Formation and propagation of cracks in RRP Nb₃Sn wires studied by deep learning applied to x-ray tomography

Abstract

This paper reports a novel non-destructive and non-invasive method to investigate crack formation and propagation in high-performance Nb3Sn wires by combining X-Ray tomography and deep learning networks. The next generation of high field magnet applications relies on the development of new Nb3Sn wires capable to withstand the large stresses generated by Lorentz forces during magnets operation. These stresses can cause a permanent reduction of the transport properties generated by residual deformation of the Nb3Sn crystal lattice as well as the formation of cracks in the brittle Nb3Sn filaments. Studies for the development of the High Luminosity LHC (HL-LHC) upgrade showed that nominal transverse compressive stresses above 150 MPa may be sufficient to generate cracks in the wires. In the case of fusion magnets, wires experience periodic bending due to the electro-magnetic cycles of the reactor which over time may induce wire deformation and filament cracks. Therefore, it has become essential to develop a quantitative method for the characterization of crack formation and propagation under compressive loads. The X-Ray tomographic data of a series of Restacked-Rod-Process (RRP) Nb3Sn wires was acquired at the microtomography beamline ID19 of the European Synchrotron Radiation Facility (ESRF), after intentionally inducing a broad spectrum of cracks in the Nb3Sn sub-elements. The samples were submitted to transvers compressive stresses, with and without epoxy impregnation, at different pressures, up to 238 MPa. The resulting tomographic images were analysed by means of deep learning semantic segmentation networks, using U-net, a Convolutional Neural Network (CNN), to identify and segment cracks inside the wires. The trained CNN was able to analyse large volumes of tomographic data, thus enabling a systematic approach for investigating the mechanical damages in Nb3Sn wires. We will show the complete three-dimensional (3D) reconstruction of various cracks and discuss their impact on the electro-mechanical performance of the analysed wires.

Numerical simulation of mechanical behaviors and intergranular fracture of polycrystalline Nb3Sn and superconducting filaments

“…The study pointed out that the irreversible degradation of the critical current under the transverse stress of 180 MPa is mainly caused by the plastic deformation of the copper matrix, and the effect of filament fracture becomes obvious above this stress. Bagni et al [42,43] investigated sub-elements voids, crack formation and propagation in Nb 3 Sn wires by combining x-ray micro-tomography and machine learning. All these studies significantly contribute to the understanding of strain sensitivity and irreversible degradation analysis.…”

Degradation of I c due to residual stress in high-performance Nb3Sn wires submitted to compressive transverse force

“…An independent confirmation of the dominant role of residual stresses on the degradation of I c came from a study combining x-ray tomography and deep learning Convolutional Neural Networks, reported in [33]. Tomography images were taken at the European Synchrotron Radiation Facility on the RRP wire sample at 0.7 mm extracted from the I c vs transverse stress probe at the end of the experiment after the final unload from 240 MPa.…”

“…The wire volume examined by tomography corresponds to a scan length of about 1.5 mm. More details about the methods of detection and image recognition are reported in the [29,33,34]. Only very few cracks are present in the examined sample after unload from 240 MPa.…”

Roadmap on artificial intelligence and big data techniques for superconductivity

“…For this reason, the voids need to be considered in a wire mechanical FE model to reproduce the wire properties, faithfully. ML and CNN can detect and separate the voids from the other components allowing the 3D reconstruction of the wire's internal structures (see figure 24) [133,134].…”