FE-Simulation Of Hemming In The Automotive Industry

Mats Sigvant *,*** and Kjell Mattiasson **,***

* Volvo Cars Body Components Dept 34406 Sheet Materials Technology

SE 293 80 Olofstrm, Sweden e-mail : msigvan1@volvocars.com

** Volvo Car Corporation

Dept 91420 Crash Simulation SE 405 31 Gteborg, Sweden

*** Department of Applied Mechanics Chalmers University of Technology

SE 412 96 Gteborg, Sweden

Abstract. This paper summarizes and presents the most important results from a research project on FE simulation of hemming carried out at Volvo Cars Body Components and Chalmers University of Technology. In the automotive industry, hemming is used to join two sheet metal panels by bending the flange of the outer panel over the inner one. The final goal of the project was to simulate all of the hemming steps of production parts. In order to make three-dimensional simulations of hemming possible within reasonable simulation times, it is necessary to use shell elements and not solid elements. On the other hand, the radius of curvature of the outer part in the folded area is very small, normally of the same order of magnitude as the sheet thickness. This fact raises the question if shell elements are applicable in FE simulation of hemming. One part of the project was therefore a thorough investigation of the order of magnitude of the errors resulting from the use of shell elements in FE simulation of hemming. Another part of the project was devoted to three-dimensional simulations of the hemming of an automotive hood. The influence on the roll-in from several parameters, such as shell element formulation, adhesives, and anisotropy was studied. Finally, results from a forming simulation were also mapped to the flanging and hemming models in order to study the influence from the stamping of the outer panel on the roll-in.

INTRODUCTION

There is a strong demand in the automotive industry today to develop new products in a shorter time and at lower cost. A way to facilitate this is to carry out simulations of manufacturing processes in early stages of car projects, to assure that the process chosen will work in production. During the past ten years, simulations of sheet metal forming with explicit FE methods have grown rapidly, and today they are commonly used in the automotive industry. The results show good agreement with practical tests. Together with parallel computing, it is now possible to get results fast, even for very large FE models.

Since sheet metal forming is just one of many processes used in the manufacturing of automotive body parts, it is also of interest to simulate other processes. This paper deals with simulations of hemming, which is a method used to join two sheet metal panels by bending the flange of the outer panel over the inner panel. Therefore, hemming is considered by many people to be a joining method. Nevertheless, as hemming also has many properties in common with sheet metal forming, knowledge gained in research on sheet metal forming can also be applied to hemming and vice versa. The method is described in Atzema et al. [1], Livatyali et al. [2], Svensson [3] and Sigvant [11].

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Hemming is used mainly for assembly of closures in automotive bodies. The advantage of this assembly method is that it gives a neat and compact joint. Such a joint is not as strong as a welded joint, but it is possible to combine hemming with other assembly methods, for instance adhesive bonding, to increase its strength.

Although there are different ways to make a hem, all of the methods have in common that the hemming operation is performed in two steps. First, the flange of the outer panel is bent down to an angle of approximately 45 from the visible surface, the pre-hemming operation, and in a second step the flange of the outer part is bent down to the final position, the final hemming.

There are several defects associated with the hemming operation. The work presented in this paper concentrates on predicting the reduction in size of the outer panel during the operation, known as roll-in. This reduction in size has to be compensated for in the flange die for the outer panel, to get an assembled part with the correct dimensions.

PRESENTATION OF THE WORK

The work presented in this paper is divided in two studies, one considering a two-dimensional approach, and one considering three-dimensional hemming. The two-dimensional one studies hemming of a flat test panel with a straight flange, while the three dimensional one analyses hemming of the hood of the previous Volvo 70-series.

The Two-Dimensional Study

The purpose of this study was to investigate the order of magnitude of the errors resulting from the use of shell elements in FE simulation of hemming. The study involves the hemming of a 290 mm long test panel, used at Volvo Cars Body Components to evaluate both new hemming methods and new materials. Four different materials are used in the study; DC06, ZStE220P, ZstE260 and AA6016. Furthermore, four different set-ups of the hemming unit was studied.

The hemming experiments were performed by means of a bi-axial MTS machine located at Chalmers University of Technology, see Figure 1. Pre- and final hemming are done with two kinds of test equipment. Common for both types is a plate with three clamps,

an adjustable support, and two guiding pins. The test panels are clamped to the plate during the experiment. The plate is then mounted on top of either of two shelves depending on whether pre- or final hemming is to be performed. The pre-hemming shelf has an inclination of 30, giving an angle of attack of 30, while the final hemming shelf is horizontal. The tip of the pre-hemming steel has a radius of 1.5 mm and can be adjusted so that different strike heights can be tested. The angle of the flange after pre-hemming is adjusted by altering the maximum displacement of the horizontal cylinder. The final hemming steel is a flat surface. During the experiments both roll-in and forces are measured continuously. Furthermore, all panels are measured before and after each operation in three sections in a CMM.

FIGURE 1. The MTS machine, at Chalmers University of Technology, used for the hemming experiments). The photograph shows the set-up for a pre-hemming experiment.

The Three-Dimensional Study

The purpose of this study was to verify that it is possible to predict all of the roll-in for a part. Therefore, all parts used in this study are manufactured with production dies, and assembled in the production line. Twenty hoods were used in this study, of which ten were made with adhesives and ten without. To join the outer and the inner parts before the first measurements, five hoods of each type were hemmed completely at the front and rear edges, while the other five were completely hemmed along the sides. The parts that were hemmed at the front and rear edges were then used for measurements on the sides. Similarly, the parts that were hemmed on the sides were used for measurements at front and rear edges.

The parts were measured after each operation, i.e. after joining, after pre hemming, and after final hemming. During the measurements the hoods were placed in an inspection fixture, the same as the one used for inspecting the outer panel in production, and

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the experimental results were obtained with a CMM. The accuracy of these measurements in this study is 0.05 mm.

THE FE-MODELS

All flanging and hemming FE-models used in the project have several common features. All the simulations were performed with the explicit software LS-DYNA. In order to reduce the simulation time, all tooling surfaces modelled by shell elements were given rigid properties. The speed of each tool was also increased compared to reality. Furthermore, mass scaling was also used to further reduce simulation time.

The Two-Dimensional Models

The FE model represents the centre cross section of the test panel with plane strain boundary conditions. The deformable parts, i.e. the outer and the inner panel, are modelled using either fully integrated, first order shell elements with five integration points through the thickness or first order, 8-node, hexahedron solid elements with eight integration points.

The outer part has an adaptive mesh with both shell and solid elements. In the shell element model the free nodes are constrained to the midpoints along the edges of the neighbouring larger elements. In the solid element model the free nodes in the mesh are constrained to the surface of the neighbouring larger elements.

The Hill 48 material model is used for steel grades, and the Barlat and Lian model for the aluminium in the shell element model. The solid model uses an implementation of the Barlat '91 material model assuming plane strain conditions.

The Three-Dimensional Model

The hood, see Figure 2, was assumed to be symmetrical. Consequently, only one half of the hood was modelled with symmetric boundary conditions on the symmetry plane. The FE-analyses were divided in two separate FE models, the first FE model simulated the flanging of the outer panel, while the second one simulated all hemming of the hood. The final geometry, stresses, and effective plastic strain in the

outer panel after flanging were transferred from the first model and entered as input to the second one. The surfaces of the FE models were based on the CAD data of the outer and the inner panels, the flange dies, and the hemming equipment. These FE models were then modified so that the geometries of the panels in the simulation were the same as in the corresponding experiments. The roll-in was measured both after pre-hemming and after final hemming. The simulation results were finally compared with those from the corresponding experiments.

FIGURE 2. The FE model of the hood in the three-dimensional study.

RESULTS

The results presented below are only the most important ones. More information about the project and the results from the studies can be found in Sigvant [11].

The Two-Dimensional Study

The presentation in this paper will focus on the mild steel results, but the conclusions are similar for the other three grades, unless anything else is stated.

Figure 3 shows the calculated roll-in from solid elements and shell elements, together with the CMM measurements for the mild steel. The numerical results, from both solid and shell elements, show good agreement with experimental results. Generally, the agreement is better after pre-hemming than after final hemming. Furthermore, the divergence between shell and solid element results is generally very small after pre-hemming, but somewhat larger after final hemming. Finally, the influence of the m-exponent in the Barlat '91 material model, on the roll-in is small.

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FIGURE 3. Roll-in after both pre- and final hemming with solid and shell elements together with CMM measurements for the mild steel.

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FIGURE 5. Final hemming forces for the mild steel in Case 3. The upper curves are vertical forces, while the lower ones are horizontal forces.

The pre-hemming forces in Case 3 are presented in Figure 4 and the final hemming forces are presented in Figure 5. There is a marked difference between the deforming forces, i.e. horisontal forces during pre-hemming and vertical forces during final hemming, calculated with solid and shell elements. The solid elements yield the highest force. The explenation can either be that shell elements are used here in an application that is beyond the limits for the shell

theory, or that the fully integrated solid elements are too stiff, which means that they yield forces that are too large. Clearly, the element type has a greater influence on the calculated forces than on the roll-in.

The simulations also underestimate the forces in comparison with the experimental ones. This can be explained by problems with the measuring equipment and technique. It is a difficult task to accurately measure forces during the experiments: for instance, the force gauges are subjected to bending moments during the experiments, which are not accounted for.

The study also showed that the supporting forces, i.e. the vertical force during pre-hemming, and the horizontal force during final hemming, are largely influenced by the friction conditions during these operations. These results could therefore indicate that the assumption of constant friction coefficients during the hemming operations is too crude. Numerical tests with different friction coefficients in different areas of the hemming steel improved the accuracy of the simulations, which underlines the conclusion above. An interesting observation was that the agreement between the calculated and experimental vertical force curves during pre-hemming for the aluminium alloy were excellent.

Finally, the study showed that the deforming forces are determined by the mechanical properties of the material. The difference between simulated forces and measured forces could therefore also indicate that the tensile test data are incorrect and/or the constitutive model cannot accurately model the material behaviour is this application. The m exponent in the material model, has also a strong influence on the horizontal forces in pre-hemming, and this underlines the conclusion above.

The Three-Dimensional Study

The two tested versions of LS-DYNA, the serial and the MPP version, give almost identical roll-in and hemming forces. Consequently, the MPP version can be used for these simulations. Without the possibility of parallel processing, the computation time would be devastating.

Four underintegrated shell elements were tested in order to determine which one was preferable. No major differences in results were obtained with initial tensile test data. But in a model with a uniformly pre-strained outer panel the flange along the side showed large wrinkles during pre-hemming with the Belytschko-Leviathan element, see Figure 6. This was

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a problem since no wrinkles were observed after pre-hemming in the experiments. On the other hand, the same model using fully integrated elements displayed no wrinkles. Similar results, i.e. wrinkles with underintegrated elements and no wrinkles with fully integrated elements, has also been observed when simulating the hemming of aluminium panels. Based on these results the fully integrated element was used for the rest of this study.

FIGURE 6. The shape of the flange along the side of the hood with 5 % pre-straining. The left picture shows the results with the Belytschko-Leviathan element and the right figure shows the results with the fully integrated element.

A model with planar anisotropy improved the accuracy of the FE results for some cross sections in comparison with a model with normal anisotropy. This indicates that a material model with full anisotropy should be used in three-dimensional simulations of hemming.

The effects on roll-in of the adhesives between the panels were modelled with a smaller friction coefficient for the contacts between the two parts. The roll-in in the simulations was almost unaffected by this modification, but the experimental results showed a dissimilar influence of the adhesives in different areas. When adhesives were included the agreement between simulation and experimental results was better along the sides of the hood, but were poorer at the rear edge. Since the adhesives function as a lubricant between the parts, and also reinforce the complete part, the experimental results from hoods with adhesives are probably more reliable than those from ones without them.

It was also considered to be of great interest to investigate the effects of including the real strain distribution after forming. To do this, the first stamping operation of the outer panel was simulated

with the implicit FE code AUTOFORM. Thereafter, the sheet thickness and effective plastic strain after forming were mapped from the AUTOFORM result file to the mesh used for flanging and hemming simulation in LS-DYNA. The results after final hemming of the side are presented in Figure 7

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FIGURE 7. Roll-in after final hemming along the sides of the hood. Effects of mapping of stamping results of the outer panel .

The results from this simulation show that the agreement between the results from the FE model, taking the preceding sheet metal forming into account, and the experimental results is good along the sides and acceptable at the rear edge. It is also evident that the difference between these results and the previous ones is small. The only exception is at the rear edge, where the new results show a little better agreement with experiments than the previous ones. Nevertheless, these results are encouraging, and it would be interesting to continue this work with other parts to investigate the effects of the forming process on the roll-in. For certain shapes of panels and/or certain sheet materials, e.g. aluminium, the influence from stamping can be large.

CONCLUSIONS

The predicted roll-in, after both pre- and final hemming, modelled with solid and shell elements, was almost identical for all four materials in the two-dimensional study. Furthermore, the agreement between predicted roll-in from the FE simulations and measured roll-in from experiments was generally good. Surprisingly, for the mild steel the accuracy of the results from shell elements was a bit higher than that from the solid and plane strain elements.

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There was a deviation between the predicted forces for solid and shell elements, respectively. This deviation can maybe be attributed to the fact that, due to the high curvature/thickness ratio, shell elements are used beyond its theoretical range of applicability. The study also showed that friction mainly influences the supporting forces and that the friction conditions are very complecated. An interesting observation is, though, that the differences in results are much more pronounced for forces than for roll-in.

The conclusion drawn from all the results in this project is that shell elements in combination with a plane stress material model can be used, with acceptable accuracy, for the simulation of hemming of anisotropic materials, even though all conditions for the shell theory to be valid are not fulfilled. This way of modelling the problem has major advantages, such as shorter simulation times and smaller model sizes.

Mapping the results from the forming of the outer panel to the mesh in the FE-models for the flanging and hemming simulations was done in the three-dimensional study. The roll-in in this simulation showed acceptable agreement with experimental results, and the conclusion drawn is, therefore, that it is possible to simulate all steps in the manufacturing of closures. In fact, the overall accuracy of the three-dimensional simulation results is judged to be good enough to motivate the use of numerical simulations as an efficient, industrial tool to predict roll-in for the hemming of real production parts. Including the influence of the preceding stamping operations has further improved the accuracy of this technique.

The final result from this project is a technique for simulating all hemming steps of a closure to an automotive body. Nevertheless, further research and development is recommended in order to make it easier and faster to perform the hemming simulation and to further improve the accuracy. It would also be interesting to develop similar methods for other types of hemming than tabletop hemming, which was the method used in the current work. An example of a new hemming method that should be interesting to simulate is robot hemming. In this method, the hemming tool is displaced along the edge of the part by a robot.

ACKNOWLEDGMENTS

The authors like to thank Volvo Car Corporation and Chalmers University of Technology for giving us the opportunity to perform this study. Volvo Car Corporation and The Swedish Research Council should also be acknowledged for its financial support.

REFERENCES

1. E.H.Atzema, R. Baartman & A.J.H. Klomp, Finite element simulations of the hemming process, Proceedings of NUMIFORM98, 933-939,Balkema (1998).

2. H. Livatyali, Computeraided process design of selected sheet metal bending processes: flanging and hemming, Dissertation, The Ohio State University, Ohio ( 1998 ).

3. M. Svensson, Hemming Simulation, Proceedings of NUMIFORM '98, 925-931, (1998).

4. C. Holmr, C. and A. Larbrant, Finite Element analyses of the hemming process, Master thesis, Department of Mechanical Engineering, University of Karlskrona/Ronneby, Karlskrona ( 2000 )

5. M. Svensson and K. Mattiasson, Simulation of hemming of automotive body components with the explicit FE-method, Proceedings of ECCOMAS 2000, (2000).

6. M. Svensson and K. Mattiasson, Simulation of hemming with different element formulations and time integration methods, Proceedings of NUMIFORM 2001, (2001).

7. M. Svensson, FE-simulation of hemming in the automotive industry, Thesis for the degree of Licentiate of Engineering, Department of Structural Mechanics, Chalmers University of Technology, (2001).

8. M. Svensson and K. Mattiasson, Three-dimensional simulation of hemming with the explicit FE-method, Journal of Materials Processing Technology 128, 142-154, (2002).

9. J.O. Hallquist,. LS-DYNA Theoretical Manual. LSTC (1998)

10. J.O. Hallquist,. LS-DYNA Keyword Users Manual, Version 970. LSTC (2003).

11. M Sigvant, The Hemming Process, A Numerical and Experimental Study, Ph.D.-thesis, Computational Mechanics, Department of Structural Design and Mechanics, Chalmers University of Technology, (2003).

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Welcome ScreenPART A: Main MenuTitle PageCopyrightPrefaceAcknowledgmentsOrganization of NUMISHEET 2005

PART B: Main MenuTitle PageCopyrightPreface

ContentsPART A: GENERAL PAPERSCHAPTER 1. KEYNOTE PROGRAM LECTURESOverview - Simulation of Sheet Metal FormingTechnology Innovation and Future Research Needs in Net Shape ManufacturingExperimentally- and Dislocation-Based Multi-scale Modeling of Metal Plasticity Including Temperature and Rate EffectsAdvances of Plasticity Experiments on Metal Sheets and Tubes and Their Applications to Constitutive ModelingDirect Design Method Based on Ideal Forming Theory for Hydroforming and Flanging Processes

CHAPTER 2. COMPUTER AIDED DIE TRYOUTImpact of Simulation Technology on Die and Stamping BusinessCAE Based Die Face Engineering Development to Contribute to the Revitalization of the Tool & Die IndustryFinite Element Simulation of the Stretch-Forming of Aircraft SkinsDraw-in MapA Road Map for Simulation-Guided Die Tryout and Stamping Process ControlIntegrated Stamping Simulation Using State of the Art Techniques to Fulfill Quality Assessment RequirementsEvolutions of Advanced Stamping CAETechnology Adventures and Business Impact on Automotive Dies and StampingDevelopment of JSTAMP-Works/NV and HYSTAMP for Multipurpose Multistage Sheet Metal Forming SimulationSimulation of Stamping Process of Automotive Panel Considering Die DeformationIntegrated Forming Simulations and Die Structural Analysis for Optimal Die DesignsModelling and Simulation of the Influence of Forming Processes on the Structural Behavior of High Strength SteelsA Benchmark Study for Different Numerical Parameters and their Impact on the Calculated Strain Levels for a Model Part Door OuterEvaluation and Visualization of Surface DefectsA Numerical and Experimental Study on Sheet-Metal PartsComparison of the Deep Drawability of Aluminum and Steel using Numerical Simulation ExperimentsControlled FEM Simulation Ways of Blank Holding Force in Sheet Metal Forming ProcessObtaining Formability Characteristics of Automotive Materials Using On-Line Strain Imaging SystemEvaluating the Dynamic Character of Friction during Metal Forming

CHAPTER 3. FINITE ELEMENT ANALYSISVisualization of the Invisible, Explanation of the Unknown, Ruggedization of the UnstableMassively Parallel Processing for Fast and Accurate Stamping SimulationsStiffness Simulation using Non-linear FEAFEA and Multivariate Statistical Data Analysis of Polypropylene Tube Forming ProcessCrashworthiness Assessment of Auto-Body Members Considering the Fabrication HistoriesApplication of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing ProcessesNumerical Simulation of Temperature Controlled Solid Phase Forming Process of Polymeric PlateFinite Element Simulation of Sheet Metal Forming Process Using Local Interpolation for Tool SurfacesFE-Analysis of the Sheet Metal Forming Processes using Continuous Contact TreatmentSimulation of Roll Forming with Dynamic Explicit Finite Element MethodMechanical Field Interpolation

CHAPTER 4. SPRINGBACK PREDICTIONAdvances in SpringbackDesign of Experiments and Springback Prediction for AHSS Automotive Components with Complex GeometryThrough-Thickness Residual Stress Measurements on Springback Test SpecimensSpringback Prediction on Slit-Ring TestInfluence of Stamping Rate upon SpringbackModeling and Simulation of Induced Anisotropic Hardening and Springback in Sheet Metals during Non-Proportional LoadingEffect of Plastic Deformation and Strain History on X-ray Elastic ConstantsAn Anisotropic Hardening Model for Springback PredictionProbabilistic Design of Aluminum Sheet Drawing for Reduced Risk of Wrinkling and FractureStudy on the Influence of the Work Hardening Models Constitutive Parameters Identification in the Springback PredictionModeling Pseudo-elastic Behavior of SpringbackA Study of FEA Springback Predictability with Channel Draw TestRobustness Evaluation and Tolerance Prediction for a Stamping Process with Springback Calculation by the FEMA Sensitivity Analysis on the Springback Behavior of the Unconstrained Bending ProblemSpringback Prediction in Sheet Metal Forming Process Based on the Hybrid SASpringback Calibration using Pulsed Electronmagnetic FieldSpringback Simulation: Impact of Some Advanced Constitutive Models and Numerical Parameters

CHAPTER 5. SPRINGBACK COMPENSATIONPossibilities and Strategies for Simulations and Compensation for SpringbackSpringback Reduction in Stamping of Front Side Member with a Response Surface MethodStructure of Complementary Surface and Numerical Simulation on Forming Process of Cover PanelDie Face Engineering Based Springback Compensation Strategy and ImplementationCompensating Springback in the Automotive Practice using MASHALIterative Springback Compensation of Numisheet Benchmark #1Springback Simulation and Tool Surface Compensation Algorithm for Sheet Metal FormingSpringback Prediction and Compensation for a High Strength Steel Side Impact BeamSpringback Prediction, Compensation and Correlation for Automotive Stamping

CHAPTER 6. CONSTITUTIVE MODELSConstitutive Modeling for Sheet Metal FormingSuitability of the Yield Criterion in Numerical Simulation of Stretch Bending of Aluminum ExtrusionsAdvancing Material Models for Automotive Forming SimulationsModel Identification and FE Simulations: Effect of Different Yield Loci and Hardening Laws in Sheet FormingExplicit Analysis of Transversely Anisotropic and Axisymmetric Sheet Metal Forming Process using 6-Component Barlat Yield FunctionDirect Measurement of Multiaxial Yield Loci as a Function of Plastic StrainDetermination of Anisotropic Hardening of Sheet Metals by Shear TestsOn the Influence of the Yield Locus Shape in the Simulation of Sheet Stretch FormingLS-DYNA Simulation of Hemispherical-Punch Stamping Process Using an Efficient Algorithm for Continuum Damage Based Elastoplastic Constitutive Equation

CHAPTER 7. MICRO-LEVEL AND MULTILEVEL MODELSAnalysis of Texture Evolution and Hardening Behavior during Deep Drawing with an Improved Mixed Type FEM ElementMulti-Scale Sheet Metal Forming Analyses by Using Dynamic Explicit Homogenized Finite Element MethodMulti Scale Finite Element Analyses by Using SEM-EBSD Crystallographic Modeling and Parallel ComputingUnit Cell Definition of Polycrystal Sheet Material based on SEM-EBSD AnalysesGrain Interactions in Crystal PlasticityTexture Evolution of FCC Sheet Metal during Deep Drawing Based on Rate Independent FEM AnalysisEffects of Texture on Mechanical Properties of Aluminum Alloy Sheets and Texture Optimization StrategyParallel Computing of Multi-scale Finite Element Sheet Forming Analyses Based on Crystallographic Homogenization Method

CHAPTER 8. FORMING LIMITSA Path-Independent Forming Limit Criterion for Stamping SimulationsForming Limits in Sheet Metal Forming for Non-Proportional Loading Conditions Experimental and Theoretical ApproachRecent Developments in the Formability of Aluminum AlloysA Comparative Study between Strain and Stress Based Forming Limit Analysis by Applying Several Phenomenological Yield CriteriaForming Limit Stresses of Sheet Metal under Proportional and Combined LoadingsAdvanced Line Die Forming Simulation Technology and its Impact on Stamping Automotive Body PanelsForming Limit Diagram of Titanium and Stainless Steel Alloys to Study the Formability of Hydro-Mechanical Deep Drawing PartsMaterial Selection for an Ultra High Strength Steel Component Based on the Failure Criteria of CrachFEMAnalytical Prediction of Forming Limits for Thermoplastic TubesA Simulation for the Punchless Piercing Process Using Lemaitre Damage ModelApplication of an Extended Stress-based Flow Limit Curve to Predict Necking in Tubular Hydroforming

CHAPTER 9. HYDROFORMING PROCESSESFundamental Issues in Hydroforming of Deep Drawing ProcessesHydroforming of Patchwork Blanks - Numerical Modeling and Experimental ValidationResearch on the Effect of the Local Constraints on Sheet Hydroforming with the Movable DieDesign of Hydroforming Processes for Metallic Liners Used in High Pressure Hydrogen StorageDeep Drawing for High LDR by a New Hydro-Rim Forming Process with Differential Temperature-Analysis and ExperimentsNumerical Investigation on Formability of Ellipse Deep Drawing by Sheet HydroformingAn Improved Hydroforming Process for "Unlimited" Drawing RatiosShear Deformation and Thickness Stress in Corner FillComparison of Conventional Deep Drawing, Hydromechanical Deep-Drawing and High Pressure Sheet Metal Forming by Numerical ExperimentsNumerical Study of Hydroforming with Tailor-Welded Tubular BlanksHydroforming Simulations and Applications in Product Design, Die Development, and Production Trouble ShootingNumerical Simulation of Hydro-Mechanical Deep Drawing A Study on the Effect of Process Parameters on Drawability and Thickness VariationOptimization of Tube Hydroforming with Consideration of Manufacturing Effects on Structural PerformanceDesign and Optimization of Sheet Hydroforming Process for Manufacturing Oil TankNumerical Simulation of Hydroforming a Double Conical TubeNumerical Self-Regulation of Time-Dependent Parameters in Tube Hydroforming Processes

CHAPTER 10. SUPERPLASTIC AND WARMING FORMINGAnalytical Formability Model for Elevated Temperature Sheet Metal Forming ProcessesMaterial Behavior Based Hybrid Process for Sheet Draw-Forging Thin Walled Magnesium AlloysStamping of Thin-Walled Structural Components with Magnesium Alloy AZ31 SheetsModeling for the FE-Simulation of Warm Metal Forming ProcessesFinite Element Analysis on Warm Hydroforming of Rectangular Mg Alloy Cups with a Step CavityWarm Forming of Aluminum Alloys Using a Coupled Thermo-Mechanical Anisotropic Material Model

CHAPTER 11. NON-HOMOGENEOUS MATERIALSNumerical Simulations of Formability of Multiphase SteelsInfluence of Normal Anisotropy Ratio on Lateral Normal Stress In Aluminum-Steel Clad Materials

CHAPTER 12. DRAWBEAD AND CYCLIC DEFORMATIONDrawbeads: To Be or Not to BeNon-Uniform Pressure Distribution in Draw-Bend Friction Test and its Influence on Friction MeasurementCyclic Bending and Stationary Drawing Deformation of Metal Sheets: Experiments and Associated Numerical Simulations

CHAPTER 13. HEMMING AND FLANGINGFE-Simulation of Hemming in the Automotive IndustryGuidelines for Stretch Flanging Advanced High Strength SteelsDevelopment of Sharp Flanging Technology for Aluminum PanelsNumerical Simulation of the Hemming Process in the Case of Al Alloys

CHAPTER 14. TAILOR WELDED BLANKSFormability Studies on Transverse Tailor Welded BlanksSimulation Based Control of Weld Line Movement in Tailor Welded Blanks

CHAPTER 15. METAL PACKAGINGConvolute Cut-Edge Design for an Earless Cup in Cup DrawingOptimum Design of Aluminum Beverage Can Ends Using Structural Optimization TechniquesErgonomics Designs of Aluminum Beverage Cans & BottlesUse of the Inverse Approach for the Manufacture and Decoration of Food Cans

CHAPTER 16. ELEMENT TECHNOLOGYOne Point Quadrature Shell Element with Through-Thickness StretchEffectiveness of Rotation-Free Triangular and Quadrilateral Shell Elements in Sheet-Metal Forming SimulationsFully Integrated EAS-Based Solid-Shell Finite Elements in Implicit Sheet Metal Forming SimulationsDevelopment of a One-Point Quadrature EAS Solid-Shell Element for Sheet FormingEnhanced Shell Elements for the Numerical Simulation of Industrial ProcessesAn ALE Model for Numerical Simulation of Cold Roll Forming ProcessThe Effect of Element Formulation on the Prediction of Boost Effects in Numerical Tube BendingMesh-Free Simulation of Automotive Decklid Inner Panel

CHAPTER 17. OPTIMIZATION AND INVERSE METHODSAnalytic Differentiation of Barlat/s 2D Criteria for Inverse ModelingAdvanced Gradient Based Optimization Techniques Applied on Sheet Metal FormingOn the Development of Multi-Step Inverse FEM with Shell ModelFast Simulation of 3-D Surface Flanging and Prediction of the Flanging Lines Based on One-Step Inverse Forming AlgorithmSensitivity Analysis of the Sheet Metal Stamping Processes Based on Inverse Finite Element Modeling and Monte Carlo SimulationApplication of Six Sigma Robust Optimization in Sheet Metal FormingRecent Advances in Process Optimization and Control for the Design of Sheet and Tube Hydroforming ProcessesFormability Predictions in Stamping and Process Parameter Optimization Based on the Inverse Approach Code Fast_StampTrimming Line Design using New Development Method and One Step FEMAutomatic Process Optimization of Sheet Metal Forming with Multi-ObjectiveOptimization of the Blankholder Force Distribution with Application to the Stamping of a Car Front Door Panel (Numisheet/99)Study of Various Initial Blank Shapes to Minimize the Earing in the Different Shaped Formed Parts using Finite Element AnalysisA Draw-In Sensor for Process Control and OptimizationProbabilistic Design in a Sheet Metal Stamping Process under Failure AnalysisFinite Element Analysis and Optimization for the Multi-Stage Deep Drawing of Molybdenum Sheet

PART B: BENCHMARK STUDY REPORTCHAPTER 1. BENCHMARK PHYSICAL TRYOUT REPORTSExperimental Test for Benchmark 1Deck Lid Inner PanelBackground and Tryout Report for BM2: Underbody Cross MemberDescription of Numisheet 2005 Benchmark #3 Stage-1: Channel Draw with 75% Drawbead PenetrationExperimental Procedures and Results for Benchmark 3: Stage 2 Forming Process

CHAPTER 2. BENCHMARK ANALYSISBenchmark Simulation Results: Automotive Deck Lid Inner Panel (Benchmark 1)Numisheet 2005 Benchmark Analysis on Forming of an Automotive Deck Lid Inner Panel: Benchmark 1Benchmark Simulation Results: Automotive Underbody Cross Member (Benchmark 2)Numisheet 2005 Benchmark Analysis on Forming of an Automotive Underbody Cross Member: Benchmark 2Benchmark Simulation Results: Channel Draw/Cylindrical Cup 2-Stage Test (Benchmark 3)

APPENDICESSpecification for BM1: Decklid Inner PanelSpecification for BM2: Underbody Cross Member PanelSpecification for BM3: Two-Stage Channel/Cup DrawSpecification for Benchmark MaterialsCharacterizations of Aluminum Alloy Sheet Materials: Numisheet 2005

ADDITIONAL BENCHMARK MATERIALDescription of additional data on aluminum alloysGeneral instructions for all benchmarksMeasured standard data of aluminum alloy 6111 (XLS)Measured standard data of bake-hardenable steel (XLS)Geometry files for BM1 in IGES format (ZIP)Instructions for Benchmark # 1Experimental results for Benchmark # 1 (XLS)Measured standard data of aluminum alloy AL 5182 (XLS)Uniaxial tension data in 15 degree intervals of Aluminum 5182 (XLS)Experimental crystal orientations of Aluminum 5182 (XLS)Measured standard data of 600 MPa Dual Phase Steel (XLS)Measured standard data of 965 MPa Dual Phase Steel (XLS)Geometry files for BM2 in IGES and NASTRAN format (ZIP)Instructions for Benchmark # 2Experimental results for Benchmark # 2 (XLS)Measured standard data of aluminum alloy AL6022 (XLS)Uniaxial tension data in 15 degree intervals of Aluminum 6022 (XLS)Experimental crystal orientations of Aluminum 6022 (XLS)Measured standard data of 600 MPa Dual Phase Steel (XLS)Measured standard data of low carbon mild steel (XLS)Measured standard data of high strength low alloy steel (XLS)Instructions for Benchmark # 3Experimental results for Benchmark # 3 (XLS)

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