Draw-bend Tests Research Articles

영구연화거동을 고려한 마찰교반용접(FSW)된 DP590 강판의 탄성복원 예측

In order to better predict the springback for friction stir welded DP590 steel sheet, the combined isotropic-kinematic hardening was formulated with considering the permanent softening behavior during reverse loading. As for yield function, the non-quadratic anisotropic yield function, Yld2000-2d, was used under plane stress condition. For the verification purposes, comparisons of simulation and experiments were performed here for the unconstrained cylindrical bending, the 2-D draw bending tests. For two applications, simulations showed good agreements with experiments.

Prediction of springback in sheet forming by a new finite strain model with nonlinear kinematic and isotropic hardening

The paper discusses the application of a finite strain model to predict springback in sheet forming. The concept combines both isotropic and kinematic hardening and utilizes a new algorithm based on the exponential map. A special focus is put on the simulation of the draw-bend test of DP600 dual phase steel sheets and the comparison of the numerical results with experimental data. Further, we investigate the sensitivity of the results with respect to geometry parameters as the tool radius and the sheet thickness as well as the ratio between isotropic and kinematic hardening. In addition, the model is applied to the S-rail benchmark problem and the thermoforming of thermoplastic blends, where large elastic strains occur. The simulation results match the experiments very well.

Influence of draw restraining force on the springback in advanced high strength steels

Draw beads are used in sheet metal forming processes to regulate material flow and achieve higher quality in the parts. The draw beads impose draw restraining force on the blank which eliminates defects such as wrinkling, tearing and reduces springback. In a draw-bend test, the draw restraining force is imitated by the back force applied through a hydraulic ram. As the back force increases, large strain is induced which reduces springback tendency. This study evaluates the influence of back force on the springback behavior in advanced high strength steel (AHSS). Three grades of dual-phase steel, namely DP600, DP800, DP980, are used with normalized back forces ranging from 0.5 to 1.1. The springback decreases as the back force increases. Anticlastic curvature as well as curl radius has significant influence on the springback behavior of dual phase steels.

Time-dependent Springback

Draw-bend tests performed some years ago on four aluminum alloys (2008-T4, 5182-O, 6022-T4, and 6111-T4) revealed that specimens can continue to change shape for long periods, up to 15 months, following forming and unloading [1]. Contemporaneous tests of autobody steels (DQSK, AKDQ and HSLA steels) tested under identical conditions showed no such time-dependent springback over a 7 year period [2]. Current, preliminary results for a few advanced high strength steels (DP600, DP800, DP980 and TRIP780) revealed time-dependent springback at room temperature; the sign of the springback reversing for certain combinations of process conditions. Time-dependent behavior of four advanced high strength steel was measured and creep-simulated for various test conditions. Comparisons show qualitative agreement, but the simulations over-predict the magnitude of the effect

Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets: Application to sheet springback

The constitutive model for the unusual asymmetric hardening behavior of magnesium alloy sheet presented in a companion paper (Lee, M.G., Wagoner, R.H., Lee, J.K., Chung, K., Kim, H.Y., 2008. Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheet, Int. J. Plasticity 24(4), 545–582) was applied to the springback prediction in sheet metal forming. The implicit finite element program ABAQUS was utilized to implement the developed constitutive equations via user material subroutine. For the verification purpose, the springback of AZ31B magnesium alloy sheet was measured using the unconstrained cylindrical bending test of Numisheet (Numisheet ’2002 Benchmark Problem, 2002. In: Yang, D.Y., Oh, S.I., Huh, H., Kim, Y.H. (Eds.), Proceedings of 5th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, Jeju, Korea) and 2D draw bend test. With the specially designed draw bend test the direct restraining force and long drawn distance were attainable, thus the measurement of the springback could be made with improved accuracy comparable with conventional U channel draw bend test. Besides the developed constitutive models, other models based on isotropic constitutive equations and the Chaboche type kinematic hardening model were also considered. Comparisons were made between simulated results by the finite element analysis and corresponding experiments and the newly proposed model showed enhanced prediction capability, which was also supported by the simple bending analysis adopting asymmetric stress–strain response.

Experimental Study of Springback in Draw Bend Test of AZ31B Magnesium Alloy Sheet

Springback has been measured under various process conditions corresponding to those found in real press-stamping operations. The draw bend tests originally developed at Ohio State University (Carden et al., 2002 [1]) were conducted using a range of tool radii, direct controlled constraining forces, and friction conditions. Especially, the draw-bend test was able to apply precise constant restraining force and almost negligible friction by rotating the cylindrical tool with the same speed of drawn sheet strip. Springback angle changes were measured for the bending and sidewall curl regions to find the dependence on the process variables. As expected, tensile restraining force dominates the springback sensitivity, with higher forces reducing springback. The measured springback angles and curvatures were reported for use in modeling of springback of higly anisotropic and asymmetric magnesium alloy sheets.

AZ31B 마그네슘 합금판재의 온간 성형한계도 및 스프링백 특성 시험

The effect of temperature on the forming limit diagram was investigated for AZ31B magnesium alloy sheet through the limit dome height test in the range from room temperature to <TEX>$300^{\circ}C$</TEX>. The formability of AZ31B sheet was improved significantly according to the increasing temperature. Also we studied the springback characteristics through the 2D draw bending test with different blank holding forces at elevated temperatures. Springback quantity was considerably reduced as temperature went up. The blank holding force in the range used, however, had little influence on springback. Experimental results obtained in this study may provide a material database for AZ31B sheet.

Semi-Analytic Hybrid Method to Predict Springback in the 2D Draw Bend Test

A simplified numerical procedure to predict springback in a 2D draw bend test was developed based on the hybrid method which superposes bending effects onto membrane solutions. In particular, the procedure was applied for springback analysis of a specially designed draw bend test with directly controllable restraining forces. As a semi-analytical method, the new approach was especially useful to analyze the effects of various process and material parameters on springback. The model can accommodate general anisotropic yield functions along with nonlinear isotropic-kinematic hardening under the plane strain condition. For sensitivity analysis, process effects such as the amount of bending curvature, normalized back force and friction, as well as material property effects such as hardening behavior including the Bauschinger effect and yield surface shapes were studied. Also, for validation purposes, the new procedure was applied for the springback analysis of the dual-phase high strength steel and results were compared with experiments.

Effect of hardening laws and yield function types on spring-back simulations of dual-phase steel automotive sheets

In order to simulate the spring-back of DP-steel automotive sheets, the effect of hardening laws and yield function types has been studied based on finite element simulations performed for 2-D draw bending and S-rail tests. Specifically, the performance of the combined isotropic-kinematic hardening based on the modified Chaboche model was compared with those of the pure isotropic hardening and kinematic hardening laws, along with the non-quadratic anisotropic yield (Yld2000-2d) and Mises yield functions. As for the 2-D draw bending test, numerical results were compared with experimental results for verification purposes.

Special Issue on Engineering Plasticity: Prediction of spring-back in anisotropic sheet metals

Constitutive equations for plane stress problems based on the modified form of a non-quadratic yield criterion suitable for aluminium alloy sheet were derived to account for the Bauschinger effect (BE). Numerical predictions of spring-back based on the original yield function and its modified form were performed and compared with the results of draw-bending tests. The results show the necessity of including the BE in the constitutive equations to enhance the accuracy in predicting spring-back.

Creep and anelasticity in the springback of aluminum

Draw-bend tests, devised to measure springback in previous work, revealed that the specimen shapes for aluminum alloys can continue to change for long periods following forming and unloading. Steels tested under identical conditions showed no such time-dependent springback. In order to quantify the effect and infer its basis, four aluminum alloys, 2008-T4, 5182-O, 6022-T4 and 6111-T4, were draw-bend tested under conditions promoting the time-dependent response (small tool radius and low sheet tension). Detailed measurements were made over 15 months following forming, after which the shape changes were difficult to separate from experimental scatter. Earlier tests were re-measured up to 7 years following forming. The shape changes are generally proportional to log(time) up to a few months, after which the kinetics become slower. In order to understand the basis of the phenomenon, two models were considered: residual stress-driven creep, and anelastic deformation. In the first case, creep properties of 6022-T4 were measured and used to simulate creep-based time-dependent springback. Qualitative agreement was obtained using a crude finite element model. For the second possibility, novel anelasticity tests following reverse-path loading were performed for 6022-T4 and drawing-quality silicon-killed (DQSK) steel. Based on the experiments and simulations, it appears that anelasticity is unlikely to play a large role in long-term time-dependent springback of aluminum alloys.

Prediction of spring-back in anisotropic sheet metals

Constitutive equations for plane stress problems based on the modified form of a non-quadratic yield criterion suitable for aluminium alloy sheet were derived by Barlat et al. to account for the Bauschinger effect (BE). Numerical predictions of spring-back based on the original yield function and its modified form wer performed and compared with the results of draw-bending tests. The results show the necessity of including the BE in the constitutive equations to enhance the accuracy in predicting spring-back.

알루미늄 합금박판 비등온 성형공정 스프링백 해석용 유한요소 프로그램 개발 ( 1부 : 실험 )

In order to examine the springback amount and material properties of aluminum alloy sheets (AL1050 and AL5052) in the warm forming which forms the sheet above the room temperature, the stretch bending and draw bending tests and tensile test in various high temperatures are carried out. The warm forming temperature 15<TEX>$0^{\circ}C$</TEX> is a transition in terms of the material properties: over the forming temperature 15<TEX>$0^{\circ}C$</TEX>, them <TEX>$\sigma$</TEX><TEX>$_{YS}$</TEX> , <TEX>$\sigma$</TEX><TEX>$_{TS}$</TEX> , E, K, n, etc. are bigger but <TEX>$\varepsilon$</TEX> and plastic strain ratio are smaller. Below the forming temperature 15<TEX>$0^{\circ}C$</TEX>, there are no big differences in material properties as the forming temperature changes. AL5052 sheet has more springback effect than AL1050 sheet. While the springbacks of AL5052 and AL1050 sheets show a big reduction over the warm forming temperature 15<TEX>$0^{\circ}C$</TEX> in the stretch bending test, the springback rapidly reduces in the warm forming temperature 15<TEX>$0^{\circ}C$</TEX>-20<TEX>$0^{\circ}C$</TEX> for AL5052 sheet and 20<TEX>$0^{\circ}C$</TEX>-25<TEX>$0^{\circ}C$</TEX> for AL1050 sheet in the draw bending test.

246 材料の微視構造変化を考慮した移動硬化モデルと薄板成形解析への適用

In order to predict spring back behavior of high strength steel in stamping process the kinematic hardening model, where the micro-structural change during deformation is described by evolution law of state variables, is implemented to commercial FE code by using user subroutine. Material parameters are identified by series of simple shear test. The model is validated by simple 2 dimensional hat draw bend test.

Measurement of springback

Springback, the elastically-driven change of shape of a part after forming, has been measured under carefully-controlled laboratory conditions corresponding to those found in press-forming operations. Constitutive equations emphasizing low-strain behavior were generated for three automotive body alloys: drawing-quality silicon-killed steel; high-strength low-alloy steel; and 6022-T4 aluminum. Strip draw-bend tests were then conducted using a range of die radii (3< R/ t<17), friction coefficients (0< μ<0.20), and controlled tensile forces (0.5< F b/ F y<1.5). Springback angles and curvatures were measured for bend and bend–unbend areas of the specimen, the latter corresponding to the “sidewall curl” region, which dominates the geometric change and the dependence on process variables. Friction coefficient and R/ t (die-radius-to-sheet-thickness) greater than 5 have modest but measurable effects over the ranges tested. As expected, strip tension dominates the springback sensitivity, with higher forces reducing springback. For 6022-T4, springback is dramatically reduced as the tensile stress approaches the yield stress, corresponding to the appearance of a persistent anticlastic curvature. The presence of this curvature, orthogonal to the principal curvature, violates the simple two-dimensional models of springback reported in the literature. The measured springback angles and curvatures are reported both in graphical summary and tabular form for use in assessing analytical models of springback.

Role of plastic anisotropy and its evolution on springback

Springback angles and anticlastic curvatures reported for a series of draw-bend tests have been analyzed in detail using a new anisotropic hardening model, four common sheet metal yield functions, and finite element procedures developed for this problem. A common lot of 6022-T4 aluminum alloy was used for all testing in order to reduce material variation. The new anisotropic hardening model extends existing mixed kinematic/isotropic and nonlinear kinematic formulations. It replicates three principal characteristics observed in uniaxial tension/compression test reversals: a transient region with low yield stress and high strain hardening, and a permanent offset of the flow stress at large subsequent strains. This hardening model was implemented in ABAQUS in conjunction with four yield functions: von Mises, Hill quadratic, Barlat three-parameter, and Barlat 1996. The simulated springback angle depended intimately on both hardening law after the strain reversal and on the plastic anisotropy. The springback angle at low back forces was controlled by the hardening law, while at higher back forces the anticlastic curvature, which depends principally on yield surface shape, controlled the springback angle. Simulations utilizing Barlat's 1996 yield function showed remarkable agreement with all measurements, in contrast to simulations with the other three yield functions.

A Hybrid Membrane/Shell Method for Rapid Estimation of Springback in Anisotropic Sheet Metals

A semi-analytical method to predict springback in sheet metal forming processes has been developed for the case of plane strain. In the proposed hybrid method, for each deformation increment, bending, and unbending stretches are analytically superposed on membrane stretches which are numerically obtained in advance from a membrane finite element code. Springback is then obtained by the unloading of a force and a bending moment at the boundary of each element treated as a shell. Hill’s 1948 yield criterion with normal anisotropy is used in this theory along with kinematic and isotropic hardening laws during reverse loading. The method has been applied for the springback prediction of a 2008-T4 aluminum alloy in plane-strain draw-bending tests. The results indicate the necessity of including anisotropic hardening (especially Bauschinger effects) and elastoplastic unloading in order to achieve good agreement with experimental results.