Analysis of forces and contact pressure distributions in forging processes by the finite element method.

Camacho, A.M. ; Marin, M. ; Rubio, E.M. 等

Abstract: In this work, metal forging operations between flat parallel platens are analysed under plane strain conditions. Different values of height and diameter of the billet are considered. A finite element model has been developed for obtaining platen forces and pressure distributions for different values of the friction coefficient. Also, contact pressure distributions are compared with those obtained by an analytical method. The results show the influence of the boundary conditions on the forces and pressures of the forging process.

Keywords: forging process; plane strain; platen forces; contact pressures; Finite Element Method.

1. INTRODUCTION

Multiple analytical techniques have been developed for studying metal forming processes (Sanchez & Sebastian, 1983; Rowe, 1979). Early methods are based on simple theoretical foundations, where geometrical considerations and stress distributions are only considered. These methods are the Homogeneous Deformation Method (HDM), and the Slab Method (SM), also called Sachs Method (Sachs, 1928).

In the first 70's, the Finite Element Method (FEM) was established as an indispensable tool for metal forming analysis. This numerical technique allows to define difficult geometries and boundary conditions and although a more realistic material response than with traditional methods (Rowe et al., 1991; Talbert & Avitzur, 1996). In this work, a finite element model has been carried out for analysing the compression of a billet under plane strain conditions. Additionally, the results are compared with the Slab method to validate the numerical model. In compression of solid billets between parallel flat dies, 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). 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 because divergence problems can occur (Kobayashi et al., 1989; Hartley et al., 1980). The mode of deformation is also influenced by the billet geometry, measured by the height to base ratio. The aim of this work is to evaluate all these phenomenon for a best knowledge of the forging process.

[FIGURE 1 OMITTED]

2. ANALYSIS PROCEDURE

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

In order to compare the results obtained by FEM, an analytical method is employed. The Slab Method (also called Sachs Method) 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):

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

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

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

3. RESULTS AND DISCUSSION

Figure 2 presents the predicted forces in an adimensional way. As it is shown, FEM and SM give similar results for small friction. The higher the reduction and friction, the higher the energy required, mainly for r = 50%. It is important to highlight the large influence of the height to base ratio on the platen forces. In Figure 3, 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 contact pressure distributions.

[FIGURE 2 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.

4. CONCLUSIONS

Although some works were developed previously (Sanchez & Sebastian, 1983; Bargueno & Sebastian, 1986), this is a first study for analysing the forging process with the Finite Element Method. Platen forces and contact pressure distributions have been analyzed by this numerical method.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The height to base ratio is the factor with the highest influence on the platen force, although the friction has an important influence too. The SM provides good results for forging problems with low friction. The lower the reduction, the best the obtained result. 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. It is thought that only having a good knowledge about all these factors it will be possible to improve the efficiency of this process.

5. REFERENCES

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

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, (June 1980) (743-753), ISSN 0020-7403

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

Kobayashi, S.; Oh S.-I. & Altan, T. (1989). Metal Forming and the finite-element method, Oxford University Press, ISBN 0-19-504402-9, New York

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

Sachs, G. (1928). Plasticity problems in metals, Transactions of the Faraday Society, 24, (1928) (84-92), ISSN 0014-7672

Sanchez, A.M. & Sebastian, M.A. (1983). Metodos analiticos en deformacion metalica. Desarrollo historico y actual, Deformacion Metalica, 90-91, (1983) (29-37), ISSN 0210-685X

Talbert, S.H. & Avitzur, B. (1996). Elementary mechanics of plastic flow in metal forming, John Wiley & Sons, ISBN 0 471 96003 9, Chichester

Table 1. Mechanical properties of the material.

E (Pa) [upsilon] Y (Pa)
2 x [10.sup.11] 0,3 7 x [10.sup.8]