Stress and Strain Histories of - PowerPoint Presentation

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Stress and Strain Histories ofMultiple Bending-UnbendingSpringback Process

H.-M. HuangS.-D. LiuNational Steel Corporation,12261 Market St.,Livonia, MI 48150S. JiangDaimlerChrysler Corporation,800 Chrysler Dr.,Auburn Hills, MI 48326

Daniel Morgan

21 Sept 2009Slide2

IntroductionUnderstand the springback phenomenon and to develop a numerical simulation technique for more accurate prediction of the springback process.springback often translates into costly iterative redesign, remanufacture of tooling and longer tryout times.Traditional mild steel ‘‘rules of thumb’’ is insufficient when it comes to high strength steels.Slide3

References:Slide4

Experimentation & SimulationDraw Bead TestUsually used for determining the coefficient of friction between steel sheet and a deep drawing tool in order to determine the ideal lubricant for the forming process.Slide5

Modified Draw Bead Experiment SetupA light gauge, hot dipped galvanneal (HDGA) high strength steel (HSS) was studiedThe male and female tool radii equaled 6.5 mmThe test samples were pulled through the drawbead under different drawbead setup conditions (die gaps equivalent to integer multiple of metal thicknesses)Slide6

Modified Draw Bead Experiment AnalysisTwo premarked lines (points) with a distance of 102 mm and the mid-point between them were used to measure the curvature of the sample after springbackThe springback curvatures of the samples, after being removed from the DBS, were recorded and analyzed using a CAD software packageThe data of the corresponding restraining (pulling) and the clamping (die holding) forces during forming were collected by the data acquisition system and used to compare with the simulation resultsAn ultrasonic thickness measuring device was used to evaluate the thickness strain after formingSlide7

Simulation Models:The implicit FEM (Finite Element Method) code Abaqus/Standard was used to simulate the draw bead forming processBoth Shell and Solid Models were usedNonlinear Isotropic HardeningNonlinear Kinematic Hardening*Combined Nonlinear Isotropic/KinematicTo account for the Bauschinger effect.*The evolution of the kinematic hardening component is defined in the rate form as: Where: α and σ are the backstress and stress tensors ε is the equivalent plastic strain γ determines the rate at which the kinematic hardening modulus decreases with increasing plastic

deformation σ˚ is the size of the elastic rangeSlide8

The successive expansion after initial yield is determined by the hardening parameter β Where Ck, Ci, and Ct, are the kinematic, the isotropic, and the total hardening moduli, respectively.Slide9

Results:Slide10

During the springback process, the strain gradients through the thickness increase at die gap 1t but decrease at the larger die gaps. This represents a change in the curvature from negative to positive as die gap increases.Slide11

Strain amplitude decreases as the die gap increasesComparing the results shown in Figs. 6 and 7 with the identical die gap, the kinematic hardening rule gives smaller strain (curvature) differences from step 1 to step 3 so that less thickness strain is predicted using the kinematic hardening ruleStrain data under the condition of the combined isotropic/ kinematic hardening rule (COMB-P9), are found in general between the isotropic and the kinematic hardening rules.Slide12

This data shows that the stress at the middle surface increases from step 1 to step 3 which indicates that the material experiences membrane stretching.At die gap 1t, the higher nonlinearity in the stress distribution through the thickness at step 4 indicates that an element with more integration points or a solid element may be needed to improve simulation resultsExcept the stress at themiddle surface, Fig. 8 shows that the stress magnitude at step 3 is larger than that at step 1 predicted by the isotropic hardening model. However, the stress magnitudes at steps 1 and 3 predicted by the kinematic hardening model are almost identical, as shown in Fig. 9. This may explain why the kinematic hardening model predicts lower forces and less sensitivity to die gap in springback curvature (see Fig. 2)Slide13

Comparison Between Shell & Solid ElementsCompared to the stress & strain distributions based on the shell element, a certain degree of nonlinearity is observed in the strain distributions predicted by the solid element as shownThe difference between the shell and the solid elements increases as the sheet curvature increasesIn general, the strain histories predicted by the shell and solid elements are similar. The strain magnitudes during and after the springback processes predicted by the solid

element are larger than those predicted by the shell element.Slide14

ConclusionsThe implicit FEM code Abaqus/Standard was successfully used to predict the forming and springback processes of sheet metal subjected to multiple bending-unbending cycles.Very good agreements were obtained in loads, thickness strains and springback curvatures between the experimentally measured and the numerically predicted results.Comparisons with experimental data indicate the hardening model has a very large effect on prediction accuracies in forces, thickness strains and springback curvature.Compared with the results using a solid element, very high accuracies are obtained in the predicted stresses and strains using the shell element.Slide15

Can it be used?Automotive companies are using HSS sheet metal more often now for reducing weight, greater formability, and weldabilityHelp shorten design lead times and decrease manufacturing costsIs this simulation adaptable to different types of material?Keep it