Finite Element Simulation of a Doubled Process of Tube Extrusion and Wall Thickness Reduction

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1 World Joural of Mechaics, 13, 3, 5- Published lie August 13 ( Fiite Elemet Simulatio of a Doubled Process of Tube Extrusio ad Wall Thickess Reductio Ahmed S. M. J. Agea Departmet of Mechaical Egieerig, High Istitute of Polytechic i Zawia, Zawia City, Libya ahmedajia1@yahoo.com Received Jue 5, 13; revised July 1, 13; accepted August 5, 13 Copyright 13 Ahmed S. M. J. Agea. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. ABSTRACT This research deals with the forward extrusio process of tubes. I this process, a piercig process was carried out o the billet to produce the tube, followed directly by a reductio i the wall thickess. A specific geometrical shape for the piercig zoe ad the wall thickess reductio zoe were chose ad desiged. The effects of the redudat shear strai ad the magitude of the extrusio load were ivestigated ad simulated with the fiite elemet method usig Q Form software program. Lead was used as model materials sice (if the experimets were carried out at room temperature) it has the similar behavior of the steel at high temperature. The results obtaied have show that at the piercig zoe, the lowest values of the extrusio load, the redudat strai, the total strai ad the fiite elemet effective strai were whe a piercig tool (madrel) of (C = 1.1) was used. While, at the die zoe, the lowest values of the extrusio load, the redudat strai, the total strai was whe a die of (C =.9) was used. Keywords: Tube Extrusio; Die Desig; Fiite Elemet Method 1. Itroductio I the materials sciece, deformatio is a chage i the shape or size of a object due to a applied force. This ca be a result of tesile (pullig) forces, compressive (pushig) forces, shear, bedig or torsio (twistig). Deformatio is ofte described as strai. As deformatio occurs, iteral iter-molecular forces arise which oppose the applied force. I the extrusio process, mechaical properties of the material, frictioal coditio at the tool workpiece iterface, extrusio ratio ad die profile are amog the importat parameters that sigificatly affect the desired characteristics of the product [1]. e of the most importat factors i a formig operatio is the profile of the deformatio zoe; it is a importat parameter for optimizig a process variable, such as extrusio pressure []. Extrusio die profiles ca be coical or curved. I the past, due to the difficulty i the maufacture of ocoical dies, most research cocered the optimizatio of rod extrusio die geometry, focused o coical dies [3], but i recet year due to the presece of moder machies such as the CNC machies, the curved dies were produced ad used. A mathematical formula has bee developed to calculate ad aalysis the strai, redudat strai ad geometry factor for the deformatio process []. I this work the extrusio process has bee carried out o lead metal usig a special dies which desiged with the costacy of ratio of successive geeralized homogeeous strai icremet (C.R.H.S) [5] ad compared with fiite elemet method. This paper is divided ito five mai sectios, amely: The first part is the itroductio where we dealt with previous research o the subject ad the basics of the extrusio process; the secod part is a theoretical backgroud, fudametals ad mathematical equatios of the research topic; the third part was about the experimetal equipmets ad procedure where we dealt with how the extrusio set were produced for the extrusio process; the fourth part dealt with the results ad discussio ad the fifth part was dealt with the coclusio i additio to the refereces.. Theoretical Backgroud I the extrusio of tubes, the deformatio processes that occur o metals cotai two basic types of strai: Copyright 13 SciRes.

2 A. S. M. J. Agea Costacy of Ratio of Successive Geeralized Homogeeous Strai Icremets (C.R.H.S) I this hypothesis, the ratio of homogeeous strai of the successive sectios of the deformatio zoe is costat, where the deformatio zoe (i the die ad piercig) is divided ito several sectios ad umbered as (, 1,, 3-1, ), as show i Figure 1. Where D f is the outer diameter of the tube, D is the ier diameter of the tube, t f is the fial thickess of the tube, t is the iitial thickess of the tube. The mathematical expressio of this hypothesis is HE HE 1 HE 3 HE HE 1 HE HE HE1 (1) HE HE1 c HE1 HE where HE is the total (effective) homogeeous strai, c is costat depeds o a type of (C.R.H.S). These values are equal: c > 1 c = 1 c < 1.. Strais Calculatio whe the strai ratio is accelerated whe the strai ratio is uiform whe the strai ratio is decelerated Withi the deformatio process, two types of strais are obtaied: 1) Homogeeous strais ) Redudat strai. This ca be calculated as below...1. Homogeeous Strais The total (effective) homogeeous strai ( HE ) equatio ca be writig as: 1 3 HE HL HR HC ()... Redudat Strai Calculatio This type of strai, also icludig a strai o the three directios 1) Logitudial redudat strai RL ) Circumferece redudat strai RC 3) Torsio redudat strai RT These strais ca appear i some deformatio process such as double rollig of tube or ay deformatio process that icludes tesio stress combied with torsio stress. I tube extrusio, oly the logitudial redudat strai occurs. This strai ca be calculated as: S RL cot (3) t where is the agle of grid lies, t is the tube thickess, ad S is the slidig legth of the grid lies i the deformatio zoe as show i Figure. Where parallel lies of a grid are prited o the surface of oe half of the sample, these lies are perpedicular to the directio of the ceter lie of the sample. As show i Figure Total Strai Calculatio The total strai T is icludig homogeeous ad redudat strais which ca be calculated as: Grid lie T HE RL Cotaier.5 1 Piercig Belt 5,59 S Figure. The agle of grid lies. t 5,1 5 () Die tf t t Df 1 D Figure 1. A schematic showig the dividig of the deformatio zoe i tube extrusio part. Figure 3. The grid lies o the sample. Copyright 13 SciRes.

3 5 A. S. M. J. Agea 3. Experimetal Equipmets ad Procedure I this work, a special extrusio device was desiged ad maufactured. This device cotais dies (cuttig ito two half); piercig (madrel), pisto, ier cotaier ad outer cotaier, as show i Figure Die Desig The Equatio () becomes a logarithmic formula as: l Z (5) HT where Z is a fuctio depeded o the D ad t. To produce the dies, the curves of deformatio zoe i these dies should be determied by calculatig the values of t at all sectio of deformatio zoe from equatio below []. Z where ad t D 3t 3t D D 3 t D.5.5 3t 3tD D where t is the iitial thickess of the tube ad D is the ier diameter of the tube. To apply (C.R.H.S), the vales of Z should be determied for all values of c. I this work the values of the costat c were chose as: Sample uter cotaier Die Ier cotaier Puch 3 () (7) () c = 1.1 c = 1. c =.9 whe the strai ratio is accelerated whe the strai ratio is uiform whe the strai ratio is decelerated The value of the iitial thickess t ad the thickess of the tube at the first sectio ( t 1 ) ca be calculated from []: t1 mt (9) where m ( ). []. I this work m.95 were chose. Ad the calculate the values of, 1 ad Z 1. The values of Z ca be calculated as: 1 3 c c c c 1 Z Z (1) The deformatio zoe of the dies was dividig ito 1 sectios; every sectio is 1 mm i legth. The thickess of the tube ca be calculated at all sectio, ad the the profile of the deformatio zoe of the dies ca be determied from: D D t (11) 3.. Piercig Desig By the same method, the profile of the piercig (madrel) ca be determied. The formula of Z is [7-]. Z where: 1 J K 3 1 K 3JK J (1) 3 K D J J t.5 K 3t 3t (13) is the ier diameter of cotaier as show i Figure 5. From the Figure 5, the diameter of the piercig (madrel) at all sectios ca be determied from: (1) t Cotaier Madrel Die holder 35,37 t 5,1 1 3 Piercig Base Belt Figure. Assembly of extrusio device-set. Figure 5. A schematic showig the dividig of the deformatio zoe at piercig part. Copyright 13 SciRes.

4 3, 3, 1 1 3,5 1 A. S. M. J. Agea 59 Three dies ad three piercig were produced. As show i Figure. From the calculatio, the profiles of the dies ad the piercig (madrels) were obtaied as show i the Figures 7 ad respectively Material ad Specimes The samples were made from Lead because it has mechaical properties like steel i high temperature [9]. The samples were compressed with a special dies to get high accurate dimesios ad to get rid of the porous. The chemical compositio of this alloy is give i Table Fiite Elemet Simulatios I this work, the fiite elemet method was used to simulate the forward extrusio of tube processes for all types of the dies ad the piercig usig Q-form software. I this software, a hydraulic press was applied, with coefficiet of frictio of. betwee the die ad the billet at room temperature. The software was provided with materials data that were obtaied from the upsettig test. Figure. The three types of the piercig (madrels); workspaces..5 Die profile whe C=.9.5 Die profile whe C= 1... Die diameter (mm) Diameter XD Die diameter (mm) Diameter XD XD (mm) 1 XD (mm) Die diameter (mm) Die profile whe C = XD (mm) Diameter XD Die diameter (mm) XD (mm) C =.9 C = 1. C = 1.1 Figure 7. Die profiles with (C =.9); Die profiles with (C = 1.); Die profiles with (C = 1.1); All die profiles. Copyright 13 SciRes.

5 A. S. M. J. Agea 1 C =.9 1 C = XP 9, Piercig radius (mm) 1 9, XP Piercig radius (mm) XP (mm) XP (mm) Piercig radius (mm) C = XP 9,93 Piercig radius (mm) C = 1.1 C = 1. C = XP (mm) XP (mm) Figure. Piercig profiles with (C =.9); Piercig profiles with (C = 1.); Piercig profiles with (C = 1.1); All piercig profiles. Table 1. Chemical Compositio of Pb (wt %). Pb Cu Fe Ag M Si Ni Results ad Discussio.1. Experimetal Extrusio Load Extrusio load depeds o several factors icludig: The amout strai i the sample. The amout of the yield stress of the sample material. The frictio force betwee the outer surface of the sample ad the ier surface of the extrusio dies. The geometry of the sample ad the geometry of the extrusio zoe. Practical results have show us that the largest value of the extrusio load at the begiig of the process was whe the piercig of (C =.9) with the die of (C =1.) were used, ad the lowest value of the extrusio load was whe the piercig of (C = 1.1) with the die of (C =1.1) were used. While, the largest value of the extrusio load was whe the piercig of (C = 1.) with the die of (C = 1.) were used, ad the lowest value for the extrusio load was whe the piercig of (C = 1.1 ) with the die of (C =.9 ) were used at the ed of the process. As show i Figure 9... Experimetal Redudat Strai The quality ad efficiecy of deformatio process are depedig o the amout of the redudat strais i the microstructure of the material that resultig from this process. As the redudat strais are small, the productio process is perfect. I the preset, the logitudial redudat strai was calculated for all samples as show i Figure 9. From the experimetal results we observed that the largest value of redudat strai at the begiig of the process was whe the piercig of (C =.9) with the die of (C = 1.1) were used, ad the lowest value of the redudat strai was whe the piercig of (C = 1.1) with Copyright 13 SciRes.

6 A. S. M. J. Agea 1 Extrusio load (KN) Die with (C = 1.) Die with (C =.9) Extrusio load (KN) 9 Die with (C = 1.) Die with (C =.9) Ram displacmet (mm) Ram displacmet (mm) Extrusio Load (KN) Die with (C = 1.) Die with (C =.9) Ram displacmet (mm) Extrusio load (KN) Piercig (C =.9 ) with Die (C = 1.1) Piercig (C =.9 ) with Die (C = 1.) Piercig (C =.9 ) with Die (C =.9) Piercig (C = 1. ) with Die (C = 1.1) 3 Piercig (C = 1. ) with Die (C = 1.) Piercig (C = 1. ) with Die (C =.9) Piercig (C = 1.1 ) with Die (C = 1.1) 1 Piercig (C = 1.1 ) with Die (C = 1.) Piercig (C = 1.1 ) with Die (C =.9) Ram displacmet (mm) Figure 9. Extrusio-load whe usig the piercig of (C =.9) with the three dies; Extrusio-load whe usig the piercig of (C = 1.) with the three dies; Extrusio-load whe usig the piercig of (C = 1.1) with the three dies; Extrusio-load for all process. the die of (C =1.1) were used. While, at the ed of the process, the largest value of the redudat strai was whe the piercig of (C = 1.1) with the die of (C =1.) were used, ad the lowest value for redudat strai was whe piercig of (C =.9) with the die of (C =.9) were used. As show i Figure Experimetal Total Strai From the practical results it is foud that all the curves of the total strai took the same form of homogeeous strai at the begiig of the process i the piercig zoe. While, i the dies zoes, the values of the total strai were heterogeeous ad deped o the piercig profile. The explaatio is that the values of total strai i the piercig zoe are depedig o the amout of the homogeous strai because the values of redudat strai were small, while, at the die zoe, the values of redudat strai are relatively large. It was show that the largest value of total strai at the piercig zoe was whe the piercig of (C =.9) with the die of (C = 1.1) were used, ad the lowest value of the total strai at the piercig zoe was whe the piercig of (C = 1.1) with the die of (C =.9) were used. While, at the die zoe, the largest value of the total strai was whe the piercig of (C = 1.1) with the die of (C = 1.) were used, ad the lowest value for total strai was whe piercig of (C =.9) with the die of (C =.9) were used. As show i Figure Fiite Elemet (FE) Effective Strai From fiite elemet result, it reported that the largest value of effective strai at the piercig zoe was whe the piercig of (C =.9) with the die of (C =.9) were used, ad the lowest value of the effective strai at the piercig zoe was whe the piercig of (C = 1.1) with the die of (C =.9) were used. While, at the die zoe, the largest value of the effective strai was whe the piercig of (C = 1.) with the die of (C =.9) were used, ad the lowest value for effective strai was whe piercig of (C = 1.) with the die of (C = 1.1) were used. As show i Figure 1. Copyright 13 SciRes.

7 A. S. M. J. Agea Die with C =.9) Die with C =1.) Die with C =1.1) Die with C =.9) Die with C =1.) Die with C =1.1) RL.. RL Ram displacemet (mm) Ram displacemet (mm) RL Die with C =.9) Die with C =1.) Die with C =1.1) Ram displacemet (mm) RL Piercig (C =.9 ) with Die (C = 1.1) Piercig (C =.9 ) with Die (C = 1.) Piercig (C =.9 ) with Die (C =.9) Piercig (C = 1. ) with Die (C = 1.1) Piercig (C = 1. ) with Die (C = 1.) Piercig (C = 1. ) with Die (C =.9) Piercig (C = 1.1 ) with Die (C = 1.1) Piercig (C = 1.1 ) with Die (C = 1.) Piercig (C = 1.1 ) with Die (C =.9) Ram displacemet (mm) Figure 1. Redudat strai whe usig the piercig of (C =.9) with the three dies; Redudat strai whe usig the piercig of (C = 1.) with the three dies; Redudat strai whe usig the piercig of (C = 1.1) with the three dies; Redudat strai for all piercig. T 1. Piercig Zoe Die Zoe Die with (C = 1.) Die with (C =.9) Ram displacemet (mm) T 1. Die Zoe Piercig Zoe Die with (C = 1.) Die with (C =.9) Ram displasemets (mm) T Piercig Zoe Die Zoe Die with (C = 1.) Die with (C =.9) Ram displacemet (mm) T Piercig Zoe Die Zoe Ram displasemets (mm) Piercig of (C=.9) with die of (C= 1.1) Piercig of (C=.9) with die of (C= 1.) Piercig of (C=.9) with die of (C=.9) Piercig of (C=1.) with die of (C= 1.1) Piercig of (C=1.) with die of (C= 1.) Piercig of (C=1.) with die of (C=.9) Piercig of (C=1.1) with die of (C= 1.1) Piercig of (C=1.1) with die of (C= 1.) Piercig of (C=1.1) with die of (C=.9) Figure 11. Total strai whe usig the piercig of (C =.9) with the three dies; Total strai whe usig the piercig of (C = 1.) with the three dies; Total strai whe usig the piercig of (C = 1.1) with the three dies; Total strai for all piercig ad dies Copyright 13 SciRes.

8 A. S. M. J. Agea 3 (e) (f) Piercig of ( C =.9) with the die of ( C =.9) Piercig of ( C =.9) with the die of ( C = 1.) Piercig of ( C =.9) with the die of ( C = 1.1) 3. Effective strai Ram displacemet (mm) Piercig of ( C =1.) with the die of ( C =.9) Piercig of ( C =1.) with the die of ( C = 1.) Piercig of ( C =1.) with the die of ( C = 1.1) 3. Effective strai Ram displacemet (mm) (g) (h) (i) Piercig of ( C =1.1) with the die of ( C =.9) Piercig of ( C =1.1) with the die of ( C = 1.) Piercig of ( C =1.1) with the die of ( C = 1.1). Effective strai Ram displacemet (mm) (j) Copyright 13 SciRes. (k) (l)

9 A. S. M. J. Agea (m) Figure 1. FE-effective strai distributio whe usig the piercig of (C =.9) with the die of (C =.9); FE-effective strai distributio whe usig the piercig of (C =.9) with the die of (C = 1.); FE-effective strai distributio whe usig the piercig of (C =.9) with the die of (C = 1.1); FE-effective strai whe usig piercig of (C =.9) with the three dies; (e) FE-effective strai distributio whe usig the piercig of (C = 1.) with the die of (C =.9); (f) FE-effective strai distributio whe usig the piercig of (C = 1.) with the die of (C= 1.); (g) FE-effective strai distributio whe usig the piercig of (C = 1.) with the die of (C = 1.1); (h) FE-effective strai whe usig piercig of (C = 1.) with the three dies; (i) FE-effective strai distributio whe usig the piercig of (C = 1.1) with the die of (C =.9); (j) FE-effective strai distributio whe usig the piercig of (C = 1.1) with the die of (C = 1.); (k) FE-effective strai distributio whe usig the piercig of (C = 1.1) with the die of (C = 1.1); (l) FE-effective strai whe usig piercig of (C = 1.1) with the three dies; (m) FEeffective strai for all piercig with all dies. This work ivestigated the mechaical behavior of lead material formed by forward extrusio of tube. From experimetal tests, we observed that at the piercig zoe, the miimum values of extrusio load, redudat strai, total strai ad fiite elemet effective strai was whe piercig (madrel) of (C = 1.1) were used, ad the largest value of total strai at the piercig zoe was whe the piercig of (C =.9) were used. While, at the die zoe, the miimum values of extrusio load, redudat strai, total strai ad was whe the die of (C =.9) were used, ad the largest value of total strai at the piercig zoe was whe the piercig of (C = 1.) were used. REFERENCES [1] B. Avitzur, Metal Formig Processes ad Aalysis, Mc Graw Hill, New York, 19. [] M. Sabor, M. Bakhshi-Joobari, M. Noorai-Azad ad A. Gorji, Experimetal ad Numerical Study of Eergy Cosumptio i Forward ad Backward Rod Extrusio, Joural of Materials Processig Techology, Vol. 177, No. 1-3,, pp doi:1.11/j.jmatprotec Coclusio [3] B. Barisic, G. Cukor ad M. Math, Estimate of Cosumed Eergy at Backward Extrusio Process by Meas of Modelig Approach, Joural of Materials Processig Techology, Vol ,, pp doi:1.11/j.jmatprotec...17 [] P. V. Vaidyaatha ad T. Z. Blazyskim, A Theoretical Method of Efficiet Extrusio, Die Desig, Joural of the Istitute of Metals, Vol. 11, 1973, pp [5] W. A. Khudheyera, D. C. Bartoa ad T. Z. Blazyskia, Pass Geometry ad Macroshear Redudacy Effects i a 3-Roll Coical blique Tube Pierci Process, Joural of Materials Processig Techology, Vol. 5, No. 1-, 199, pp [] A. K. A. Al-Dahwi ad T. Z. Blazyski, Ihomogeeity of Flow, Force Parameters ad Pass Geometry i Rotary Coe-Roll Tube Piercig, Materialwisseschaft ud Werkstofftechik, Vol. 3, No. 1, 199, pp doi:1.1/mawe [7] T. Z. Blazyskim, Theoretical Method of Desig Tools for Metal Formig Process, Metal Formig, Vol. 3, No. 5, 197, pp [] [9] N. Loizo ad R. B. Sims, The Yield Stress of Pure Lead i Compressio, Joural of the Mechaics ad Physics of Solids, Vol. 1, 1953, pp Copyright 13 SciRes.