Table 1. Parameters used in finite element models

a/mm

b/mm

α/deg

β/deg

h/mm

Model1

10

15

15

15

0

Model2

10

15

15

15

2*[(ba)/2]/tanα

Model3

10

15

15

15

[(ba)/2]/tanα

To verify the deformation characters of AGE as discussed in section 2, finite element analysis is proposed in this section. In order to highlight the influence of parameter h, three analysis models with different value for h were established. These three analysis models are named Model1, Model2 and Model3 respectively. Corresponding to the parameters of AGE as illustrated in Figure 1(b), their values used in the three finite element models are listed in Table 1. The first model which named Model1 is symmetry extrusion as the value 0 is used for h. In addition, the other models which named Model2 and Model3 are all asymmetry extrusion. However, a higher value h has been used in Model3 which leads to generating two independent DZs. Distinguish with Model3, the two DZs are interacted in Model2 as a small value is assigned for h.
The commercial finite element software DEFORM was used for simulation. As discussed in section 1, all the simulations are proceed based on plane strain assumption. The punch and die are all set as rigid, and an elasticplastic model is used for workpiece. A material AL1100 was chose for workpiece from the DEFORM material library. Shear friction model with a coefficient 0.12 was used for all the contact surfaces. The punch moves along channel vertical direction with a velocity of 1mm/s, and a room temperature 20oC was assigned for all simulations. Workpieces used in the three analysis modes with the same geometry dimensions and meshes, which are all meshed by mapping method and plane strain elements.
3.2 Characters of the deformation zones
Variation of mesh shape can be regarded as an indirect reflection of deformation characteristics. The results of mesh distortion with the three analysis models in extrusion process are shown in Figure 5. The significant influence of parameter h on the interaction manners of DZs is schematically verified. In Model1, two DZs are formed symmetrically about the vertical center of workpiece. With increasing h, the two DZs are gradually separated on the extrusion direction (Model3). In addition, two independent DZs would be generated as a larger value has been assigned to h (Model2). As these two independent DZs forming, a dead metal zone where materials flow rigidly is generating simultaneously. In terms of the total area of DMs in workpiece, Model2 takes the first place in value. It can be deduced that AGE (Model2) is more efficient in workpiece deformation than other conventional extrusions under one pass.
The results of velocity field in DZs of workpiece for these three analysis models are displayed in Figure 6. As discussed in section 2, due to constancy of volume, materials at die outlet should be of the same velocity as an identical moving condition implied on punches in the three analysis models. Corresponding to the results shown in Figure 5, Model1 which is a conventional symmetric extrusion has the smallest velocity variation area among the three models. Through transforming the symmetrical structure into vertical separation of channel, a larger velocity field can be formed as displayed in Model2 and Model3. However, the Model2 which is an AGE emphasized in this article produces two independent velocity variation areas. It is meaningful that materials can be shaped more smoothly in AGE, and forming defects such as cracks can be largely restrained.
Slip line field in workpiece can be reflected by the simulation results of equivalent strain rate which are displayed in Figure 7. According to the results, a higher strain rate has been generated at the entrance and exit of each deformation zones. With a larger parameter h is assigned, two independent DZs are formed in AGE (Model2). It means that materials would be suffered shear effects with four times in one pass. In other words, more works can be impacted on grains fragment. Through AGE, the efficiency of extrusion on grains refinement has be largely improved. With simulation results of equivalent strain rate, the correctness of slip line field as analyzed and discussed in section 2 has been verified.
3.2 Comparison of extrusion results
The contour plot of equivalent strain distribution in workpiece after extrusion is shown in Figure 8. The results show that for the symmetric extrusion of Model1, the formed equivalent strain field also presents a symmetric distribution. In addition, the equivalent strain field formed by asymmetric extrusion, Model2 and Model3, is larger than that by symmetric extrusion in value. However, Model2 which forms two independent plastic deformation zones, has more uniform distribution of equivalent strain than Model 3.
The results of equivalent stress distribution along the midline OP of workpieces are shown in Figure 9. Corresponding to the characteristics of deformation, the equivalent strain formed by Model1 is symmetrically distributed. The equivalent strain in two asymmetric extrusion, Model2 and Model3, is larger than that in symmetric extrusion with Model1. In addition, the equivalent strain distribution formed by Model 2 is the most uniform, and its equivalent strain fluctuation is less than 0.05. It should be emphasized that for asymmetric extrusion, the extrusion angles of two deformation zones can be independently adjusted to obtain higher and more uniform equivalent strain results.
The statistical results of the equivalent strain in workpieces after extrusion is shown in Figure 10. It can be seen from the results that the equivalent strain distribution of Model2 is the most concentrated. The average values of equivalent strain of the three models are 0.518, 0.638 and 0.607 respectively. All the analysis results show that the asymmetric extrusion with two independent plastic deformation zones, Model2, can form large and uniform equivalent strain in workpiece. Therefore, the advantage of asymmetric extrusion proposed in this paper in the preparation of ultrafinegrained materials has been verified.