A model of a polycrystalline material is studied, where each grain consists of several zones with different plastic properties. The size and configuration of the zones as well as their properties are mimicking the situation inside the crystals of artificially aged Al alloys with precipitate free zones (PFZs). The properties of the different zones are conjectured based on micromechanical models and experimental observations of the AA6000 series of Al alloys. A periodic patch of such a composite material, subjected to plane-strain tension, is modelled using the finite element method. The material behaviour is described by a single crystal plasticity model. The results of the simulations show a number of characteristic features emerging in composite material systems, including sliding and distortion of grain boundaries and shear band formation at grain boundary triple points. The assumptions made about the properties of the different zones in the crystals are evaluated. The distributions of plastic strain and deviatoric and hydrostatic stresses in the composite crystalline systems are discussed.