Eperimet () Upsettig Test of Forgeabilit of Metal Dr. Moammad Al-taat Departmet of Idustrial Egieerig. Uiversit of Jorda. Lab. Of Maufacturig Processes. Course No: 9064. Objective: Te forgeabilit of a metal ca be defied as its capabilit to udergo deformatio b forgig witout crackig. Tus a material wit good forgeabilit is oe tat ca be saped wit low forces witout crackig. A umber of tests ave bee developed to measure forgeabilit, altoug oe is uiversall accepted. Oe of te more commol used tests is te upsettig test, wic simulate te metals caracteristics durig upsettig process. Te mai objective of tis eperimet is to stud ad measure forgeabilit of metals ad teir capabilities to udergo deformatio b upsettig process witout crackig.. Backgroud: For more iformatio about te subject of te eperimets, it is recommeded for te studet to review sectio 6. of capter si of te tet. 3. Teor Forgig is a famil of processes i wic Compressive forces carr out plastic deformatio of te work piece. Tis group of operatio is oe of te oldest metalworkig operatios kow, ad is used i makig parts of widel varig sizes ad sapes from a variet of metals. Forgig ca be carried out at room temperature (cold workig), or at elevated temperatures, called warm ad ot forgig, depedig o te temperature. Simple forgigs ca be made wit a eav ammer ad a avil usuall, toug, a set of dies ad presses are required. Tere are tree mai basic categories of forgig tese are; Ope die forgig; Impressio die forgig; ad Closed die forgig. Ope-die forgig (Upsettig) I its simplest form, ope-die forgig geerall ivolves placig a solid clidrical work piece betwee two flat dies (plates) ad reducig its eigt b compressig it (Figa). Tis operatio is also kow as upsettig. FIGURE (a) Ideal deformatio of a solid clidrical specime compressed betwee flat frictioless dies. Tis process is kow as upsettig. (b) Deformatio i upsettig wit frictio at te die work piece iterfaces. Uder ideal coditios, a solid clider deforms as sow i Fig. a. Tis is kow as omogeeous deformatio. Because volume is costat, a reductio
i eigt icreases te diameter of te clider. For a specime tat as bee reduced i eigt from o to, o Reductio i eigt 00% () o o e () o ε l o (3) Wit a relative velocit v betwee te plates, te specime is subjected to a strai rate,. v v e ad ε (4) o Actuall, te specime develops a barrel sape, as sow i Fig. b. Barrelig also occurs i upsettig ot work pieces betwee cool dies. Is caused primaril b frictioal forces at te die-work piece iterfaces tat oppose te outward flow of te material at tese iterfaces. Barrelig also occurs i upsettig ot work pieces betwee cool dies. I barrelig, te material flow witi te specime becomes o uiform, or iomogeeous, as ca be i Fig.. FIGURE Grai flow lies i upsettig a solid steel clider at elevated temperatures. Note te igl iomogeeous deformatio ad barrelig. Te differet sape of te bottom sectio of te specime (as compared to te top) results from te ot specime restig o te lower cool die before deformatio proceeded. Te bottom surface was cilled; tus it eibits greater stregt ad ece deforms less ta te top surface. I additio to te sigle barrelig sow i Fig., double barrelig ca also be observed. Barrelig caused b frictio ca be miimized b, Applig a effective lubricat, or Ultrasoicall vibratig te plates. Also, Te use of eated plates, or a termal barrier at iterfaces will reduce barrelig i ot workig
Forces ad work of deformatio uder ideal coditios If frictio at te iterfaces is zero ad te material is perfectl plastic wit a ield stress of Y, te te ormal compressive stress o te clidrical specime is uiform at a level Y, Te force at a eigt is te F σa YA A (5) o o were A (Volume costac) A is te cross-sectioal area ad is obtaied from volume costac. Te ideal work of deformatio is te product of te volume of te specime ad te specific eerg u. ε ε l o Work Volume σdε Ydε Yε (6) 0 0 If te metal is strai ardeig, wit a true stress-true strai curve give b σ Kε Were K is te stregt coefficiet, is te strai-ardeig epoet, te te force at a stage durig deformatio becomes F σ A Y (7) f A Were Y f is te flow stress Te work doe ca be epressed as Work Volum Y ε ( )( )( ) K ε dε (8) 0 Kε Were, average flow stress, Y ε + Te slab metod for Aalzig stresses ad loads i forgig O of te simpler metod of aalsis, tis metod requires te selectio of a elemet i te work piece ad determiatio all ormal ad frictioal stresses o te elemet. a) Forgig of a rectagular work piece i plae strai. Let's take te case of simple compressio wit frictio (Fig. 3), wic is te basic deformatio i forgig. As te flat dies compress te part, it is reduced i tickess ad, as te volume remais costat, te part epads laterall. Tis relative movemet at te die-work piece iterfaces causes frictioal forces actig i oppositio to te movemet of te piece. Tese frictioal forces are sow b te orizotal arrows i Fig 3. For simplicit, let's also assume tat te deformatio is i plae strai; tat is, te work piece is ot free to flow i te directio perpedicular to tis page. Let's ow take a elemet ad idicate all te stresses actig o it (Fig. 3.b). Note te correct directio of te frictioal stresses. Also ote te differece i te orizotal stresses actig o te sides of te elemet; tis differece is caused b te presece of frictioal stresses o te elemet. We assume tat te lateral stress distributio σ is uiform alog te eigt. ε
Te et step i tis aalsis is to balace te orizotal forces o tis elemet, because it must be i static equilibrium. Tus, assumig uit widt, FIGURE 3 Stresses o a elemet i plae-strai compressio (forgig) betwee flat dies. Te stress σ is assumed to be uiforml distributed alog te eigt of te elemet. Idetifig te stresses o a elemet (slab) is te first step i te slab metod of aalsis. ( σ + dσ ) dσ + σ d 0 σ d d + 0 w + σ dw σ w 0 for uit widt (w ) σ (9) Note tat we ave oe equatio but two ukows: σ ad σ. We obtai te ecessar secod equatio from te ield criteria as follows. As sow i Fig 3c, tis elemet is subjected to triaial compressio i plai strai. σ 3 E Te maimum value for v (or tat value for wic volume cage is zero) is 0.50 i.e. (I te elastic rage 0< ν < 0.5 ad tere is a volume cage). Sice we ave plai strai state, te we ca write ε 0, tere we obtai I geeral ε [ σ υ( σ + )] σ.5( σ + σ ) as see i figure 3.c (0) z 0 Accordig to te distortio-eerg criterio for plae strai, we ave ' σ - σ Y Y () 3 dσ dσ (). We ow ave two equatios. Substitute equatio i equatio 9 we obtai σ d dσ + 0 (3) dσ or d (4) σ σ Ce (5)
Te boudar coditios are suc tat at a, σ 0, ad tus σ Y` at te edges of te specime. (All stresses are compressive, so we ma igore egative sigs for stresses, wic are traditioal i suc aalses.) Hece te value of C becomes a σ 0 from equatio 3. σ Y` a Y` Y ` Ce C a a e C Y`e (6) Substitute equatio 6 i equatio 5 we obtai a a ( a ) µ σ Ce Y`e e Y`e Y`e Terefore te compressio pressure, p, wic is equal to σ ca be epressed as: ( a ) p σ Y`e (7) ( a ) ad σ σ Y` Y` e (8) Equatio (7) is plotted qualitativel i Fig. 4 i dimesioless form. For a strai-ardeig material, Y' i Eqs. (7) Ad (8) is replaced b Y`f. Note tat te pressure wit frictio is iger ta it is witout frictio. Te area uder te pressure curve i Fig. 4 is te upsettig force per uit widt of te specime. Tis area ca be obtaied b itegratio, but a approimate epressio for te average pressure p av is FIGURE 4 Distributio of die pressure i terms of p/y`, i plai-strai compressio wit slidig frictio. Note tat te pressure at te left ad rigt boudaries is equal to te ield stress i plae strai, Y'. Slidig frictio meas tat te frictioal stress is directl proportioal to te ormal stress. µ a p av Y` + (9) Te forgig force F is te product of te average pressure ad te cotact area; tat is, F ( pav )( a)( widt) (0)
b) Forgig of a solid clidrical work piece Usig te slab metod of aalsis, we ca also determie te pressure distributio i forgig of a solid clidrical specime (Fig. 5). We first isolate a segmet of agle dθ i te clider of radius r ad eigt, take a small elemet of radial legt d, ad place o tis elemet all te ormal ad frictioal stresses actig o it. We te balace te forces o tis elemet i te radial directio. Tus, FIGURE 5 Stresses o a elemet i forgig of a solid clidrical work piece betwee flat dies. dθ σ r. dθ. + σ θ d σ zdθ. d ( σ r + dσ r )( + d). dθ. 0 Followig te same procedure as before, we obtai te epressio for te pressure p at a radius as z ( r ) p σ Ye () ( r ) ( r ) + + + ad σ r Y σ z Y Ye Y e () Te average pressure P av ca be give approimatel as r p av Y + (3) 3 Te forgig force F is F ( pav )( πr ) (4) For strai-ardeig materials, Y is replaced b te flow stress Y f. c) Forgig uder stickig coditio. Te product of µ ad P is te frictioal stress (surface sear stress) at te iterface at a locatio from te ceter of te specime. As P icreases toward te ceter, µp also icreases. However, te value of µp caot be greater
ta te sear ield stress k of te material. We µp k, stickig takes place. (I plae strai te value of k is Y'/. Stickig does ot ecessaril mea adesio at te iterface; it reflects te fact tat, relative to te plate surfaces, te material does ot move. For te stickig coditio, te ormal stress distributio i plae strai ca be sow to be a p Y` + (5) Te pressure varies liearl wit ; te ormal stress distributio for a clidrical specime uder stickig coditio ca be sow to be r p Y + (6) Eample: Upsettig Force A clidrical specime made of aealed 435 steel is 6 i. i diameter ad 4 i. ig. Ope-die forgig upsets it wit flat dies to a eigt of i. at room temperature. Assumig tat te coefficiet of frictio is 0., calculate te force required at te ed of te stroke. Use te averagepressure formula. Te force at te ed of te stroke? F ( pav )( πr ), r at te ed of te stroke. r r f p + + av Y Y 3 3 f Aealed 435 steel, is a strai ardeig material, terefore Y sould be replaced b Y f, oted tat Y f is te flow stress correspodig to ε as sow i te figure bellow. To determie Y f, we ave to kow ε ad te equatio of te sow true stress-true strai curve.
f l l o Simpl ε (compressio) o f 4 ε l 0.693 Te geeral formula of te curve i te figure sow is σ Kε, at ε σ Y f, tus, Y f K ε K(0.693) From tables for aealed steel 435, K05 Mpa47psi, ad 0.7, ( 0.7) Yf Kε ( 47,000) (0.693) 38,000 r f ( 0.) rf ( ) ( ) p av Yf + 38,000 + 3 f 3 We eed to fid r f, from volume costac 6 π V.4 o V f π rf rf 4 4.4i. ( 0.)( 4.4) 3( ) p ( 38,000) + 77, 000 psi av 7 F pav π r 77,000 π 4.4 0 Ib ( )( ) ( ) ( ). 4. Materials: Clidrical specimes made of lead (98% lead). 5. Equipmets: Pressig macie, Flat die, ad verier caliper ad measurig tools are required. 6. Procedures: ) Set te flat die o te pressig macie. ) Set te press for operatio. 3) Measure te diameter of te specime before ad after upsettig at various eigts. 4) Measure te eigt of te specime before ad after upsettig. 5) Perform te upsettig operatio b puttig te circular lead specime o te lower alf of te flat die ad te press te specime to te required eigt b upper alf of te flat die. 6) Repeat te upsettig sequece for differet specimes for frictio ad frictioless cases at te ier surfaces betwee te die ad te specime. 7. Requiremets: ) Describe te upsettig process. ) Sketc all te used dies, tools, ad specimes. 3) Fid te ratio of billet fial eigt to fial mea diameter to give uiform upsettig deformatio. 4) Draw te cotour patters of te outer surface for all upset specime.
8. Questios. ) W ad ow Barrelig occurs i upsettig ot work pieces betwee cool dies. ) Defie ad eplai te term double barrelig? 3) Discuss forgig metods ad forgig defects? 8. Refereces. Kalpakjia Scmid, 003. Maufacturig processes for Egieerig materials, fourt editio, Pretice all iteratioal ISBN 0-3-04087-9.. George Tlust, 000. Maufacturig Processes ad equipmet, Pretice all iteratioal. ISBN 0-0-49865-0 3. Serope Kalpakjia ad Steve R. Scmid, 003, Maufacturig egieerig tecolog, fourt editio Pretice all iteratioal. ISBN 0-3-07440-8. 4. Mikell P. Groover, 00, Fudametals of moder maufacturig materials, processes, ad sstems. Jo wile ad sos, Ic. ISBN 0-47-4005-3.