Comparison of strain scaling functions for the strain dependence of composite Nb3Sn superconductors

The observed strain dependence of the critical current of Nb3Sn composite superconductors is described by strain scaling laws in which the strain dependence of the effective upper critical field plays a prominent role. The strain dependence of the effective upper critical field is in turn given by a strain scaling function, or simply strain function. Recently, a general invariant strain function was suggested by a detailed analysis of the physical basis of strain dependence in Nb3Sn. The invariant strain function is viewed as giving a general formulation of strain dependence for all configurations of applied strain. In order to gain familiarity with the invariant strain function and to explore its range of validity, the invariant strain function is compared with previous empirical strain functions including the power law, the deviatoric description, the polynomial form, and the deviatoric power law. The invariant strain function is found to give a unified representation of strain dependence, including the characteristics that are observed for longitudinal applied strain to wires, and the observations that were made for tapes under multidimensional strain that led to the deviatoric description.