Thermal and bending strain on Nb₃Sn strands

Recent experimental results on the International Thermonuclear Experimental Reactor (ITER) Central Solenoid Model Coil and Insert Coil have shown that the critical characteristics measured on a single strand are significantly different from those of a cabled conductor. This performance degradation seems to be due mostly to the bending effects on the strands subjected to the electromagnetic forces: a strand inside the cable behaves like a beam supported by the neighboring strands and loaded by the transversal Lorentz force. Recently at the University of Twente (The Netherlands) and at the Japan Atomic Energy Research Institute (JAERI) some experimental tests have been performed to study this effect. In this study we analyze the strand strain field resulting from the cool down and the successive bending loads. Due to the material non linearity it is not possible to calculate the two effects separately. To analyze the strain field in a strand experiencing an electromagnetic load at 4.2 K, it is hence necessary to follow the evolution of the deformation from the strand reaction temperature to its working conditions. One single strand is taken into consideration, and it is studied with three different approaches: assuming Kirchhoff hypothesis, applying Timoshenko beam theory and using a composite, fibrous beam model. The resulting strain field is used as input data for the THELMA code to compare the results with the experiment performed at JAERI. This work is detailed in a companion paper.