Strain scaling law for flux pinning in practical superconductors. Part 1: Basic relationship and application to Nb3Sn conductors

Abstract Critical current and flux pinning densities have been determined for a series of Nb3Sn, V3Ga, Nb3Ge, and NbTi conductors as a function of uniaxial tensile strain in magnetic fields ranging from 4 to 19 T. An empirical relationship has been found at 4.2 K that describes these data over the entire range of field under both compressive and tensile strain. The pinning force F has been found to obey a scaling law of the form F = [B c2 ∗(ϵ)] n f(b) , where Bc2∗ is the strain-dependent upper-critical field determined from high-field critical-current measurements and f(b) is a function only of the reduced magnetic field b  B/B c2 ∗ . The detailed shape of f(b) depends on the super-conducting material and reaction conditions, but n was found to be nearly constant for a given type of superconductor. For Nb3Sn conductors n = 1 ± 0.3, for multifilamentary V3Gan≅1.3, for CVD-Nb3Ge tape n≅1.6, and for multifilamentary NbTi n≅3.3. The importance of this relationship is that, for these conductors at least, it is possible to measure F at one strain and then immediately be able to predict F (and thus the critical current) at other strain levels simply by scaling the results by [Bc2∗(ϵ)]n. Part I of this paper presents the basic uniaxial-strain scaling relationship and focuses on its application to Nb3Sn conductors. The strain scaling law with n = 1 ± 0.3 was found to hold for all Nb-Sn based conductors examined thus far, including commercial-multifilamentary conductors, extremely fine-filament composites, partially-reacted specimens, ‘insitu’ conductors, and Nb-Hf/Cu-Sn-Ga conductors. The detailed dependence of Bc2∗ on strain was-found to be nearly universal for highly-reacted commercial Nb3Sn specimens, greatly simplifying the application of the scaling law to this group of practical superconductors. These results are discussed within the context of flux pinning models and a general scaling relation is proposed which unifies the usual temperature-scaling relation with this strain-scaling relation.

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