a b s t r a c tSubsequent yielding of polycrystalline aluminum after cyclic tension-compression is studied by both experiments and finite element simulations applying crystal plasticity. The directional hardening induced by pre-deformation is particularly emphasized. By means of a sub-model method, scale-bridging analyses of a specimen containing a ring-section constructed of a number of grains re-loaded in different ratios of axial tension and torsion are carried out, after cyclic tension-compression pre-deformation. Both the Chaboche rate-dependent constitutive relation and the crystal plasticity theory extended by introducing a back stress, which relates the mechanical behavior of polycrystalline aluminum at macroscopic scale and microscopic scale, are employed. The influences of different unloading loci, pre-loading directions and yield definitions on subsequent yield surfaces are investigated in detail by comparing computational and experimental results. The results show that the shape of subsequent yield surfaces and the ''sharp corner'' appearing at the front end of a yield surface are closely related to the tensile or compressive pre-loading direction and different yield point definitions. The subsequent yielding by re-loading obviously shows deformation-induced anisotropic hardening. The main characteristics of subsequent yield surfaces observed in experiments can be satisfactorily captured by the present crystal plasticity model with the introduction of a back stress.

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This study aims at introducing the back stress of anisotropic strain-hardening into the crystal plasticity theory and demonstrating the rationality of this crystal plasticity model to describe the evolution of the subsequent yield surface of polycrystalline aluminum at the mesoscopic scale under complex pre-cyclic loading paths. By using two different scale finite element models, namely a global finite element model (GFEM) as the same size of the thin-walled tube specimen used in the experiments and a 3D cubic polycrystalline aggregate representative volume element (RVE) model, the evolution of the subsequent yield surface for different unloading cases after 30 pre-cycles is further performed by experiments and numerical simulations within a crystal plasticity finite element (CPFE) frame. Results show that the size and shape of the subsequent yield surfaces are extremely sensitive to the chosen offset strain and the pre-cyclic loading direction, which present pronounced anisotropic hardening through a translation and a distortion of the yield surface characterized by the obvious “sharp corner” in the pre-deformation direction and “flat” in the reverse direction by the definition of small offset strain, while the subsequent yield surface exhibits isotropic hardening reflected by the von Mises circle to be distorted into an ellipse by the definition of large offset strain. In addition, the heterogeneous properties of equivalent plastic strain increment are further discussed under different offset strain conditions. Modeling results from this study show that the heterogeneity of plastic deformation decreases as a law of fraction exponential function with the increasing offset strain. The above analysis indicates that anisotropic hardening of the yield surface is correlated with heterogeneous deformation caused by crystal microstructure and crystal slip. The crystal plasticity model based on the above microscopic mechanism can accurately capture the directional hardening features of the yield surface.

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