Analytical model of the critical current of a bent Nb3Sn strand

The critical current performance of a large Nb3Sn cable-in-conduit conductor (CICC) was degraded by periodic bending of strands due to a large transverse electromagnetic force. The degradation of each strand due to this bending should be evaluated in calculations of the critical current of a CICC, but a suitable model has not been developed yet. Therefore, the authors have developed a new analytical model which takes into account plastic deformation of copper and bronze and filament breakage. The calculated results were compared with test results for uniformly bent Nb3Sn bronze-route strands. The calculated results assuming a high transverse resistance model (HTRM) show good agreement with the test results, a finding which confirms the validity of the model. Because of a much shorter calculation time than for numerical simulation, the developed model seems much more practical for use in calculating the critical current performance of a Nb3Sn CICC. In addition, simulation results show that since the neutral axis of a bent strand shifts to the compressive side due to plastic deformation of the copper and bronze, and/or filament breakage, the strand is elongated by bending. This elongation may enhance the strand's critical current performance. Moreover, the calculated results indicate that the dependence of the critical current on the bending strain is affected by the bending history if the strand is excessively bent, especially when filaments are broken. In a real magnet, since a strand in a CICC is normally subject to the maximum electromagnetic force prior to an evaluation of its performance at a lower electromagnetic force, the effect of over-bending should be taken into account in calculations of its critical current performance, especially when filament breakage occurs.