Flux-pinning-induced stress and magnetostriction in a long rectangular slab superconductor: Critical-state model approach

This work investigates the irreversible behavior of the flux-pinning-induced stress and magnetostriction in a rectangular slab superconductor, placed in a strong background magnetic field Hz combined with an orthogonal transverse field (comprising a constant bias field Hax and a time-varying cyclic field Hay(t)). A solution of this three-dimensional magnetoelastic problem is found by the plane strain approach. All the stress–strain components and magnetostriction are expressed in terms of the magnetic field profile in the slab. The field distributions are obtained based on the critical-state model. We conclude that both the magnitude and location of the maximum tensile stress depend on the amplitude of Hay during different field cycles. Furthermore, the constant field Hax induces additional compressive stress components, leading to a downward shift in the magnetostriction loop and a significant reduction in the stress level within the slab (except at the slab surface). The calculated magnetostriction curve in the BaFe1.908Ni0.092As2 single crystal agrees with the measured ones in trend at 5 K. The difference in magnitude is mainly caused by the demagnetization effects of the sample and the applied field conditions. The maximum stress reaches the order of 1 MPa, which is very likely to induce the initiation and propagation of microcracks and degradation of superconducting properties. Compared to the Bean model, the critical-state model can evaluate the elastic response of the slab under arbitrary field excitation.