The critical volume for the onset of plastic strain relaxation in SiGe islands on Si(001) is computed for different Ge contents and realistic shapes by using a three-dimensional model, with position-dependent dislocation energy. It turns out that the critical bases for dome- and barnlike islands are different for any composition. By comparison to extensive atomic force microscopy measurements of the footprints left on the Si substrates by islands grown at different temperatures (and compositions), we conclude that, in contrast with planar films, dislocation nucleation in 3D islands is fully thermodynamic.