The overall behaviour of metals composed of grains with different sizes is simulated as well as the evolution of their internal structure making use a self-consistent modelling for elasticviscoplastic materials. The Representative Volume Element is composed of isotropic spherical grains randomly distributed with a grain size distribution following a log-normal statistical function. Thus the heterogeneity of the RVE comes only from the grain size dependence of the local flow stress. The viscoplastic strain rate of the grains is modelled through a classic isotropic power law involving a reference stress depending on the individual grain size and the local plastic strain. Numerical results applied to IF steels firstly display that the overall yield stress depends not only on the mean grain size but also on the dispersion of the grain diameter distribution. The role of the grain size dispersion becomes significant when the mean grain size is on the order of "m, and, a decrease of the overall yield stress with an increase of the dispersion is observed. Secondly, prediction of the evolution of the internal structure indicates an increase of second order internal stresses with grain size dispersion. When this one is large enough and the mean grain size is on the order of "m, residual stresses due to heterogeneities arising from the grain size distribution are on the same order than the ones related to heterogeneities associated with plastic anisotropy found for polycrystalline IF steels.