Aluminium sheet drawing processes can be improved by manipulating local flow behaviour\ud
by means of elevated temperatures and temperature gradients in the tooling. Forming tests\ud
showed that a substantial improvement is possible not only for 5xxx but also for 6xxx series\ud
alloys. Finite element method simulations can be a powerful tool for the design of warm\ud
forming processes and tooling. Their accuracy will depend on the availability of materials\ud
models that are capable of describing the influence of temperature and strain rate on the flow\ud
stresses. Two models, an adapted Nadai power law and a dislocation based Bergström type\ud
model, are compared by means of simulations of a cup drawing process. Experimental\ud
drawing test data are used to validate the modelling approaches, whereas the model parameters\ud
follow from tensile tests

Bolt, P.J.

Boogaard, A.H. van den

Werkhoven, R.J.

English

van den Boogaard, Antonius H.

University of Twente Research Information

Warm deep drawing of aluminium sheet

Aluminium sheet drawing processes can be improved by manipulating local flow behaviour by means of elevated temperatures and temperature gradients in the tooling. Forming tests showed that a substantial improvement is possible not only for 5xxx but also for 6xxx series alloys. Finite element method simulations can be a powerful tool for the design of warm forming processes and tooling. Their accuracy will depend on the availability of materials models that are capable of describing the influence of temperature and strain rate on the flow stresses. Two models, an adapted Nadai power law and a dislocation based Bergström type model, are compared by means of simulations of a cup drawing process. Experimental drawing test data are used to validate the modelling approaches, whereas the model parameters follow from tensile tests

van den Boogaard, A.H.

Warm Deep Drawing of Aluminium SheetP.J. Bolt1, R.J. Werkhoven1, A.H. van den Boogaard21 TNO Industrial Technology, The Netherlands, 2 University of Twente, The NetherlandsAbstractAluminium sheet drawing processes can be improved by manipulating local flow behaviourby means of elevated temperatures and temperature gradients in the tooling.  Forming testsshowed that a substantial improvement is possible not only for 5xxx but also for 6xxx seriesalloys. Finite element method simulations can be a powerful tool for the design of warmforming processes and tooling. Their accuracy will depend on the availability of materialsmodels that are capable of describing the influence of temperature and strain rate on the flowstresses.  Two models, an adapted Nadai power law and a dislocation based Bergström typemodel, are compared by means of simulations of a cup drawing process. Experimentaldrawing test data are used to validate the modelling approaches, whereas the model parametersfollow from tensile tests.Keywords: aluminium, warm forming, simulation1 IntroductionThe need for lighter car bodies on the one hand side and the complicated shapes of car partson the other hand side result in a quest for improving the formability of aluminium sheet.Aluminium has a large potential for weight reduction, but press operations are more criticalthan with steel. The alloys used for automotive sheet components are mostly 5xxx and 6xxxalloys. The 5xxx alloys have the best formability, but cannot be used for outer panelsbecause of stretcher strains. These are mostly made from 6xxx alloys, which are howeverless suitable for complicated inner parts because of a lesser formability.The formability can be improved by using elevated temperatures and temperature gradientsin the tooling and blank, which make it possible to manipulate local flow [1-3]. An extrabenefit of warm forming is that stretcher strains do not occur in 5xxx series alloys atelevated temperatures.In this paper the effect of warm drawing (in the temperature range up to 250oC) on theprocess limits of a 1.2 mm gauge 5754-O and 6016-T4 alloy sheet and on the mechanicalproperties of the formed material are demonstrated. The introduction of warm drawingtechnology will be greatly helped if finite element method simulations are available forprocess and tooling design. Hence FEM simulations, including material models of warmflow behaviour, are developed and validated.2 Effect of temperature on formability of aluminium2.1 Flow behaviourThe temperature affects the plastic deformation of aluminium in two ways: by changing thework hardening and the ductility. How depends strongly on the alloy system.Fig. 1 depicts flow curves of 5754-O sheet for a series of temperatures and strain rates. Theflow curves do not change significantly between RT and 100oC. At a higher temperaturethe serrated flow (due to dynamic strain ageing, which may result in stretcher strains indrawn products) disappears.  For a strain rate of 0.02 s-1 this occurred at 137oC. The flowstress and work hardening decrease, due to dynamic recovery, and the fracture strainincreases proportionally to the temperature - especially at the lower strain rate. The latterresults from an increased positive strain rate sensitivity. The dynamic recovery resultafterwards in a higher room temperature ductility but lower yield strength relative to coldformed aluminium [4].The 6016-T4 alloy behaves differently, see Fig. 2. The flow stress is already significantlylower at 100oC and the fracture strain decreases with temperature (especially for the lowstrain rate). The latter results from the increased precipitation rate of Mg2Si particles(ageing) at higher temperatures. The higher the temperature and longer the process timeare, the larger the precipitates will be, with more loss of ductility. The room temperaturestrength afterwards will be less than after cold forming, but to a lesser degree than for5754-O. But contrary to 5754-O, the remaining fracture strain after warm forming will besmaller than after cold forming [4].2.2 Process limitsThe lower flow stress and hardening at elevated temperature can be used to control andimprove deep drawing processes. A heated die and blankholder results in a softer flangeand a lower draw-in force. If the punch is kept at a lower temperature, an increase indrawability can be expected. In order to test this, products were drawn with partially heatedtooling. Heat rods warmed die and blankholder, whereas water cooling kept the punch  atroom temperature.  Products were round cups and rectangular conical shapes. The latter aremade by a combination of deep drawing and stretching, which is often encountered instamping of automotive panels. Lubricant was a water based paste. The punch speed was120 mm/min unless otherwise stated. The corresponding strain rate in the drawn-in flangeis in the order of magnitude of 0.02 s-1. The die and blankholder heated the blanks; noheating outside the tooling was used. The products were air cooled afterwards.Figs. 3 and 4 show the effect of the die and blankholder temperature on the limit draw ratiofor cylindrical products without tears or wrinkles. The punch diameter was 110 mm and thepunch and draw-in radii were 10 mm and 15 mm respectively.Presented are data from tests with a blankholder force at which the largest limit draw ratiois obtained. This force decreases actually with temperature. Fig. 5 shows the effect of thepunch speed on the limit draw ratio. The flange heating results as expected also in a lowerhardness of the cup wall, although it is still harder than the undeformed material, see Fig. 6.Figure 1:   Engineering flow curves for 5754-O at a strain rate of 0.002 s-1 (top) or 0.1 s-1                (bottom)5754-O, strain rate 0.1 s-10501001502002500 0.2 0.4 0.6 0.8 1engineering strain [-]engineering stress [MPa]25oC175oC100oC225oC250oC200oC5754-O, strain rate 0.002 s-10501001502002500 0.2 0.4 0.6 0.8 1engineering strain [-]engineering stress [MPa] 25oC225oC200oC175oC150oC100oC250oCFigure 2:  Engineering flow curves for 6016-T4 at strain rate of 0.002 s-1 (black lines) or                  0.02 s-1   (grey lines)Figs. 7 and 8 depict the effect of partial heating on stretch-drawing of the conical box shape(210 mm by 130 mm): an increase in maximum drawing depth of 65%. In this case themaximum depth is either limited by tearing due to a draw-in restriction (blankholder forceor blank too large) or by wrinkling in the die clearance due to a too easy draw-in(blankholder force too low, blank too small). At 250oC, 6016-T4 becomes so weak thatnear the draw-in radius the product tears. But a smaller blank gave a sound part, whichcould not be drawn at room temperature, due to excessive flange draw-in.3 Modelling of temperature dependent flow behaviourThe accuracy of finite element method simulations will greatly depend on the models thatdescribe the influence of temperature and strain rate on the flow stresses, which are governedby time dependent recovery and/or ageing processes. In this study two strain hardeningmodels are tested for the 5754-O alloy, which are introduced only briefly in this paper.More details and parameter values, which follow from tensile tests, are presented in [5,6].The first is based on the Nadai flow curve fit:mn ε/εεεCσ )()( 00+= (1)Temperature dependence is introduced by defining C, n and m as exponential functions ofthe temperature.01002003000 10 20 30engineering strain [ %]engineering stress [MPa] 100 oC175 oC 250 oC25 oC6016-T4Figure 3: Limit draw ratio versus die temperature     Figure 4:  Deepest 5754-O cups        drawn at RT and 250 oCFigure 5: 5754-O limit draw ratio         Figure 6: Effect of die temperature on the                versus punch speed; die                                         wall of a cup with a 2.09 draw                temperature is 250 oC             ratioFigure 7: Stretch-drawing: limit depth for         Figure 8:Deepest 6016-T4 productat RT (left) and  at 250oC (right)1.822.22.42.62.80 100 200 300die temperature [oC]limit draw ratio5754-O6016-T41.822.22.42.62.81 10 100 1000punch speed [mm/min]limit draw ratio50607080901001100 100 200 300die temperature [oC]hardness [Brinell]5754 - wall6016 - wall5754  -initially6016 - initially2030405060700 100 200 300die temperature [oC]maximum drawing depth [mm5754-O6016-T4Figure 9:  Measured and calculated (with Bergström en extended Nadai model) force –      displacement curves and true thickness strain distribution when deep drawing a                 80 mm deep cup with draw ratio 2.09. Initial blankholder pressure is 1.0 MPaThe second model is dislocation based and is originally proposed by Bergström [7,8]. Itdescribes the flow stress as a function of dislocation density ρ and drag:))()(( 0 ,TεσρbαGσTgσ*ref ++=        (2)The function g(T) is the ratio of elastic shear modulus G(T) at temperature T and Gref at areference temperature. The first term is a strain and strain rate independent stresscontribution, the second describes work hardening due to micro-structural evolution and thethird models the effect of strain rate and temperature on the required driving force fordislocation movement. The last term, the dynamic stress, is neglected in this paper on basisof the small effect of strain rate on the yield stress in the considered temperature interval(see Fig. 1). The second term is the Taylor equation (b is the Burgers vector, α a scalingfactor close to unity) and links flow stress to dislocation density [9]. The evolution of thedislocation density ρ is described by:20oC0204060801001200 50 100punch displacement [mm]punch force [kN]measuredBergstroemext. Nadai175oC0204060801001200 50 100punch displacement [mm]punch force [kN]measuredBergstroemext. Nadai250oC0204060801001200 50 100punch displacement [mm]punch force [kN]measuredBergstroemext. Nadai20oC-0.2-0.10.00.10.20.30 50 100 150centre to rim  [mm]thickness strain [-]experimentBergstroemext. Nadai175oC-0.2-0.10.00.10.20.30 50 100 150centre to rim  [mm]thickness strain [-]experimentBergstroemext. Nadai250oC-0.2-0.10.00.10.20.30 50 100 150centre to rim  [mm]thickness strain [-]experimentBergstroemext. Nadai−+−=RTQCΩρUερ v3exp(dd00 )31/ε −      (3)The first term in this equation represents storage (immobilisation) of dislocations (whichincreases work hardening), the second dynamic recovery by remobilisation and annihilationof dislocations (which decreases work hardening). The appeal of this approach is that it ispotentially applicable for a wider range of forming process conditions and histories becauseit models the underlying physical phenomena of the macroscopic behaviour.Fig. 9 depicts measured and calculated drawing force-ram displacement curves andthickness strain distributions in deep drawn cups. The extended Nadai model wasimplemented in a MSC.MARC model, which included the punch, die and blankholder withcooling channels and heating elements. The Bergström model was implemented in aDIEKA code (from University Twente) model. The local sheet temperature was set equal tothat of tooling contact surfaces, which were set constant. Although the MSC.MARCsimulations as well as measurements show that the local tooling temperatures vary duringthe process, this assumption is a good approximation [3]. Von Mises isotropic hardeningwas used in both cases. The friction coefficient was set at 0.06 in all simulations.Measurements showed however an increase between 150oC and 175oC to an average valueof 0.12, which is not taken into account here.Both models underestimate the drawing force, extended Nadai more than Bergström, andoverestimate the thinning of the cup bottom. The effect of temperature is calculatedqualitatively well, though. More detailed information on the relationship between frictionand temperature together with more advanced modelling of the yield surface are likely toimprove the quantitative agreement.4 ConclusionsTests showed that temperature gradients in stamping tooling can yield a large increase(>65%) in drawing depth of 5754-O and 6016-T4 sheet. This effect is based on the localreduction of flow stresses. For 5754-O, but not for 6016-T4, the higher strain ratesensitivity at elevated temperature will improve stretchability, especially at low strain rates.A heuristic and a dislocation based material model were compared for FEM processsimulation purposes. Based on cup test simulations, both seem capable of qualitativelycorrect predictions, but drawing force and strains were predicted quantitatively onlymoderately. It is recommended to improve the friction and anisotropy models as well asexplore more advanced (physically based) work hardening models.5 References[1] F. Shebata, M.J. Painter, M.J., R. Pearce, Warm forming of aluminium/magnesiumalloy sheet, Journal of Mechanical Working Technology, Vol. 2, 1978, pp  279-291.[2] D. Schmoeckel, B.C. Liebler, F.-D. Speck, Temperaturgeführter Stofffluβ beimTiefziehen von Al-Blech - Realversuche, Bänder Bleche Rohre, Vol. 36, No. 7/8,1995, pp 24 – 27.[3] P.J. Bolt, N.A.P.M. Lamboo, P.J.C.M. Rozier, Feasibility of warm drawing ofaluminium products, Journal of Materials Processing, Vol. 115, 2001, pp. 118-121.[4] P.J. Bolt, R.Werkhoven, A.H. van den Boogaard, Effect of elevated temperatureson the drawability of aluminium sheet components, Proceedings Esaform, Liège,2001, pp. 309-312.[5] A.H. van den Boogaard, P.J. Bolt, R. Werkhoven, Modelling of AlMg sheetforming at elevated temperatures, Int. Journal of Forming Processes, Vol. 4, No2/4 2001, pp 361-375.[6] A.H. van den Boogaard, Thermally enhanced forming of aluminium sheet, Ph. D.thesis, University Twente, 2002.[7] Y. Bergström, Dislocation model for the stress-strain behaviour of polycrystallineα-Fe with special emhasis on the variation of the densities of mobile and immobiledislocations, Mater. Sci. Eng., Vol. 5, 1969, pp. 193-200.[8] Y. Bergström, The plastic deformation of metals – a dislocation modeland itsapplicability, Reviews on Powder Metallurgy and Physical Ceramics, Vol. 2,1983, pp. 105-115.[9] Y. Estrin, Dislocation-density-related constitutive modeling. In A.S. Krausz and K.Krausz, editors, Unified Constitutive Laws of Plastic Deformation, AcademicPress, San Diego, ISBN 0-12-425970-7, 1996, pp. 69–104.

Warm Deep Drawing of Aluminium Sheet

Dislocation model for the stress-strain behaviour of polycrystalline α-Fe with special emhasis on the variation of the densities of mobile and immobile dislocations,

Dislocation-density-related constitutive modeling.

Effect of elevated temperatures on the drawability of aluminium sheet components,

Warm Deep Drawing of Aluminium Sheet

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University of Twente Research Information

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