  We examine the interaction between precipitates and grain boundaries, which
undergo shear-coupled motion. The elastic problem, emerging from grain boundary
perturbations and an elastic mismatch strain induced by the precipitates, is
analysed. The resulting free elastic energy contains interaction terms, which
are derived numerically via the integration of the elastic energy density. The
interaction of the shear-coupled grain boundary and the coherent precipitates
leads to potential elastic energy reductions. Such a decrease of the elastic
energy has implications on the grain boundary shape and also on the solubility
limit near the grain boundary. By energy minimisation we are able to derive the
grain boundary shape change analytically. We apply the results to the Fe-C
system to predict the solubility limit change of cementite near an
$\alpha$-iron grain boundary.
