CONTROLLING GALLING IN SHEET METAL FORMING OF HIGH STRENGTH STEELS: A NUMERICAL APPROACH

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1 CONTROLLING GALLING IN SHEET METAL FORMING OF HIGH STRENGTH STEELS: A NUMERICAL APPROACH Edwn Gelnck TNO, Endhoven, The Netherlands Emle van der Hede TNO, Endhoven, The Netherlands Matthjn de Rooj Unversty o Twente, Enschede, The Netherlands Dk Schpper Unversty o Twente, Enschede, The Netherlands ABSTRACT In many ormng processes gallng s a wear process that lmts producton velocty and ormablty o parts. Gallng lmts the letme o tools and the qualty o the products s aected. For hgh strength steels problems wth gallng are o major nterest, snce ormng pressures are hgh, as well as shear stresses. In ths paper a numercal model s presented, whch descrbes the ntaton o gallng and ollows the growth o the gallng lumps. Flash temperatures are calculated and compared to the crtcal temperature o the boundary layer at the nterace o the and ndvdual tool summts. In case gallng occurs at an nterace, lump growth can be calculated, as well as the rate o lump growth. In some cases lump growth can cease. KEYWORDS Gallng, ormng, numercal model, lump growth, lubrcant alure INTRODUCTION Hgh strength steels are subjected to hgh pressures and hgh shear stresses n ormng processes. In order to study the nluence o the derent materal propertes o the tool and materal and the operatonal condtons on the tendency o gallng a numercal approach s chosen. Experments on laboratory scale and on eld scale are costly and tme consumng. The numercal model presented n ths paper s one o the nstruments or desgnng tools or the ormng o hgh strength steels. The model s based on the models developed by Van der Hede [1] or gallng ntaton and by De Rooj [] or lump growth. These models have been combned nto one model n whch the gallng ntaton stage s coupled wth the lump growth stage. 1. MODEL The model s based on the models developed by Van der Hede [1] or gallng ntaton and by De Rooj [] or lump growth. These models have been combned nto one model n whch the gallng ntaton stage s coupled wth the lump growth stage. Both models are based on the wear mode map based on the work o Hokkrgawa & Kato [3]. Ths wear mode map descrbes the three wear modes o a tool asperty n contact wth materal: Cuttng mode (c): materal s removed rom the sot surace n the orm o long rbbon-lke chps; Wedge ormaton (w): a wedge o materal lows n ront o the summt;

2 Ploughng mode (pl): materal o the sot surace s dsplaced to the rdges o the wear track and no materal s removed rom the surace. In Fg. 1 an asperty n contact wth materal s shown. The asperty has a radus β, normal orce F n, sldes wth a velocty v and has a projected contact radus a s. In Fg. the wear mode dagram s plotted. In the wear mode dagram the transton between the derent wear modes are plotted. The attack angle θ (Fg. 1) s shown on the vertcal axs and the dmensonless shear strength on the horzontal axs. The dmensonless shear strength s the quotent o the nteracal shear stress and the shear strength o the sot materal (the blank o hgh strength steel). Fg. 1 Tool summt contact cuttng 0.7 Attack angle, θ wedgng ploughng Dmensonless shear strength, [-] Fg. Wear mode dagram

3 Aspertes n the wedge mode have the potental to ntate or mantan materal transer. However, when lubrcant s appled, the local surace temperature T also should exceed the crtcal temperature T cr o the lubrcant to be gallng. The lubrcant breaks down at the specc asperty. The alure crteron s thereore dened as: T > T cr and the contact operates n wedge ormaton mode ater removal o boundary layers. For lubrcated contact s between 0.4 and 0.7. In ths paper s used or the lubrcated contacts. Ths s denomnated also as 1. For unlubrcated contacts s globally between 0.9 and In ths paper 0.9 s used or the unlubrcated contact. An unlubrcated contact s a contact wthout lubrcant (dry), but also a contact wth a alng lubrcant: T > T cr.. CALCULATIONS The teraton procedure or calculatons s as ollows: 1. The roughness o the tool s measured. Asperty heghts and asperty curvatures are calculated rom the roughness measurement. The startng values and nput are determned. The nput values or the reerence case are lsted n Table 1.. For each step the value o the separaton s calculated. In ths step the value or the real area o contact s kept constant. 3. Usng the separaton o the suraces the attack angle θ per asperty s calculated. 4. The lash temperature per asperty can be calculated usng the theory o Bos and Moes [4], whch s based on the theory o Carslaw and Jeager [5]. For ths purpose the coecent o rcton o the approprate regme n the wear mode map s calculated. Usng the thermal conductvty values o the tool and the heat transer rom the contact can be calculated and thus usng the specc heat o the the local temperature can be calculated. These calculatons are perormed or the lubrcated contact stuaton. In case the contact s lubrcated the 1 value s between 0.4 and 0.7. In the present case s taken. 5. For all aspertes n whch the lash temperature exceeds the crtcal temperature are vrtually unlubrcated. At all other aspertes no gallng can occur. 6. For all aspertes that can potentally be gallng (T > T cr ) the value o s set to 0.9, snce ths s the value o or unlubrcated contacts. It s then checked whether at 0.9 the asperty s n the wedge regme. I not n the wedge regme no gallng on that asperty. In case the asperty s n the wedge regme gallng occurs at that asperty. 7. In case gallng occurs on an asperty the summt rse s s calculated or that asperty. 8. Fnally the new separaton and attack angles per asperty are calculated keepng the real area o contact constant at each teraton step. 9. Return to number In case no asperty s gallng (anymore) the teraton s stopped. The complete mathematcs s gven below. Input: roughness The nput n the program s a measured roughness and the load on the contact. The surace o the tool s measured n 3D. The roughness measurement s used to determne whch measured ponts on the surace are summts and the radus o each summt. Ths can be done n accordance wth an oten used 8-ponts crteron n whch a pont s a summt when t s hgher than ts eght surroundng ponts.

4 Calculaton: racton o contact area, separaton It s assumed that the load, F N, on the contact s constant. Ths constrant s equvalent to the demand, that α*, the racton o area n contact, should reman constant. The normal load s: F πha η β s h (1) N nom ( ) Wth H hardness, A nom nomnal area and η summt densty, β summt radus per summt, s summt heght and h the separaton between the contactng suraces. Or n term o α*: α* πη β () By assumng a normal load, the separaton h can be calculated usng a root-ndng procedure. Calculaton: attack angle The attack angles θ per summt (Fg. 1) are calculated accordng to: arctan θ π (β + h s) β + h s s-h < otherwse (3) Calculaton: lash temperature Calculaton o the lash temperature s done n more steps. The lash temperature s calculated per ndvdual summt. Frst the coecent o rcton s calculated. Ths coecent o rcton depends on the wear mode o the specc summt. The transtons can not only be depcted n a wear mode dagram, but are also avalable as a mathematcal expresson: θ 0.5( π arccos w, pl c ) (4) and θ pl w 0.5arccos (5) The coecents o rcton n each wear regme: c π 1 tan θ + arccos 4 (6) w 1 sn ξ1 + 1 sn ξ sn θ + cosθ cosθ sn θ (7) pl wth: ξ snθ + cos(arccos ξ cosθ + sn(arccos θ ) θ ) (8)

5 π 1 ξ1 θ 4 arccos + arcsn snθ 1 (9) and π ξ arccos θ arcsn snθ 1 In order to calculate the lash temperatures, the eectve conductvty K e s needed as well: (10) K e wth.746 K K κ ρ c tool p, + K a v κ (11) (1) and 1 a β sn θ The load per summt s: F 1 π a n H (13) (14) The lash temperature per summt can now be calculated: T F n a K v e (15) For the approprate coecent o rcton rom the wear regme applcable or the specc summt should be used (Eqs. 6, 7 and 8). Check: summt lubrcated or not lubrcated The value or appled n the temperature calculatons s the at lubrcated condtons ( 1 0.6, or between 0.4 and 0.7), snce the contacts o the summts are consdered to be lubrcated, unless the lash temperature exceeds the crtcal temperature o the lubrcant. I the lash temperature at a summt exceeds the crtcal temperature a contact als and the contact s consdered to be vrtually unlubrcated. Check: summt gallng or not gallng In the case the lash temperature on a summt exceeds the crtcal temperature, t has to be checked whether the summt s n the wedge regme. Snce the summt s vrtually unlubrcated (lubrcant aled) the hgh value s used or unlubrcated contacts, e.g The boundares o the wedge regme are agan gven n eq. 4 and 5 (wth 0.9). Summts that exceed the crtcal temperature and are n the wedgng regme are gallng and or those summts the ncrease n heght has to be calculated.

6 Calculaton: heght ncrease o gallng summts The ncrease n heght s o a gallng summt s gven by [] as: m 6 3πH s * γe m 6 6 H wth 1 sn θ sn θ Q 1 ++ sn θ β Q 3 Q H H * γe < π β * γe π β and γ the specc adheson energy and E* the reduced elastc modulus. The value o m s gven by [] as constant n the gallng model (unt: N -1 ). The value or m gven by []: m 10-4 N -1. Ths value s vald or non-coated steels. Ths ncrease s s added to the current heght o the summt to obtan the new summt heght, and thus a new summt heght dstrbuton. Ths new summt heght dstrbuton s used or the next pass. (16) (17) 3. Results Usng the parameters o Table 1 calculatons have been perormed. Varous parameters can be studed n ths process, e.g. the number o aspertes that s gallng per summt, the growth per asperty, the attack angle vs. heght o an asperty and the temperature per asperty. These parameters can all be ollowed when beng calculated. Each summt has ts own attack angle, lash temperature and ncrease n heght at each pass. A cloud o ponts, whch develops per pass (teraton), can thereore be ollowed. An example o the representaton o ponts s gven n Fgs. 3 to 6. In these gures the cloud o ponts s gven at a sngle pass. In the current case pass number 100. Fg. 3 gves the attack angles o the ndvdual summts as uncton o the heght. At the begnnng o each cycle the attack angles have to be recalculated, snce the reerence heght (h 0 ) o the surace has changed. Thereore the attack angles o the summts that have not been gallng n the last teraton decrease slghtly, whlst the attack angles o the summts that have been gallng n the last teraton wll ncrease, eq. (3)). The summts that have been gallng wll go deeper nto the materal, caused by the ncrease n heght. These summts are denoted n the gures as the gallng summts. In Fg. 4 the lash temperatures that have been calculated are depcted as uncton o the attack angle o the summt. In ths gure the role o the wear mode dagram (Fg. ) can be clearly seen. In the cuttng regme the lash temperatures are relatvely low. Ths explans the drop n the temperatures above the attack angle θ 1 ( 1 ),.e. at the transton rom wedgng to cuttng n the lubrcated case (vertcal lne n Fg. 4). Above the crtcal temperature o 60 ºC the lubrcant als, and thus these summts are vrtually unlubrcated. A ew summts whch are n the cuttng mode when lubrcated ( 1 0.6) do reach a temperature above the crtcal temperature o the lubrcant. Snce the wedge

7 regme dverges or ncreasng values o, some o these summts are n the wedge regme at 0.9, combned wth the act that these summts are vrtually unlubrcated, results n gallng o these summts as well. Table 1 Parameters used n reerence case Quantty Symbol Value Unt Tool propertes WN Thermal conductvty tool K t 0 W m -1 K -1 Sheet propertes 1400 M cold rolled Thermal conductvty K s 64 W m -1 K -1 Densty ρ 8000 kg m -3 Specc heat c p 460 J kg -1 K -1 Hardness H 1.8 GPa Temperature T s 0 C Combned propertes Reduced elastc modulus E* 69 GPa Specc adheson energy γ.5 N m -1 Constant n gallng model m N Dmensonless shear strength 1 (lubrcated) (unlubrcated) Lubrcant property Crtcal Temperature T cr 60 C Operatonal condtons Velocty v 1.0 m s -1 Startng value h 0 h 0,start - σ m Fg. 3 Attack angle vs. heght at pass 100

8 Fg. 4 Temperature o summts vs. attack angle at pass 100 T cr 60 C Fg. 5 Temperature o summts vs. summt heght at pass 100 The lash temperatures o the summts are plotted aganst the summt heght n Fg. 5. In ths gure the crtcal temperature T cr 60 C s ndcated. It shows that not all summts that exceed the crtcal temperature gall. In Fg. 3 t can be seen that most o these summts are n the cuttng regme and some n the ploughng regme.

9 At the end o each teraton the change n heght s calculated or each o the summts that s gallng. In Fg. 6 the change n heght o all summts s gven as uncton o the heght o the summt. O course the summts whch are gallng have a non-zero change n heght. The gure shows that the hgher summts that gall have a larger change n heght. Because o the larger change n heght, the attack angle wll ncrease subsequently and most o these summts wll not gall n one o the subsequent passes. Other summts that do not gall n the current pass can gall n one o the subsequent passes. The attack angle o these summts decreases n the current pass, and ther attack angle can cross the crtcal attack angle o cuttng or wedgng n the wear mode dagram. Then ths summt s n the wedge regme at the next pass. Fg. 6 Change n heght o summts vs. summt heght at pass 100 Over the subsequent passes hgh summts (lumps) wll arse, whch wll cause deep scratches. In the ormng process the depth o the scratches let behnd on the product s the most nterestng crteron or approval o a product. In case a scratch s too deep the scratch can not be masked wth lacquer. A crteron used n the ndustry s a maxmum depth o the scratch o 10 µm. Deeper scratches lead to rejecton o the product. The depth o the scratch s thereore used as crteron n ths paper as well. In Fg. 7 the calculated separaton s plotted aganst the pass number. The program calculates the lump growth on the tool. The lumps on the tool cause scratches n the materal. These scratches wll be just as deep, as the lump s hgh. As crteron or the lump growth the change n heght o the hghest asperty has been chosen. There are two possble crtera or the lump heght. The rst s the change n heght o the hghest asperty. The second s the change n the value or the separaton. In ths paper the latter had been chosen, snce the heght o the hghest asperty s a more subject to statstcal nose. The depth o the scratch s equal to the ncrease n the separaton, snce the lump growth s equal to the change n separaton. The separaton starts at h µm and thereore the end crteron or dsapproval or a product s h µm. Ths value s reached ater 8 passes or the reerence case n Table 1. Ths number o passes s related to the tool le, the number o products that can be made wth the tool.

10 14 1 Separaton, h 0 [µm] Pass number [-] Fg. 7 Separaton or lump growth or the reerence case (h 0 -σ) In cases the load s less severe the startng value o h 0 wll be hgher. In Fg. 8 t s shown, that gallng can stop ater a lmted number o cycles (ths case 67), and that the depth o the scratch that s made wth the tool s only very small, less then 0.01 µm or ths case. The case shown n Fg. 8 wll thereore not lead to rejecton o the product Separaton, h 0 [µm] Pass number [-] Fg. 8 Separaton or lump growth or h 0 -σ.

11 4. Conclusons A mathematcal model has been presented, whch combnes gallng ntaton and lump growth n ormng processes. Ths model has been appled to the ormng process o super hgh strength steel. The model can be used to predct whether gallng n deep drawng wll occur and at whch rate t wll take place. Acton can be taken to decrease the probablty o gallng. The model can be appled as an nstrument to predct the letme o the tool used n the ormng process. An nterestng result o the calculatons shown s that the gallng process can stop under certan condtons. The heght o the hghest summt s only slghtly above ts startng value, and thus t can be sad that n that case no scorng has occurred. The products wll not be rejected. A parameter study o the most mportant parameters s oreseen. Expermental valdaton o both the ntaton model and the lump growth model has been perormed. Currently measurements are perormed on super hgh strength steels as well. REFERENCES 1) E. van der Hede and D.J. Schpper, On the rctonal heatng n sngle summt contacts: towards alure at asperty level n lubrcated systems, Journal o Trbology, 16 (). (004), p.75. ) M.B. de Rooj, Trbologcal aspects o unlubrcated deep drawng processes, PhD Thess, Unversty o Twente (1998). 3) K. Hokkrgawa and K. Kato, An expermental and theoretcal nvestgaton o ploughng, cuttng and wedge ormaton durng abrasve wear, Trbology Internatonal, 1 (1), (1988) p ) J. Bos and H. Moes, Frctonal heatng o trbologcal contacts, Journal o Trbology, 117, (1995), p ) H.S. Carslaw and J.C. Jaeger, Conducton o heat n solds, Oxord Unversty Press, Oxord (1959).