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NIPPON STEEL TECHNICAL REPORT No. 102 JANUARY 2013 Technical Report UDC 539 . 413 . 072 Material Modeling for Accuracy Improvement of the Springback Prediction of High-strength Steel Sheets Tohru YOSHIDA* Eiji ISOGAI Shigeru YONEMURA Akihiro UENISHI Koichi SATO Abstract Improving the prediction accuracy of springback simulation are one of the most important problem because springback is major forming defect in sheet metal forming using high strength steel sheets. By applying the mixed harden
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  NIPPON STEEL TECHNICAL REPORT No. 102 JANUARY 2013 - 63 - *Chief Researcher, Dr., Forming Technologies R&D Center, Steel Research Laboratories20-1, Shintomi, Futtsu, Chiba 293-8511 UDC 539 . 413 . 072 Material Modeling for Accuracy Improvement of theSpringback Prediction of High-strength Steel Sheets Tohru YOSHIDA*Akihiro UENISHIEiji ISOGAIKoichi SATOShigeru YONEMURA Abstract  Improving the prediction accuracy of springback simulation are one of the mostimportant problem because springback is major forming defect in sheet metal formingusing high strength steel sheets. By applying the mixed hardening model by Lemaitre-Chaboche, which is possible to consider the Bauschinger effect under reverse loading path, prediction accuracy of springback were improved. And influences of material  parameters of this model on springback deformation are investigated. To investigate the mechanism of the 3D springback, theoretical evaluation of simulation results before springback is carried out. It was found that 3D springback were reduced effectively by countermeasures obtained from that analytical results applied to the rear member model tests. 1.Introduction Weight reduction for environmental considerations and enhancedcollision safety are major current issues in the automotive industry,and as a solution for both, use of steel materials of higher strengthfor car bodies is increasing. 1)  The main problem with the use of high-strength steel sheets as compared with those of ordinary strength isits poor shape fixability due to springback. A common countermeasureagainst springback is to design forming dies that anticipate thisbehavior (springback compensation), but how much compensationis necessary is a difficult question, even for experienced die designers,and therefore actual field practice is largely based on trial and error.On the other hand, accurate prediction of springback based onthe simulation of forming, which has advanced remarkably in thelast few years, would enable optimum die design with respect tospringback compensation. An important point for forming simula-tions is how accurately the work hardening models used in springback analysis can reflect the yield stress decrease resulting from the de-formation path (typically the Bauschinger effect). There have beensome studies on the application of high-accuracy work hardeningmodels to springback analysis. 2-4)  Herein is presented a study on theeffects of the material parameters on the accuracy of springback analy-sis using work hardening models that can take the Bauschinger ef-fect into account. A factor analysis based on the change of materialparameters due to higher material strength, the analysis results, andexamples of countermeasures against springback are also discussed. 2.Accuracy Improvement of Springback PredictionUsing Work Hardening Models that Consider theBauschinger Effect Springback is the elastic deformation of a steel sheet resultingfrom the release of stress that has accumulated in it during the strokeof a forming die down to the bottom dead center. For high-accuracyspringback analysis, it is essential to correctly take into consider-ation the deformation path that the material sheet has undergone dur-ing the forming process. In a press forming process, in particular, a Technical Report   NIPPON STEEL TECHNICAL REPORT No. 102 JANUARY 2013 - 64 -steel sheet undergoes bending and unbending work when it entersthe gap between the dies around a shoulder; during this process, thedeformation mode changes from tension to compression on one sideof the sheet, and from compression to tension on the other. Fig. 1 shows the stress-strain relationship during a reverse loading test (inred) compared with the curve (in blue) generated from a simulationbased on the isotropic hardening model, a commonly used work hard-ening model that does not take the Bauschinger effect into account.As can be seen in the figure, the section after load reversal of thestress-strain curve obtained from the test deviates significantly fromthat of the simulated curve. Because it is impossible to accuratelycalculate the stress distribution at the bottom dead center based onthe isotropic hardening model, the accuracy of the springback pre-diction by this model is naturally poor. Fig. 2  shows the characteristics of typical work hardening mod-els used for forming simulations. According to the isotropic harden-ing model (a), the yield surface expands concentrically regardless of the mode of deformation, while according to the kinematic harden-ing model (b), the center of the yield surface shifts as deformationadvances, and for this reason, this model can express the deforma-tion condition where the amount of work hardening is different de-pending on the deformation mode. Thus, the latter model is knownto be capable of reflecting the Bauschinger effect. In addition, asshown in Fig. 2 (c), mixed hardening models that combine isotropicand kinematic hardening have been proposed. Specifically, the mixedhardening model proposed by Lemaitre-Chaboche (hereafter calledthe L-C model) is expressed as follows  5) :  f   =  σ e  σσ ,  X   −  R  ε   p  (1)  R  ε   p  =  Y   +  R sat   1  −  e  −  C r  ε   p  (2) d   X  =  C   x   X  sat   d  ε   p  −  C   x   X  d  ε   p  (3)where σ e ( σ ,  X  ) is the equivalent stress, ε  p  is the equivalent plasticstrain,  X   is the back stress,  R   ( ε  p ) is the isotropic hardening stress, Y  is the yield stress,  R sat   and C  r   are the material parameters for theisotropic hardening model representing the critical stress and work hardening ratio, respectively, under infinite strain, and  X  sat   and C   x   arethe material parameters for the kinematic hardening model. When  R sat   = 0, this model is equivalent to the kinematic hardening model,and when  X  sat   = 0, it is equivalent to the isotropic hardening model.The number of material parameters used for this model is five.In order to examine the effects of the isotropic, kinematic, andmixed hardening models on the results of a springback simulationusing the L-C model, the parameters were defined such that the val-ues of the stress calculated according to the three hardening modelswere the same before, but different after, load reversal . Table 1  showsthe parameter values thus determined, and Fig. 3  depicts the stress-strain relationship after the load reversal. According to the isotropichardening model, the stress after load reversal is always the same asthe stress before it in terms of absolute value, while a stress decreaseafter load reversal is clear in the kinematic and mixed hardeningmodels. For the springback analysis, a simulation of hat-shape bend-ing was conducted by applying the above parameter values and basedon the die dimensions given in Fig. 4 .In the hat-shape bending test, the occurrence of wall warpingdepends largely on the fitting of the material sheet with the die shoul-der. Based on this fact, the die shoulder radius R was changed in Fig. 2 Schematic illustration of work hardening modelsFig. 1 Stress-strain relations under reverse deformationsTable 1Material parameters for stress-strain relations in reverse loadingpath C X 06.520Isotropic hardeningKinematic hardeningMixed hardeningY(MPa)260260260R sat (MPa)3400240C r 905X sat (MPa)0340100  NIPPON STEEL TECHNICAL REPORT No. 102 JANUARY 2013 - 65 - Fig. 3Stress-strain relations of each work hardening models in reverseloading pathFig. 6Comparison of stress-strain relations between experiment andcalculation results by simple sear testsFig. 4 Tool dimensions of hat shape bendingFig. 5Influence of die radius on wall curvature after springback in hatshape bending relation to the sheet thickness t, and the effects of the ratio R/t wasinvestigated. Fig. 5  shows the wall warping obtained through form-ing and springback analyses. When R/t was 3 or less, the curvatureof the wall warping was larger in the mixed hardening model than inthe isotropic hardening model. When R/t was approximately 2 inparticular, the wall curvature for the isotropic hardening model be-came negative, indicating internal warping. When the ratio was 4 to5 or more, in contrast, the curvature in the isotropic hardening modelwas larger than that in the mixed hardening model. Thus, the magni-tude of the relationship between the wall curvature estimated ac-cording to the different hardening models is inversely proportionalto the value of R/t. This result is presumably due to the differentyielding behaviors after load reversal, which lead to different fit-tings of the material sheet with the die shoulder. It should be noted,therefore, that the change in wall warping is not determined solelyby the work hardening model used for the simulation.In addition, partly because of the difficulties associated withreverse loading tests for steel sheets, a method for obtaining thematerial parameters for use as input in the constitutive equations forthe materials has not been well established. In fact, regarding theuniaxial deformation test under reverse tension-compression loading,there have been some proposed methods for suppressing bucklingduring compression, 6, 7)  but even with these methods, the measurementover large-deformation ranges is not easy with high-strengthspecimens. In the shear test, in contrast, buckling and fracture areunlikely to occur, even under large plastic deformation, and reverseloading over large deformation ranges corresponding to bending andunbending is applicable. Therefore, the shear test is more suitablefor the measurement of work hardening behavior, including theBauschinger effect, over wide ranges of strain. 4)   Fig. 6  shows theresults of reverse loading tests for 590-MPa high-strength steel sheetspecimens using the simple shear method, along with the calculatedresults for the mixed hardening model obtained using these test results.The graph clearly shows good agreement between the experimentaland calculated results from the transitory softening region to the  NIPPON STEEL TECHNICAL REPORT No. 102 JANUARY 2013 - 66 -permanent softening region. 3.Change in the Bauschinger Effect Due to HigherMaterial Strength and Shape Fixability The problem of poor shape fixability is more conspicuous withhigh-strength materials, and for this reason, it is important to under-stand how high material strength influences the Bauschinger effect.Therefore, a systematic investigation of solid-solution hardening, abasic steel strengthening method, was conducted. Solid-solution-hardened specimen sheets of different strengths were prepared bychanging the Mn and Si content in an interstitial-free steel, and thesematerials were subjected to tensile and simple shear tests. Table 2 compares the specimens in terms of the increase in the flow stressdue to solid solution hardening as measured by the tensile test; here,Steel A is the reference specimen. The Bauschinger effect was seenin all of the specimens at reverse loading using the simple shear test.The parameters for the L-C model were defined based on these testresults.The parameters thus defined are given in Table 2. Here, the val-ues of C r  and C X  as defined according to the test results for Steel Awere used for all of the other specimens. Even so, the simulationsagreed well with the test results, which seems to indicate that, as faras these specimens are concerned, the elementary processes that gov-ern softening after load reversal do not change significantly. In addi-tion, the parameters defined according to the test rests were com-pared with the increase in flow stress due to solid solution hardening(see Fig. 7 ). It was found that the increase in the flow stress due tosolid solution hardening changed substantially in a linear fashionwith respect to the parameters of the L-C model. The slope of thelinear relationship, however, was different for each parameter. Spe- Fig. 7Lemaitre-Chaboche model parameters vs. the increase in flowstress due to solid-solution hardeningFig. 8Opening width in vertical wall side ( ΔΔΔΔΔ W 1 ) vs. blank holding force(BHF) cifically, the ratio X sat  /R sat  was found to increase with increasingstrength, which indicates that kinematic hardening is more conspicu-ous in solid-solution-hardened materials. Microscopically, kinematichardening is considered to result from interactions directional tomobile dislocations, such as elastic stress fields resulting from dislo-cations accumulated in obstacles.Springback analysis was conducted using the material param-eters in Table 2. Here, the values of R sat  and X sat  of Steel A’ weredetermined such that the ratio of the kinematic hardening compo-nent (X sat  /R sat ) was the same as that for Steel C. Springback evalua-tion was conducted assuming that 1.8 ×  280 ×  100 mm specimensheets were subjected to hat-shaped bending (with two vertical walls)using dies with a width of 80 mm and a shoulder radius of 5 mm. Fig. 8  shows the width opening ( Δ W 1 ) on one side. As has beenpreviously observed, the springback amount increased as the mate-rial strength increased. However, Steel A’, which had the samestrength as that of Steel A and the same value of X sat  /R sat  as that of Steel C, tended to exhibit a larger wall opening with a low blank holding force (BHF) compared to that of Steel A. This result is pre-sumably because the Steel A and A’ specimens deformed differentlyat the die shoulders because of their different flow stresses duringbending and unbending. As stated above, it became clear that, al-though the amount of springback was predominantly influenced bythe material strength, it was also affected by the ratio of the kine-matic hardening component (X sat  /R sat ). 4.Application of the Springback Simulation andFactor Analysis There are no all-purpose measures to prevent three-dimensionalforming problems such as torsion, camber, etc. from occurring in Table 2 Increase in flow stress of materials due to solid-solution hardening and material parameters of Lemaitre-Chaboche model X sat  /R sat ASteel BSteel CSteel A' Δσ (MPa)-41219-C r 6.24R sat (MPa)246256334222C X 142X sat (MPa)525910569Y(MPa)8111017481 Δσ : Increase in flow stress
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