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The refinement of grains in a polycrystalline material leads to an increase in strength but as a counterpart to a decrease in elongation to fracture. Different routes are proposed in the literature to try to overpass this strength-ductility dilemma, based on the combination of grains with highly contrasted sizes. In the simplest concept, coarse grains are used to provide relaxation locations for the highly stressed fine grains. In this work, a model bimodal polycrystalline system with a single coarse grain embedded in a matrix of fine grains is considered. Numerical full-field micro-mechanical analyses are performed to characterize the impact of this coarse grain on the stress-strain constitutive behavior of the polycrystal: the effect on plasticity is assessed by means of crystal plasticity finite element modeling [B. Flipon, C. Keller, L. Garcia de la Cruz, E. Hug and F. Barbe, Tensile properties of spark plasma sintered AISI 316L stainless steel with unimodal and bimodal grain size distributions, Mater. Sci. Eng. A 729 (2018) 248–256] while the effect on intergranular fracture behavior is studied by using boundary element modeling [I. Benedetti and V. Gulizzi, A grain-scale model for high-cycle fatigue degradation in polycrystalline materials, Int. J. Fract. 116 (2018) 90–105]. The analysis of the computational results, compared to the experimentally characterized tensile properties of a bimodal 316L stainless steel, suggests that the elasto-plastic interactions taking place prior to micro-cracking may play an important role in the mechanics of fracture of this steel.