A generalised self-consistent like homogenisation for non linear thermo-mechanical analyses

For electrical and thermal stability, in superconducting strands 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 depending upon the state of reaction of the filaments. It is based on a generalised self-consistent like homogenisation, suitably developed to deal with heterogeneous inclusions, material non-linearity and coupling between 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