Analytical and Numerical Methods to Estimate the Effective Mechanical Properties of Rutherford Cables

Superconducting Nb₃Sn Rutherford cables can be used in the accelerator magnets above 10 T regions that cannot be reached with NbTi. These cables are composed of superconducting multifilamentary strands, interstitial epoxy, and insulation materials. To properly design the magnets made from these cables, it is essential to analyze their mechanical behavior. The prerequisite for this is the knowledge of the mechanical performance of Rutherford cables. In large magnets, these cables cannot be modeled with all details but effective properties and homogenization are typically required. In this work, an analytical model and numerical approach for predicting the effective mechanical properties of Rutherford cables are developed. The analytical model is established on a two-step homogenization and mechanical analysis for composite. The effective mechanical properties of the filament area and the transverse Young's modulus of the strand are first determined by means of utilizing the mechanical theory of the unit cell approach. The composite effective mechanical properties of the strand and interstitial epoxy are homogenized in the first step. The second step homogenization derives the effective mechanical properties of the strands epoxy composite and insulation layers. The numerical approach to determine the effective mechanical properties is based on the finite-element analysis. The developed methodologies are used to obtain the effective mechanical properties of two Nb₃Sn Rutherford cables. The influence of the insulation thickness and modulus, the strand's modulus, is studied.