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Experimental investigation and numerical simulation of plastic flow behavior during forward-backward-radial extrusion process
Progress in Natural Science: Materials International (xxxx) xxxx–xxxx
Contents lists available at ScienceDirect
HOSTED BY
Progress in Natural Science: Materials International journal homepage: www.elsevier.com/locate/pnsmi
Original Research
Experimental investigation and numerical simulation of plastic flow behavior during forward-backward-radial extrusion process☆ ⁎
A. Farhoumand , R. Ebrahimi Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran
A R T I C L E I N F O
A BS T RAC T
Keywords: Finite element analysis Extrusion Forming Plastic deformation Strain heterogeneity
Finite element method was employed to investigate the effect of process parameters of plastic deformation behavior in Forward-Backward-Radial Extrusion (FBRE) process. The result of an axisymmetric model shows that the friction between die components and the sample has a substantial effect on the material flow behavior. Although strain heterogeneity index (SHI) slightly decreases with an increase in friction, large portion of the sample experiences significant strain heterogeneity. Increasing the friction factor also localizes the strain heterogeneity effect in the backward section, and spread the effect in the forward section. Decreasing the friction in the FBRE process can reduce the amount of the strain heterogeneity in the product while decreases the required punch force substantially. Furthermore, an increase in gap thickness increases the deformation in the area close to the lower punch at the expense of the area in the vicinity of the upper punch. The numerical simulation has a good agreement with the experimental results which confirms the accuracy of the proposed finite element model.
1. Introduction
In a study by Kim et al. [10], the effect of friction on the material deformation during equal channel angular pressing process was investigated using a 2D finite element model. It was found that friction intensifies the shear deformation for the surface elements. This is due to substantial effect of friction acting on the opposite direction of the moving surfaces during the process. Thus, the friction can decrease the extent of the less-deformed shared zones in the process. Altan et al. utilized finite element analysis of an axisymmetric model for a deep cup drawing process to investigate the effect of friction [11]. It was concluded that the variation in the friction coefficient over a small range, in which the coefficients are close to the actual values, does not significantly affect the deformation, as long as the material is not within the instability limit [11]. In contrary where material instability is likely to occur due to the large tensile stresses associated with a great punch force or a large blank diameter or small sheet thickness the sensitivity of the process to changes in the conditions of friction becomes significant. Farhoumand et al. employed a 3D finite element analysis of a novel extrusion process for quantitative assessment of strain accumulation in relation to the process parameters [12,13]. More recently, in an effort to increase the accumulated plastic strain and obtain a more uniform distribution, a modified backwards extrusion was proposed by Shatermashhadi et al. [14] and, Finite Element (FE) analysis results confirmed the successful
Extrusion in comparison to other manufacturing methods used in industrial application has many advantages such as: minimum material waste, high dimensional accuracy, reduction or complete elimination of machining, good surface finish, better mechanical properties of products than those of the parent material. The basic processes involving cold extrusion are classified based on their forming direction as forward, backward and radial/lateral extrusion [1]. Radial extrusion process can be used to manufacture complex parts such as collar flanges, spur gears, splines with shafts and tube fittings [1–3]. Besides, combinations of extrusion processes in which a billet is extruded simultaneously in forward, backward and radial directions can also facilitate to eliminate the need for multistep forming of relatively complex shaped parts [4]. For instance backward-forward extrusion [5], radial forward extrusion [6,7], radial backward extrusion [4] and double backward extrusion [8] are some of these processes. Since most of the components are produced on the basis of experience and trial-and-error [5], it is imperative to eliminate the unnecessary production cost by modeling the process and optimizing the parameters. The significance of an analysis for a forming process lies in the determination of required punch force, flow behavior as well as stress-strain state during the process [9].
Peer review under responsibility of Chinese Materials Research Society. ⁎ Corresponding author. E-mail address: [email protected] (A. Farhoumand). http://dx.doi.org/10.1016/j.pnsc.2016.12.005 Received 20 September 2015; Received in revised form 5 November 2016; Accepted 13 December 2016 1002-0071/ © 2016 Chinese Materials Research Society. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Please cite this article as: Farhoumand, A., Progress in Natural Science: Materials International (2016), http://dx.doi.org/10.1016/j.pnsc.2016.12.005
Progress in Natural Science: Materials International (xxxx) xxxx–xxxx
A. Farhoumand, R. Ebrahimi
implementation of the modified process. In another research by Ebrahimi et al. FE analysis was employed to investigate the uniformity of strain distribution in extrusion of copper with optimization of various sample and process geometries [15]. Furthermore, numerical simulation of copper deformation in compression-extrusion was performed by Babaei et al. using commercial FE software ABAQUS [16]. Forward-backward-radial extrusion process (FBRE) can be used to manufacture components that feature a hoop protrusion like gears and flanges that come with hollow shafts [17]. A quantitative study of FBRE was performed to investigate the effect of process parameters on the final dimensions of the product. But, the effect of process parameters on the material flow behavior, strain distribution and thus the strain heterogeneity within the final product has not been investigated. It is imperative to have a clear understanding of the strain distribution within the final product which can affect the mechanical properties and microstructure of the product. Hence, in this study, the effect of processing parameters on strain heterogeneity within the product processed by FBRE was investigated by implementation of FE method. Quantitative analysis of strain heterogeneity was performed by utilizing an axisymmetric FE model. A number of numerical simulations were performed and the results were compared with experimental work to verify the accuracy of the FE model.
Fig. 2. The schematic of the die assembly used in FBRE process and the geometrical parameters (gap and wall thickness and die corner fillet).
its axi-symmetrical nature similar to that of the double cup extrusion process. Several parameters in FBRE can influence the material deformation behavior. Friction as a process parameter along with geometrical parameters such gap thickness and die corner fillet can influence the material deformation behavior in FBRE. Fig. 2 illustrates the aforementioned parameters schematically. Several simulations were performed to analyze the effect of friction and geometrical parameters on the FBRE deformation behavior and the corresponding punch force.
2. Finite element analysis An Axisymmetric FBRE model was analyzed in ABAQUS FE software [18] using explicit algorithm. Punches and dies were assumed to be rigid due to negligible elastic deformation whereas the sample material (commercially pure aluminum) was considered as deformable in the model. The kinematic relation of the sample was obtained from a compression test, Fig. 1, which represented by a power law equation as σ=133ε 0.3 (MPa). The kinematic behavior in FE model was incorporated with the von Misses yield criterion and isotropic hardening. The contact condition between sample and surfaces of die and punches were assumed to follow coulomb friction law. Barrel compression test [19] was utilized to measure the experimental friction factor (m). The experimental friction factor (m) was found 0.13. However, it should be noted that the acquired value is only pertinent to the performed FBRE process, used lubricant and the existing surface condition of the FBRE die components and sample. Due to the limitations in ABAQUS software input variables, Eq. (1) was used to convert the measured friction factor (m) to coefficient of friction (μ ) for numerical simulations,
μ=
m0.9 2.72(1 − m )0.11
3. Experimental procedures To perform the FBRE process experimentally, a proper die set was designed and manufactured. The punches and dies were machined from cold-worked alloy steel (Grade: X210Cr12 No. 1.2080) while the other die components were manufactured from medium carbon steel (Grade: CK45 No. 1.1191). The heat treatment of alloy steel parts was performed at 970 °C followed by an oil quenching and subsequent tempering at 250 °C. The assembly of the die setup under a screw press is shown in Fig. 3(a). The die was designed with an adjustable gap thickness that eliminates the need for additional die sets. The gap thickness has been shown by the arrow in Fig. 3(b). Cylindrical samples with 24 mm diameter and 20 mm in length
(1)
Although Eq. (1) has been derived for double cup extrusion process [20], this equation is considered to be applicable to FBRE process due
Fig. 3. FBRE setup under a screw press in (a) and the gap between upper and lower dies in (b).
Fig. 1. Before and after a compression test of a commercially pure aluminum sample, utilized to obtain the kinematic of the material.
2
Progress in Natural Science: Materials International (xxxx) xxxx–xxxx
A. Farhoumand, R. Ebrahimi
Fig. 4. Cross section view of FBRE processed aluminum samples for gap thicknesses of 2 mm (a) and 4 mm (b).
were machined from commercially pure aluminum (grade 1100). FBRE process was performed in a 200 kN capacity screw press machine with the crosshead speed of 0.2 mm/sec at ambient temperature. The die corner fillet and the wall thickness in the experimental setup were 1 mm and 2 mm, respectively, while samples with two different gap thicknesses of 2 mm and 4 mm, were processed. The cross sections of the processed samples are shown in Fig. 4. 4. Results and discussion Variation of frictional conditions during forming processes can significantly alter the rate of strain hardening and subsequently the mechanical properties of different sections within the product. Considering the application of the product, these variations of mechanical properties within the product shall be thoroughly examined to assure its compliance with the engineered design limits. Hence, in case of FBRE product and considering the presence of three different sections, namely forward, backward and radial, this frictional variation needs more in depth investigation. Therefore, analysis of plastic strain distribution in different sections of FBRE product was performed in several frictional conditions. The quantitative assessment was fulfilled by defining Strain Heterogeneity Index, SHI as below,
SHI =
(εmax − εmin ) εave
Fig. 5. Meshed model with defined paths for various sections for the strain heterogeneity analysis (Un-deformed and Deformed Mesh geometry on the left and right of Axisymmetric axis, respectively.).
(2)
increases from 0 to 0.13, the location of the maximum SHI in Fig. 6(a) shifts towards point B. With further increase of friction factor, m=0.8, the maximum SHI for backward section increases significantly which shows the significant effect of friction on deformation behavior in backward section of FBRE sample. Furthermore, not only the SHI increases with increase of frictional conditions, but also the height of the material in backward section decreases. Therefore, not only an increase in friction factor in backward section intensifies the strain heterogeneity but also it restricts the material progress into backward section. In frictionless condition, the SHI in forward section, Fig. 6(b), is much more intense in the vicinity of the lower punch, (point C in Fig. 5). However, as the friction factor increases, the SHI decreases slightly, but wider section of the sample experiences significant strain heterogeneity. It was also observed that an increase in friction factor promotes the material progress into forward section which is in contrast to that of backward section, as previously discussed. Therefore, an increase in friction in FBRE process has opposing effects for backward and forward sections. Increasing the friction factor will promote the material progress into forward section at the expense of the backward one. Besides, increasing the friction factor narrows the strain heterogeneity curve in backward section while increasing its maximum which is in contrary for that of forward section. For the center section, the equivalent plastic strain for various frictional conditions has been depicted in Fig. 7. When the frictionless conditions prevails (m=0), the accumulated strain is higher in the vicinity of the upper and lower punches (point E and F) in comparison to that of middle section (normalized distance 0.4–0.8 in Fig. 7). As the
where εmax , εmin and εave denote the maximum, minimum and average effective plastic strain over a path, respectively. Different paths in cross section of the FBRE sample were defined and mapped in the deformed mesh as shown in Fig. 5. For the backward section, paths were defined along the wall thickness of the simulated deformed mesh with 1 mm spacing. As shown in Fig. 5, a typical path in backward section is from point ai to bi while the range of i was chosen according to the extent of this section from point A to B. For each frictional condition, SHI was calculated along each path by using the FE simulation results as per Eq. (2). Similar approach was applied for the forward section as paths were annotated as cj to dj from point C to D as shown in Fig. 5. For the center section, only one path was considered on the axisymmetric axis of the sample from the upper punch (point E) towards the lower punch (point F) as indicated in Fig. 5. 4.1. Effect of friction between sample and the surfaces of die and punches in FBRE process The effect of different frictional conditions on the heterogeneity of the accumulated strain in backward and forward sections of FBRE sample is depicted in Fig. 6(a) and (b), respectively. In frictionless case SHI is the maximum in the vicinity of point A which rapidly declines towards point B. This strain heterogeneity adjacent to point A is due to intense deformation at the corner of the punch which causes localized strain heterogeneity. As the friction factor 3
Progress in Natural Science: Materials International (xxxx) xxxx–xxxx
A. Farhoumand, R. Ebrahimi
Fig. 6. Effect of friction on strain heterogeneity, (a) in backward section and (b) in forward section of a FBRE sample.
Fig. 9. Effect of friction factor on the FBRE punch force.
Fig. 7. Effect of friction on the equivalent plastic strain at center region of a FBRE processed sample.
decreases significantly which give rise to substantial plastic strain accumulation in the middle of the center section. This shows a shift in material flow preferences as the friction factor increases. In frictionless
friction factor increases, the plastic strain in the vicinity of the punches
Fig. 8. Equivalent plastic strain contours (PEEQ) and dead zones in a FBRE sample. Cross section views of the sample for a friction factor of (a) m=0, (b) m=0.13, (c) m=0.38 and (d) m=0.8.
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Progress in Natural Science: Materials International (xxxx) xxxx–xxxx
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Fig. 10. Equivalent plastic strain (PEEQ) contours in different stages of a sample formation during frictionless (m=0) FBRE at different punch strokes (in mm) of (a) 0, (b) 1, (c) 1.5, (d) 2.5, (e) 6 and (f) 15.
3 Gap Thickness = 1 mm Gap Thickness = 2 mm Gap Thickness = 4 mm
Equivalent Plastic Strain, ε
2.5
2
1.5
1
0.5
0 Fig. 11. Effect of gap thickness on the FBRE punch force, simulation and experimental results.
0
0.2
0.4
0.6
0.8
1
Nomalized Distance (From E to F) Fig. 12. Effect of gap thickness on the equivalent plastic strain in the center section of FBRE processed samples.
condition, the material plastic flow occurs in two discrete regions in the vicinity of upper and lower punches. As friction increases, these two discrete regions form separate dead-zones with no further material flow while one central region in the material becomes responsible for further plastic flow of the material during FBRE. The extent of dead-zones adjacent to the upper and lower punches for various frictional conditions is shown in Fig. 8(a)–(d). Regardless of the friction factor, the extent of the dead zone adjacent to the upper punch is much more noticeable than that of the lower punch. But, as the friction factor increases this difference abates. It can be established from Fig. 8 that as the friction factor increases, the extent of the dead zone adjacent to the upper punch extends which limits the material flow into the backward section. Consequently, the restriction of material flow into backward section, promotes the material flows into forward section and therefore, the difference between the height of forward and backward sections decreases as
the friction factor increases. The effect of friction on the required FBRE punch force is also investigated as shown in Fig. 9. The difference in punch force between friction less condition and m=0.13 case is not significant. This is due to similarity of the deformation behavior in the aforementioned frictional conditions. As the friction increases further to m=0.38, the material plastic flow localizes in central areas, which in turn increases the FBRE required load as can be seen in Fig. 9. Further increase of the friction from m=0.38 to m=0.8 has a significant effect on the increase of punch force. This increase could be solely due to redundant frictional losses along die/sample. interface since there is no significant change in material flow behavior between m=0.38 and 0.8. Hence, increase of FBRE punch force with an increase in friction 5
Progress in Natural Science: Materials International (xxxx) xxxx–xxxx
A. Farhoumand, R. Ebrahimi
2 1.8
Equivalent Plastic Strain , ε
deformation path. Hence, the error/noise, propagated incrementally when the effective strain was recovered via integration during the FBRE process. This could also be correlated to the noise in the calculation of the punch force for FBRE as shown in Fig. 11. The effect of gap thickness is also investigated on the equivalent plastic strain in center section of the sample as illustrated in Fig. 12. When the gap thickness is 1 mm, the equivalent plastic stain is homogenously disturbed in the sample and only areas in the vicinity of the lower and upper punches, Point E and F which corresponds to normalized distance 0 and 1, respectively, experiences less deformation. As the gap thickness increases to 2 mm, an obvious change in material flow behavior can be seen from Fig. 12. A narrow gap thickness, for instance 1 mm, restricts the material flow into the radial section. Hence, the material tends to flow more into backward and forward sections. As the gap thickness increases, the material tends to progress more into radial section due to an easier flow. Hence, the area closer to the lower punch, flows in both forward and radial directions and therefore accumulates more plastic strain inside the material. This on the other hand, causes the restriction of the material flow in the vicinity of the upper punch hence causing lower strain accumulation in backward section. Therefore, as the gap thickness increases, the area in the vicinity of lower punch experiences more deformation at the expense of the area in the vicinity of the upper punch which corresponds to point F and E in Fig. 11, respectively.
r = 1 mm r = 3 mm r = 5 mm
1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
0
0.2
0.4
0.6
0.8
1
Normalized Distance (From E to F) Fig. 13. Effect of die corner fillet on the equivalent plastic strain in the center section of FBRE processed samples.
factor can be the contribution of two factors. Firstly, increasing the friction is increasing the required redundant work to overcome the frictional force between the die surfaces and the material. Secondly, increasing the friction in FBRE causes a shift in material flow to be restricted in the central regions which also limits the deformation hence giving rise to an increase of required punch force. It can be deducted that the effect of the former is much more pronounced than that of the latter on FBRE punch force requirements. Equivalent plastic strain contours of the sample in frictionless conditions are shown in Fig. 10 in six different stages of FBRE. It could be seen that the highest values of strains occur where the maximum deformation exists. The plastic equivalent effective strain is higher in the areas where the sample is in contact with the punch corners than anywhere else. In addition, at the initial stage of the process, contours of strains are distributed in extensive areas which gradually decrease towards the end of the process.
4.3. Effect of die corner fillet in equivalent plastic strain in FBRE process The effect of die corner fillet on the equivalent plastic strain in the center section is not as significant as that of the gap thickness. As illustrated in Fig. 13, a change in die corner fillet from 1 to 5 mm does not change the material flow behavior significantly. 5. Conclusion A reliable axisymmetric FE model was developed to investigate the effect of process parameters on the material flow behavior in FBRE, and the results of which were verified experimentally. It is found that the friction between the die components namely punches and dies, and sample has a significant effect on the material flow in FBRE. The strain heterogeneity index, SHI, was defined for quantitative analysis of frictional effect on plastic deformation. An increase in friction factor increases the SHI for both backward and forward sections. But, intense friction confines the extent of strain heterogeneity in backward section, while it has an opposite effect for that of forward section. Besides, the minimization of friction in the FBRE process reduces the required punch force significantly. As the gap thickness increases, the area in the vicinity of lower punch accumulates more plastic strain in comparison to that of the upper punch. Hence, more uniform deformation is achieved with smaller gap thickness. The presented FE model can be used to predict the plastic deformation behavior within the process parameters which in turn can dictate the mechanical properties of the FBRE process products.
4.2. Effect of gap thickness in punch force and equivalent plastic strain in FBRE process Another geometrical parameter that was considered to influence the material deformation behavior in FBRE is gap thickness. The effect of gap thickness on the accumulated effective plastic strain in center section is shown in Fig. 11. During the FBRE, similar to conventional extrusion, the punch force increases significantly with punch stroke at the start of the process while after certain punch stroke, the required extrusion force reaches a steady state. As can be seen from Fig. 11, regardless of the gap thickness, the location of this transition in punch force is somehow constant which occurs at point of about 8 mm of punch stroke. Besides, as the gap thickness decreases the punch force increase, which is due to the restriction of the material flow into the gap between the upper and lower dies. Reasonable agreement between the simulations results and the experimental data confirms the validity of the finite element model and the accuracy of the simulation results. The proposed grid size in the axisymmetric model gave a convergent and stable solution while minimizing the computational cost. To solve the problem, the punch displacement is typically divided into a large number of infinitesimal time steps each corresponding to a small stroke increment. An incremental displacement field solution was obtained for each time step while the total strain corresponding at a given time was calculated by integrating the strain rate along the
References [1] B.D. Ko, et al., J. Mater. Process. Technol. 113 (1–3) (2001) 109–114. [2] Y. Çan, T. Altınbalık, H.E. Akata, J. Mater. Process. Technol. 166 (1) (2005) 128–134. [3] Y. Can, C. Misirli, Mater. Des. 29 (4) (2008) 829–838. [4] H.-J. Choi, J.-H. Choi, B.-B. Hwang, J. Mater. Process. Technol. 113 (1–3) (2001) 141–147. [5] H.Y. Cho, et al., J. Mater. Process. Technol. 135 (2–3) (2003) 375–381. [6] Y.S. Lee, et al., J. Mater. Process. Technol. 113 (1–3) (2001) 136–140. [7] R. Ebrahimi, M. Reihanian, M.M. Moshksar, Mater. Des. 29 (9) (2008) 1694–1700. [8] A. Buschhausen, et al., J. Mater. Process. Technol. 33 (1–2) (1992) 95–108. [9] D.Y. Yang, K.J. Kim, J. Mater. Process. Technol. 191 (1–3) (2007) 2–6. [10] H.S. Kim, M.H. Seo, S.I. Hong, J. Mater. Process. Technol. 113 (1–3) (2001)
6
Progress in Natural Science: Materials International (xxxx) xxxx–xxxx
A. Farhoumand, R. Ebrahimi [15] [16] [17] [18] [19] [20]
622–626. [11] H. Darendeliler, T. Altan, J. Mater. Process. Technol. 58 (2–3) (1996) 293–301. [12] A. Farhoumand, S. Khoddam, P. Hodgson, Model. Simul. Mater. Sci. Eng. 20 (8) (2012) 085005. [13] A. Farhoumand, P.D. Hodgson, S. Khoddam, 48 (6) (2013) 2454–2461. [14] V. Shatermashhadi, et al., Mater. Des. 62 (0) (2014) 361–366.
7
M. Ebrahimi, F. Djavanroodi, Prog. Nat. Sci.: Mater. Int. 24 (1) (2014) 68–74. A. Babaei, M.M. Mashhadi, Prog. Nat. Sci.: Mater. Int. 24 (6) (2014) 623–630. A. Farhoumand, R. Ebrahimi, Mater. Des. 30 (6) (2009) 2152–2157. V. Abaqus/Explicit, Dassault Systèmes Inc., USA, 2009. R. Ebrahimi, A. Najafizadeh, J. Mater. Process. Technol. 152 (2) (2004) 136–143. S.H. Molaei, M. Shahbaz, R. Ebrahimi, Iran. J. Mater. Form. 1 (2) (2014) 14–22.
Contents lists available at ScienceDirect
HOSTED BY
Progress in Natural Science: Materials International journal homepage: www.elsevier.com/locate/pnsmi
Original Research
Experimental investigation and numerical simulation of plastic flow behavior during forward-backward-radial extrusion process☆ ⁎
A. Farhoumand , R. Ebrahimi Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran
A R T I C L E I N F O
A BS T RAC T
Keywords: Finite element analysis Extrusion Forming Plastic deformation Strain heterogeneity
Finite element method was employed to investigate the effect of process parameters of plastic deformation behavior in Forward-Backward-Radial Extrusion (FBRE) process. The result of an axisymmetric model shows that the friction between die components and the sample has a substantial effect on the material flow behavior. Although strain heterogeneity index (SHI) slightly decreases with an increase in friction, large portion of the sample experiences significant strain heterogeneity. Increasing the friction factor also localizes the strain heterogeneity effect in the backward section, and spread the effect in the forward section. Decreasing the friction in the FBRE process can reduce the amount of the strain heterogeneity in the product while decreases the required punch force substantially. Furthermore, an increase in gap thickness increases the deformation in the area close to the lower punch at the expense of the area in the vicinity of the upper punch. The numerical simulation has a good agreement with the experimental results which confirms the accuracy of the proposed finite element model.
1. Introduction
In a study by Kim et al. [10], the effect of friction on the material deformation during equal channel angular pressing process was investigated using a 2D finite element model. It was found that friction intensifies the shear deformation for the surface elements. This is due to substantial effect of friction acting on the opposite direction of the moving surfaces during the process. Thus, the friction can decrease the extent of the less-deformed shared zones in the process. Altan et al. utilized finite element analysis of an axisymmetric model for a deep cup drawing process to investigate the effect of friction [11]. It was concluded that the variation in the friction coefficient over a small range, in which the coefficients are close to the actual values, does not significantly affect the deformation, as long as the material is not within the instability limit [11]. In contrary where material instability is likely to occur due to the large tensile stresses associated with a great punch force or a large blank diameter or small sheet thickness the sensitivity of the process to changes in the conditions of friction becomes significant. Farhoumand et al. employed a 3D finite element analysis of a novel extrusion process for quantitative assessment of strain accumulation in relation to the process parameters [12,13]. More recently, in an effort to increase the accumulated plastic strain and obtain a more uniform distribution, a modified backwards extrusion was proposed by Shatermashhadi et al. [14] and, Finite Element (FE) analysis results confirmed the successful
Extrusion in comparison to other manufacturing methods used in industrial application has many advantages such as: minimum material waste, high dimensional accuracy, reduction or complete elimination of machining, good surface finish, better mechanical properties of products than those of the parent material. The basic processes involving cold extrusion are classified based on their forming direction as forward, backward and radial/lateral extrusion [1]. Radial extrusion process can be used to manufacture complex parts such as collar flanges, spur gears, splines with shafts and tube fittings [1–3]. Besides, combinations of extrusion processes in which a billet is extruded simultaneously in forward, backward and radial directions can also facilitate to eliminate the need for multistep forming of relatively complex shaped parts [4]. For instance backward-forward extrusion [5], radial forward extrusion [6,7], radial backward extrusion [4] and double backward extrusion [8] are some of these processes. Since most of the components are produced on the basis of experience and trial-and-error [5], it is imperative to eliminate the unnecessary production cost by modeling the process and optimizing the parameters. The significance of an analysis for a forming process lies in the determination of required punch force, flow behavior as well as stress-strain state during the process [9].
Peer review under responsibility of Chinese Materials Research Society. ⁎ Corresponding author. E-mail address: [email protected] (A. Farhoumand). http://dx.doi.org/10.1016/j.pnsc.2016.12.005 Received 20 September 2015; Received in revised form 5 November 2016; Accepted 13 December 2016 1002-0071/ © 2016 Chinese Materials Research Society. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Please cite this article as: Farhoumand, A., Progress in Natural Science: Materials International (2016), http://dx.doi.org/10.1016/j.pnsc.2016.12.005
Progress in Natural Science: Materials International (xxxx) xxxx–xxxx
A. Farhoumand, R. Ebrahimi
implementation of the modified process. In another research by Ebrahimi et al. FE analysis was employed to investigate the uniformity of strain distribution in extrusion of copper with optimization of various sample and process geometries [15]. Furthermore, numerical simulation of copper deformation in compression-extrusion was performed by Babaei et al. using commercial FE software ABAQUS [16]. Forward-backward-radial extrusion process (FBRE) can be used to manufacture components that feature a hoop protrusion like gears and flanges that come with hollow shafts [17]. A quantitative study of FBRE was performed to investigate the effect of process parameters on the final dimensions of the product. But, the effect of process parameters on the material flow behavior, strain distribution and thus the strain heterogeneity within the final product has not been investigated. It is imperative to have a clear understanding of the strain distribution within the final product which can affect the mechanical properties and microstructure of the product. Hence, in this study, the effect of processing parameters on strain heterogeneity within the product processed by FBRE was investigated by implementation of FE method. Quantitative analysis of strain heterogeneity was performed by utilizing an axisymmetric FE model. A number of numerical simulations were performed and the results were compared with experimental work to verify the accuracy of the FE model.
Fig. 2. The schematic of the die assembly used in FBRE process and the geometrical parameters (gap and wall thickness and die corner fillet).
its axi-symmetrical nature similar to that of the double cup extrusion process. Several parameters in FBRE can influence the material deformation behavior. Friction as a process parameter along with geometrical parameters such gap thickness and die corner fillet can influence the material deformation behavior in FBRE. Fig. 2 illustrates the aforementioned parameters schematically. Several simulations were performed to analyze the effect of friction and geometrical parameters on the FBRE deformation behavior and the corresponding punch force.
2. Finite element analysis An Axisymmetric FBRE model was analyzed in ABAQUS FE software [18] using explicit algorithm. Punches and dies were assumed to be rigid due to negligible elastic deformation whereas the sample material (commercially pure aluminum) was considered as deformable in the model. The kinematic relation of the sample was obtained from a compression test, Fig. 1, which represented by a power law equation as σ=133ε 0.3 (MPa). The kinematic behavior in FE model was incorporated with the von Misses yield criterion and isotropic hardening. The contact condition between sample and surfaces of die and punches were assumed to follow coulomb friction law. Barrel compression test [19] was utilized to measure the experimental friction factor (m). The experimental friction factor (m) was found 0.13. However, it should be noted that the acquired value is only pertinent to the performed FBRE process, used lubricant and the existing surface condition of the FBRE die components and sample. Due to the limitations in ABAQUS software input variables, Eq. (1) was used to convert the measured friction factor (m) to coefficient of friction (μ ) for numerical simulations,
μ=
m0.9 2.72(1 − m )0.11
3. Experimental procedures To perform the FBRE process experimentally, a proper die set was designed and manufactured. The punches and dies were machined from cold-worked alloy steel (Grade: X210Cr12 No. 1.2080) while the other die components were manufactured from medium carbon steel (Grade: CK45 No. 1.1191). The heat treatment of alloy steel parts was performed at 970 °C followed by an oil quenching and subsequent tempering at 250 °C. The assembly of the die setup under a screw press is shown in Fig. 3(a). The die was designed with an adjustable gap thickness that eliminates the need for additional die sets. The gap thickness has been shown by the arrow in Fig. 3(b). Cylindrical samples with 24 mm diameter and 20 mm in length
(1)
Although Eq. (1) has been derived for double cup extrusion process [20], this equation is considered to be applicable to FBRE process due
Fig. 3. FBRE setup under a screw press in (a) and the gap between upper and lower dies in (b).
Fig. 1. Before and after a compression test of a commercially pure aluminum sample, utilized to obtain the kinematic of the material.
2
Progress in Natural Science: Materials International (xxxx) xxxx–xxxx
A. Farhoumand, R. Ebrahimi
Fig. 4. Cross section view of FBRE processed aluminum samples for gap thicknesses of 2 mm (a) and 4 mm (b).
were machined from commercially pure aluminum (grade 1100). FBRE process was performed in a 200 kN capacity screw press machine with the crosshead speed of 0.2 mm/sec at ambient temperature. The die corner fillet and the wall thickness in the experimental setup were 1 mm and 2 mm, respectively, while samples with two different gap thicknesses of 2 mm and 4 mm, were processed. The cross sections of the processed samples are shown in Fig. 4. 4. Results and discussion Variation of frictional conditions during forming processes can significantly alter the rate of strain hardening and subsequently the mechanical properties of different sections within the product. Considering the application of the product, these variations of mechanical properties within the product shall be thoroughly examined to assure its compliance with the engineered design limits. Hence, in case of FBRE product and considering the presence of three different sections, namely forward, backward and radial, this frictional variation needs more in depth investigation. Therefore, analysis of plastic strain distribution in different sections of FBRE product was performed in several frictional conditions. The quantitative assessment was fulfilled by defining Strain Heterogeneity Index, SHI as below,
SHI =
(εmax − εmin ) εave
Fig. 5. Meshed model with defined paths for various sections for the strain heterogeneity analysis (Un-deformed and Deformed Mesh geometry on the left and right of Axisymmetric axis, respectively.).
(2)
increases from 0 to 0.13, the location of the maximum SHI in Fig. 6(a) shifts towards point B. With further increase of friction factor, m=0.8, the maximum SHI for backward section increases significantly which shows the significant effect of friction on deformation behavior in backward section of FBRE sample. Furthermore, not only the SHI increases with increase of frictional conditions, but also the height of the material in backward section decreases. Therefore, not only an increase in friction factor in backward section intensifies the strain heterogeneity but also it restricts the material progress into backward section. In frictionless condition, the SHI in forward section, Fig. 6(b), is much more intense in the vicinity of the lower punch, (point C in Fig. 5). However, as the friction factor increases, the SHI decreases slightly, but wider section of the sample experiences significant strain heterogeneity. It was also observed that an increase in friction factor promotes the material progress into forward section which is in contrast to that of backward section, as previously discussed. Therefore, an increase in friction in FBRE process has opposing effects for backward and forward sections. Increasing the friction factor will promote the material progress into forward section at the expense of the backward one. Besides, increasing the friction factor narrows the strain heterogeneity curve in backward section while increasing its maximum which is in contrary for that of forward section. For the center section, the equivalent plastic strain for various frictional conditions has been depicted in Fig. 7. When the frictionless conditions prevails (m=0), the accumulated strain is higher in the vicinity of the upper and lower punches (point E and F) in comparison to that of middle section (normalized distance 0.4–0.8 in Fig. 7). As the
where εmax , εmin and εave denote the maximum, minimum and average effective plastic strain over a path, respectively. Different paths in cross section of the FBRE sample were defined and mapped in the deformed mesh as shown in Fig. 5. For the backward section, paths were defined along the wall thickness of the simulated deformed mesh with 1 mm spacing. As shown in Fig. 5, a typical path in backward section is from point ai to bi while the range of i was chosen according to the extent of this section from point A to B. For each frictional condition, SHI was calculated along each path by using the FE simulation results as per Eq. (2). Similar approach was applied for the forward section as paths were annotated as cj to dj from point C to D as shown in Fig. 5. For the center section, only one path was considered on the axisymmetric axis of the sample from the upper punch (point E) towards the lower punch (point F) as indicated in Fig. 5. 4.1. Effect of friction between sample and the surfaces of die and punches in FBRE process The effect of different frictional conditions on the heterogeneity of the accumulated strain in backward and forward sections of FBRE sample is depicted in Fig. 6(a) and (b), respectively. In frictionless case SHI is the maximum in the vicinity of point A which rapidly declines towards point B. This strain heterogeneity adjacent to point A is due to intense deformation at the corner of the punch which causes localized strain heterogeneity. As the friction factor 3
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Fig. 6. Effect of friction on strain heterogeneity, (a) in backward section and (b) in forward section of a FBRE sample.
Fig. 9. Effect of friction factor on the FBRE punch force.
Fig. 7. Effect of friction on the equivalent plastic strain at center region of a FBRE processed sample.
decreases significantly which give rise to substantial plastic strain accumulation in the middle of the center section. This shows a shift in material flow preferences as the friction factor increases. In frictionless
friction factor increases, the plastic strain in the vicinity of the punches
Fig. 8. Equivalent plastic strain contours (PEEQ) and dead zones in a FBRE sample. Cross section views of the sample for a friction factor of (a) m=0, (b) m=0.13, (c) m=0.38 and (d) m=0.8.
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Fig. 10. Equivalent plastic strain (PEEQ) contours in different stages of a sample formation during frictionless (m=0) FBRE at different punch strokes (in mm) of (a) 0, (b) 1, (c) 1.5, (d) 2.5, (e) 6 and (f) 15.
3 Gap Thickness = 1 mm Gap Thickness = 2 mm Gap Thickness = 4 mm
Equivalent Plastic Strain, ε
2.5
2
1.5
1
0.5
0 Fig. 11. Effect of gap thickness on the FBRE punch force, simulation and experimental results.
0
0.2
0.4
0.6
0.8
1
Nomalized Distance (From E to F) Fig. 12. Effect of gap thickness on the equivalent plastic strain in the center section of FBRE processed samples.
condition, the material plastic flow occurs in two discrete regions in the vicinity of upper and lower punches. As friction increases, these two discrete regions form separate dead-zones with no further material flow while one central region in the material becomes responsible for further plastic flow of the material during FBRE. The extent of dead-zones adjacent to the upper and lower punches for various frictional conditions is shown in Fig. 8(a)–(d). Regardless of the friction factor, the extent of the dead zone adjacent to the upper punch is much more noticeable than that of the lower punch. But, as the friction factor increases this difference abates. It can be established from Fig. 8 that as the friction factor increases, the extent of the dead zone adjacent to the upper punch extends which limits the material flow into the backward section. Consequently, the restriction of material flow into backward section, promotes the material flows into forward section and therefore, the difference between the height of forward and backward sections decreases as
the friction factor increases. The effect of friction on the required FBRE punch force is also investigated as shown in Fig. 9. The difference in punch force between friction less condition and m=0.13 case is not significant. This is due to similarity of the deformation behavior in the aforementioned frictional conditions. As the friction increases further to m=0.38, the material plastic flow localizes in central areas, which in turn increases the FBRE required load as can be seen in Fig. 9. Further increase of the friction from m=0.38 to m=0.8 has a significant effect on the increase of punch force. This increase could be solely due to redundant frictional losses along die/sample. interface since there is no significant change in material flow behavior between m=0.38 and 0.8. Hence, increase of FBRE punch force with an increase in friction 5
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2 1.8
Equivalent Plastic Strain , ε
deformation path. Hence, the error/noise, propagated incrementally when the effective strain was recovered via integration during the FBRE process. This could also be correlated to the noise in the calculation of the punch force for FBRE as shown in Fig. 11. The effect of gap thickness is also investigated on the equivalent plastic strain in center section of the sample as illustrated in Fig. 12. When the gap thickness is 1 mm, the equivalent plastic stain is homogenously disturbed in the sample and only areas in the vicinity of the lower and upper punches, Point E and F which corresponds to normalized distance 0 and 1, respectively, experiences less deformation. As the gap thickness increases to 2 mm, an obvious change in material flow behavior can be seen from Fig. 12. A narrow gap thickness, for instance 1 mm, restricts the material flow into the radial section. Hence, the material tends to flow more into backward and forward sections. As the gap thickness increases, the material tends to progress more into radial section due to an easier flow. Hence, the area closer to the lower punch, flows in both forward and radial directions and therefore accumulates more plastic strain inside the material. This on the other hand, causes the restriction of the material flow in the vicinity of the upper punch hence causing lower strain accumulation in backward section. Therefore, as the gap thickness increases, the area in the vicinity of lower punch experiences more deformation at the expense of the area in the vicinity of the upper punch which corresponds to point F and E in Fig. 11, respectively.
r = 1 mm r = 3 mm r = 5 mm
1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
0
0.2
0.4
0.6
0.8
1
Normalized Distance (From E to F) Fig. 13. Effect of die corner fillet on the equivalent plastic strain in the center section of FBRE processed samples.
factor can be the contribution of two factors. Firstly, increasing the friction is increasing the required redundant work to overcome the frictional force between the die surfaces and the material. Secondly, increasing the friction in FBRE causes a shift in material flow to be restricted in the central regions which also limits the deformation hence giving rise to an increase of required punch force. It can be deducted that the effect of the former is much more pronounced than that of the latter on FBRE punch force requirements. Equivalent plastic strain contours of the sample in frictionless conditions are shown in Fig. 10 in six different stages of FBRE. It could be seen that the highest values of strains occur where the maximum deformation exists. The plastic equivalent effective strain is higher in the areas where the sample is in contact with the punch corners than anywhere else. In addition, at the initial stage of the process, contours of strains are distributed in extensive areas which gradually decrease towards the end of the process.
4.3. Effect of die corner fillet in equivalent plastic strain in FBRE process The effect of die corner fillet on the equivalent plastic strain in the center section is not as significant as that of the gap thickness. As illustrated in Fig. 13, a change in die corner fillet from 1 to 5 mm does not change the material flow behavior significantly. 5. Conclusion A reliable axisymmetric FE model was developed to investigate the effect of process parameters on the material flow behavior in FBRE, and the results of which were verified experimentally. It is found that the friction between the die components namely punches and dies, and sample has a significant effect on the material flow in FBRE. The strain heterogeneity index, SHI, was defined for quantitative analysis of frictional effect on plastic deformation. An increase in friction factor increases the SHI for both backward and forward sections. But, intense friction confines the extent of strain heterogeneity in backward section, while it has an opposite effect for that of forward section. Besides, the minimization of friction in the FBRE process reduces the required punch force significantly. As the gap thickness increases, the area in the vicinity of lower punch accumulates more plastic strain in comparison to that of the upper punch. Hence, more uniform deformation is achieved with smaller gap thickness. The presented FE model can be used to predict the plastic deformation behavior within the process parameters which in turn can dictate the mechanical properties of the FBRE process products.
4.2. Effect of gap thickness in punch force and equivalent plastic strain in FBRE process Another geometrical parameter that was considered to influence the material deformation behavior in FBRE is gap thickness. The effect of gap thickness on the accumulated effective plastic strain in center section is shown in Fig. 11. During the FBRE, similar to conventional extrusion, the punch force increases significantly with punch stroke at the start of the process while after certain punch stroke, the required extrusion force reaches a steady state. As can be seen from Fig. 11, regardless of the gap thickness, the location of this transition in punch force is somehow constant which occurs at point of about 8 mm of punch stroke. Besides, as the gap thickness decreases the punch force increase, which is due to the restriction of the material flow into the gap between the upper and lower dies. Reasonable agreement between the simulations results and the experimental data confirms the validity of the finite element model and the accuracy of the simulation results. The proposed grid size in the axisymmetric model gave a convergent and stable solution while minimizing the computational cost. To solve the problem, the punch displacement is typically divided into a large number of infinitesimal time steps each corresponding to a small stroke increment. An incremental displacement field solution was obtained for each time step while the total strain corresponding at a given time was calculated by integrating the strain rate along the
References [1] B.D. Ko, et al., J. Mater. Process. Technol. 113 (1–3) (2001) 109–114. [2] Y. Çan, T. Altınbalık, H.E. Akata, J. Mater. Process. Technol. 166 (1) (2005) 128–134. [3] Y. Can, C. Misirli, Mater. Des. 29 (4) (2008) 829–838. [4] H.-J. Choi, J.-H. Choi, B.-B. Hwang, J. Mater. Process. Technol. 113 (1–3) (2001) 141–147. [5] H.Y. Cho, et al., J. Mater. Process. Technol. 135 (2–3) (2003) 375–381. [6] Y.S. Lee, et al., J. Mater. Process. Technol. 113 (1–3) (2001) 136–140. [7] R. Ebrahimi, M. Reihanian, M.M. Moshksar, Mater. Des. 29 (9) (2008) 1694–1700. [8] A. Buschhausen, et al., J. Mater. Process. Technol. 33 (1–2) (1992) 95–108. [9] D.Y. Yang, K.J. Kim, J. Mater. Process. Technol. 191 (1–3) (2007) 2–6. [10] H.S. Kim, M.H. Seo, S.I. Hong, J. Mater. Process. Technol. 113 (1–3) (2001)
6
Progress in Natural Science: Materials International (xxxx) xxxx–xxxx
A. Farhoumand, R. Ebrahimi [15] [16] [17] [18] [19] [20]
622–626. [11] H. Darendeliler, T. Altan, J. Mater. Process. Technol. 58 (2–3) (1996) 293–301. [12] A. Farhoumand, S. Khoddam, P. Hodgson, Model. Simul. Mater. Sci. Eng. 20 (8) (2012) 085005. [13] A. Farhoumand, P.D. Hodgson, S. Khoddam, 48 (6) (2013) 2454–2461. [14] V. Shatermashhadi, et al., Mater. Des. 62 (0) (2014) 361–366.
7
M. Ebrahimi, F. Djavanroodi, Prog. Nat. Sci.: Mater. Int. 24 (1) (2014) 68–74. A. Babaei, M.M. Mashhadi, Prog. Nat. Sci.: Mater. Int. 24 (6) (2014) 623–630. A. Farhoumand, R. Ebrahimi, Mater. Des. 30 (6) (2009) 2152–2157. V. Abaqus/Explicit, Dassault Systèmes Inc., USA, 2009. R. Ebrahimi, A. Najafizadeh, J. Mater. Process. Technol. 152 (2) (2004) 136–143. S.H. Molaei, M. Shahbaz, R. Ebrahimi, Iran. J. Mater. Form. 1 (2) (2014) 14–22.