Analysis of the distribution of critical current of bent Bi2223 composite tape based on a unifying parameter approach

Abstract

A modeling study was carried out to provide a description of the critical current distribution of bent multifilamentary Bi2223/Ag/Ag alloy superconducting composite tape samples. In the modeling, the difference between the tensile fracture strain of the Bi2223 filaments along the sample length under no residual strain and residual strain was used as a unifying parameter for the description of the damage evolution. The unifying parameter was treated to be different from sample to sample and also from position to position in each sample. The statistics of the unifying parameter were combined with the shape of the core and exerted tensile strain of the Bi2223 filaments, from which the relation of the heterogeneous damage evolution to the distribution of the critical current was formulated. The proposed model was applied to the reported data of 33 samples of the round robin test of VAMAS (Versailles project on advanced materials and standard)/TWA16 (Technical working area 16, superconducting materials) in 2000-2001. The reported distributions of the critical current of the bent-damaged samples were described well by the present model.

Applicability of Weibull Distribution to Description of Distributed Normalized Critical Current of Bent-Damaged Bi2223 Composite Tape

“…The cumulative (F) and density ( f ) probability of the critical current (I c =I c0 ) values at " B ¼ 0:6, 0.8 and 1.0%, taken from Fig. 1(a 15) This function has been used to describe the transport critical current distribution [11][12][13][14] and the critical current distribution at weak links for analysis of V (voltage)-I (current) curve near the transition from superconducting to normal conductive state. 16,17) The three-parameter Weibull distribution function is characterized by three parameters (ðI c =I c0 Þ min is the minimum (lower limit) value of critical current, ðI c =I c0 Þ 0 is the scale parameter, and m is the shape parameter).…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14] Heterogeneous damage occurs, and the damage evolution behavior differs from specimen to specimen and from location to location within a specimen. [9][10][11][12][13][14] Accordingly, when a number of specimens are tested, the critical current differs from specimen to specimen.…”

“…11,12,14) In this approach, the " f À " r value, where " f is the fracture strain of the bare Bi2223 filaments and " r is the residual strain of the filaments in the current transport direction, was treated as a variable; using this value, the difference in damage amount among the specimens was expressed. The " f À " r value corresponds to the tensile strain at which the filaments embedded in the composite tape are fractured.…”

“…Because the " r is negative (compressive) in the Bi2223 composite tape, as has been demonstrated by X ray diffraction analysis, 7,8) the actual fracture strain of the filaments in the composite tape is by À" r higher than the intrinsic fracture strain " f of the filaments alone. 2,4,[6][7][8]11,14) The " f À " r value is different from location to location within a specimen as well as from specimen to specimen. In the preceding works, 11,12) the heterogeneous damage behavior was formulated by the distributed " f À " r values and was correlated to the distribution of critical current values.…”

“…2,4,[6][7][8]11,14) The " f À " r value is different from location to location within a specimen as well as from specimen to specimen. In the preceding works, 11,12) the heterogeneous damage behavior was formulated by the distributed " f À " r values and was correlated to the distribution of critical current values. The procedure for application and the features of this approach (hereinafter ''damage approach'') is presented later in Section 3.2.…”