Analytical model of the critical current of a bentNb3Sn strand

Abstract

The critical current performance of a largeNb3Sn cable-in-conduit conductor (CICC) was degraded by periodic bending of strands due to alarge transverse electromagnetic force. The degradation of each strand due to this bendingshould be evaluated in calculations of the critical current of a CICC, but a suitable modelhas not been developed yet. Therefore, the authors have developed a new analytical modelwhich takes into account plastic deformation of copper and bronze and filamentbreakage. The calculated results were compared with test results for uniformly bentNb3Sn 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 themodel. Because of a much shorter calculation time than for numerical simulation, the developedmodel seems much more practical for use in calculating the critical current performance of aNb3Sn CICC. In addition, simulation results show that since the neutral axis of a bent strandshifts to the compressive side due to plastic deformation of the copper and bronze, and/orfilament breakage, the strand is elongated by bending. This elongation may enhance thestrand’s critical current performance. Moreover, the calculated results indicate thatthe dependence of the critical current on the bending strain is affected by thebending history if the strand is excessively bent, especially when filaments arebroken. In a real magnet, since a strand in a CICC is normally subject to themaximum electromagnetic force prior to an evaluation of its performance at a lowerelectromagnetic force, the effect of over-bending should be taken into account incalculations of its critical current performance, especially when filament breakage occurs.