Analysis of upsetting processes by the finite element method.

Camacho, Ana M. ; Marin, Marta ; Rubio, Eva M. 等

Abstract: In this work, metal forging operations between flat parallel platens are analysed under plane strain conditions. Several parameters are considered in order to observe general trends on forces and contact pressure distributions: the friction between the die-workpiece interface ([mu]), the reduction in height (r) and the shape factor (h/b). A finite element model has been developed for obtaining platen forces and pressure distributions for different values of these parameters. Thus, forces are obtained for three reductions and different values of the friction coefficient, assuming two values of the shape factor. Otherwise, contact pressures are calculated for different values of friction, being constant the reduction and the shape factor. Besides, contact pressure distributions are compared with those obtained by an analytical method: the Slab Method. Results show the influence of the most relevant variables of this compression process on forces and die pressures.

Key words: upsetting process, plane strai, planten forces, contact pressures, Finite Element Method

1. Introduction

Multiple analytical techniques have been developed for studying metal forming processes (Sanchez & Sebastian, 1983; Rubio et al., 2003; 2005). Early methods are based on simple theoretical foundations, where geometrical considerations and stress distributions are only considered (Avitzur, 1968; Slater, 1977; Rowe, 1977; 1979; Johnson & Mellor, 1983; Kalpakjian, 1997). These methods are the Homogeneous Deformation Method (HDM), and the Slab Method (SM), also called Sachs Method (Sachs, 1927; 1928).

In the first 70's, the Finite Element Method (FEM) is established as an indispensable tool in metal forming analysis. This numerical technique allows to define difficult geometries and boundary conditions and also a more realistic material response than with traditional methods (Rowe et al., 1991; Talbert & Avitzur, 1996; Camacho et al., 2005a). In compression of solid billets between parallel flat dies (or upsetting process), the deformation is homogeneous when there is not friction, but with friction the distribution of the compressive stresses is not uniform and the free surface barrels (Figure 1).

[FIGURE 1 OMITTED]

The complexity of non uniform deformation is not only represented by this barreling phenomenon but also by the fact that a part of the initially free surface comes into contact with the platen during compression. This phenomenon is called folding, and it has been studied since years by other authors because divergence problems can occur (Kobayashi et al., 1989; Hartley et al., 1980).

Some preliminary studies have been done using FEM in analysis of compression processes (Camacho et al., 2005b; 2005c; Martin et al., 2006). This paper is one of these previous works: a finite element model has been carried out for analysing upsetting processes under plane strain conditions. Additionally, FEM results are compared with those obtained with Slab Method. Several variables are considered in order to observe general trends: friction ([mu]), reduction (r) and shape factor (h/b). The aim of this work is to evaluate all these factors for a best knowledge of the upsetting process.

2. Methodology

2.1 Geometry of the problem

Rectangular billets of dimensions [2b.sub.i] and [2h.sub.i], width and height respectively, are considered. This billets present double symmetry, and this allows to consider a quarter of the original workpiece in the model in order to simplify the calculations (Figure 2).

[FIGURE 2 OMITTED]

2.2 Numerical method

A finite element model has been developed. For this purpose ABAQUS/Standard has been employed (Hibbitt et al., 2004). It is a general purpose code of implicit methodology. The billet has been meshed by means of the CPE4R element type. It is a continuum, plane strain, linear interpolation and reduced integration element. These properties are highly recommended to problems where large deformations and contact non linearities are involved, as in the present case. Regarding the material, the billet has been modeled with an aluminium alloy, which main mechanical properties are shown in Table 1.

2.3 Analytical method

In order to compare the results obtained by FEM, an analytical method is employed. The Slab Method, also called Sachs Method (Sachs, 1927; 1928), can be applied easily, and provides a good approach in metal forming analysis. For plane strain problems, the analytical expressions of the slab method are as follows (Bargueno & Sebastian, 1986; 1987):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for platen forces (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for exponential contact pressures (2)

p/2k = 1 + 2[mu]/[h.sub.f]([b.sub.f]/2 - x) for lineal contact pressures (3)

2.4 Applications

Platen forces and contact pressure distributions have been obtained for different Coulomb friction values (0 < [mu] < 0,3). Several height to base ratios has been considered: h/b = 1 and h/b = 0,5 for the platen force calculations; and h/b = 2 for contact pressure distributions.

On the other hand, the reduction in height is defined in equation (4):

r (%) = [h.sub.i] - [h.sub.f] / [h.sub.i] x 100 (4)

Three values of the reduction are analysed for evaluating the platen forces: r = 5%, r = 25% and r = 50 %. The forces have been expressed in terms of the dimensionless ratio F/[A.sub.i]S, where Ai is the initial contact area, and S = 2k is the yield stress under plane strain conditions. Contact pressures are represented in an absolute scale.

3. Results and discussion

Figure 3 presents the predicted forces in an adimensional way.

As it is shown, FEM and SM give similar results for small coefficients of friction. The higher the reduction and friction, the higher the energy required, and also the differences encountered between FEM and SM.

It is important to highlight the large influence of the height to base ratio on the platen forces. Thus, platen forces are much higher for h/b = 0,5 than for h/b = 1 (see scale in Figure 3).

[FIGURE 3 OMITTED]

In Figure 4, different profiles of contact pressure have been obtained by both methods. As the friction grows, the differences between them are more significant. Up to [mu] = 0,1, the distribution is horizontal, but a descent trend is observed for friction values higher than [mu] = 0,1. According to FEM results, friction increases the peak of contact pressure distributions at the center of the die.

[FIGURE 3 OMITTED]

Finally, Figure 4 shows the predicted grid distortions at 5, 25 and 50% reduction in height for the friction coefficient [mu] = 0,05. In this figure, stress and strain distributions are represented.

[FIGURE 4 OMITTED]

5. Conclusion

Although some works were developed previously (Sanchez & Sebastian, 1983; Bargueno & Sebastian, 1986), this paper is included in a set of preliminary studies for analysing upsetting processes with the Finite Element Method (Camacho et al., 2005b; 2005c; Martin et al., 2006). The influence of several variables on platen forces and contact pressure distributions has been considered. The height to base ratio is the factor with the highest influence on the platen forces. Thus, the higher the shape factor, the lower the platen forces. Friction has an important influence too. The SM provides good results for forging problems with low friction. However, differences between FEM and SM are higher as friction and reduction increases. On the other hand, friction increases the peak of contact pressure distributions at the center of the die.

In future works other conditions of the forging process will be analyzed. In this sense, the influence of the height to base ratio on variables such as the contact distributions or the platen forces will be studied in a spread way. Also, an strain hardened material could be considered in order to analyse the influence of the material model. It is thought that only having a good knowledge about all these factors it will be possible to improve the efficiency of this process.

This Publication has to be referred as: Camacho, A.M.; Marin, M.; Rubio, E.M. & Sebastian, M.A. (2006). Analysis of Upsetting Processes by the Finite Element Method, Chapter 11 in DAAAM International Scientific Book 2006, B. Katalinic (Ed.), Published by DAAAM International, ISBN 3-901509-47-X, ISSN 1726-9687, Vienna, Austria

DOI: 10.2507/daaam.scibook.2006.11

8. References

Avitzur, B. (1968). Metal Forming: Processes and Analysis, McGraw-Hill, ISBN 007002510X, New York

Bargueno, V. & Sebastian, M.A. (1986). Estudio de la interaccion prensa-proceso en operaciones elementales de recalcado. Anales de Ingenieria Mecanica, 2, 59-63, ISSN-0212-5072

Bargueno, V. & Sebastian, M.A. (1987). Evaluacion de la influencia del rozamiento y del endurecimiento en procesos de forja en frio. Anales de Ingenieria Mecanica, 1, 105-109, ISSN 0212-5072

Camacho, A.M.; Domingo, R.; Rubio, E.M. & Gonzalez, C. (2005a). Analysis of the influence of back-pull in drawing process by the finite element method. Journal of Materials Processing Technology, 164-165, 1167-1174, ISSN 0924-0136

Camacho, A.M.; Marin, M.; Gonzalez, C. & Sebastian, M.A. (2005b). Study of technological parameters in compression processes by FEM, Proceedings of the TCNCAE, pp. 1-4, Convento di San Domenico, October 2005, Lecce

Camacho, A.M.; Marin, M.; Rubio, E.M. & Sebastin, M.A. (2005c). Analysis of forces and contact pressure distributions in forging proceses by the finite element method, Proceedings of the 16th International DAAAM Symposium "Intelligent Manufacturing & Automation: focus on young researchers and scientists", Katalinic,

B. (Ed.), pp. 53-54, ISBN 3-901509-46-1, University of Rijeka, October 2005, Opatija Hartley, P.; Sturgess, C.E.N. & Rowe, G.W. (1980). Influence of friction on the prediction of forces, pressure distributions and properties in upset forging. International Journal of Mechanical Sciences, 22, 743-753, ISSN 0020-7403

Hibbitt, D.; Karlsson, B. & Sorensen, P. (2004). ABAQUS v6.4, User's Manuals, Providence (RI)

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Martin, F.; Camacho, A.M.; Marin, M. & Sevilla, L. (2006). Parametrization of analytical and numerical methods in plane strain forging. Materials Science Forum, In press

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Rowe, G.W. (1979). Elements of metalworking theory, Edward Arnold, ISBN 0 471 96003 9, London

Rowe, G.W.; Sturgess, C.E.N.; Hartley, P. & Pillinger, I. (1991). Finite-element plasticity and metalforming analysis, Cambridge University Press, ISBN 0 521 38362 5, Cambridge

Rubio, E.M.; Camacho, A.M.; Sevilla, L. & Sebasti n, M.A. (2005). Calculation of the forward tension in drawing processes. Journal of Materials Processing Technology, 162-163, 551-557, ISSN 0924-0136

Rubio, E.M.; Sebasti n, M.A. & Sanz, A. (2003). Mechanical solutions for drawing processes under plane strain conditions by the upper-bound. Journal of Materials Processing Technology, 143-144, 539-545, ISSN 0924-0136

Sachs, G. (1927). Beitrag zur Theorie des Ziehvorganges, Zeitschrift fuer Angewandte Mathematik und Mechanik, 7, 235, ISSN 0044-2267

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Authors' data: Assist. Prof. Dr. Camacho A.[na] M., Ph.D. Student Marin M.[arta], M. Prof. Dr. Rubio E[va] M., Prof. Dr. Sebastian M[iguel] A., Universidad Nacional de Educacion a Distancia (UNED), ETS de Ingenieros Industriales; Departamento de Ingenieria de Construccion y Fabricacion, Madrid, Spain, amcamacho@ind.uned.es, soldadura@ind.uned.es, erubio@ind.uned.es, msebastian@ind.uned.es

Table 1. Mechanical properties of the material

E (Pa) v Y(Pa)

2 x [10.sup.11] 0,3 7 x [10.sup.8]