A hybrid approach for the efficient computation of polycrystalline yield loci with the accuracy of the crystal plasticity finite element method

Direct experimental evaluation of the anisotropic yield locus of a given material, representing the zeros of the material's yield function in the stress space, is arduous. It is much more practical to determine the yield locus by combining limited measurements of yield strengths with predictions from numerical models based on microstructural features such as the orientation distribution function (ODF; also referred to as the crystallographic texture). For the latter, several different strategies exist in the current literature. In this work, we develop and present a new hybrid method that combines the numerical efficiency and simplicity of the classical crystallographic yield locus (CYL) method with the accuracy of the computationally expensive crystal plasticity finite element method (CPFEM). The development of our hybrid approach is presented in two steps. In the first step, we demonstrate for diverse crystallographic textures that the proposed hybrid method is in good agreement with the shape of the predicted yield locus estimated by either CPFEM or experiments, even for pronounced plastic anisotropy. It is shown that the calibration of only two parameters of the CYL method with only two yield stresses for different load cases obtained from either CPFEM simulations or experiments produces a reliable computation of the polycrystal yield loci for diverse crystallographic textures. The accuracy of the hybrid approach is evaluated using the results from the previously established CPFEM method for the computation of the entire yield locus and also experiments. In the second step, the point cloud data of stress tensors on the yield loci predicted by the calibrated CYL method are interpolated within the deviatoric stress space by cubic splines such that a smooth yield function can be constructed. Since the produced yield locus from the hybrid approach is presented as a smooth function, this formulation can potentially be used as an anisotropic yield function for the standard continuum plasticity methods commonly used in finite element analysis.

Investigation on Plastic Flow Behaviors of FCC Polycrystalline Aluminum under Pre-Cyclic Tension-Compression Loading: Experiments and Crystal Plasticity Modeling

The plastic flow behaviors of FCC polycrystalline aluminum after pre-cyclic tension-compression deformation are mainly investigated in tension–torsion stress space by the physically based crystal plasticity model introducing a back-stress. A global finite element model (GFEM) constructed of sufficient grains was established to simulate the same-size thin-walled tube specimen constrained and loaded as the experiments of yield surfaces. The computational results showed that the shape of subsequent yield surfaces and the plastic flow directions directly depended on the given offset strain levels and the applied re-loading paths under different pre-cyclic deformations. The angle deviation between the plastic flow direction and the theoretical orthogonal direction further indicated that there was a large difference between them in the inverse pre-straining direction, but the difference was negligible in the pre-straining direction. From the influence of the anisotropic evolution of the subsequent yield surfaces on plastic flow, we found that the plastic normality rule followed the smooth yield locus; conversely, the significant non-associated flow was attributed to the distorted yield locus. Furthermore, it was also demonstrated that the anisotropic evolution and the plastic flow trend of the subsequent yield surfaces obtained by experiments can be better reproduced by the crystal plasticity model.

Prediction of Wrinkling of a Beverage Can Subjected to the Redrawing Process by J2 Deformation Theory

Wrinkling of beverage cans is one of the problems faced by can manufacturers and aluminum suppliers. The bottom of an aluminum can is wrinkled by compression during the forming process. In this study, to predict the occurrence of wrinkles during the redrawing process of AA3104 (t = 0.265 mm), which is the material used to fabricate aluminum cans, the classical plasticity J2 deformation theory (J2D) and flow theory (J2F) were considered. J2F considers only the deformation perpendicular to the yield locus, whereas J2D considers the deformation perpendicular to the yield locus and that tangential to the yield locus. Wrinkles are predicted using finite element (FE) analyses based on J2D and J2F, and the results are compared. J2F could not predict the number and amplitude of wrinkles. By contrast, the wrinkles predicted using J2D exhibited good agreement with sample data obtained for a real can. To find the difference between the results obtained using J2F and J2D, evolutions of stress path in a wrinkled element are compared. It was confirmed that compressive stress is more dominant in the J2D case than in the J2F case. Moreover, the measured effective strain of the element is small, under 0.04. In conclusion, J2D is more suitable for predicting the wrinkling behavior of aluminum cans than J2F. In addition, ANOVA and ANOM analysis are performed to evaluate the influence of the design parameters, namely friction coefficient, thickness, and outer profile angle, and the parameters are optimized to reduce wrinkles by combining the Taguchi method with FE simulation based on the J2D theory.