A micro-mechanically motivated phenomenological yield function, for polycrystalline cubic metals is presented. In the suggested yield function microstructure is taken into account by the crystallographic orientation distribution function in terms of tensorial Fourier coefficients. The yield function is presented in a polynomial form in powers of the stress state. Known group-theoretic results are used to identify isotropic and anisotropic parts in the yield function, whereby anisotropic parts are characterized by tensorial Fourier coefficients. The form of the presented yield function is inspired by the classic, phenomenological von Mises -Hill yield function first published in 1913. For a specific choice of material parameters, both functions coincide, thus a micro-mechanically motivated generalization of the von Mises -Hill yield function is presented. For the given yield function, two dimensional experimental results are sufficient, to identify a three dimensional anisotropic yield behavior. The work concludes with a treatment of the isotropic special case, i.e. a tension-compression split in yield behavior as well as parameter ranges for convexity and shapes of the yield surface. K E Y W O R D Sanisotropic yield function, crystallographic texture, orientation distribution function, plastic anisotropy, tensorial texture coefficients This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
In scientific studies, sheet metal is usually considered as a two-dimensional body. Thus, it is accepted that material properties are in most cases regarded homogeneous in thickness direction. However, a gradation of certain properties becomes apparent when going beyond the standard characterization methods for sheet metals, which can for example, influence the springback behavior and the thinning of the sheet after forming. Thus, the aim of this work is to further improve the prediction accuracy of springback after forming in simulations, by implementing several inhomogeneous properties over the sheet thickness in an existing material model. For this purpose, the entire procedure from the identification of the inhomogeneous properties for describing the gradation to the implementation in a numerical model and its validation by comparing experimental and simulated bending operations is carried out on a DC04 cold-forming steel in order to prove its influence on the springback behavior. It is shown that including graded material properties in simulations does indeed have an impact on the prediction quality of springback and that the information about inhomogeneous properties can be provided by existing characterization methods with a high local resolution like electron backscatter diffraction or X-ray stress analysis. In a further step, it was possible to validate the improvement in numerical accuracy by comparing the prediction of the springback angle from both the existing and the extended model with experimental bending results. Both the initial model as well as the model supplemented with the 3D properties provide a good prediction accuracy in the solution heat treated material state. For the predeformed material, however, the initial numerical model predicts a springback angle of about 13°, which deviates remarkably from the experimentally obtained mean value of about 17°. The extended model delivers a significantly improved accuracy in springback prediction in relation to the initial prediction (deviation of 4°) with a minor deviation of only about 0.8°, which proves the importance of considering the gradation of material properties in thickness direction for an overall higher dimensional accuracy of sheet metal products.
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