Elastoplastic stress analysis of Nb3Sn superconducting magnet

The plastic behavior of a superconducting material is investigated and the corresponding elastoplastic formulation for the distribution of stress and strain in a superconducting solenoid magnet is presented. The analysis calculates stress and strain at the midsection, where tangential stress exhibits its maximum value and shear stress is negligible. The prediction of stress and strain is essential for both the mechanical and electrical design of high-field superconducting magnets containing Nb3Sn superconductor. The concept of plasticity is introduced for the first time in the context of magnet design for Nb3Sn conductor and compared to alternative approaches using conventional elasticity theory. Individual coil sections of a superconducting magnet can be reinforced by an outer section of structural material, the effect of which is included in this formulation. The results show that the elasticity approach using the ‘‘secant modulus method’’ does not fully predict the strain distribution; however, it can be used to approximate the stresses. It is shown that for an accurate strain prediction the true nonlinear elastoplastic nature of the superconducting materials should be considered and proper yield criteria should be used. The inaccurate prediction of strains (tangential or radial) can affect critical current density and the evaluation of the reinforcements.