Bulge testing of copper and niobium tubes for hydroformed RF cavities

Abstract

The heat treatment, tensile testing, and bulge testing of Cu and Nb tubes has been carried out to gain experience for the subsequent hydroforming of Nb tube into seamless superconducting radio frequency (SRF) cavities for high energy particle acceleration. In the experimental part of the study samples removed from representative tubes were prepared for heat treatment, tensile testing, residual resistance ratio measurement, and orientation imaging electron microscopy (OIM). After being optimally heat treated Cu and Nb tubes were subjected to hydraulic bulge testing and the results analyzed. In the final part of the study finite-element models (FEM) incorporating constitutive (stress-strain) relationships analytically derived from the tensile and bulge tests, respectively, were used to replicate the bulge test. As expected, agreement was obtained between the experimental bulge parameters and the FEM model based on the bulge-derived constitutive relationship. Not so for the FEM model based on tensile-test data. It is concluded that a constitutive relationship based on bulge testing is necessary to predict a material's performance under hydraulic deformation.

Development of a multi-scale simulation model of tube hydroforming for superconducting RF cavities

“…The experimental tensile and bulge data of Nb samples heat treated for 2h/1000°C in previous work was used for this study [9]. For the Nb samples heat treated multiple times, numerical analysis based on the microstructure and tensile test was performed.…”

“…We first examined the validity of various analytical models for obtaining the flow stress curve from the tube bulge test results [8]. Subsequently, the constitutive relationships of tubular materials were obtained from the tensile and tube bulge tests using a previous verified and selected analytical model [9]. The continuum numerical simulation analyses were performed using these constitutive equations.…”

“…Tables I and II list the sample dimension, preparation, testing, and numerical simulation analyses performed in this and related studies. Some data from [9] were used in this study.…”

“…In Tables Table I Dimensions of starting Cu alloy and Nb tubes Table II Materials, experiments, and numerical simulations included in this and related [9] studies Table III Material parameters for CP-FEM Figure 1. Evolution of our research on the hydroforming of tubular materials Figure 2.…”

The automatic optimization of metal forming processes: Inverse identification of constitutive parameters for tubular materials based on hydraulic bulge test

“…The above equations 2.1 and 2.2 lay the foundation to calculate the circumferential and longitudinal stress components and fit the flow stress curve, which are first derived by Woo et al [50] and then used in many studies [23,56,66,[88][89][90][91][92][93]. Fuchizawa et al [53] improve this stress model by taking into account the wall thickness of metal tubes, and following re-searchers [54,55,58,59,63,71,72,81,87,[94][95][96][97][98][99][100] recommend this new formula because it is more in line with the actual situation.…”