Strain Hardening of Carbon Steel During Wire Drawing

Transcription

1 Mterils Reserch. 08 (): e0700 DOI: Strin Hrdening of Cron Steel During Wire Drwing Umerto Prisco * Diprtimento di Ingegneri Chimic, dei Mterili e dell Produzione Industrile, Università degli Studi di Npoli Federico II, Pizzle Vincenzo Tecchio, 80, 805 Npoli, Itli Received: Mrch, 07 Revised: Decemer, 07 Accepted: Ferury 07, 08 The Avitzur's limit nlysis for the clcultion of the drwing force in wire drwing process is used to study the rel ehviour of cron steel in n industril cse. The liner hrdening ssumption, used y Avitzur only for the first step, is extended to the whole process nd tested ginst experimentl dt. The result shows tht the predictions resulting from this extension re in good greement with the experimentl results nd re, s rule, conservtive. Keywords: wire drwing, strinhrdening, Avitzur's limit nlysis, cron steel.. Introduction Drwing is cold metl forming technique widely used to otin rods, pipes, nd wires. It is used to mnufcture prts with fine microstructure which improves the mechnicl properties of the product, such s its tensile strength. It is very useful to otin products with smll section. The drwing force is fundmentl prmeter for the optimiztion of the process nd of the production costs. Vrious nlyticl models hve een proposed for the foreseeing of the drwing force, ut the one proposed y Avitzur, sed on the limit nlysis, is very effective ecuse it ccounts for the strin hrdening effects on the mteril. In this pper the hypothesis of strin hrdening used y Avitzur for the clcultion of force in wire drwing is compred with the rel ehviour of cron steel sujected to n industril drwing process. Fig. show sketch of the die nd of the workpiece. In regrd to the model dopted in this pper, the fctors involved during the process re:. reduction re it cn e evluted with the R i /R f rtio etween entrnce nd exit rdius, or using the rtios (R i /R f ) nd (A i A f )/A i. semiconicl ngle of the die, α. sher fctor, m 4. coefficient of friction, µ 5. yield limit t unixil lod, σ 0 6. wire stress t the exit of the die, σ xf 7. wire stress t the entrnce of the die, σ x 8. length of the lnd of the die, L 9. initil nd finl rdius of the wire, R i ndr f 0. entrnce nd exit velocity of the wire, v i nd v f, respectively. Plstic work nd friction t the workpiecedie interfce generte the het in cold wire drwing. The het generted induces temperture grdient, in oth the workpiece nd *emil: umerto.prisco@unin.it Figure. Geometry of the rod nd the die the die, which influences therml expnsion, deformtion pttern, nd elstic recovery. The determintion of the two shres of the drwing force, the one due to the plstic work nd the one due to the friction, is very importnt to uild predictive models of the drwing process. In prticulr, the forecst of the plstic work plys fundmentl role in considertion of the fct tht the drwn mteril experiences work hrdening long the vrious steps of the wire drwing, so tht its yield strength is not constnt. The most interesting results, with regrd to the clcultion of drwing force, were otined y Avitzur,, even if Sieel nd Sch offered solutions still used in prctice nd in some theoreticl formultion due to their esy implementtion. On the other hnd, the prolem of the friction in wire drwing ws ddressed, mong the others reserchers, y Moon nd Kim 4 who, using procedures of inverse engineering, determined the friction nd therml conditions y compring esytomesure vriles with the computtionl results of the drwing power nd the temperture distriution of the die. Dixit et l. 5 studied the effect of the coefficient of friction t the interfce on the qulity of the drwn product nd oserved tht decrese in the coefficient of friction tends to mke the product more homogeneous nd consequently of higher qulity. By mesuring the temperture in the

2 Prisco et l. Mterils Reserch deformtion zone nd the drwing force y chnging the drwing velocity, Veg et l. 6 confirmed from their experiment tht the temperture nd the drwing force were function of the interfce conditions. To clculte the friction coefficient mny method hd een proposed: for exmple, Leu 7 used model of plstic hemisphericl contct ginst rigid flt nd descried the deformed shpe s the frctionl profile of n ellipsoid, while Ajioyeet l. 8 performed n ANOVA nlysis compring two regression models to predict the sher friction fctor t the punch interfce. Similr models nd experimentl nlyses re presented y Prid et l. 7,8, Souz et l. nd Andrde et l. 4. The principl im of this pper is to compre the hypothesis of strin hrdening used y Avitzur in the model proposed in for the clcultion of the force in wire drwing with the rel ehviour of cron steel sujected to n industril drwing process. In prticulr, the fesiility of the extension of the liner hrdening hypothesis, used y Avitzur only in the first step of the wire drwing, to the whole process is nlysed nd tested ginst experimentl dt. This study cn provide simple nd useful model to predict the drwing force nd power in multipss wire drwing process.. Clcultion procedures Avitzur used n pproch tht produced two solutions: the upperound solution gives, in regrd of the predicted drwing power, vlue greter or t lest equl to the rel one the lower ound solution gives vlue lower or t lest equl to the rel one. Fig. shows the cinemtic field used in Avitzur's theory. He defined the cinemtic field s sphericl nd considered the die s rigid ody. By choosing kinemtic field congruent with the oundry conditions, he ws le to clculte the force needed for the drwing process. Two different models re dopted for the study of the friction 9,0. The first one uses constnt sher fctor the second one is the clssicl Coulom lw. The present work mkes reference only to the first model. Strin hrdening modelling is fundmentlin the precise clcultion of the drwing force. Avitzur's method ssumes tht the liner strin hrdening follow the function: Q v = S { Where S is Avitzur initil flow stress, β is the strin hrdening coefficient nd φ is the instntneous effective strin expressed y: S sin ix { = cos i # () () where θ is the ngle of the deforming fire, see Fig.. The solution of the integrl yields the expression: V dr r S sin ix r0 { = cos i r () Under the hypothesis of liner strin hrdening, the upper ound solution hs the expression: where A is given y: v xf = vx A Z f( ) cot i _ T Y f sin ] A = S[ m( cot ) i L ] m f R f Z \ ( cos 6 sin _ i # 4 & T Y FQV f ] i [ f i T Y ] f \ In the expression (5) F() is represented y: while E() is given y: Eq. () sttes tht the centrl fire (chrcterized y the ngle θ equl to 0) hs the following mteril chrcteristic curve: Eq. (8) cn lso e written s : The die semingle commonly employed in industril prctice re rther smll, thus the strinhrdening effects in peripherl zone cn e considered equl of those present in the core.. Experiments S sin X m sin 4 S sin L X m R cos i f f A series of tensile tests for 0.8 cron steel wire in vrious steps of complete drwing process were crried out, ccording to the industril prctise,4,5. From the results of the tests it ws possile to evlute deformtion nd strin hrdening effects on the mechnicl chrcteristics of mterils,,6. The drwing ench, where the wire ws drwn, consists of ten steps. The initil dimeter of the rod E( ) F( ) = sin 5 sin E( ) sin = TS sin $ X Y S sin X S sin sin X cos r0 v = S( r ) A0 v = S( l n A (4) (5) (6) (7) (8) (9)

3 Strin Hrdening of Cron Steel During Wire Drwing use sodium sterte. The solid luricnts ensure oundry luriction. The clcium sterte gurntees good protection in spite of the oxide lyer lwys present on the rod the sodium sterte is more resistnt t the high tempertures found during the lter stges of the process.. Results nd Discussion Fig. shows the σε digrm for the strting (7.00 mm dimeter) nd the finl (.6 finl dimeter) geometry. It is evident tht the strinhrdening cused y the drwing doule the yield limit of the wire. Figure. Admissile cinemtic field is 7.00 mm nd the finl one is.6 mm, ech die hving t their end cylindricl zone / of finl dimeter long. The die semingle is 5. Tle reports the entrnce nd the exit dimeter for ech of the ten steps. Tle reports the yield strength fter ech step. Tle. Entrnce nd exit dimeter t ech of the ten drwing steps. Entrnce Dimeter (mm) Exit dimeter (mm) Step I Step II Step III Step IV Step V Step VI.54. Step VII..79 Step VIII Step IX.50.6 Step X.6.6 Tle. Yield strength fter ech step. Ln(A 0 /A) Yield strength (MP) The rod mteril is cron steel (0.8% C), its rw tensile stress is 60 Mp. After the drwing to the finl dimeter of.6 mm, its mesured tensile stress is 600 MP. The preliminry opertions, to which the rods re suject efore the drwing process, re:. pickling in hydrochloric cid. tretment using Bonder slt in hot wter c. phosphtiztion t 80ºC d. dipping in orx solution. A zinc triphosphte lyer is pplied to gurntee high luricnt dhesion. The first two dies of the process use clcium sterte s dry luricnt while the other eight Figure. σε digrm for 7 mm nd.6 mm wire dimeter Fig. 4 reports the correltion, fter six steps, etween the yield limit t the end of ech drwing step nd the rtio etween the ctul nd the strting re of the wire. Ech point is the verge over ten mesures tken for ech single step. When plotted on semilogrithmicl scle the experimentl points cn e pproximted with stright line. Using liner fitting,it is possile to otin the eqution tht est fits the experimentl results: A v = 60(. 5) A (0) The correltion coefficient of the dopted regression model ( mesure of the cpcity of the regression to fit the phenomenon, it hs limit vlue equl to ) is This result permits to stte tht the liner strin hrdening hypothesis, dopted y Avitzur for single step, is extensile to multistep drwing. Further, the liner strin hrdening prmeters, S nd β, re constnt within ll the steps of the exmined drwing process, nd they re equl to those found for the first step. 0

4 4 Prisco et l. Mterils Reserch. Conclusions Figure 4. Experimentl results relting σ/s to Ln (A 0 /A i ) Strting from this ssumption,it is possile to evlute the mteril chrcteristic prmeters S nd β needed to clculte the drwing force for ech step. The knowledge of the drwing force nd of the strin hrdening properties llows the clcultion of the friction coefficient. In this wy, ll process prmeters cn e clculted in our condition, for exmple, the computed sher fctor clculted using the Avitzur model is m= 0.,9. In Fig. 5 the predicted drwing stress for 0.8 cron steel with reduction re of 5% in function of the semingleα is shown (friction fctor m= 0. nd length of the die equl to / of the finl dimeter) Fig. 6 show the drwing stress for the sme mteril with m= 0. nd α= 5 in function of the reduction re. In oth csesavitzur's formultion for strin hrdening mterils ws used together with second formultion tht utilizes s yield limit n verge vlue otined using for ech step the entrnce nd finl tensile strength. The difference etween the two is no more thn %. The experimentl tests crried out were focused on evluting if the model dopted y Avitzur for the strin hrdening effects is useful in the industril prctice of wire drwing. The experimentl dt otined re in good greement with the theoreticl model. It is proven tht the chrcteristic prmeters of the rw mteril cn e utilized not only for single step ut lso for the entire multistep process. Indeed, the vlues of yield strength fter ech step vs. the logrithm of rtio etween ctul re nd the strting re of wire converge to stright line. As consequence of these tests it is shown the fesiility to predict the ehviour of n industril multistep process y testing the sme process prmeters in n experimentl singlestep setup nd then extending the otined results to the whole multistep process. This should llow to reduce oth the mount of test trils on the production line nd to void teething troules when some chnges in the process re introduced. 4. References. Avitzur B. StrinHrdening nd StrinRte Effect in Plstic Flow Through Conicl Converging Dies. Journl of Engineering for Industry (): Avitzur B. Anlysis of Wire Drwing nd Extrusion Through Conicl Dies of Smll Cone Angle. Journl of Engineering for Industry. 9685(): Lnge K, ed. Hndook of Metl Forming. New York: McGrw Hill Moon C, Kim N. Anlysis of wiredrwing process with friction nd therml conditions otined y inverse engineering. Journl of Mechnicl Science nd Technology. 06(9): Dixit US, Dixit PM. An nlysis of the stedystte wire drwing of strinhrdening mterils. Journl of Mterils Processing Technology (4): Veg G, Hddi A, Imd A. Temperture effects on wiredrwing process: experimentl investigtion. Interntionl Journl of Mteril Forming. 009(Suppl ):9. 7. Leu DK. Evlution of friction coefficient using simplified deformtion model of plstic hemisphericl contct with rigid flt. Journl of Mechnicl Science nd Technology. 004(8): Figure 5. Drwing stress σ xf for reduction re of 5% nd m= Ajioye JS, Jung KH, Im YT. Sensitivity study of frictionl ehvior y dimensionl nlysis in cold forging. Journl of Mechnicl Science nd Technology.004: Bowden FP, Tor D. The Friction nd Luriction of Solids. Oxford: Clrendon Press Avitzur B. The upper ound pproch to the friction wve model. Journl of Mterils Processing Technology. 994( 4):009. Figure 6. Drwing stress σ xf for 5 die semingle nd m= 0.. Cstro ALR, Cmpos HB, Cetlin PR. Influence of die semingle on mechnicl properties of single nd multiple pss drwn copper. Journl of Mterils Processing Technology ( 4):798.

5 Strin Hrdening of Cron Steel During Wire Drwing 5. Snidle RW. Contriution to the theory of frictionl heting nd the distriution of temperture in wires nd strips during drwing. Wer (): Souz TF, Sores CAT, Zottis J, Nunes RM, Roch AS, Hirsch T. Comprison etween Neutron Diffrction mesurements nd numericl simultion of residul stresses of WireDrwing process. Mterils Reserch. 06(): Andrde EC, Bernrdi HH, Otuo J. microstructurl evlution on shpe recovery in stinless FeMnSiCrNiCo SMA processed y wire drwing. Mterils Reserch. 047(): Prisco U. Sizedependent distriutions of prticle velocity nd temperture t impct in the coldgs dynmicspry process. Journl of Mterils Processing Technology. 056: Kym LK, Tguchi SP, Mrtínez GAS. The influence of die geometry on stress distriution y experimentl nd FEM simultion on electrolytic copper wiredrwing. Mterils Reserch. 009(): Prid AK, Soren S, Jh RN, Sdhukhn S. mm Thick Circulr Blnks of Alkilled AISI 00 Steel Applied for Cylindricl Cup Mnufcturing y Multistge Deep Drwing with Simultneous Ironing. Mterils Reserch. 069(5): Prid AK, Soren S, Jh RN, Sdhukhn S, Krishnmurthy N. Multistge Deep Drwing with Ironing of Alkilled AISI 040 Grded Medium Cron Steel: Prmetric Study. Mterils Reserch. 070(4):0. 9. Serroni G, Squillce A, Prisco U, Bitondo C, Prisco A. Pnnelli eronutici rinforzti con prti estruse sldte medinte FSW: crtterizzzione meccnic. L Metllurgi Itlin. 00():59.