Distribution of thermal and bending strain in Nb3Sn strands

For electrical and thermal stability the Nb3Sn compound is distributed into fine filaments (up to about 50 micrometers diameter) and embedded in a resistive matrix. Nb3Sn formation requires a solid state diffusion reaction at high temperature, which causes transformation strains in each material during cool down. The energisation modifies this initial strain field because Lorentz forces act as bending loads on the strands inside the cable. In this work we present a thermo-mechanical model to compute the strand initial strain field and the distribution of strain due to the following bending. It is based on a generalized self-consistent like homogenisation, suitably developed to deal with the material non-linearity and the coupling between the thermal and mechanical field. Attention is focused on the various components of the strain in the strand and their distribution. An appropriate unsmearing technique gives finally the strain state in the real, not homogenized materials. The numerical results are compared with the experimental tests recently performed on a single strand subject to bending loads.