Sensitivity analysis on elastic-plastic properties of superconducting strands

Scientific and medical equipment may require the generation of high magnetic fields. To this purpose superconducting (SC) magnets wound with SC wires are mainly used. Superconducting wires are made of SC filaments embedded in a bronze/copper matrix. Bronze and copper typically show elastic-plastic behavior with hardening, while filaments remains in elastic conditions. Because of their manufacturing process, SC wires experience a wide thermal variation: from reaction temperature (900-950K) to working conditions (4-7K). Due to its heterogeneity, a straightforward numerical simulation of a coil, taking into account all the details of the microstructure, would result in an enormous number of unknowns. In some previous works homogenization methods were proposed to address this problem. In particular in [D.P. Boso, Superconductor Science & Technology, 2013] it is presented that our model can reproduce well the stress and strain curves of wires by means of virtual testing and finite element method. However, it is very difficult to find a consistent set of thermal and elastic-plastic material data over the whole temperature range needed. In this work we address this problem. We investigate how the variability and uncertainty on the measured samples reflect on the obtained homogenized behavior. A parametric study is performed, with variations up to 30% on the elastic properties of each component to see the overall effects on the elastic behavior. Concerning the plastic field, yielding stress is increased of 30% and tangent moduli are increased up to 300%. Variations of the properties of a single material as well as simultaneous variations of the properties of different components are considered. As far as the elastic field is concerned, some regularity is found for a single increment: the leading factor for the global behavior is the volume fraction. Out of the regularities found in the results, it is possible to obtain a relationship to correlate the variation of the Young modulus of one material to the simultaneous variation of the Young modulus of different components. With respect to the plastic field, very different performances between the wire longitudinal behavior and the cross-section behavior are observed. Along the longitudinal axis SC filaments show their influence on the global plastic behavior, while in the wire cross-section bronze and copper materials lead the nonlinear mechanics.