This article details the ESAFORM Benchmark 2021. The deep drawing cup of a 1 mm thick, AA 6016-T4 sheet with a strong cube texture was simulated by 11 teams relying on phenomenological or crystal plasticity approaches, using commercial or self-developed Finite Element (FE) codes, with solid, continuum or classical shell elements and different contact models. The material characterization (tensile tests, biaxial tensile tests, monotonic and reverse shear tests, EBSD measurements) and the cup forming steps were performed with care (redundancy of measurements). The Benchmark organizers identified some constitutive laws but each team could perform its own identification. The methodology to reach material data is systematically described as well as the final data set. The ability of the constitutive law and of the FE model to predict Lankford and yield stress in different directions is verified. Then, the simulation results such as the earing (number and average height and amplitude), the punch force evolution and thickness in the cup wall are evaluated and analysed. The CPU time, the manpower for each step as well as the required tests versus the final prediction accuracy of more than 20 FE simulations are commented. The article aims to guide students and engineers in their choice of a constitutive law (yield locus, hardening law or plasticity approach) and data set used in the identification, without neglecting the other FE features, such as software, explicit or implicit strategy, element type and contact model.
The main objective of this study is to accurately predict the thinning behavior of AA6016-O aluminum alloy in the hole expansion test. In order to perform this aim, three yield functions, namely isotropic von Mises, quadratic Hill48 and non-quadratic Yld91, are considered and their prediction capabilities are evaluated in this study. Firstly, finite element (FE) model of hole expansion test is created by implicit FE software Marc, then FE simulations are performed with each yield criterion. In order to assess prediction capabilities of these yield criteria, thickness strain distributions along the three directions of the sheet (rolling, diagonal and transversal) and punch force–displacement curves are investigated. The results predicted from FE analyses are compared with experimental results. From the comparisons, it is observed that Yld91 yield criterion could successfully predict the thickness strain distributions along the rolling and transverse directions, whereas the other two criteria could only predict the thickness strain distributions along the diagonal direction. On the other hand, it is determined that punch force–displacement curves predicted from three models are identical and these predictions are overestimated compared to experimental data.
Various numerical parameters such as element size, mesh topology, element formulations effect the prediction accuracy of sheet metal forming simulations and wrong selection of these parameters can lead to inaccurate predictions. Therefore, selection of proper numerical parameters is crucial for obtaining of realistic results from finite element (FE) analyses. In the present work, influence of the number of through-thickness integration points from the numerical parameters was investigated on the cup drawing simulation. Highly anisotropic AA 2090-T3 aluminum alloy was selected as test material and the anisotropic behavior of the material was defined with Barlat 91 yield criterion. Firstly, cup drawing model was created with implicit code Marc and then FE analyses were performed with five, seven and nine layers to investigate the effect of number of throughthickness integration points. The computed earing profiles and thickness strain distributions were compared with measurements. Comparisons showed that the angular locations of maximum cup heights and thickness strain distributions along rolling and transverse directions were captured accurately by Yld91 yield criterion and also it was observed that the layer number effects the maximum cup height and thickness strain distribution along the rolling direction.
Earing can be described as difference in cup wall height due to planar anisotropy of the sheet metals, and both prediction and minimization of this defect are critical steps of drawing process design to save material and production costs due to additional trimming operations. The finite element (FE) method is a practical design tool in this context. The accuracy of FE analyses is directly dependent on modeling material deformations using an effective plasticity model. In this study, a homogeneous orthotropic fourth-order polynomial stress function is presented and implemented into Ls-Dyna FE software by a user-defined material subroutine to predict the earing evolution of a strongly anisotropic aluminum alloy (AA2090-T3) in cup drawing. Primarily, the parameters of the function were calibrated using test data. The effects of element size, number of through-thickness integration points, and time-step size were investigated separately on the drawn cup’s earing profile and thickness strain distributions. It was observed that mass scaling factor related to time step size has a significant impact on the cup height and profile. Finally, simulations were repeated with optimum parameters to assess the performance of the plasticity model. The yield criterion successfully predicted the cup profile, earing amplitude, and thickness strain distributions.
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