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Experimental study and FEM analysis of redundant strains in flow forming of tubes
Journal of Materials Processing Technology 210 (2010) 389–395
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Experimental study and FEM analysis of redundant strains in flow forming of tubes M.S. Mohebbi, A. Akbarzadeh ∗ School of Materials Science and Engineering, Sharif University of Technology Azadi Ave., P.O. Box 11155-9466, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 2 May 2009 Received in revised form 30 September 2009 Accepted 30 September 2009
Keywords: Flow forming Tube spinning Incremental forming FEM analysis Redundant strains
a b s t r a c t Flow forming, as a kind of metal spinning processes, is mainly used to produce thin-walled high-precision tubular components. In this study a coupled set of experiments and numerical simulations using the commercial finite element code ABAQUS/Explicit was used to study the evolution of redundant strains in a single-roller flow forming process in one pass. The modified embedded pins were used to evaluate the shear strains. It is shown that high shear strains occur not only at the longitudinal but also at the cross section. Sketched longitudinal lines also show that εz of the cylindrical coordinate system cannot be neglected. Beside of the shear strains, reversal straining is recognized as another type of redundant work. It is shown that this type of redundant strain results from the incremental nature of flow forming process in which the deformation is highly localized. Good agreements between the force measurements of frictionless model simulations with the experiment imply that the frictional work can be neglected in comparison to the redundant work. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Flow forming, as a kind of metal spinning processes, is mainly used to produce thin-walled high-precision tubular components. In this process the thick-walled workpiece rotates with the mandrel while one or more rollers, which revolve about their own axis, move axially along the workpiece axis reduce its thickness. Kobayashi and Thomsen (1962) imply the incremental nature of this process and complexity of this type of deformation. Actually the deformation area is limited to a part of workpiece which is in contact to the roller, so that the deformation is constrained strongly by surrounding metals. This is why the stress and strain have such a complicated distribution in this incremental process. There is always an inhomogeneous material flow due to the local deformation between the roller and the preform surface (Chang et al., 1998). The flow forming process has been already studied by three approaches: theoretical analyses (lower bound, upper bound and slip line field methods), numerical method (FEM analysis) and experimental works. The most considerable analytical analyses were developed by Kobayashi and Thomsen (1962) and Hayama (1966). These analyses evaluate the power and load requirements in the process. While Kobayashi and Thomsen did not verify their calculations, Hayama validated his results with experimental works on aluminum. Anyway, their analytical methods were
∗ Corresponding author. Tel.: +98 21 66165206; fax: +98 21 66005717. E-mail address: [email protected] (A. Akbarzadeh). 0924-0136/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2009.09.028
incapable of considering some complexity of the process especially in case of redundant strain. In fact, Hayama has verified his calculations with experimental measurements assigning all power to the ideal and frictional works and not the redundant strains. Gur and Tirosh (1982) used upper bound method to calculate the power consumption in flow forming process. They considered the velocity field with discontinuities in both cross and longitudinal sections, so accounted only two possible shear strains of three. The total power consumption resulted from their analysis was in good agreement with experimental measurements. In contrast with Hayama (1966), their study implied that the frictional work has a negligible part of power consumption and the redundant strains are the significant parts. Beside of this upper bound analysis, Park et al. (1997) adopted the upper bound stream function method to calculate the required total power and the related tangential force. In their study, the shear strain is only considered in the longitudinal section. Wang et al. (1989) conducted a plane strain model and calculated the forces by slip line field method. As can be seen in the mentioned studies, there are a lot of simplifications in order to analyze this complicated process theoretically. Although those analyses have some successes in estimating the required force and power consumption, they are insufficient in understanding the mechanism and phenomenological aspects of the process. Kemin et al. (1997) have studied the sequence of plastic deformation, residual stresses and diametral growth utilizing an elasto-plastic FEM analysis in the process. Xu et al. (2001) built a rigid-plastic FEM and analyzed the distribution of stress and
390
M.S. Mohebbi, A. Akbarzadeh / Journal of Materials Processing Technology 210 (2010) 389–395
Fig. 1. (a) Schematic illustration of modified pins and (b) prepared workpiece by exerting the pins and sketching the longitudinal lines.
strain rate of the deformation field for forward and backward tube spinning. They classified the deformation area into three regions according to different deformations in the radial, tangential and axial directions. Wong et al. (2004) have reported the use of explicit FE code and demonstrated the influence of mass scaling on dynamic effects which may lead to unreliable simulation results. Hua et al. (2005) used the FEM analysis for three-roller backward tube spinning and studied the differences of strain history between the inner and outer surface elements as well as some phenomena such as the bell-mouth, build-up and diametral growth. Wong et al. (2008) used the FE implicit code to analyze forming a tube from a thick circular plate. Several researchers have conducted experimental works in the flow forming of tubes to evaluate the effects of process variables such as feed rate, attack angle and reduction on quality and soundness of the product. In spite of these studies, there is a little work regarding the redundant strain and its distribution through the thickness of the tube. Kalpakcioglu (1962) used the grid lines inscribed within the tube and clay model test to study the both conical and tubular metal flow in spinning process. His results were not quantitative and also the mechanism and history of shear strain was not studied. The through-thickness distribution of texture and its relation to the distribution of plastic strain have been studied by Brandon et al. (1980). They inserted cylindrical pins into the material prior to tube spinning to study the shear strains by attention to their inclined profile. As the pins inclined in both axial and tangential directions, they could not measure the shear strains and conducted only a qualitative study. Roy et al. (2009) measured the local micro-indentation hardness of a flow formed plate in order to study the distribution of plastic strain across the tube wall thickness. The work presented in this paper is aimed at improving the understanding of local plastic deformation and its evolution during a single-roller flow forming process in one pass. Redundant strains were studied both experimentally and numerically with a more systematic and detailed examination of the mechanisms and phenomenological aspects of the flow forming.
more than one direction of the flow forming process, the cylindrical pin would not stay in a plane. In fact, thickness of the pin would not be uniform at any section (Brandon et al., 1980) and measurement of the shear strains is not possible in that way. This method is modified for flow forming of tubes in the work presented here. To solve this problem, noncylindrical pins in two directions are used. The method is schematically illustrated in Fig. 1. The longitudinal and circumferential pins are used to measure the shear strains in the cross and longitudinal sections respectively. Those pins were prepared from the same directions in the tube and were embedded in the same holes made by machining. The tube was machined after assembling the pins on it to make the surface even and smooth. Moreover, some longitudinal lines were sketched on the surface of the workpiece in order to study the shear strain in the –z plane of the cylindrical coordinate system (Fig. 1). 2.2. Flow forming process In this work, a common lathe was utilized as a flow forming machine (Fig. 2). Dimensions of the tools and workpiece and the process conditions are given in Table 1. A single-roller tool was designed and built to accommodate the lathe tool post. The mandrel was clamped into the chuck of the lathe and the workpiece was fixed by the tail stock. The mandrel-tube interface was lubricated as good as the roller-tube one to minimize the shear stress at contact surfaces. The process was carried out at such a small speed that the heat of deformation and the effect of strain rate can be neglected.
2. Experimental methods 2.1. Study of shear strain distribution Measurement of shear strain distribution across the thickness of flow formed tube was carried out by the embedded pins. Though cylindrical pin has been used successfully in rolling process (Lee et al., 2002), it is not applicable here. Since there is no shear strain in the transverse direction of rolling process, the embedded pin distorts just in the rolling direction and stays in the plane perpendicular to transverse direction. So, it is possible to cut the sheet in the plane including the pin axis. As, there are shear strains in
Fig. 2. Set-up for flow forming experiments on an NC lathe.
M.S. Mohebbi, A. Akbarzadeh / Journal of Materials Processing Technology 210 (2010) 389–395
391
Table 1 Dimensions of tools and workpiece and the process conditions. Parameter
Value
Workpiece Inner diameter (mm) Wall thickness (mm) Initial length (mm)
35 2.5 50
Roller Diameter (mm) Attack angle (◦ ) Smoothing angle (◦ )
54 25 5
Flow forming conditions Feed rate (mm/rev) Reduction (%) Speed of rotation (rpm)
0.1 40 30 Fig. 4. The model used for FEM.
Table 2 Chemical composition of the AA 6063 alloy.
The material used in this study was the extruded AA 6063 alloy with the chemical composition illustrated in Table 2. Workpiece was solution heat treated at 450 ◦ C for 2 h just before the process.
on inertia forces as speeding up the time of simulation (Abaqus Analysis User’s Manual, 2003). In the simulation presented here step time of 10 s and mass scaling factor of 100 were chosen. Mass of the roller supposed to be 10−5 kg, to decrease its revolution effect on the kinetic energy. Fig. 3 shows that the ratio of the kinetic energy to the internal energy is quite negligible, confirming the quasi static response of the explicit method with used step time and mass scaling factor (Wong et al., 2004).
3. Development of FEM model
3.2. Proposed FEM model
3.1. Analysis procedure
The initial model set-up is shown in Fig. 4. All dimensions were similar to the experimental conditions (Table 1) except that the length of the tube was 24 mm. The tube was considered as an elastoplastic model with elastic modulus of 70 GPa and Poisson’s ratio of 0.33. The plastic relation is illustrated in Fig. 5. This curve consists of tension test results of tube material for the strains bellow 0.2 combined with the reported data of a torsion test for the strains over 0.2 (Totik et al., 2004). The roller and the mandrel were modeled as rigid surfaces. As Wong et al. (2004) have suggested, the workpiece and the mandrel were fixed and the roller was chosen to rotate about their axes. By adopting this method, not only the volume can be controlled, but also a significant reduction in computational time can be achieved. The roller appointed to rotate 942 rad (150 revolution) while it is traveling 15 mm in the axial direction to make a feed rate of 0.1 mm/rev. About 20,000 elements were distributed on the tube as illustrated in Fig. 4. As half of the tube did not undertake the
Element
Cu
Zn
Si
Mn
Mg
Fe
wt.%
0.069
0.1
0.34
0.013
0.42
0.1
ABAQUS/Explicit commercial code was used to simulate the flow forming process. It has been mentioned by Wong et al. (2004) that the flow forming process by nature, like other incremental forming processes, is very difficult to model. They have confirmed that the explicit FE code is ideal to tackle some issues in simulating flow forming process; the main drawback has always been the inherent existence of the dynamic effects which has to be controlled by user. Computational cost of the simulation in the explicit procedure can be reduced by either speeding it up compared to the time of actual process or artificially increasing the material density by a factor called mass scaling. If the simulation speed is too much increased, the increased inertia forces will change the predicted response (in an extreme case the problem will exhibit wave propagation response). The only way to avoid this error is to choose a speed-up that is not too large. Mass scaling also has the same effect
Fig. 3. (a) Kinetic energy and (b) internal energy.
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Fig. 5. True stress–true strain curve of the AA 6063 alloy.
deformation, it was meshed with bigger elements. The friction at the roller-tube and mandrel-tube interfaces was assumed to be quite low so all contact areas were modeled as frictionless interfaces. After several FEM analyses on different flow forming models, these conditions were applied to the model in order to cover the realistic conditions of the process at the steady state: • The length of the tube was considered to be more than the axial movement of the roller (length of deformation). The reason for applying this surplus region of tube is that in the incremental deformations like flow forming, materials out of the deformation zone may have some elastic effect on it. This point would be more discussed later. To consider these effects, the length of modeled tube was more than the length of deformation zone. • Internal edge of the end of the tube was constrained in the rdirection to have the role of removed length of the tube. Several simulations showed that the tube would undertake diametral growth by reaching the roller to its end. This phenomenon would be the object of more discussion later. Under the steady state conditions, the diameter of tube would be constrained by material far from the deformation zone. • The head of tube was constrained in the r, and z directions to have the role of the flange (Fig. 4). Although, these constraints do not have the exact effects of the flange, the results of simulation confirm that at a distance from the head of tube, strains and deformation conditions are quite the same, whether using a flange or the mentioned constraint with the advantage of smaller cost of computations for the latter one. It is easy to discern this distance regarding where the steady state conditions start (Fig. 6(a))
Fig. 6. (a) Longitudinal section and (b) cross section of the spun tube; including both the simulation and experimental results.
spinning and extrusion. However, the present results show that the very large shear at the external surface in the tangential direction would have strong effect on textural evolution, as Brandon et al. (1980) predicted. The distribution of equivalent plastic strain through the thickness of spun tube is illustrated in Fig. 7. Although high equivalent strain on the surface could be attributed to the high shear strains (Fig. 6), more detailed analyses are necessary. Fig. 8 demonstrates the evolution of equivalent plastic strain at three elements of the tube thickness. Tiny intervals in recording the results have made it possible to observe the step like nature of the process in these diagrams. The time of deformation for surface element is obviously higher than others. Its plastic deformation starts sooner than the others and keeps going after they stop. These comments are based on the so-called “pile-up” phenomenon. Fig. 9 shows that the material in front of the roller tends to accumulate and make a pile on the surface. In this study it is attempted to analyze this phenomena with more details especially regarding its effect on the redundant work.
By applying these three conditions it is possible to decrease the model size as far as it is close to the real conditions. The stresses and strains of all elements and reaction forces of the roller reference point at the 500 equally time intervals were assigned to be recorded for the postprocessing. 4. Results and discussion The longitudinal and cross sections of the spun tube are shown in Figs. 6(a) and (b), respectively. The flections of the embedded pins show a good agreement between the experimental and simulation results. It is seen that high shear strains exist not only in the longitudinal section but also in the cross section. The very large shear in cross section had already predicted by Brandon et al. (1980). Their textural studies on spun tube did not confirm the previous studies on the process that had concluded similarities between the tube
Fig. 7. Distribution of equivalent plastic strain across the thickness of tube.
M.S. Mohebbi, A. Akbarzadeh / Journal of Materials Processing Technology 210 (2010) 389–395
Fig. 8. Records of equivalent plastic strain versus time for three elements at different distances from the surface.
The piled-up region sweeps all the surface elements. It means that the surface materials should undertake some positive radial strain coming toward the pile-up and some negative radial strain leaving it. This remark is illustrated in Fig. 10. This figure shows the logarithmic radial strain computed from the nodal displacements in the radial direction. It can be deduced from this figure that another type of redundant strain can be distinguished from the common redundant shear strains. This strain is known as the so-called “reversal straining”, which arises and revokes in opposite directions with no contribution to the final deformation. It can be recognized only by the strain history of the material. In fact, the equivalent plastic strain at the surface of spun tube is higher than the other points due to not only its high level of shear but also its reversal straining by pile-up. The results in this study show that other types of reversal straining can occur in the flow forming process. For instance, Fig. 11 illustrates the recorded εz of a mid-thickness element during the process time. This strain is observed as the distortion of longitudinal lines sketched on the surface of workpiece (Fig. 12). It can be seen in this figure that the elements undertake high shear strains entering the deformation zone and returning to a lower level at the end of their deformation, as depicted in Fig. 11. It can be said that when an element is closing to the deformation zone, its front side shears toward the -direction as a result of tangential stress caused by circumferential movement of the roller, while the other side is constrained by non deforming part of the tube. So, the element undergoes a shear strain in the –z plane. When the element is deforming and leaving the deformation zone, its front side leaves the deformation zone and then is constrained by the surrounding materials while the other side is shearing in the -direction by the roller. This shear which imposes a shear strain in the opposite direction with respect to the previous strain, reduces the shear strain in the –z plane resulting in the strain reversal illustrated in Fig. 11.
393
Fig. 10. Evolution of radial strain at a surface element.
Fig. 11. Evolution of εz at a mid-thickness element.
In the present model, no friction is considered. So, frictional work is not taken into account in the force calculations. The comparison depicted in Fig. 13 shows a good agreement between the FEM analysis and experimental results by Hayama (1966) with similar processing conditions to this work. These results imply that the frictional work does not cover a significant portion of the power consumption. This remark had already demonstrated with upper bound analysis by Gur and Tirosh (1982). However, it should be noted here that this conclusion is not generalized for other processing conditions. For instance, in case of low thickness to diameter ratio more frictional work can be expected. It is interesting to note that two types of short and long period serrations are observed in Fig. 13. Short period serrations may result from the numerical calculations and elastic stress waves. Long period serrations, however, result from the distortion of elements at the deformation time. This is illustrated in Fig. 14 which depicts tip of the pile-up. As the roller sweeps the tube, surface of the elements rotate. This rotation changes the area of contact surface between the roller and the tube, so changes the deformation forces. Since the roller sweeps more elements in the tangential
Fig. 9. Pile-up of material at the surface of spinning tube; (a) simulation and (b) experimental results.
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Fig. 12. Distortion in –z plane; (a) simulation and (b) experimental results. Dashed line punctuates one of the distorted longitudinal lines sketched on the surface of workpiece.
Fig. 15. Longitudinal section of a spun tube with elastic modulus of 10 GPa.
Fig. 13. (a) Radial, axial and (b) tangential forces resulted from the FEM analysis and experiments.
direction than the axial one, periods of these serrations in the tangential force diagram are shorter than the radial and axial forces. So far, the redundant strains in the flow forming are classified as two types of shear and reversal straining. Also, it is shown that the effect of pile-up on these redundant strains leads to high equivalent plastic strain on the surface of spun tube. It is interesting now to analyze the phenomenological aspects of the pile-up. In fact, this phenomenon is resulted from the incremental nature of this forming process in which the deformation of material is localized. Flow of the material in this type of deformation is highly constrained by the surrounding regions. This flow can be accommodated by the surrounding regions in four ways: elastic deformation of not deformed part of the tube, pile-up, diametral growth and thickening of the deformed part of tube. Fig. 15 shows the longitudinal section of a supposed spun tube with elastic modulus of 10 GPa. Other conditions of this simulation are similar to what mentioned
Fig. 14. Tip of the pile-up: rotation of the surface of the elements makes the long period serrations in the force diagrams.
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The following conclusions may be drawn by outcomes:
Fig. 16. Longitudinal section of the end of tube.
in Section 3. It can be seen that the lower elastic modulus make the capacity of not deformed materials to accommodate more elastic deformation so that it prevents the pile-up formation. In other words, pile-up occurs when the deformation zone is highly constrained in all directions except r. This comment shows that in the FEM analysis of the flow forming, it is necessary to consider the effect of not deformed materials. That is why a surplus region of tube is considered in the present analysis (Section 3.2). The other way of accommodation of material flow by the materials out of the deformation zone is the diametral growth. As previously mentioned (Section 3), in order to analyze the steady state deformation, it is necessary to consider a constraint in the r-direction at the internal edge of the end of tube. At the end of deformation, however, the steady state condition does not exist. Fig. 16 illustrates the longitudinal section of the end of tube. The surplus region of tube and constraint in the r-direction are not considered in the analyze presented in this figure. It can be seen that materials at the end of tube has a diametral growth instead of pile-up. By passing the roller through this region, its diameter would return to its initial value. It means that this region undertakes the positive and then negative strain in the -direction, a reversal straining that is as effective as the pile-up on redundant work. It should be noted here that diametral growth is not just a type of strain occurring at the end of tube. In fact both diametral growth (Kemin et al., 1997) and thickening of deformed part of the tube (ASM Handbook, 1988), as processes defects, may happen during the process, the analysis of which is not the scope of this paper. 5. Conclusions A coupled set of experiments and finite element simulations were conducted to study the evolution of redundant strains in a single-roller flow forming process.
1. It is observed that high shear strains occur not only at the longitudinal but also at cross section. Also, the existence of εz is shown by the sketched longitudinal lines. 2. Beside of shear strains, reversal straining has a significant role on redundant work of the process. It arises and revokes in opposite directions and do not contribute to the final deformation. 3. The “pile-up” increases the reversal straining on the surface of tube. This phenomenon beside the high shear strains in the surface of tube results in a very high equivalent plastic strain. 4. While frictional work was not considered in the present simulations, the force measurements are in good agreement with the experiment results. This implies that under the conditions of this study, frictional work is negligible in comparison to the redundant work. References Abaqus Analysis User’s Manual, 2003, ABAQUS Inc. Version 6.4. ASM Handbook, 1988. Forming and Forging, vol. 14, 9th ed., pp. 675–679. Brandon, D.G., Ari-gur, P., Bratt, Z., Gur, M., 1980. Texture inhomogeneity and the strain distribution in shear-spun steel tubes. Mater. Sci. Eng. 44 (2), 185–194. Chang, S.C., Huang, C.A., et al., 1998. Tube spinnability of AA 2024 and 7075 aluminum alloys. J. Mater. Process. Technol. 80–81, 676–682. Gur, M., Tirosh, J., 1982. Plastic flow instability under compressive loading during shear spinning process. J. Eng. Ind. 104, 17–22. Hayama, M., 1966. Theoretical Study of tube spinning. Bull. Fac. Eng. 15, 33–48. Hua, F.A., Yang, Y.S., et al., 2005. Three-dimensional finite element analysis of tube spinning. J. Mater. Process. Technol. 168 (1), 68–74. Kalpakcioglu, S., 1962. An experimental study of plastic deformation in power spinning. C.I.R.P. Anna. 10, 58–65. Kemin, X., Zhen, W., Yan, Lu., Kezhi, Li., 1997. Elasto-plastic FEM analysis and experimental study of diametral growth in tube spinning. J. Mater. Process. Technol. 69 (1–3), 172–175. Kobayashi, S., Thomsen, E.G., 1962. Theory of spin forging. C.I.R.P. Anna. 10, 114–123. Lee, S.H., Saito, Y., et al., 2002. Role of shear strain in ultragrain refinement by accumulative roll-bonding (ARB) process. Scripta Mater. 46 (4), 281–285. Park, J.W., Kim, Y.H., Bae, W.B., 1997. Analysis of tube-spinning processes by the upper-bound stream-function method. J. Mater. Process. Technol. 66 (1–3), 195–203. Roy, M.J., Klassen, R.J., Wood, J.T., 2009. Evolution of plastic strain during a flow forming process. J. Mater. Process. Technol. 209, 1018–1025. Totik, Y., Sadeler, R., et al., 2004. The effect of homogenisation treatment on cold deformations of AA 2014 and AA 6063 alloys. J. Mater. Process. Technol. 147, 60–64. Wang, T., Wang, Z.R., et al., 1989. The slip line fields of thickness reduction spinning and the engineering calculation of the spinning forces. In: Proceedings of the fourth International Conference on Rotary Forming, pp. 89–93. Wong, C.C., Danno, A., et al., 2008. Cold rotary forming of thin-wall component from flat-disc blank. J. Mater. Process. Technol. 208, 53–62. Wong, C.C., Dean, T.A., Lin, J., 2004. Incremental forming of solid cylindrical components using flow forming principles. J. Mater. Process. Technol. 153–154, 60–66. Xu, Y., Zhang, S.H., et al., 2001. 3D rigid-plastic FEM numerical simulation on tube spinning. J. Mater. Process. Technol. 113 (1–3), 710–713.
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Experimental study and FEM analysis of redundant strains in flow forming of tubes M.S. Mohebbi, A. Akbarzadeh ∗ School of Materials Science and Engineering, Sharif University of Technology Azadi Ave., P.O. Box 11155-9466, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 2 May 2009 Received in revised form 30 September 2009 Accepted 30 September 2009
Keywords: Flow forming Tube spinning Incremental forming FEM analysis Redundant strains
a b s t r a c t Flow forming, as a kind of metal spinning processes, is mainly used to produce thin-walled high-precision tubular components. In this study a coupled set of experiments and numerical simulations using the commercial finite element code ABAQUS/Explicit was used to study the evolution of redundant strains in a single-roller flow forming process in one pass. The modified embedded pins were used to evaluate the shear strains. It is shown that high shear strains occur not only at the longitudinal but also at the cross section. Sketched longitudinal lines also show that εz of the cylindrical coordinate system cannot be neglected. Beside of the shear strains, reversal straining is recognized as another type of redundant work. It is shown that this type of redundant strain results from the incremental nature of flow forming process in which the deformation is highly localized. Good agreements between the force measurements of frictionless model simulations with the experiment imply that the frictional work can be neglected in comparison to the redundant work. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Flow forming, as a kind of metal spinning processes, is mainly used to produce thin-walled high-precision tubular components. In this process the thick-walled workpiece rotates with the mandrel while one or more rollers, which revolve about their own axis, move axially along the workpiece axis reduce its thickness. Kobayashi and Thomsen (1962) imply the incremental nature of this process and complexity of this type of deformation. Actually the deformation area is limited to a part of workpiece which is in contact to the roller, so that the deformation is constrained strongly by surrounding metals. This is why the stress and strain have such a complicated distribution in this incremental process. There is always an inhomogeneous material flow due to the local deformation between the roller and the preform surface (Chang et al., 1998). The flow forming process has been already studied by three approaches: theoretical analyses (lower bound, upper bound and slip line field methods), numerical method (FEM analysis) and experimental works. The most considerable analytical analyses were developed by Kobayashi and Thomsen (1962) and Hayama (1966). These analyses evaluate the power and load requirements in the process. While Kobayashi and Thomsen did not verify their calculations, Hayama validated his results with experimental works on aluminum. Anyway, their analytical methods were
∗ Corresponding author. Tel.: +98 21 66165206; fax: +98 21 66005717. E-mail address: [email protected] (A. Akbarzadeh). 0924-0136/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2009.09.028
incapable of considering some complexity of the process especially in case of redundant strain. In fact, Hayama has verified his calculations with experimental measurements assigning all power to the ideal and frictional works and not the redundant strains. Gur and Tirosh (1982) used upper bound method to calculate the power consumption in flow forming process. They considered the velocity field with discontinuities in both cross and longitudinal sections, so accounted only two possible shear strains of three. The total power consumption resulted from their analysis was in good agreement with experimental measurements. In contrast with Hayama (1966), their study implied that the frictional work has a negligible part of power consumption and the redundant strains are the significant parts. Beside of this upper bound analysis, Park et al. (1997) adopted the upper bound stream function method to calculate the required total power and the related tangential force. In their study, the shear strain is only considered in the longitudinal section. Wang et al. (1989) conducted a plane strain model and calculated the forces by slip line field method. As can be seen in the mentioned studies, there are a lot of simplifications in order to analyze this complicated process theoretically. Although those analyses have some successes in estimating the required force and power consumption, they are insufficient in understanding the mechanism and phenomenological aspects of the process. Kemin et al. (1997) have studied the sequence of plastic deformation, residual stresses and diametral growth utilizing an elasto-plastic FEM analysis in the process. Xu et al. (2001) built a rigid-plastic FEM and analyzed the distribution of stress and
390
M.S. Mohebbi, A. Akbarzadeh / Journal of Materials Processing Technology 210 (2010) 389–395
Fig. 1. (a) Schematic illustration of modified pins and (b) prepared workpiece by exerting the pins and sketching the longitudinal lines.
strain rate of the deformation field for forward and backward tube spinning. They classified the deformation area into three regions according to different deformations in the radial, tangential and axial directions. Wong et al. (2004) have reported the use of explicit FE code and demonstrated the influence of mass scaling on dynamic effects which may lead to unreliable simulation results. Hua et al. (2005) used the FEM analysis for three-roller backward tube spinning and studied the differences of strain history between the inner and outer surface elements as well as some phenomena such as the bell-mouth, build-up and diametral growth. Wong et al. (2008) used the FE implicit code to analyze forming a tube from a thick circular plate. Several researchers have conducted experimental works in the flow forming of tubes to evaluate the effects of process variables such as feed rate, attack angle and reduction on quality and soundness of the product. In spite of these studies, there is a little work regarding the redundant strain and its distribution through the thickness of the tube. Kalpakcioglu (1962) used the grid lines inscribed within the tube and clay model test to study the both conical and tubular metal flow in spinning process. His results were not quantitative and also the mechanism and history of shear strain was not studied. The through-thickness distribution of texture and its relation to the distribution of plastic strain have been studied by Brandon et al. (1980). They inserted cylindrical pins into the material prior to tube spinning to study the shear strains by attention to their inclined profile. As the pins inclined in both axial and tangential directions, they could not measure the shear strains and conducted only a qualitative study. Roy et al. (2009) measured the local micro-indentation hardness of a flow formed plate in order to study the distribution of plastic strain across the tube wall thickness. The work presented in this paper is aimed at improving the understanding of local plastic deformation and its evolution during a single-roller flow forming process in one pass. Redundant strains were studied both experimentally and numerically with a more systematic and detailed examination of the mechanisms and phenomenological aspects of the flow forming.
more than one direction of the flow forming process, the cylindrical pin would not stay in a plane. In fact, thickness of the pin would not be uniform at any section (Brandon et al., 1980) and measurement of the shear strains is not possible in that way. This method is modified for flow forming of tubes in the work presented here. To solve this problem, noncylindrical pins in two directions are used. The method is schematically illustrated in Fig. 1. The longitudinal and circumferential pins are used to measure the shear strains in the cross and longitudinal sections respectively. Those pins were prepared from the same directions in the tube and were embedded in the same holes made by machining. The tube was machined after assembling the pins on it to make the surface even and smooth. Moreover, some longitudinal lines were sketched on the surface of the workpiece in order to study the shear strain in the –z plane of the cylindrical coordinate system (Fig. 1). 2.2. Flow forming process In this work, a common lathe was utilized as a flow forming machine (Fig. 2). Dimensions of the tools and workpiece and the process conditions are given in Table 1. A single-roller tool was designed and built to accommodate the lathe tool post. The mandrel was clamped into the chuck of the lathe and the workpiece was fixed by the tail stock. The mandrel-tube interface was lubricated as good as the roller-tube one to minimize the shear stress at contact surfaces. The process was carried out at such a small speed that the heat of deformation and the effect of strain rate can be neglected.
2. Experimental methods 2.1. Study of shear strain distribution Measurement of shear strain distribution across the thickness of flow formed tube was carried out by the embedded pins. Though cylindrical pin has been used successfully in rolling process (Lee et al., 2002), it is not applicable here. Since there is no shear strain in the transverse direction of rolling process, the embedded pin distorts just in the rolling direction and stays in the plane perpendicular to transverse direction. So, it is possible to cut the sheet in the plane including the pin axis. As, there are shear strains in
Fig. 2. Set-up for flow forming experiments on an NC lathe.
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Table 1 Dimensions of tools and workpiece and the process conditions. Parameter
Value
Workpiece Inner diameter (mm) Wall thickness (mm) Initial length (mm)
35 2.5 50
Roller Diameter (mm) Attack angle (◦ ) Smoothing angle (◦ )
54 25 5
Flow forming conditions Feed rate (mm/rev) Reduction (%) Speed of rotation (rpm)
0.1 40 30 Fig. 4. The model used for FEM.
Table 2 Chemical composition of the AA 6063 alloy.
The material used in this study was the extruded AA 6063 alloy with the chemical composition illustrated in Table 2. Workpiece was solution heat treated at 450 ◦ C for 2 h just before the process.
on inertia forces as speeding up the time of simulation (Abaqus Analysis User’s Manual, 2003). In the simulation presented here step time of 10 s and mass scaling factor of 100 were chosen. Mass of the roller supposed to be 10−5 kg, to decrease its revolution effect on the kinetic energy. Fig. 3 shows that the ratio of the kinetic energy to the internal energy is quite negligible, confirming the quasi static response of the explicit method with used step time and mass scaling factor (Wong et al., 2004).
3. Development of FEM model
3.2. Proposed FEM model
3.1. Analysis procedure
The initial model set-up is shown in Fig. 4. All dimensions were similar to the experimental conditions (Table 1) except that the length of the tube was 24 mm. The tube was considered as an elastoplastic model with elastic modulus of 70 GPa and Poisson’s ratio of 0.33. The plastic relation is illustrated in Fig. 5. This curve consists of tension test results of tube material for the strains bellow 0.2 combined with the reported data of a torsion test for the strains over 0.2 (Totik et al., 2004). The roller and the mandrel were modeled as rigid surfaces. As Wong et al. (2004) have suggested, the workpiece and the mandrel were fixed and the roller was chosen to rotate about their axes. By adopting this method, not only the volume can be controlled, but also a significant reduction in computational time can be achieved. The roller appointed to rotate 942 rad (150 revolution) while it is traveling 15 mm in the axial direction to make a feed rate of 0.1 mm/rev. About 20,000 elements were distributed on the tube as illustrated in Fig. 4. As half of the tube did not undertake the
Element
Cu
Zn
Si
Mn
Mg
Fe
wt.%
0.069
0.1
0.34
0.013
0.42
0.1
ABAQUS/Explicit commercial code was used to simulate the flow forming process. It has been mentioned by Wong et al. (2004) that the flow forming process by nature, like other incremental forming processes, is very difficult to model. They have confirmed that the explicit FE code is ideal to tackle some issues in simulating flow forming process; the main drawback has always been the inherent existence of the dynamic effects which has to be controlled by user. Computational cost of the simulation in the explicit procedure can be reduced by either speeding it up compared to the time of actual process or artificially increasing the material density by a factor called mass scaling. If the simulation speed is too much increased, the increased inertia forces will change the predicted response (in an extreme case the problem will exhibit wave propagation response). The only way to avoid this error is to choose a speed-up that is not too large. Mass scaling also has the same effect
Fig. 3. (a) Kinetic energy and (b) internal energy.
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Fig. 5. True stress–true strain curve of the AA 6063 alloy.
deformation, it was meshed with bigger elements. The friction at the roller-tube and mandrel-tube interfaces was assumed to be quite low so all contact areas were modeled as frictionless interfaces. After several FEM analyses on different flow forming models, these conditions were applied to the model in order to cover the realistic conditions of the process at the steady state: • The length of the tube was considered to be more than the axial movement of the roller (length of deformation). The reason for applying this surplus region of tube is that in the incremental deformations like flow forming, materials out of the deformation zone may have some elastic effect on it. This point would be more discussed later. To consider these effects, the length of modeled tube was more than the length of deformation zone. • Internal edge of the end of the tube was constrained in the rdirection to have the role of removed length of the tube. Several simulations showed that the tube would undertake diametral growth by reaching the roller to its end. This phenomenon would be the object of more discussion later. Under the steady state conditions, the diameter of tube would be constrained by material far from the deformation zone. • The head of tube was constrained in the r, and z directions to have the role of the flange (Fig. 4). Although, these constraints do not have the exact effects of the flange, the results of simulation confirm that at a distance from the head of tube, strains and deformation conditions are quite the same, whether using a flange or the mentioned constraint with the advantage of smaller cost of computations for the latter one. It is easy to discern this distance regarding where the steady state conditions start (Fig. 6(a))
Fig. 6. (a) Longitudinal section and (b) cross section of the spun tube; including both the simulation and experimental results.
spinning and extrusion. However, the present results show that the very large shear at the external surface in the tangential direction would have strong effect on textural evolution, as Brandon et al. (1980) predicted. The distribution of equivalent plastic strain through the thickness of spun tube is illustrated in Fig. 7. Although high equivalent strain on the surface could be attributed to the high shear strains (Fig. 6), more detailed analyses are necessary. Fig. 8 demonstrates the evolution of equivalent plastic strain at three elements of the tube thickness. Tiny intervals in recording the results have made it possible to observe the step like nature of the process in these diagrams. The time of deformation for surface element is obviously higher than others. Its plastic deformation starts sooner than the others and keeps going after they stop. These comments are based on the so-called “pile-up” phenomenon. Fig. 9 shows that the material in front of the roller tends to accumulate and make a pile on the surface. In this study it is attempted to analyze this phenomena with more details especially regarding its effect on the redundant work.
By applying these three conditions it is possible to decrease the model size as far as it is close to the real conditions. The stresses and strains of all elements and reaction forces of the roller reference point at the 500 equally time intervals were assigned to be recorded for the postprocessing. 4. Results and discussion The longitudinal and cross sections of the spun tube are shown in Figs. 6(a) and (b), respectively. The flections of the embedded pins show a good agreement between the experimental and simulation results. It is seen that high shear strains exist not only in the longitudinal section but also in the cross section. The very large shear in cross section had already predicted by Brandon et al. (1980). Their textural studies on spun tube did not confirm the previous studies on the process that had concluded similarities between the tube
Fig. 7. Distribution of equivalent plastic strain across the thickness of tube.
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Fig. 8. Records of equivalent plastic strain versus time for three elements at different distances from the surface.
The piled-up region sweeps all the surface elements. It means that the surface materials should undertake some positive radial strain coming toward the pile-up and some negative radial strain leaving it. This remark is illustrated in Fig. 10. This figure shows the logarithmic radial strain computed from the nodal displacements in the radial direction. It can be deduced from this figure that another type of redundant strain can be distinguished from the common redundant shear strains. This strain is known as the so-called “reversal straining”, which arises and revokes in opposite directions with no contribution to the final deformation. It can be recognized only by the strain history of the material. In fact, the equivalent plastic strain at the surface of spun tube is higher than the other points due to not only its high level of shear but also its reversal straining by pile-up. The results in this study show that other types of reversal straining can occur in the flow forming process. For instance, Fig. 11 illustrates the recorded εz of a mid-thickness element during the process time. This strain is observed as the distortion of longitudinal lines sketched on the surface of workpiece (Fig. 12). It can be seen in this figure that the elements undertake high shear strains entering the deformation zone and returning to a lower level at the end of their deformation, as depicted in Fig. 11. It can be said that when an element is closing to the deformation zone, its front side shears toward the -direction as a result of tangential stress caused by circumferential movement of the roller, while the other side is constrained by non deforming part of the tube. So, the element undergoes a shear strain in the –z plane. When the element is deforming and leaving the deformation zone, its front side leaves the deformation zone and then is constrained by the surrounding materials while the other side is shearing in the -direction by the roller. This shear which imposes a shear strain in the opposite direction with respect to the previous strain, reduces the shear strain in the –z plane resulting in the strain reversal illustrated in Fig. 11.
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Fig. 10. Evolution of radial strain at a surface element.
Fig. 11. Evolution of εz at a mid-thickness element.
In the present model, no friction is considered. So, frictional work is not taken into account in the force calculations. The comparison depicted in Fig. 13 shows a good agreement between the FEM analysis and experimental results by Hayama (1966) with similar processing conditions to this work. These results imply that the frictional work does not cover a significant portion of the power consumption. This remark had already demonstrated with upper bound analysis by Gur and Tirosh (1982). However, it should be noted here that this conclusion is not generalized for other processing conditions. For instance, in case of low thickness to diameter ratio more frictional work can be expected. It is interesting to note that two types of short and long period serrations are observed in Fig. 13. Short period serrations may result from the numerical calculations and elastic stress waves. Long period serrations, however, result from the distortion of elements at the deformation time. This is illustrated in Fig. 14 which depicts tip of the pile-up. As the roller sweeps the tube, surface of the elements rotate. This rotation changes the area of contact surface between the roller and the tube, so changes the deformation forces. Since the roller sweeps more elements in the tangential
Fig. 9. Pile-up of material at the surface of spinning tube; (a) simulation and (b) experimental results.
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Fig. 12. Distortion in –z plane; (a) simulation and (b) experimental results. Dashed line punctuates one of the distorted longitudinal lines sketched on the surface of workpiece.
Fig. 15. Longitudinal section of a spun tube with elastic modulus of 10 GPa.
Fig. 13. (a) Radial, axial and (b) tangential forces resulted from the FEM analysis and experiments.
direction than the axial one, periods of these serrations in the tangential force diagram are shorter than the radial and axial forces. So far, the redundant strains in the flow forming are classified as two types of shear and reversal straining. Also, it is shown that the effect of pile-up on these redundant strains leads to high equivalent plastic strain on the surface of spun tube. It is interesting now to analyze the phenomenological aspects of the pile-up. In fact, this phenomenon is resulted from the incremental nature of this forming process in which the deformation of material is localized. Flow of the material in this type of deformation is highly constrained by the surrounding regions. This flow can be accommodated by the surrounding regions in four ways: elastic deformation of not deformed part of the tube, pile-up, diametral growth and thickening of the deformed part of tube. Fig. 15 shows the longitudinal section of a supposed spun tube with elastic modulus of 10 GPa. Other conditions of this simulation are similar to what mentioned
Fig. 14. Tip of the pile-up: rotation of the surface of the elements makes the long period serrations in the force diagrams.
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The following conclusions may be drawn by outcomes:
Fig. 16. Longitudinal section of the end of tube.
in Section 3. It can be seen that the lower elastic modulus make the capacity of not deformed materials to accommodate more elastic deformation so that it prevents the pile-up formation. In other words, pile-up occurs when the deformation zone is highly constrained in all directions except r. This comment shows that in the FEM analysis of the flow forming, it is necessary to consider the effect of not deformed materials. That is why a surplus region of tube is considered in the present analysis (Section 3.2). The other way of accommodation of material flow by the materials out of the deformation zone is the diametral growth. As previously mentioned (Section 3), in order to analyze the steady state deformation, it is necessary to consider a constraint in the r-direction at the internal edge of the end of tube. At the end of deformation, however, the steady state condition does not exist. Fig. 16 illustrates the longitudinal section of the end of tube. The surplus region of tube and constraint in the r-direction are not considered in the analyze presented in this figure. It can be seen that materials at the end of tube has a diametral growth instead of pile-up. By passing the roller through this region, its diameter would return to its initial value. It means that this region undertakes the positive and then negative strain in the -direction, a reversal straining that is as effective as the pile-up on redundant work. It should be noted here that diametral growth is not just a type of strain occurring at the end of tube. In fact both diametral growth (Kemin et al., 1997) and thickening of deformed part of the tube (ASM Handbook, 1988), as processes defects, may happen during the process, the analysis of which is not the scope of this paper. 5. Conclusions A coupled set of experiments and finite element simulations were conducted to study the evolution of redundant strains in a single-roller flow forming process.
1. It is observed that high shear strains occur not only at the longitudinal but also at cross section. Also, the existence of εz is shown by the sketched longitudinal lines. 2. Beside of shear strains, reversal straining has a significant role on redundant work of the process. It arises and revokes in opposite directions and do not contribute to the final deformation. 3. The “pile-up” increases the reversal straining on the surface of tube. This phenomenon beside the high shear strains in the surface of tube results in a very high equivalent plastic strain. 4. While frictional work was not considered in the present simulations, the force measurements are in good agreement with the experiment results. This implies that under the conditions of this study, frictional work is negligible in comparison to the redundant work. References Abaqus Analysis User’s Manual, 2003, ABAQUS Inc. Version 6.4. ASM Handbook, 1988. Forming and Forging, vol. 14, 9th ed., pp. 675–679. Brandon, D.G., Ari-gur, P., Bratt, Z., Gur, M., 1980. Texture inhomogeneity and the strain distribution in shear-spun steel tubes. Mater. Sci. Eng. 44 (2), 185–194. Chang, S.C., Huang, C.A., et al., 1998. Tube spinnability of AA 2024 and 7075 aluminum alloys. J. Mater. Process. Technol. 80–81, 676–682. Gur, M., Tirosh, J., 1982. Plastic flow instability under compressive loading during shear spinning process. J. Eng. Ind. 104, 17–22. Hayama, M., 1966. Theoretical Study of tube spinning. Bull. Fac. Eng. 15, 33–48. Hua, F.A., Yang, Y.S., et al., 2005. Three-dimensional finite element analysis of tube spinning. J. Mater. Process. Technol. 168 (1), 68–74. Kalpakcioglu, S., 1962. An experimental study of plastic deformation in power spinning. C.I.R.P. Anna. 10, 58–65. Kemin, X., Zhen, W., Yan, Lu., Kezhi, Li., 1997. Elasto-plastic FEM analysis and experimental study of diametral growth in tube spinning. J. Mater. Process. Technol. 69 (1–3), 172–175. Kobayashi, S., Thomsen, E.G., 1962. Theory of spin forging. C.I.R.P. Anna. 10, 114–123. Lee, S.H., Saito, Y., et al., 2002. Role of shear strain in ultragrain refinement by accumulative roll-bonding (ARB) process. Scripta Mater. 46 (4), 281–285. Park, J.W., Kim, Y.H., Bae, W.B., 1997. Analysis of tube-spinning processes by the upper-bound stream-function method. J. Mater. Process. Technol. 66 (1–3), 195–203. Roy, M.J., Klassen, R.J., Wood, J.T., 2009. Evolution of plastic strain during a flow forming process. J. Mater. Process. Technol. 209, 1018–1025. Totik, Y., Sadeler, R., et al., 2004. The effect of homogenisation treatment on cold deformations of AA 2014 and AA 6063 alloys. J. Mater. Process. Technol. 147, 60–64. Wang, T., Wang, Z.R., et al., 1989. The slip line fields of thickness reduction spinning and the engineering calculation of the spinning forces. In: Proceedings of the fourth International Conference on Rotary Forming, pp. 89–93. Wong, C.C., Danno, A., et al., 2008. Cold rotary forming of thin-wall component from flat-disc blank. J. Mater. Process. Technol. 208, 53–62. Wong, C.C., Dean, T.A., Lin, J., 2004. Incremental forming of solid cylindrical components using flow forming principles. J. Mater. Process. Technol. 153–154, 60–66. Xu, Y., Zhang, S.H., et al., 2001. 3D rigid-plastic FEM numerical simulation on tube spinning. J. Mater. Process. Technol. 113 (1–3), 710–713.