Relation of the strength distribution of Nb3Sn to the critical current of a pre-stressed multifilamentary composite superconductor

From an analysis of the change in the superconducting critical current at 4.2 K caused by pre-stressing treatment at room temperature, the distribution of tensile strength of Nb3Sn in multifilamentary bronze-processed composite wires heat-treated at 973 K for 8.6 (sample A), 43 (B) and 260 ks (C) is estimated using the two-parameter Weibull distribution function. The shape parameters of the Weibull distribution are 7.2, 12. and 14, and the average strengths of the Nb3Sn are 1.3, 1.0 and 0.79 GPa for samples A, B and C respectively for the present specimen length of 25 mm. This means that the scatter of strengths and also the average strength for specimens of length 25 mm decrease with increasing heat-treatment time. An attempt to predict the length dependence of the critical current of pre-stressed specimens from the data for short specimens is presented. It seems that the permissible pre-stress below which there is no breakage of Nb3Sn (for all Nb3Sn transport currents) is reduced by 20-30% when the specimen is lengthened from 25 mm to 300 m, while the average strength of Nb3Sn is reduced by 50-70%.