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Numerical and physical modelling of plastic deformation in 2-turn equal channel angular extrusion
Journal of Materials Processing Technology 125–126 (2002) 309–316
Numerical and physical modelling of plastic deformation in 2-turn equal channel angular extrusion A. Rosochowskia,*, L. Olejnikb a
University of Strathclyde, Glasgow, UK Warsaw University of Technology, Warsaw, Poland
b
Received 6 December 2001; accepted 24 January 2002
Abstract A new process of 2-turn equal channel angular extrusion (ECAE) was simulated by finite element method with a view to providing an insight into the mechanics of the process. The stress results obtained gave indication of expected forces and tool contact stresses. Plastic flow sensitivity analysis, with respect to geometrical features of the die, enabled process and tool design guidelines to be formulated. Two methods of increasing productivity of 2-turn ECAE were presented and simulated using finite element method. Physical modelling experiments with wax billets validated the results of numerical simulation and also gave indication of possible problems with the real process. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Equal channel angular extrusion; Finite element modelling; Physical modelling; Simulation of metal forming
1. Introduction Development in materials can be achieved by either introducing new materials, which is often problematic and expensive, or improving existing materials. Recently, the latter method has been extensively used to improve mechanical and processing properties of metals by reducing their grain size. Very small (including sub-micron) grains can be produced by a number of non-conventional methods such as rapid solidification, powder metallurgy and vapour condensation. However, most of these methods are only used for the production of very small quantities of material, often of unusual compositions. A new group of methods, which enable the realization of the benefits of small grains on a big scale, is based on large strain deformation of bulk metal. These methods are universal in terms of the metallurgical systems they can be applied to (e.g. fcc aluminium, bcc iron and hexagonal magnesium). Obtaining large plastic deformation is a difficult task since it is limited by strain localization and ductile fracture in normal metal forming processes. Therefore, special processes are used which enable severe or unlimited plastic deformation to be achieved without changing the shape of the billet. Currently, there are three such processes. * Corresponding author. E-mail address: [email protected] (A. Rosochowski).
The first one is based on the combination of torsion and hydrostatic compression (TC) and was inspired by the work of Bridgeman in the early 1950s [1]. Due to the strain gradient in the sample and technical difficulties associated with the high pressure required, this technique cannot be readily scaled up and is therefore most suitable for smallscale laboratory investigations. In the late 1970s, J. Richert, M. Richert, Zasadzinski and Korbel, introduced a process, known as cyclic extrusion compression (CEC) [2]. It involves the cyclic flow of metal between the alternating extrusion and compression chambers. This process seems to be better suited for industrial applications, but has only been used in laboratory trials. The third process, called equal channel angular extrusion (ECAE) or equal channel angular pressing (ECAP), was invented by Segal [3] roughly at the same time as the previous one. ECAE is based on simple shear taking place in a thin layer at the crossing plane of the channels. The billet is then released from the die, rotated by a certain angle about its axis and the operation is repeated (Fig. 1). After several such cycles one can obtain large deformation and a fine grain structure. ECAE is most popular of the three methods.
2. Problem Over the last two decades, TC, CEC and ECAE have been used to produce laboratory specimens with a view to
0924-0136/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 3 3 9 - 4
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Fig. 1. A typical sequence of ECAE.
providing adequate description and interpretation of the structural changes observed. Although this is still a valid research subject, the evidence gathered is strong enough to justify industrial applications. From the three processes available, ECAE seems to be the closest to industrial implementation. However, ECAE realized according to the sequence illustrated in Fig. 1, is cumbersome and inefficient. In this form, it is hardly a process to be accepted by industry. Therefore, there is a need for a more efficient and industrially friendly solution. Some recent research is directed to more practical aspects of ECAE. For example, Utsunomiya et al. [4] introduced continuous ECAE, in which the billet is fed into a die by rolls. Nishida et al. [5] invented a rotating die, which enables large plastic deformation to be consecutively applied to a billet without reintroducing it into the die. Liu et al. [6] were probably the first to use 2-turn ECAE (Fig. 2). This idea was developed further by Nakashima et al. [7], who added more turns to the channel in order to achieve larger strain in one pass. The above alterations to the original ECAE improve the chance of successful industrial applications. However, there are still no guidelines for process and tool design for ECAE. The research presented in this paper addresses this problem by simulating and analysing the mechanics of 2-turn ECAE, illustrated schematically in Fig. 2. The simulation techniques used are finite element analysis (FEM) and physical modelling (PM).
Fig. 3. FEM model.
ECAE. The tools were assumed to be rigid. Fig. 3 shows the geometry of the tools and the initial position of the billet. The die channel had a square cross-section of 8 8 mm2. The length of the input segment of the channel was set to fit a billet 7 units long (1 unit ¼ 8 mm) and the output segment was 5 units long. These segments were offset by 2 units by connecting them with a middle, horizontal segment. The inner and the outer corners of the channel bends were rounded with 1.5 and 1.0 mm radius, respectively. The billet was divided into about 900 plane-strain, bilinear, quadrilateral elements with reduced integration. Despite large strains in the process, no re-meshing was attempted so the material flow was easier to observe and interpret. The material used in the simulation was commercially pure aluminium. It was modelled as an elastic–plastic, isotropic, Huber/Mises material with a strain-hardening curve described by
3. FEM simulation
s ¼ 159ð0:02 þ eÞ0:27 MPa
3.1. FEM model
Friction was assumed to follow Coulomb’s law with friction coefficient m ¼ 0:05. The process velocity was increased to 1 m/s to reduce the computation time.
A commercial FEM program Abaqus/Explicit was used to simulate the elastic/plastic flow of the material in 2-turn
3.2. FEM results
Fig. 2. A 2-turn ECAE.
Fig. 4 presents the simulation results in terms of mesh deformation and equivalent plastic strain. The displayed area is limited to the middle segment and the adjacent sections of the input and output segments of the channel. The second snapshot (Fig. 4(b)) refers to the initial stage of the process, when the material is sheared only across the first bend of the die. Features characteristic for classical ECAE can be observed here, such as unfilled inner corner of the die and undeformed end of the billet. When the material reaches the second bend of the die (Fig. 4(c)), the gap in the
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Fig. 4. Evolution of billet mesh and equivalent plastic strain in 2-turn ECAE.
first bend closes. The inner corner of the second bend becomes filled soon after that (Fig. 4(d)). However, the end effect remains in place. Looking at the mesh in the output segment it is difficult to distinguish between the undeformed end of the billet and the material which is sheared at the second bend. This is because this shearing reverses mesh distortion which occurred at the first bend (the second turn of the billet is equivalent to a 1808 rotation of the billet about its axis between two passes in classical ECAE). The extension of the end effect can be better assessed by the contours of plastic strain. These contours also show strain variation in the direction normal to the billet axis. The strain variation can be seen, for example, along Section 1 going across the middle segment of the die and Section 2 crossing the output segment (Fig. 4(e)). Plastic strain for these sections is shown in Fig. 5. Following Section 1, plastic strain produced by shearing at the first bend of the die is smaller at the ‘‘0’’ end of the section. This is followed by a peak of strain and a strain plateau which extends to the ‘‘8’’ end of the section. The average strain along the plateau is about 1.15. The distribution of plastic strain in Section 2 becomes more symmetrical after the material passes the second bend. Now, both sides of the billet exhibit smaller strain. The average strain along the plateau reaches the value of about 2.3.
As far as the forming force and tool stresses are concerned, classical ECAE is not a demanding process. However, due to the doubled plastic strain and also strain hardening, the forming force in 2-turn ECAE is more than twice of that in a 1-turn process. This is illustrated in Fig. 6, where after the first turn of the billet the maximum forming
Fig. 5. Strain distribution across the billet.
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Fig. 8. Distribution of equivalent stress.
Fig. 6. History of the forming force in 2-turn ECAE.
force is 16 kN, while after the second turn it reaches 37 kN. Fig. 7 displays the distribution of tool contact stress which results from the maximum forming force in the process. The punch and the input segment of the channel are subjected to the contact stress approaching 600 MPa. Stress distribution in the input segment is relatively uniform. The maximum contact stress for the upper wall of the middle segment and
the whole output segment does not exceed 300 MPa. This suggests that 2-turn ECAE can still be treated as a low tool pressure process compared to, for example, extrusion. However, this could change for harder materials, materials undergoing intensive strain hardening as well as for less favourable friction conditions. In addition to higher mean stress, 2-turn ECAE has different distribution of equivalent stress (Fig. 8). What in classical ECAE is split into two passes of the billet, in 2-turn ECAE takes place in one process. Thus, in 2-turn ECAE, after primary yielding at the first bend, the material undergoes unloading in the middle segment of the channel and finally yields again at the second bend. This secondary yielding takes place on the opposite side of the yield surface compared to primary yielding. What happens here is qualitatively similar to secondary yielding in CEC [8] or in close-die calibration [9]. It seems that this kind of process reversal may result in a more complex change of the yield surface than just isotropic expansion. This could be a possible explanation of the saturation of the yield stress observed after several passes of classical ECAE or several cycles of CEC [10]. 3.3. Parameter analysis
Fig. 7. Distribution of tool contact stress, for the maximum forming force.
In order to gain better understanding of 2-turn ECAE, as well as formulate design guidelines for tooling, two geometrical parameters of the channel were tested; they were the radius of inner corners and the length of middle segment. Like in the original model, introduced in previous sections, the radius of outer corners was 1 mm. The radius of inner corners was changed from the original value of 1.5– to 1– and then to 2 mm. Fig. 9 presents the results of mesh deformation for roughly the same instant of the process, and strain distribution along Section 1 at that instant, for all three radii of the inner corners. While the deformed meshes for 1.5 and 2 mm case look similar, the deformation pattern for 1 mm case reveals strain concentration along the bottom side of the middle segment (mesh density for this case was increased). This is confirmed by the curves of strain distribution along Section 1 where the maximum equivalent plastic strain for 1 mm radius is about 30% higher than for
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Fig. 10. Distribution of equivalent plastic strain for three offset lengths and a counter-punch. Fig. 9. Strain distribution across the billet for different radii of the inner corner of the channel.
1.5 mm radius. The peak strain for 1 mm radius is nearly twice as high as the strain plateau, which is roughly the same for all the three cases. The strain concentration described above occurs only after the billet takes the second turn, i.e. after the inner corner at the first bend becomes filled with the material. It seems that for a sharper inner corner there is a tendency for the material to stay there instead of flowing with the rest of the billet. For a very sharp corner this might lead to the creation of a dead metal zone and the accompanying layer of extreme shear deformation along that zone. This leads to the conclusion that, in 2-turn ECAE, the inner corners of the channel should be rounded with a radius equal to about 20% of the channel thickness. The radius of the outer corners of the channel could be smaller than that but not too sharp, since this would adversely affect surface finish of the billet and decrease tool life. Taking into account uniform deformation along the horizontal segment of the channel, it seems to be possible to reduce the length of this segment. In order to check how far this reduction could go, the offset distance between the input and output segment was decreased from 2 to 1.5 units and further to 1 unit. Fig. 10 contains strain distribution results for the original offset distance as well as the two new distances. It is clear
that decreasing the offset from 2 to 1.5 changes neither mechanics of plastic flow nor strain distribution. However, this is not the case with the smallest offset of 1 unit. The character of plastic flow becomes dramatically different. Instead of shearing there is a lot of bending. The inner corner, at the second bend of the channel, is entirely unfilled. There is also a small gap below the outer corner of this bend. The maximum strain is localized around this corner. It is obvious that the process with the offset of 1 unit cannot be treated as ECAE, as it no longer contains its characteristic shear planes. At this stage of this research, it was considered whether supporting the billet in the output segment could help. The idea was tested by simulating the process for 1 unit offset with an added counter-punch. It was assumed that the punch was passive and moved back only when the force on it reached 10 kN. The result of this simulation is also shown in Fig. 10. The application of a counter-punch causes the material to fill in the corner of the die, so geometrically the billet seems to be all right. However, a closer look at strain contours reveals the lack of regular, highly concentrated zones of simple shear so characteristic for 2-turn ECAE. Moreover, there is strain localization around the outer corner of the second bend which resembles what happened to the unsupported billet. Taking all this into account, as well as the fact
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that the counter-force adds up to the forming force and increases tool contact stresses, the idea of 1 unit offset and a counter-punch has to be abandoned. Thus, the recommendation is to have the input and output segment of the channel at least 1.5 units apart. The application of a counter-punch in ECAE might be useful in other situations though. These would be the cases of deforming brittle materials, sintered billets or even particulate materials, where high mean stress helps avoid fracture. Since the main punch and the counter-punch are parallel to each other in 2-turn ECAE, it should be possible to carry out the process on a normal press. This is not the case with classical ECAE, where the punches would be perpendicular. 3.4. Productivity problems The equivalent plastic strain produced by one pass of the billet through a 2-bend channel is about 2.3. This might not be enough for desirable structural changes to occur. The solution could be, like in the case of laboratory experiments with classical ECAE, to remove the billet from the die (open a split die?) and to feed it again to the same die. This is obviously not the most efficient procedure. Below, two alternatives to this procedure are analysed, with a view to checking their viability in 2-turn ECAE. The first one is based on removing the processed billet by pushing it out of the channel with another billet. This would create a semi-continuous feeding system for discrete billets transferred from die to die until a required strain is achieved. Fig. 11 shows the case of two billets subjected to 2-turn ECAE. Despite imperfect contact between the billets, they behave as if they were one body. This result can be easier achieved for the billet length exceeding the length of the horizontal segment of the channel, so that the second turn of the first billet creates enough contact pressure between the billets. In classical ECAE the same effect might require the
application of a counter-punch. In addition to increased productivity, semi-continuous feeding reduces end effects, except the first and the last billet in the series. Another possible productivity improvement is based on pushing a single billet forward and backward along the same channel of the die. This cycle could be repeated as many times as necessary to achieve a required strain. Cyclic ECAE cannot deal with end effects so it would be used for longer billets. Kinematically, cyclic ECAE can be compared to CEC. It remains to be seen if this kind of process reversal is less efficient with respect to grain refinement than other deformation sequences (as sometimes claimed). In terms of plastic flow of the material, cyclic ECAE is not expected to create problems (Fig. 12). It is even possible that it will make plastic strain distribution more symmetrical with reference to both billet sides and billet ends.
4. Physical modelling experiments Physical modelling (PM) is a technique used to simulate plastic flow of metal in real metal forming operations. The materials used for PM are usually composed of a mixture of waxes, while the modelling tools are made of plastic or aluminium. Although PM can be used to measure forces, strains and calculate stresses, in this research, it was employed just for visualization purposes as a complementary tool to FEM simulation. The experimental rig used enabled plane-strain conditions to be realized. The experimental procedure involved putting a wax billet with a printed mesh into an aluminium die, covering it with a glass plate and pushing it by an aluminium punch driven by an electric motor and a gearbox. A similar driver unit was used to push the wax back in cyclic experiments. Since the wax material used was not intended to represent any particular metal, its composition and properties were not addressed in this experiment.
Fig. 11. Distribution of equivalent plastic strain in 2-turn ECAE of two billets.
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Fig. 12. Evolution of billet mesh and equivalent plastic strain in 2-turn cyclic ECAE.
There were some practical problems encountered in the experiment which resulted from large plastic deformation and a large relative movement of the material with reference to the die. For example, the wax taken directly from the fridge appeared to be too brittle and the one heated to the room temperature had a tendency to stick to the die. A remedy was generous lubrication with vaseline. Unfortunately, this led to some lubricant becoming entrapped in the corners of the die. This caused the actual increase of the corners’ radii, with the corner in the second bend being more affected. Despite the difficulties, some reasonably good runs were obtained. For example, Fig. 13 illustrates a cyclic process where the snapshots (a)–(d) refer to the first pass of the billet travelling down the channel while the snapshots (e) and (f) show the billet on its way up. The deformation pattern of the mesh resembles that presented in Fig. 12. This includes end
Fig. 13. PM of 2-turn cyclic ECAE.
effects, shearing zones and the restoration of the mesh after an even number of billet turns. Less successful runs can also be useful because they may indicate possible problems with the real process. Fig. 14 contains three such examples, incidentally obtained for billets with different meshes. Fig. 14(a) illustrates a fold which develops at the bottom of the billet in the first, upsetting stage of the process. This fold may subsequently be sheared off the main body of the billet and stay in the die corner. Fig. 14(b) shows the case of the die corner well filled, probably due to higher friction. However, the same friction leads to the concentration of shear along the side of the channel adjacent to this corner. In Fig. 14(c), some material
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The analysis of strain distribution has shown that it is not uniform and it depends on geometrical features of the die. In particular: in order to avoid strain concentration along the sides of the middle segment of the channel, the radius of inner corners of the die should not be smaller than about 20% of the channel thickness, and to maintain the character of the process, the minimum offset distance between the input and output segment of the channel should be 1.5 units (where 1 unit equals the channel thickness). Productivity of 2-turn ECAE can be increased by semi-continuous feeding of consecutive billets into a die and, after one pass, transferring them to a next die; the number of dies depends on plastic strain required, and cyclic deformation of the billet in one die by using two reciprocating punches. PM is a bit difficult but useful tool which can be used for the visualization of plastic flow. Applied to 2-turn ECAE, it basically confirmed the results of FEM simulations and also revealed potential problems with the real process.
References Fig. 14. Potential problems revealed by PM.
is stacked in the corner and the rest of the billet is sliding along it. This is, in effect, a dead zone like the one created in hot forward extrusion of aluminium.
5. Conclusions The analysis of the mechanics of plastic flow in 2-turn ECAE. It revealed that after the first turn of the billet, characterizing classical ECAE, the second turn
causes the material to fill in the corners of the die, doubles the plastic strain, more than doubles the forming force, and increases tool contact stresses which however remain relatively low and uniformly distributed.
The observed sequence of primary yielding at the first bend of the die, unloading and secondary yielding at the second bend, allows new interpretation of the mechanics of the process to be considered.
[1] S. Erbel, Mechanical properties and structure of extremely strainhardened copper, Met. Technol. 6 (1979) 482–486. [2] A. Korbel, M. Richert, Formation of shear bands during cyclic deformation of aluminium, Acta Metall. 33 (11) (1985) 1971–1978. [3] V.M. Segal, Materials processing by simple shear, Mater. Sci. Eng. A 197 (1995) 157–164. [4] H. Utsunomiya, Y. Saito, H. Suzuki, T. Sakai, Continuous ECAE (conshearing) process of aluminium strip, in: Proceedings of the Eighth International Conference on Metal Forming, Krakow, September 3–7, 2000, pp. 337–342. [5] Y. Nishida, S. Kume, T. Imai, Large deformation apparatus, the deformation method and the deformed metallic materials, US patent 6,209,379 B1 (April 3, 2001). [6] Z.Y. Liu, G.X. Liang, E.D. Wang, Z.R. Wang, The effect of cumulative large plastic strain on the structure and properties of a Cu–Zn alloy, Mater. Sci. Eng. A 242 (1998) 137–140. [7] K. Nakashima, Z. Horita, M. Nemoto, T.G. Langdon, Development of a multi-pass facility for equal-channel angular pressing to high total strains, Mater. Sci. Eng. A 281 (2000) 82–87. [8] A. Rosochowski, R. Rodiet, P. Lipinski, Finite element simulation of cyclic extrusion compression, in: Proceedings of the Eighth International Conference on Metal Forming, Krakow, September 3– 7, 2000, pp. 253–259. [9] A. Rosochowski, R. Balendra, Secondary yielding of forged components due to unloading, J. Mater. Process. Technol. 115 (2) (2001) 233–239. [10] M. Richert, Changes in structure and properties of metals due to large deformation, Inz. Mater. 2 (1998) 59–70 (in Polish).
Numerical and physical modelling of plastic deformation in 2-turn equal channel angular extrusion A. Rosochowskia,*, L. Olejnikb a
University of Strathclyde, Glasgow, UK Warsaw University of Technology, Warsaw, Poland
b
Received 6 December 2001; accepted 24 January 2002
Abstract A new process of 2-turn equal channel angular extrusion (ECAE) was simulated by finite element method with a view to providing an insight into the mechanics of the process. The stress results obtained gave indication of expected forces and tool contact stresses. Plastic flow sensitivity analysis, with respect to geometrical features of the die, enabled process and tool design guidelines to be formulated. Two methods of increasing productivity of 2-turn ECAE were presented and simulated using finite element method. Physical modelling experiments with wax billets validated the results of numerical simulation and also gave indication of possible problems with the real process. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Equal channel angular extrusion; Finite element modelling; Physical modelling; Simulation of metal forming
1. Introduction Development in materials can be achieved by either introducing new materials, which is often problematic and expensive, or improving existing materials. Recently, the latter method has been extensively used to improve mechanical and processing properties of metals by reducing their grain size. Very small (including sub-micron) grains can be produced by a number of non-conventional methods such as rapid solidification, powder metallurgy and vapour condensation. However, most of these methods are only used for the production of very small quantities of material, often of unusual compositions. A new group of methods, which enable the realization of the benefits of small grains on a big scale, is based on large strain deformation of bulk metal. These methods are universal in terms of the metallurgical systems they can be applied to (e.g. fcc aluminium, bcc iron and hexagonal magnesium). Obtaining large plastic deformation is a difficult task since it is limited by strain localization and ductile fracture in normal metal forming processes. Therefore, special processes are used which enable severe or unlimited plastic deformation to be achieved without changing the shape of the billet. Currently, there are three such processes. * Corresponding author. E-mail address: [email protected] (A. Rosochowski).
The first one is based on the combination of torsion and hydrostatic compression (TC) and was inspired by the work of Bridgeman in the early 1950s [1]. Due to the strain gradient in the sample and technical difficulties associated with the high pressure required, this technique cannot be readily scaled up and is therefore most suitable for smallscale laboratory investigations. In the late 1970s, J. Richert, M. Richert, Zasadzinski and Korbel, introduced a process, known as cyclic extrusion compression (CEC) [2]. It involves the cyclic flow of metal between the alternating extrusion and compression chambers. This process seems to be better suited for industrial applications, but has only been used in laboratory trials. The third process, called equal channel angular extrusion (ECAE) or equal channel angular pressing (ECAP), was invented by Segal [3] roughly at the same time as the previous one. ECAE is based on simple shear taking place in a thin layer at the crossing plane of the channels. The billet is then released from the die, rotated by a certain angle about its axis and the operation is repeated (Fig. 1). After several such cycles one can obtain large deformation and a fine grain structure. ECAE is most popular of the three methods.
2. Problem Over the last two decades, TC, CEC and ECAE have been used to produce laboratory specimens with a view to
0924-0136/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 3 3 9 - 4
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Fig. 1. A typical sequence of ECAE.
providing adequate description and interpretation of the structural changes observed. Although this is still a valid research subject, the evidence gathered is strong enough to justify industrial applications. From the three processes available, ECAE seems to be the closest to industrial implementation. However, ECAE realized according to the sequence illustrated in Fig. 1, is cumbersome and inefficient. In this form, it is hardly a process to be accepted by industry. Therefore, there is a need for a more efficient and industrially friendly solution. Some recent research is directed to more practical aspects of ECAE. For example, Utsunomiya et al. [4] introduced continuous ECAE, in which the billet is fed into a die by rolls. Nishida et al. [5] invented a rotating die, which enables large plastic deformation to be consecutively applied to a billet without reintroducing it into the die. Liu et al. [6] were probably the first to use 2-turn ECAE (Fig. 2). This idea was developed further by Nakashima et al. [7], who added more turns to the channel in order to achieve larger strain in one pass. The above alterations to the original ECAE improve the chance of successful industrial applications. However, there are still no guidelines for process and tool design for ECAE. The research presented in this paper addresses this problem by simulating and analysing the mechanics of 2-turn ECAE, illustrated schematically in Fig. 2. The simulation techniques used are finite element analysis (FEM) and physical modelling (PM).
Fig. 3. FEM model.
ECAE. The tools were assumed to be rigid. Fig. 3 shows the geometry of the tools and the initial position of the billet. The die channel had a square cross-section of 8 8 mm2. The length of the input segment of the channel was set to fit a billet 7 units long (1 unit ¼ 8 mm) and the output segment was 5 units long. These segments were offset by 2 units by connecting them with a middle, horizontal segment. The inner and the outer corners of the channel bends were rounded with 1.5 and 1.0 mm radius, respectively. The billet was divided into about 900 plane-strain, bilinear, quadrilateral elements with reduced integration. Despite large strains in the process, no re-meshing was attempted so the material flow was easier to observe and interpret. The material used in the simulation was commercially pure aluminium. It was modelled as an elastic–plastic, isotropic, Huber/Mises material with a strain-hardening curve described by
3. FEM simulation
s ¼ 159ð0:02 þ eÞ0:27 MPa
3.1. FEM model
Friction was assumed to follow Coulomb’s law with friction coefficient m ¼ 0:05. The process velocity was increased to 1 m/s to reduce the computation time.
A commercial FEM program Abaqus/Explicit was used to simulate the elastic/plastic flow of the material in 2-turn
3.2. FEM results
Fig. 2. A 2-turn ECAE.
Fig. 4 presents the simulation results in terms of mesh deformation and equivalent plastic strain. The displayed area is limited to the middle segment and the adjacent sections of the input and output segments of the channel. The second snapshot (Fig. 4(b)) refers to the initial stage of the process, when the material is sheared only across the first bend of the die. Features characteristic for classical ECAE can be observed here, such as unfilled inner corner of the die and undeformed end of the billet. When the material reaches the second bend of the die (Fig. 4(c)), the gap in the
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Fig. 4. Evolution of billet mesh and equivalent plastic strain in 2-turn ECAE.
first bend closes. The inner corner of the second bend becomes filled soon after that (Fig. 4(d)). However, the end effect remains in place. Looking at the mesh in the output segment it is difficult to distinguish between the undeformed end of the billet and the material which is sheared at the second bend. This is because this shearing reverses mesh distortion which occurred at the first bend (the second turn of the billet is equivalent to a 1808 rotation of the billet about its axis between two passes in classical ECAE). The extension of the end effect can be better assessed by the contours of plastic strain. These contours also show strain variation in the direction normal to the billet axis. The strain variation can be seen, for example, along Section 1 going across the middle segment of the die and Section 2 crossing the output segment (Fig. 4(e)). Plastic strain for these sections is shown in Fig. 5. Following Section 1, plastic strain produced by shearing at the first bend of the die is smaller at the ‘‘0’’ end of the section. This is followed by a peak of strain and a strain plateau which extends to the ‘‘8’’ end of the section. The average strain along the plateau is about 1.15. The distribution of plastic strain in Section 2 becomes more symmetrical after the material passes the second bend. Now, both sides of the billet exhibit smaller strain. The average strain along the plateau reaches the value of about 2.3.
As far as the forming force and tool stresses are concerned, classical ECAE is not a demanding process. However, due to the doubled plastic strain and also strain hardening, the forming force in 2-turn ECAE is more than twice of that in a 1-turn process. This is illustrated in Fig. 6, where after the first turn of the billet the maximum forming
Fig. 5. Strain distribution across the billet.
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Fig. 8. Distribution of equivalent stress.
Fig. 6. History of the forming force in 2-turn ECAE.
force is 16 kN, while after the second turn it reaches 37 kN. Fig. 7 displays the distribution of tool contact stress which results from the maximum forming force in the process. The punch and the input segment of the channel are subjected to the contact stress approaching 600 MPa. Stress distribution in the input segment is relatively uniform. The maximum contact stress for the upper wall of the middle segment and
the whole output segment does not exceed 300 MPa. This suggests that 2-turn ECAE can still be treated as a low tool pressure process compared to, for example, extrusion. However, this could change for harder materials, materials undergoing intensive strain hardening as well as for less favourable friction conditions. In addition to higher mean stress, 2-turn ECAE has different distribution of equivalent stress (Fig. 8). What in classical ECAE is split into two passes of the billet, in 2-turn ECAE takes place in one process. Thus, in 2-turn ECAE, after primary yielding at the first bend, the material undergoes unloading in the middle segment of the channel and finally yields again at the second bend. This secondary yielding takes place on the opposite side of the yield surface compared to primary yielding. What happens here is qualitatively similar to secondary yielding in CEC [8] or in close-die calibration [9]. It seems that this kind of process reversal may result in a more complex change of the yield surface than just isotropic expansion. This could be a possible explanation of the saturation of the yield stress observed after several passes of classical ECAE or several cycles of CEC [10]. 3.3. Parameter analysis
Fig. 7. Distribution of tool contact stress, for the maximum forming force.
In order to gain better understanding of 2-turn ECAE, as well as formulate design guidelines for tooling, two geometrical parameters of the channel were tested; they were the radius of inner corners and the length of middle segment. Like in the original model, introduced in previous sections, the radius of outer corners was 1 mm. The radius of inner corners was changed from the original value of 1.5– to 1– and then to 2 mm. Fig. 9 presents the results of mesh deformation for roughly the same instant of the process, and strain distribution along Section 1 at that instant, for all three radii of the inner corners. While the deformed meshes for 1.5 and 2 mm case look similar, the deformation pattern for 1 mm case reveals strain concentration along the bottom side of the middle segment (mesh density for this case was increased). This is confirmed by the curves of strain distribution along Section 1 where the maximum equivalent plastic strain for 1 mm radius is about 30% higher than for
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Fig. 10. Distribution of equivalent plastic strain for three offset lengths and a counter-punch. Fig. 9. Strain distribution across the billet for different radii of the inner corner of the channel.
1.5 mm radius. The peak strain for 1 mm radius is nearly twice as high as the strain plateau, which is roughly the same for all the three cases. The strain concentration described above occurs only after the billet takes the second turn, i.e. after the inner corner at the first bend becomes filled with the material. It seems that for a sharper inner corner there is a tendency for the material to stay there instead of flowing with the rest of the billet. For a very sharp corner this might lead to the creation of a dead metal zone and the accompanying layer of extreme shear deformation along that zone. This leads to the conclusion that, in 2-turn ECAE, the inner corners of the channel should be rounded with a radius equal to about 20% of the channel thickness. The radius of the outer corners of the channel could be smaller than that but not too sharp, since this would adversely affect surface finish of the billet and decrease tool life. Taking into account uniform deformation along the horizontal segment of the channel, it seems to be possible to reduce the length of this segment. In order to check how far this reduction could go, the offset distance between the input and output segment was decreased from 2 to 1.5 units and further to 1 unit. Fig. 10 contains strain distribution results for the original offset distance as well as the two new distances. It is clear
that decreasing the offset from 2 to 1.5 changes neither mechanics of plastic flow nor strain distribution. However, this is not the case with the smallest offset of 1 unit. The character of plastic flow becomes dramatically different. Instead of shearing there is a lot of bending. The inner corner, at the second bend of the channel, is entirely unfilled. There is also a small gap below the outer corner of this bend. The maximum strain is localized around this corner. It is obvious that the process with the offset of 1 unit cannot be treated as ECAE, as it no longer contains its characteristic shear planes. At this stage of this research, it was considered whether supporting the billet in the output segment could help. The idea was tested by simulating the process for 1 unit offset with an added counter-punch. It was assumed that the punch was passive and moved back only when the force on it reached 10 kN. The result of this simulation is also shown in Fig. 10. The application of a counter-punch causes the material to fill in the corner of the die, so geometrically the billet seems to be all right. However, a closer look at strain contours reveals the lack of regular, highly concentrated zones of simple shear so characteristic for 2-turn ECAE. Moreover, there is strain localization around the outer corner of the second bend which resembles what happened to the unsupported billet. Taking all this into account, as well as the fact
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that the counter-force adds up to the forming force and increases tool contact stresses, the idea of 1 unit offset and a counter-punch has to be abandoned. Thus, the recommendation is to have the input and output segment of the channel at least 1.5 units apart. The application of a counter-punch in ECAE might be useful in other situations though. These would be the cases of deforming brittle materials, sintered billets or even particulate materials, where high mean stress helps avoid fracture. Since the main punch and the counter-punch are parallel to each other in 2-turn ECAE, it should be possible to carry out the process on a normal press. This is not the case with classical ECAE, where the punches would be perpendicular. 3.4. Productivity problems The equivalent plastic strain produced by one pass of the billet through a 2-bend channel is about 2.3. This might not be enough for desirable structural changes to occur. The solution could be, like in the case of laboratory experiments with classical ECAE, to remove the billet from the die (open a split die?) and to feed it again to the same die. This is obviously not the most efficient procedure. Below, two alternatives to this procedure are analysed, with a view to checking their viability in 2-turn ECAE. The first one is based on removing the processed billet by pushing it out of the channel with another billet. This would create a semi-continuous feeding system for discrete billets transferred from die to die until a required strain is achieved. Fig. 11 shows the case of two billets subjected to 2-turn ECAE. Despite imperfect contact between the billets, they behave as if they were one body. This result can be easier achieved for the billet length exceeding the length of the horizontal segment of the channel, so that the second turn of the first billet creates enough contact pressure between the billets. In classical ECAE the same effect might require the
application of a counter-punch. In addition to increased productivity, semi-continuous feeding reduces end effects, except the first and the last billet in the series. Another possible productivity improvement is based on pushing a single billet forward and backward along the same channel of the die. This cycle could be repeated as many times as necessary to achieve a required strain. Cyclic ECAE cannot deal with end effects so it would be used for longer billets. Kinematically, cyclic ECAE can be compared to CEC. It remains to be seen if this kind of process reversal is less efficient with respect to grain refinement than other deformation sequences (as sometimes claimed). In terms of plastic flow of the material, cyclic ECAE is not expected to create problems (Fig. 12). It is even possible that it will make plastic strain distribution more symmetrical with reference to both billet sides and billet ends.
4. Physical modelling experiments Physical modelling (PM) is a technique used to simulate plastic flow of metal in real metal forming operations. The materials used for PM are usually composed of a mixture of waxes, while the modelling tools are made of plastic or aluminium. Although PM can be used to measure forces, strains and calculate stresses, in this research, it was employed just for visualization purposes as a complementary tool to FEM simulation. The experimental rig used enabled plane-strain conditions to be realized. The experimental procedure involved putting a wax billet with a printed mesh into an aluminium die, covering it with a glass plate and pushing it by an aluminium punch driven by an electric motor and a gearbox. A similar driver unit was used to push the wax back in cyclic experiments. Since the wax material used was not intended to represent any particular metal, its composition and properties were not addressed in this experiment.
Fig. 11. Distribution of equivalent plastic strain in 2-turn ECAE of two billets.
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Fig. 12. Evolution of billet mesh and equivalent plastic strain in 2-turn cyclic ECAE.
There were some practical problems encountered in the experiment which resulted from large plastic deformation and a large relative movement of the material with reference to the die. For example, the wax taken directly from the fridge appeared to be too brittle and the one heated to the room temperature had a tendency to stick to the die. A remedy was generous lubrication with vaseline. Unfortunately, this led to some lubricant becoming entrapped in the corners of the die. This caused the actual increase of the corners’ radii, with the corner in the second bend being more affected. Despite the difficulties, some reasonably good runs were obtained. For example, Fig. 13 illustrates a cyclic process where the snapshots (a)–(d) refer to the first pass of the billet travelling down the channel while the snapshots (e) and (f) show the billet on its way up. The deformation pattern of the mesh resembles that presented in Fig. 12. This includes end
Fig. 13. PM of 2-turn cyclic ECAE.
effects, shearing zones and the restoration of the mesh after an even number of billet turns. Less successful runs can also be useful because they may indicate possible problems with the real process. Fig. 14 contains three such examples, incidentally obtained for billets with different meshes. Fig. 14(a) illustrates a fold which develops at the bottom of the billet in the first, upsetting stage of the process. This fold may subsequently be sheared off the main body of the billet and stay in the die corner. Fig. 14(b) shows the case of the die corner well filled, probably due to higher friction. However, the same friction leads to the concentration of shear along the side of the channel adjacent to this corner. In Fig. 14(c), some material
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The analysis of strain distribution has shown that it is not uniform and it depends on geometrical features of the die. In particular: in order to avoid strain concentration along the sides of the middle segment of the channel, the radius of inner corners of the die should not be smaller than about 20% of the channel thickness, and to maintain the character of the process, the minimum offset distance between the input and output segment of the channel should be 1.5 units (where 1 unit equals the channel thickness). Productivity of 2-turn ECAE can be increased by semi-continuous feeding of consecutive billets into a die and, after one pass, transferring them to a next die; the number of dies depends on plastic strain required, and cyclic deformation of the billet in one die by using two reciprocating punches. PM is a bit difficult but useful tool which can be used for the visualization of plastic flow. Applied to 2-turn ECAE, it basically confirmed the results of FEM simulations and also revealed potential problems with the real process.
References Fig. 14. Potential problems revealed by PM.
is stacked in the corner and the rest of the billet is sliding along it. This is, in effect, a dead zone like the one created in hot forward extrusion of aluminium.
5. Conclusions The analysis of the mechanics of plastic flow in 2-turn ECAE. It revealed that after the first turn of the billet, characterizing classical ECAE, the second turn
causes the material to fill in the corners of the die, doubles the plastic strain, more than doubles the forming force, and increases tool contact stresses which however remain relatively low and uniformly distributed.
The observed sequence of primary yielding at the first bend of the die, unloading and secondary yielding at the second bend, allows new interpretation of the mechanics of the process to be considered.
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