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Two-phase composites, which consist of polycrystalline -iron and copper particles, are studied mechanically under large plastic deformation. Due to the significant difference of the yield stress in the iron and the copper phase in which the slip system geometry is also dissimilar, a high heterogeneity and anisotropy characterize the plastic deformation behaviour. In this work, an elasto-viscoplastic material model is applied in finite element simulations, whereas the macroscopic material behaviour is established based on constitutive equations of the single crystal. Due to the natural spatial character of the slip system mechanisms of crystal plasticity, the numerical calculation must be performed fully 3D. However, since it is hardly possible to determine the grain geometry of a real material in 3D without destroying the sample by slicing or the like, real 2D cross-sections have been modelled and extended to the third dimension in an axisymmetric way producing an annular pattern, which comes closer to reality than a 2D structure. Numerical predictions include the grain deformation behaviour, the flow behaviour, the crystallographic texture, and the local strain in Fe–Cu composites. In particular, a quantitative study is performed for the mean value of the local strain in both phases, which shows a good agreement with the experimental result for the Fe17–Cu83 composite under tension.