Fractal analysis of the role of the rough interface between Bi ₂Sr₂CaCu₂O_x filaments and the Ag matrix in the mechanical behavior of composite round wires

Multifilamentary round wires (RWs) of Bi₂Sr₂CaCu ₂O_x (Bi2212) superconductor in a Ag/AgMg matrix have complex microstructures that strongly influence their electrical and mechanical behavior. The Bi2212/Ag interfaces, which in some locations are characterized by Bi2212 growths into the Ag matrix that result in rough, jagged interfaces, and in other locations are characterized by Bi2212 growths that bridge and connect to neighboring Bi2212 filaments, are believed to be amongst the most important microstructural features; yet their role is not well understood. In this work, a fractal-based framework is created in an effort to understand the role of the structure of individual filaments and the Bi2212/Ag interfaces in determining the macroscopic electromechanical behavior of Bi2212 RW. Scanning electron micrographs of an individual Bi2212 filament extracted from a Bi2212 RW are used to analyze the rough Bi2212/Ag interface and develop a fractal model using the Weierstrass-Mandelbrot (W-M) fractal function. The W-M fractal function is then used to generate simulated Bi2212/Ag microstructures. Finally, the mechanical behavior of the microstructures is investigated. It is found that the interfilamentary bridges which play a significant role in Bi2212 transport are not likely to be the cause of electromechanical degradation and failure. Instead, large stress concentrations are identified at the concave tips that occur along the jagged Bi2212/Ag interface. In particular, locations where the concave tips are within the Bi2212 filament are the likely initiation points of failure in Bi2212 RWs.