Quantitative correlation between the void morphology of niobium-tin wires and their irreversible critical current degradation upon mechanical loading

Abstract

Understanding the critical current performance variation of Nb3Sn superconducting wires under mechanical loading is a crucial issue for the design of next generation accelerator and fusion magnets. In these applications, the mechanical properties of the conductors may become a limiting factor due to the strong electro-magnetic forces resulting from the combination of large magnets and intense magnetic fields. In particular, the presence of voids in the superconducting filament structure, which are formed during the fabrication and the reaction heat treatment, determines localized stress concentrations and possibly the formation of cracks. In this work, we demonstrate a quantitative correlation between the void morphology and the electro-mechanical limits measured on different Bronze route Nb3Sn wires. Hot Isostatic Pressing (HIP) prior to the reaction heat treatment is utilized to partially eliminate the voids. The wires’ void distributions - with and without HIP treatment - are detected and statistically analyzed using high energy X-ray micro tomography. The stress concentration due to the shape and distribution of the voids as well as their impact on the electro-mechanical properties are determined through finite element method modeling. Finally, the results are quantitatively correlated with the experimentally determined limits of the irreversible critical current degradation upon mechanical loading.

Machine learning applied to X-ray tomography as a new tool to analyze the voids in RRP Nb3Sn wires

“…The tomography post-process was begun exploiting a dedicate algorithm written in MATLAB and already tested in 21 . The MATLAB tool analyses the 2D tomography’s cross-sections one by one.…”

“…one wire cannot be used as mechanical model scale for the others 48 . In this context a simple mechanical model based only on the sub-elements design cannot provide reliable results, because the sub-elements voids cannot be neglected, as they can act as nucleation point for the cracks in Nb 3 Sn 21 . Therefore to study and enhance the mechanical properties of RRP wires, a more complex mechanical model, capable to include the Kirkendall voids in the sub-elements, is necessary.…”

“…A possible application could be to use the tool to quantify the impact of voids on the electro-mechanical behavior of the wire and, as consequence, to improve the mechanical limits of RRP Nb 3 Sn wires. As matter of fact a clear quantitative correlation between voids and mechanical limits was obtained for Bronze route wires 21 while for the other types of internal tin wires, such as RRPs, the correlation has yet to be demonstrated. It was shown that varying the dopants (Ti or Ta) and the temperature of the heat treatment final plateau (600–750 °C), the axial irreversible limit of RRP wire changes 49 .…”

“…Synchrotron tomography was successfully used in the past to study and characterize the voids formation of Internal-Tin Nb 3 Sn wires 24 , 25 . Furthermore, a more recent study focused on bronze route Nb 3 Sn wires 26 was able to correlate the void morphology to the critical current degradation upon mechanical load 21 showing that the non-destructive synchrotron X-ray tomography is extremely effective to study Nb 3 Sn voids. Our analysis tool is the combination of micro-tomographies with an unsupervised machine learning algorithm, which is able to autonomously isolate, reconstruct and analyze the voids.…”

Tomography analysis tool: an application for image analysis based on unsupervised machine learning

“…In addition to the Nb 3 Sn phase, the reaction heat treatment generates Kirkendall voids [8] in the wire subelements that can have a detrimental impact on mechanical performances of the wires [9], see figure 1 3 for an example of Nb 3 Sn wire cross section. As said, Nb 3 Sn is a brittle and strain sensitive compound, this imply that it is prone to fracture and its critical current density strongly depends on the mechanical strain applied to the superconducting wire.…”