Development of machine learning model for predicting powder density during drawing process of superconducting ${MgB_2}$ wire

Abstract

After the discovery of superconductivity in magnesium diboride (MgB2), significant efforts have been made to develop the MgB2 wires for replacing low-temperature superconductors in large-scale applications like magnetic resonance imaging (MRI) because MgB2 can maintain the superconducting state without expensive liquid helium. The powder-in-tube (PIT) method is widely used to fabricate the MgB2 wires due to the inferior formability of the synthesized MgB2 itself. In the PIT process, the raw precursor powders are inserted into a diffusion barrier surrounded by an outer sheath. This composite billet is deformed into a wire by cold working processes including drawing, swaging, and rolling. In the subsequent heat treatment process, the unreacted Mg+2B powder mixture is synthesized into MgB2, in which the volume shrinkage as a result of synthesizing MgB2 induces the formation of voids. It is well known that the formation of voids and nucleation of MgO layers at the grain boundaries can deteriorate the grain connectivity of MgB2. Based on Rowell’s model, most of the commercial PIT-processed wires exhibited 5-15% of full-grain connectivity. In other words, less than 15% of the total cross-sectional superconducting area may play a role in carrying the transport currents. It is known that the enhancement of grain connectivity of MgB2 wire can be achieved by increasing the powder packing density of the wire. Therefore, it is quite essential to predict and control the packing density of the powder mixture during the manufacturing process to improve the superconducting properties of MgB2 wire. For this aim, the powder density prediction model in the drawing process of PIT-processed MgB2 wire was established by machine learning (ML) with a drawing simulation model in the current study. As the first step, a series of PIT-processed mono-filamentary MgB2 wires with different initial filling densities of powder mixture was fabricated. The effect of initial filling density on the deformation behavior of the sheath materials and the powder mixture during the drawing was investigated by means of microstructural analysis. In addition, by estimating the grain connectivity based on the site percolation model, it was found that the increase in the packing density of the Mg+2B powder mixture enhanced the grain connectivity and consequently resulted in improving the critical current properties of the MgB2 wire. For the next step, the FE simulation model for the multi-pass drawing process of MgB2 wire was built by the modified Drucker-Prager Cap model. To capture the anisotropic hardening behavior of the powder mixture, a number of uniaxial die compaction and cold isostatic pressing tests were conducted with different powder densities of the powder mixture. The drawing simulation model was verified by comparing the density obtained by simulation with experimental values. Finally, the drawing simulations were conducted by changing the design parameters of the MgB2 wire drawing to establish ML models for predicting powder density. Of the output features, the rarely observed data was resampled by a distance-based linear interpolating method and introducing Gaussian noise. The prediction results by the artificial neural network algorithm showed good consistency with the simulation results. By using the model interpretation method, the effect of design parameters on model output representing superconducting performances of MgB2 wire was investigated in terms of the powder density. In addition, the underlying mechanism of the initiation and development of wavy shape non-uniform deformation, namely sausaging phenomenon, was explained by simulation results.