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Equal channel angular extrusion deformation mechanism simulation and process parameter optimization

1 introduction

ultra fine grain materials (including submicron materials) have important and broad industrial application prospects, and their preparation technology has an important impact on the application of this material. In recent years, severe plastic deformation (SPD) is one of the important methods to prepare ultra-fine grain materials. It includes equal channel angular pressing (ECAP), high press torsion ARB, cumulative rolling bonding ARB, etc. The equal channel angular pressing (ECAP) process proposed by Segal, a scholar of the former Soviet Union, is a process with the most industrialized prospects for preparing block ultrafine grain materials through severe plastic deformation. Compared with other processes, severe plastic deformation has attracted people's attention because its process is not complex and it can produce massive and dense ultra-fine structural materials. Compared with other samples, the strength, hardness and plasticity of the ultra-fine grain block samples prepared by severe plastic deformation are greatly improved in terms of heat dissipation. The equal channel angular extrusion process is shown in Figure 1. Its working principle is that two pipes with equal cross-sectional area intersect at a certain angle, and the metal sample is extruded continuously through two intersecting pipes of the die to obtain sufficient cumulative strain and achieve grain refinement. Due to different channel sections, it is generally divided into square section channels and circular section channels. Equal square channel angular extrusion is a typical plane deformation problem, and equal circular channel angular extrusion is a three-dimensional extrusion deformation problem

the intersection angle of two equal cross-section pipes shown in Figure 1 Φ It is called the mold corner, and the center angle of the arc at the corner Ψ It is called the center angle of the mold, Ψ From 0 ° ~ (180 °- Φ） Between, and Ψ The radius of the center angle of the die in a one-to-one correspondence is r. Because ECAP process mainly relies on the equal effect deformation accumulated by the extrusion to effectively refine its grains, therefore, the die corner Φ、 Center angle Ψ Die geometric parameters such as center angle radius r have an important influence on the grain refinement of extruded parts. Quantitatively understanding and mastering the influence law of die parameters on the internal strain distribution and strain size of extruded parts is very important for effectively determining the extrusion process and making the extruded parts obtain reasonable strain distribution and size, so as to obtain the required grain refinement effect. In order to obtain the optimized geometric parameters of the die, it is usually obtained by experiment or numerical simulation. Experimental research requires a certain amount of cost and a lot of time, and it is difficult to fully grasp the distribution of various fields in the extrusion part and the changes of material flow law in the extrusion process. The special finite element numerical simulation technology can comprehensively grasp the flow law of metal and the size and distribution of field quantity in the whole process of extrusion, and can quickly obtain the influence of die geometric parameters on the field quantity distribution of extruded parts, so as to achieve the purpose of optimizing die parameters

people have carried out some experimental and analytical research on the equal channel angular extrusion process, but have not carried out a detailed and comprehensive numerical simulation analysis. In this paper, the commercial finite element simulation software casform is used to carry out a large number of process simulations for different mold geometric parameters. Through data analysis, the theoretical results that can be used to guide the actual process and mold design are obtained, and the optimal design scheme of mold geometry is given

2 finite element simulation software and mathematical model

channel angular extrusion process to prepare ultra-fine grain materials is mainly to obtain large strain through severe plasticity, and try to ensure that the equivalent strain distribution inside the extrusion is uniform. Japanese scholar ahashi et al. Put forward the theoretical formula for calculating the cumulative equal effect change:

where n represents the number of extrusion, and the cumulative equal effect change ε Follow the mold corner Φ And center angle Ψ Increase and decrease; When Φ Certain and Ψ At 0 °, ε Take the maximum value, when Ψ= 180°- Φ When, ε Take the minimum value; However, the strain obtained by the theoretical formula is different from the strain distribution in the actual deformation process. Due to the uneven deformation distribution of the extrusion, the numerical expression of the deformation process is quite complex, so the finite element simulation can more intuitively and dynamically analyze the whole process of ECAP extrusion deformation

in this paper, the simulation research is carried out for the equal square channel angular extrusion process, so the extrusion process is a plane deformation problem, which is simulated by the commercial finite element software casform-2d/pc. Casform is developed by the mold engineering technology research center of Shandong University and is mainly used for the simulation software of industrial forging, extrusion and other metal forming processes. The shape of the sample is rectangular, and its size is 10mm × 10mm × 80mm, the extrusion material is aluminum (al99, Cu 0.1, si0.15, fe0.5). The extrusion material can be regarded as rigid plastic material, and its stress-strain relationship is, where c=170kg/mm2, n=0.24, the friction factor M is 0.20, and the downward extrusion speed of the punch is 2mm/s

The finite element simulation model of the equal square channel angular extrusion process is shown in Figure 2, in which only two cases of 90 ° and 120 ° die corners are given, and the number of element divisions is 1100. The situation and parameter changes of the whole process simulation are as follows:mold corner Φ Changing from 90 ° to 150 °, every 5 ° is a case, and the radius r of the center angle of the die is taken as 2, 4, 5, 6, 8 and 10mm respectively, a total of 6 cases. Therefore, 78 different combinations of die parameters are simulated in this paper. Therefore, through simulation, we can fully grasp the panorama of equal channel angular extrusion process

3 distribution law of equivalent stress and strain in extrusion process

Figure 3 is the equivalent stress distribution diagram of equal channel angular extrusion process, in which figure 3A shows that the maximum equivalent stress in the deformation area is 141.67mpa when the die corner is 90 °, and the maximum equivalent stress in the deformation area is 127.62mpa when the die corner is 120 °, The equivalent stress at 90 ° of the die corner is about 11% higher than that at 120 ° of the die corner, which indicates that when the corner is 90 °, the deformation resistance of the material increases and the required extrusion force increases significantly. From the contour shown in Figure 3, the deformation is mainly concentrated at the corner of the mold, and the deformation gradient is large

Figure 4 shows the isostrain contour map of the equal channel bend extrusion when the die corner is 90 °. When the material is squeezed through the bend, the strain distribution along the pipe direction of the extrusion is almost uniform, that is, the strain distribution and its size are almost independent of the pipe length. On the cross section of the extrusion, the deformation distribution of the material accounting for about 3/4 of the cross section is relatively uniform, Only the material close to the upper and lower surfaces accounting for about 1/4 of the height of the material section has uneven deformation. The strain distribution on the cross section of the extrusion is shown in Figure 5, and the maximum equivalent effect in the deformation zone becomes 1.116

4 influence of die corner on extrusion process

as shown in Figure 6, the effect change relationship curve between die corner and main deformation area of extrusion is shown, and the figure shows the simulation results of sand rattling from 90 ° to 150 ° of die corner. The main deformation zone is defined as equal effect deformation, which is distributed in the larger and more uniform part of the extrusion, accounting for about 3/4 of the cross-section height of the extrusion. The liquid metal in the terminator in the figure also gives the curve corresponding to equation (1). According to the finite element simulation results, with the corner Φ With the gradual increase of, the equivalent effect obtained by the extrusion decreases gradually, and the equivalent effect obtained by the extrusion decreases from 1.116 at 90 ° to 0.306 at 150 °. The strain distribution obtained by this simulation scheme is quite consistent with the theoretical derivation formula (1). Both methods give the equal effect variation angle of the main deformation zone Φ Change law of

Figure 7 shows the relationship between the mold corner obtained by simulation and the maximum extrusion force. It can be seen that with the mold corner Φ When the angle is 90 °, the maximum extrusion force reaches 15.90kn; When the corner is 120 °, the extrusion force is 9.385kn, almost 1/2 of that when the corner is 90 °; When the corner decreases to 150 °, the extrusion force decreases to 4.507kn. It can be seen that the extrusion force of ECAP process decreases rapidly with the increase of the die corner, that is, the die corner is an important factor affecting the extrusion force

Table 1 shows the values of extrusion force and equivalent strain corresponding to different die corners. It can be seen that if you want to obtain an extruded part with a cumulative strain of 4, it takes about 4 times of extrusion to achieve the required cumulative equivalent strain with a 90 ° die corner, while it takes about 6 ~ 7 times to achieve the equivalent cumulative equivalent strain with a 120 ° die corner. Therefore, when the strength of the mold can meet the requirements, the mold with a corner of 90 ° should be used as far as possible to improve the efficiency of cumulative deformation; For extrusion materials with large deformation resistance, the die strength and equivalent strain should be comprehensively considered, and the ideal choice is the die with a corner of 120 °. Table 1 Effect of die corner on extrusion force and equivalent strain

die corner (°)

90

100

110

120

130

140

150 extrusion force (KN)

15.90

14.84

10.63

9.385

8.185

6.296

4.507 equivalent strain

1.116

1.087

0.809

0.755

0.649

0.420

0.306

5 Influence of die center angle radius on extrusion process

another important process of ECAP die is die center angle radius R. Figure 8 shows the distribution of equivalent strain of the extrusion corresponding to different center angle radius r when the die corner is 90 °. The distribution of equivalent strain in the main deformation area of the extrusion tends to be uniform with the increase of the center angle radius of the die, and the maximum equivalent strain decreases accordingly. Figure 9 shows the influence of different center angle radius on the equivalent strain of the section of the main deformation area of the extrusion when the die corner is 90 ° and 120 °. The value range of the radius r of the center angle of the die is 0 ~ 10mm, and the equivalent strain of the main deformation area of the extrusion decreases with the increase of the radius of the center angle. With the decrease of the radius of the center angle, on the one hand, the whole extrusion gradually tends to be uniform, that is, the variation of the maximum and minimum equivalent effects decreases; On the other hand, the equivalent effect variables obtained in the main deformation zone gradually increase, so the ECAP process design should comprehensively consider or balance the influence of the die center angle radius on the deformation distribution uniformity and strain size of the extrusion

Fig. 10 and FIG. 11 show the distribution law curve of equal effect variation of extrusion cross section corresponding to different center angle radii when the die corner is 90 ° and 120 ° respectively. The curve can be divided into three stages. The first stage represents the upper surface part close to the cross section of the extrusion, which accounts for less section height; The second stage means that the central part of the extrusion occupies about 3/4 of the section; The third stage means that the lower surface of the extrusion cross section accounts for about 1/5 of the cross section. The distribution of curves in the first stage shown in Figure 10 is relatively smooth. When R is 4mm and 6mm, the first and second stages are more than 2mm and 8mm of R. at the same time, it is necessary to collect real-time data on working parameters or tribological characteristic parameters such as friction force, impact force, temperature, load, speed and wear rate in the experiment. The degree of data collection is gentle, and the strain obtained in the main deformation area is large. The equivalent strain drop gradient of curves in the third stage is large, and the deformation distribution is uneven. Therefore, considering the influence of obtaining higher strain and deformation uniformity, when the die corner is 90 °, it is better to choose R between 4mm and 6mm. The curves in the first stage shown in Figure 11 rise slowly. When R is 2mm and 4mm, the transition of the curve in the first and second stages is smooth, especially when R is 2mm and 4mm in the second stage, the curve is smoother than that of R is 6mm and 8mm. The strain value obtained by applying windows98/me/2000/xp operating system platform

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