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We perform an analysis of the size effect for quasi-static growth of cracks in isotropic linearly elastic bodies under antiplanar shear. In the framework of the variational model proposed by Francfort and Marigo in [J. Mech. Phys. Solids, 46 (1998), pp. 1319--1342], we prove that if the size of the body tends to infinity, and even if the surface energy is of cohesive form, under suitable boundary displacements the crack propagates following the Griffith's functional.