The aim of this article is to study the accuracy of finite element simulations in predicting the tool force occurring during the single point incremental forming (SPIF) process. The forming of two cones in soft aluminum was studied with two finite element (FE) codes and several constitutive laws (an elastic-plastic law coupled with various hardening models). The parameters of these laws were identified using several combinations of a tensile test, shear tests, and an inverse modeling approach taking into account a test similar to the incremental forming process. Comparisons between measured and predicted force values are performed. This article shows that three factors have an influence on force prediction: the type of finite element, the constitutive law and the identification procedure for the material parameters. In addition, it confirms that a detailed description of the behavior occurring across the thickness of the metal sheet is crucial for an accurate force prediction by FE simulations, even though a simple analytical formula could provide an otherwise acceptable answer.

This paper describes a stress-strain interpolation method to model the macroscopic anisotropic elasto-plastic behavior of polycrystalline materials. Accurate analytical descriptions of yield loci derived from crystallographic texture [Int. J. Plasticity 19 (2003) This identification method depends on the crystallographic texture and should be applied each time that the plastic strain has induced a significant texture evolution. The stress-strain interpolation method accurately describes the anisotropic material behavior in a narrow stress direction defined by only five stress points. The cost of texture updating is then greatly reduced compared to a full analytical function of the yield locus. After the mathematical description of the stress-strain interpolation method, its validity is demonstrated on two non-radial strain paths. The simulations of a deep drawing experiment allow comparing model predictions and measurements. Accuracy and CPU time of the interpolation stress-strain method are judged against two other models, respectively based on a complete analytical yield locus and on the averaging of crystallite stresses.

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.

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