Micromechanical modelling on the elastoplastic damage and irreversible critical current degradation of the twisted multi-filamentary Nb₃Sn superconducting strand

Nb₃Sn is widely accepted as the enabling technology for high field superconducting magnets. However, it is brittle and with strain-sensitive superconducting properties. In high field applications, Nb₃Sn strand experiences significant elastoplastic strain or even damage which causes degradation in its current carrying capacity. In this work, a 3D mean-field homogenization model based on the incremental micromechanics scheme is developed to investigate the elastoplastic damage and irreversible degradation of the twisted multifilamentary Nb₃Sn strand. The effective stress-strain curves and strain distribution in the Nb₃Sn filaments are calculated for the strand under monotonic and cyclic loads. The invariant strain scaling law supplemented with the damage-induced reduction is adopted to characterize the irreversible degradation of the critical current. It is found that twisting plays an important role in elastoplastic damage and strain-induced critical current degradation. With the increasing of twist pitch, the strand becomes stiffer and the strain limit surpasses which the filaments start to damage sharply decreases. Both the accumulated residual strain and damage of the filaments contribute to the irreversible degradation of the critical current. The experimentally observed “strain irreversibility cliff” is the result of damage to the Nb₃Sn filaments. From a mechanical point of view, a short twist pitch will be a good choice to alleviate the strain-induced irreversible degradation of the Nb₃Sn strands.