Study On The Scaling Relation And The Strain Dependence Of The Critical Properties Of Nb₃Sn Superconducting Wires

The A15 phase Nb3 Sn superconducting wire is widely used in a variety of large-scale high-field superconducting magnets(above 13T) because of its good superconducting properties. However, since the critical superconducting properties(critical temperature cT, critical upper field c2 B and critical current cI) of Nb3 Sn are strongly dependent on the applied strain on account of its strain sensitivity, an overall performance degradation can take place when the magnets are strained. This applied strain usually comes from the mechanical loads during cooling(due to different thermal contractions between the composite) and operation(due to Lorentz forces). Hence, it is of importance to have knowledge of the strain dependence of the superconducting critical parameters, especially for the critical current.Scaling law is the basic theory to describe the critical current density with field, temperature and strain. The key of the calculation of the critical current density in Nb3 Sn strands is the so called ‘strain function’ which describes the strain-dependent upper critical field in the series of equations of scaling law. Several strain function models have been proposed based on theoretical analysis or experiments over the last decades of years. However, there is still not a perfect model which can describe the strain dependence of the upper critical field both theoretically and experimentally.In this paper, we first propose a simple form of the strain function based on Migdal-Eliashberg theory with the results of first principles calculations in the case of the most common uniaxial strain situation. From the McMillan Equation, we derive a method to bond the axial strain a? to the critical temperature cT, with the electron-phonon coupling ? and the averaged phonon frequency ln?. As the ‘bell shape’ of the curves of these two parameters with the applied uniaxial strain can be approximated as parabolic, we then connect cT with a? following the McMillan formula. With the relationship between cT and c2 B, we give the upper critical field with the axial strain(expresses by percentage and all in this paper). In this way, we derive the scaling law for the strain dependence of Nb3 Sn.From the view of invariants of the strain tensor, we derive a new invariant strain function model according to the consistency of the relationship between the critical temperature, the averaged phonon frequency and the electron-phonon with general strain state respectively. Both of above theoretical models show good fit with the measurements data of different kinds of Nb3 Sn strands and have a quite easy form compared to lots of previous models. Moreover, the invariant model has a better ability of extrapolation for the measurement ofc2 B.We also do lots of work on the simulations of transverse load effects on Nb3 Sn strands using finite element analysis. We take consideration of the shape of the contact surface, which has dependence on the mechanical response and the strain distribution of the strained Nb3 Sn strands. By refining the distribution of Nb3 Sn superconducting filaments inside the strand, we find the optimization of modeling of the strands and verify our two strain function models eventually.