Optimized Design of an ECAP Die Using the Finite Element Method for Obtaining Nanostructured Materials

Patricia Ponce-Peña, Edgar López-Chipres, Edgar García-Sánchez, Miguel Angel Escobedo-Bretado, Brenda Xiomara Ochoa-Salazar, and María Azucena González-Lozano 1Departamento de Ciencia de Materiales, Facultad de Ciencias Quı́micas, UJED, Avenida Veterinaria S/N, Circuito Universitario, 34120 Durango, DGO, Mexico 2Facultad de Ingenieŕıa Mecánica y Eléctrica, Universidad Autónoma de Nuevo León, Avenida Universidad, S/N, Ciudad Universitaria, 66451 San Nicolás de Los Garza, NL, Mexico 3Departamento de Ingenieŕıa Ambiental, Facultad de Ciencias Forestales, UJED, Rio Papaloapan y Bulevar Durango, 34120 Durango, DGO, Mexico


Introduction
The development of improved properties in nanostructured materials produced by severe plastic deformation (SPD) and the selection of the deformation mechanisms in these materials is a relatively new field of knowledge in recent years, and it has been of great interest to the scientific community, due to the unique and special properties that these materials present.
Research into the production and properties of nanostructured materials in bulk or ultrafine grain (UFG) materials was first initiated in Russia 20 years ago and has continued to the present day [1,2].Out of the processes of nanostructured materials in bulk, the current effective approaches include synthesis of powders, amorphous cast, and severe plastic deformation [3].Within these methods, severe plastic deformation (SPD) is the easiest and lowest cost-benefit structure, consisting of a simple die [3].The SPD processing refers to the metal formation experimental procedures that could be used to impose a very high deformation on the materials for an exceptional refinement of the grain, a unique SPD processing feature, the high deformation imposed without any significant change in the overall dimensions of the workpiece.Another feature is that the shape is retained, when the materials are processed with special geometry tools that prevent their free flow and produce a significant hydrostatic pressure.The presence of this hydrostatic pressure is essential to achieve a high level of deformation and introduce high defect density in the network, required for grain refinement [4].
As one of the most promising SPD techniques, equal channel angular pressing (ECAP), which was developed by Segal et al. (1981) [5], has become a more and more popular method in producing UFG materials.
On the other hand, some researchers studied the deformation behavior of the sample during ECAP by finite element method (FEM) simulation.For example, Semiatin et al. (2000) [6] investigated the effects of material constitutive behavior, tooling design, and friction conditions on metal flow, stress fields, and the tendency for tensile fracture during equal channel angular extrusion, Lapovok (2005) [7] simulated the stress-strain state of aluminum alloy 2024, and Son et al. (2006) [8] investigated the material behavior and strain distribution of the commercially available pure titanium (CP-Ti) specimen.
Although the ECAP technique is of great importance, there are not many works that focus on the design of dies and its analysis by FEM, considering both frictions as die geometry parameters; likewise, only few works have been reported in which the effect of die shape is analyzed, for example, the experiments conducted by pressing the alloy through dies having angles of 90 ∘ , 110 ∘ , and 135 ∘ [9] and the escaped Cu and Al at curved and sharp dies [10], among others.Thus, in order to generate information on the design of dies and to evaluate the advantages and disadvantages of a modified conventional die channel (ECAP) and the processing conditions as well, in this study, finite element simulations of one pass ECAP route for six die configurations and three friction coefficients, which have not been reported previously, have been carried out.

Experimental Development
As can be seen in Figure 1, to conduct the ECAP process simulation, with the help of commercial design software and assisted by a SolidWorks 2008 computer, it is first necessary to define the workpiece geometry, the punch type, and die.
To design and optimize the ECAP conventional die's channel, using finite element method, six different configurations were designed, as shown in Figure 2.
To perform ECAP process simulations, first, analytical commercial software with DEFORM-3D finite element was used.Secondly, a 3D simulation was conducted, and, lastly, an isothermal and adiabatic process with one pass was recorded.The geometry of the set to DEFORM-3D had been drawn previously in SolidWorksTM (see Figure 1) as independent solids which were then exported as triangles in STL format and imported finally in DEFORM-3D.For the ECAP process simulation, it has been found that with the different types of defined mesh the results obtained are similar, and, therefore, it was decided to use the mesh which translates into less computing time as can be seen in Figure 3.
Similarly, various friction coefficients were used ( = 0, 0.05, and 0.1) to study their effect on the deformation behavior of the Al6060 workpiece.The simulations were carried out at room temperature (25 ∘ C).The Von Misses failure criterion was also considered, and the heating of the workpiece due to plastic deformation was not taken into account.To model the alloy (Al6060) mechanical behavior, stress-strain curves were used, which were obtained through a compression test executed at room temperature (see Figure 4).

Results and Discussion
Generally the ECAP die's tensile stress area (see red area, Figure 5) was presented in the simulations with the FEM for the six configurations utilized, at the top of the workpieces in the area known as severe plastic deformation as can be seen in Figure 5.It is well known that the tensile forces increase the fracture and cracking tendency, which can be prevented with processing the materials with the ECAP technique [11].
Likewise, the finite element method analysis in parts processed with the ECAP technique indicated that the stress state changed from tension to compression when the ECAP die's channel configuration four was used, reducing considerably the red zone as shown in Figure 5. Similarly, the shear strain (red zone) focused evenly on the ECAP die corner's diagonal plane for all of the ECAP die configurations studied as can be seen in Figure 6; this result is consistent with the conventional theory for metallic materials processing technique ECAP [4,[11][12][13].
On the other hand, the results, obtained with the finite element method analysis on the deformation distribution in the six configurations of the ECAP die's channel, as a function of the friction coefficients (), used during the ECAP processing after one pass (as can be seen in Figure 6), showed that a very significant influence due to the effect of the friction coefficient is not present, resulting in the presence of red zones with similar magnitudes in the workpieces processed with ECAP.The red areas represent in the simulation with DEFORM-3DTM the areas of highest deformation after one ECAP pass.In Figure 6, you can also see that after an ECAP pass regardless of the coefficient friction () used in the Step 210 Step 210 Step 210 Step 210 Step 205 Step 210 simulation the deformation exhibited throughout the entire workpiece was always heterogeneous regardless of the ECAP die configuration utilized.Similarly, in Figure 7, the distribution level curves of the deformation as a function of the friction coefficient during the ECAP processing after one pass are being displayed for the six configurations of the ECAP die.In these figures, we can visualize the trend to the deformation being better distributed on the long side of the pieces that were deformed with the die 4 configuration regardless of the coefficient friction used.Presenting the best distribution for the die 4 case 11, where the intermediate friction coefficient of 0.05 was used for the simulation, which indicates that the friction must be kept within this range, which will encourage better Step 210

Stress-mean
Die 4,  = 0.05 Step 210 Die 5,  = 0.05 Step 210 Die 6,  = 0.05 Step 207 Die 2,  = 0.05 homogeneous distribution of deformation throughout the workpiece, resulting in a smaller grain size, which directly affects the mechanical properties of the alloy of Al6060.

Conclusions
One ECAP pass was unable to produce homogeneous deformation and nanostructures in the workpiece; although the deformation distribution can be improved by selecting the appropriate processing parameters, it is recommended to perform multiple passes.
The FEM analysis showed that the state of tensile stress was reduced, and the compression state increased when the modified ECAP die was used (die 4).
The presence of a high friction coefficient between the contact surfaces of the workpiece and the ECAP die slightly  increases the deformation homogeneity.However, for practical considerations, heat generation caused by this damage of the surface of the workpiece and wear of the die should be avoided by the use of lubricants.
In the FEM simulation, it was found that the die's geometry has a strong influence on the deformation homogeneity, resulting in a better distribution of the shear deformation on die 4 with a coefficient friction of 0.05, due to the effects of channel geometry used in the ECAP die.

Figure 2 :Figure 3 :Figure 4 :
Figure 2: ECAP die's channel geometry and dimensions of the six configurations used in the simulations.

Figure 5 :
Figure 5: Results of the finite element method simulation showing the tensile stress areas distribution (red area) and compression (blue zone) during the ECAP six configurations of the die's channel processing as a function of the friction coefficient () after one pass.

Figure 6 :
Figure 6: Results of the finite element method analysis of the deformation distribution in the workpieces as a function of the intermediate friction coefficient utilized during the processing with the six-channel configurations of the ECAP die after one pass.

Figure 7 :
Figure 7: Deformation distribution curves level as a function of the friction coefficient during the ECAP processing, after one pass with the ECAP die's six-channel configurations.