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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The plastic crack tip opening displacement (CTODp) is considered to replace ΔK in the study of fatigue crack propagation. The cyclic plastic deformation of the 7050‐T6 aluminium alloy was determined experimentally and modeled analytically. Then, a three‐dimensional elastic–plastic numerical model which included crack growth was developed in order to predict the plastic CTOD for different loading conditions. In a parallel study, crack growth rates were determined experimentally in M(T) specimens with a thickness of 6 mm. A relation was subsequently established between da/dN and plastic CTOD for the 7050‐T6 aluminium alloy, independent of stress ratio, showing that the CTOD is a viable alternative to ΔK in the analysis of fatigue crack propagation.

The present paper focuses on the application of the total strain energy density approach to assess fatigue life in notched samples subjected to multiaxial loading. This approach requires, as a starting point, a fatigue master curve defined in terms of total strain energy density versus number of cycles to failure, which is usually determined from a set of uniaxial fatigue tests using smooth standard specimens. In order to reduce the time and cost associated with the generation of the fatigue master curve, a straightforward methodology based on the outcomes of only two uniaxial straincontrolled tests is proposed. The methodology is applied to round bars with U-shaped notches subjected to proportional bending-torsion loading histories. A very good correlation between the experimental and the predicted life of the notched specimens is observed. In addition, the theoretical predictions are nearly independent of the pairs of uniaxial strain-controlled tests selected to obtain the fatigue master curve, which indicates a good robustness of the suggested methodology.

This article is a review regarding recently developed inverse strategies coupled with finite element simulations for the identification of the parameters of constitutive laws that describe the plastic behaviour of metal sheets. It highlights that the identification procedure is dictated by the loading conditions, the geometry of the sample, the type of experimental results selected for the analysis, the cost function, and optimization algorithm used. Also, the type of constitutive law (isotropic and/or kinematic hardening laws and/or anisotropic yield criterion), whose parameters are intended to be identified, affects the whole identification procedure.

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