a b s t r a c tThe details concerning the implementation of the yield criterion developed by Cazacu et al. 2006 (CPB06) [1], which accounts for both tension-compression asymmetry and orthotropy of the plastic flow, in the fully implicit FE solver DD3IMP (contraction of 'Deep Drawing 3-D IMPlicit') are presented in this work. The implemented constitutive model is extensively described, including the analytical first and second order derivatives required to the stress update algorithm. A set of anisotropy parameters describing the mechanical behavior of two metallic materials at room temperature, namely Zirconium and AZ31-Mg alloy, are identified with the DD3MAT (contraction for 'Deep Drawing 3-D MATerial') in-house code (Alves, 2004) [2]. The anisotropy parameters are identified for both the CPB06 and the Cazacu and Barlat (2001) (CB2001) [3] yield criteria, in order to emphasize the importance and role of the strength differential effect. The results clearly show that the CPB06 yield criterion is able to accurately describe both the in-plane anisotropy and tension-compression asymmetry, as well a different anisotropic behavior in uniaxial tension and uniaxial compression. The numerical simulation of a four-point bending test is performed, considering different orientations of the beam, i.e. of the hard/soft to deform direction relatively to the load direction, allowing to validate the implementation. The results obtained with the CPB06 show its ability to describe with accuracy the strain fields in the beam's central cross-section, the distribution of the tensile and compressive layers and, consequently, the shift of the neutral layer. The comparison with the results obtained with CB2001 indicates that the strength differential effect affects the final deformed shape of the beam, particularly for materials exhibiting strong tension-compression asymmetry.

The recent trend to reduce the thickness of metallic sheets used in forming processes strongly increases the likelihood of the occurrence of wrinkling. Thus, in order to obtain defect-free components, the prediction of this kind of defect becomes extremely important in the tool design and selection of process parameters. In this study, the sheet metal forming process proposed as a benchmark in the Numisheet 2014 conference is selected to analyse the influence of the tool geometry on wrinkling behaviour, as well as the reliability of the developed numerical model. The side-wall wrinkling during the deep drawing process of a cylindrical cup in AA5042 aluminium alloy is investigated through finite element simulation and experimental measurements. The material plastic anisotropy is modelled with an advanced yield criterion beyond the isotropic (von Mises) material behaviour. The results show that the shape of the wrinkles predicted by the numerical model is strongly affected by the finite element mesh used in the blank discretization. The accurate modelling of the plastic anisotropy of the aluminium alloy yields numerical results that are in good agreement with the experiments, particularly the shape and location of the wrinkles. The predicted punch force evolution is strongly influenced by the friction coefficient used in the model. Moreover, the two punch geometries provide drawn cups with different wrinkle waves, mainly differing in amplitude.

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This work aims to contribute to the understanding of the role/influence of advanced yield criteria on the earing profile prediction after drawing and ironing, for a cylindrical cup benchmark proposed at the NUMISHEET 2011 conference [1]. Two typical materials used for can-making were considered and studied: an AA5042 aluminum alloy and an AKDQ steel. The drawing and ironing operations are performed on a special die which allows drawing and ironing in one single punch stroke in order to simplify the real process. The benchmark results report include, for each material: (i) the earing profile after drawing and ironing, presenting the cup height evolution with the angle from the rolling direction, and (ii) the evolution of punch force with punch stroke. This work presents a comparison between experimental and numerical results obtained for the aforesaid benchmark with DD3IMP in-house solver, using two sets of parameters for the Cazacu and Barlat 2001 [2] yield criterion, identified based on uniaxial tensile, equi-biaxial tension and disc compression test results. The first set uses the initial yield stress values while the second one used the flow stress values for an accumulated plastic work of 20 MPa. The results highlight the different impact of the experimental data in the earing prediction for both materials: the results for the second set are slightly improved for the AKDQ steel while for AA5042 the effect is negligible. The improved earing prediction obtained with the second set for the AKDQ steel seems to result from a better description of the stress states that occur in the flange zone.

This work presents a study concerning both the deep drawing and ironing processes. The process conditions considered are the ones of the BENCHMARK 1-Earing Evolution During Drawing and Ironing Processes, proposed under the NUMISHEET 2011 conference. The deep drawing and ironing operations are performed considering two typical body stock materials: AA5042 aluminum alloy and AKDQ steel. The results analyzed are the average cup heights after drawing and ironing processes as well as the required punch load. Two yield criteria were considered: Hill'48 [9] and Cazacu and Barlat, 2001 [3]. The constitutive parameters for the Hill'48 and the Cazacu and Barlat, 2001 were determined based on the experimental results for tensile tests with different orientations to the rolling direction, disk compression test and the equibiaxial tension test, using DD3MAT in-house code. The numerical simulations of the forming process are performed using DD3IMP in-house code. The blank sheet is discretized using 3D solid elements, allowing the accurate description of the contact conditions during the ironing process. The numerical results are compared with the experimental and numerical ones reported in the NUMISHEET 2011 conference proceedings [7]. Globally, the numerical results show that the earing prediction is sensitive to the blank holder modeling, the yield criterion selected, the work hardening law and the strategy used to identify the materials parameters.

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The accurate prediction of forming defects is fundamental for the virtual try-out of metallic sheet components. However, the constitutive model can have a strong impact on the numerical predictions, namely the cup earing, the occurrence of wrinkles and the tearing failure. The process conditions considered in this work are the ones established for the “Benchmark 2 – Cup Drawing of Anisotropic Thick Steel Sheet”, proposed under the Numisheet 2018 international conference. The axisymmetric cups are obtained from a steel sheet with 2.8 mm of thickness, resorting to different process conditions to induce different defects. The advanced yield criterion proposed by Cazacu and Barlat is used to define the anisotropic behavior of the blank. The calibration of the material parameters is carried out by fitting the following experimental data from: (i) uniaxial tensile tests performed in every 15º to the rolling direction; (ii) biaxial tension tests to evaluate the directions of the plastic strain rates in the first quadrant of the yield loci. The numerical predictions are compared with the experimental measurements, allowing to assess the accuracy of the finite element model to predict each type of forming defect. The cup earing and the strain localization are accurately predicted, while the wrinkles amplitude is clearly underestimated.

Over the last years, the numerical simulation of integrated processes has become the major challenge in virtual try-out of sheet metal components, including trimming operations that may occur between forming steps. Detailed simulation of trimming processes is a challenging task, particularly when integrated with other forming operations such as deep drawing or hemming. A simplified approach can be adopted in which elements outside the trim surface are deleted from the finite element (FE) model adjusting the remaining to the surface. Following this approach, the state variables are mapped from the old FE mesh to the new trimmed mesh to continue the simulation. This paper addresses this simplified approach to the trimming process exploring a previously presented algorithm (Finite Elem Anal Des 42: 1053-1060, Baptista et al. 2006), which allows the treatment of hexahedral finite element meshes. Particularly, it focuses on the performance evaluation of the implemented strategies for correcting the FE mesh to the trimming surface, including the treatment of pentahedral-shaped elements. Different correction and treatment strategies are evaluated on different types of meshes, based on numerical simulation results of simple mechanical tests: uniaxial tensile test and simple bending test. Finally, two practical applications are given where the local effect of the trimming algorithm is highlighted.