paper to calculate the thermal stress of inhomogeneous HTS when temperature decreases from ambient to operating conditions (cryogenic temperatures). By fitting a second order polynomial to the experimental data, value of the material properties of inhomogeneous HTS can be obtained. Then, through the proposed graded finite element method, the coupled thermo-mechanical equations were solved numerically. The numerical results show that the temperature profiles distribute the function of time after soaking. It is notable that the temperature profile reaches steady in a very short period of time, so the thermal stress suddenly increases to a very high level for a bulk superconductor. It is also shown that the closer to the sample internal region it is, the larger the heat fluxes are. Besides, the maximum tensile stresses, i.e. the peeling stresses, occur near bottom corner of inhomogeneous HTS. It is intended that the model presented in this paper could be useful to researchers who are interested in mechanical properties of inhomogeneous HTS.