Evaluation of forces in indentation processes considering geometric parameters of the workpiece.

Marin, Marta ; De Agustina, Beatriz ; Camacho, Ana 等

1. INTRODUCTION

Among the different compression processes, indentation was considered because of its similarity to other processes such as forging, that is widely used in the industry field. Usually, indentation processes are used as a method for estimating material hardening (Minh-Quy, 2008), (Kucharski & Mroz, 2007). However, in this work, indentation process will be considered as a manufacturing process (Camacho et al., 2008), (Sebastian & Camacho, 2007).

In conventional compression processes the flow of information is mainly restricted to design and manufacturing (Camacho et al., 2006a); (Camacho et al, 2006b). For this reason, it is important to see how such processes are influenced by the size of the workpiece. Based on the use of dies with simple shapes it is intended to analyze what parameters of the indentation processes can be modified in order to achieve more economic processes (Camacho et al., 2007).

In this work, the dimensions of the punch will remain constant while the dimensions of the billet are changed. The approached problem was studied assuming ideal conditions such as plain strain ones. Different cases were analyzed according to different geometrical values of the workpiece by means of the Finite Element Method (FEM).

2. METHODOLOGY

2.1. Parameters

At first, a rectangular section of the punch is considered, where B is the width. This dimension remains constant throughout the whole study.

Similarly, the workpiece is considered a rectangular billet but its dimensions (w, h, width and height respectively) change throughout the analysis (see Figure 1). These geometrical parameters are chosen as follows:

w = B + 2 x x = B + 2 x n x B = B x (1 + 2 x n) h = x = n x B (2)

The value of the parameter n changes from 1 to 5. From now on the ratio w/h is used in order to quantify the influence of the geometry of the billet and it is called the "shape factor".

[FIGURE 1 OMITTED]

In all the cases, the friction at the punch-workpiece interface is considered null and the reduction in height applied is 5%.

2.2. Cases of Study

In a first approach and according to its previous definition, different shape factors are obtained varying the values of n (Table 1). This will be the first group of cases to be analyzed, and it means a simultaneous increase of both dimensions, the width and the height of the billet.

Afterwards, a second group of geometries of the workpiece were studied. Assuming different values of the height but keeping each one constant, and varying the width of the billet while the parameter n is gradually increased, it is possible to obtain the geometric values of Table 2, where the second group of cases to be analyzed are summed up.

3. FINITE ELEMENT MODEL

This study was completed using the Finite Element Method (FEM). A general purpose software of implicit methodology, ABAQUS/Standard (Hibbit et al., 2007), was used. The puch was designed as a rigid part and the workpiece was modeled as a deformable body. The type of element is CPE4R and consists of a continuous, plain strain, linear interpolation and reduced integration element. The billet was modeled with an aluminum alloy. The type of material was considered as a strain hardened one. A linear behaviour of strain hardening was assumed for the material. Finally, a Coulomb friction model was assumed by the Finite Element Software. As a first approach in this work, a frictionless problem was assumed for all the cases, simulating a well lubricated process.

4. RESULTS

In this work the variable that was analyzed is the required force to develop the indentation processes. As it was explained, this study was divided into two groups of cases. In the first one, forces were obtained for the shape factors given in Table 1, and the results are showed in the figure 2.

[FIGURE 2 OMITTED]

In this figure it can be observed that the greater the shape factor, the greater the forces required to carry out the process, so it means that as the dimensions of the workpiece increase, the necessary energy also increases for the same conditions of the process.

[FIGURE 3 OMITTED]

For the second group of cases, the influence of the width and the height of the billet on the forces were studied (see Table 2). The figure 3 represents the forces that were obtained and the width was represented in the x axis. The analysis was carried out in the same conditions as in the first group of cases.

[FIGURE 4 OMITTED]

This figure shows that the greater both the width and the height, the greater the required force, until a value where forces keep constant and there is not variation with the width. The graph shows that this value is reached when n = 4. This behaviour means that if n [greater than or equal to] 4 forces do not depend on the width, for the conditions of the problem that were analyzed.

An example of the numerical simulation that was developed, is shown in figure 4. In this illustration the case where h = 2B and w = 5B, the mesh of the model and a strain diagram are represented.

5. CONCLUSIONS

This paper studied the influence of geometrical parameters on the forces of an indentation process. In a first analysis, a shape factor was chosen as the geometric parameter, in order to evaluate the influence of a simultaneous variation of both dimensions, height and width. In a second analysis, the dimensions of the workpiece were changed independently. The first conclusion is that the obtained forces increase when the dimensions of the workpiece increase simultaneously. Looking at the influence of each dimension, it is observed that the greater the height, the greater the force, and also the greater the width, the greater the force. But this effect is greater when there is a change in the height. In fact, starting from a value n, force is not affected by the width. Therefore, for each geometry of kind of workpiece this, it would be possible to predict the value of the force starting from that width, if the rest of conditions keep constant. Additionally, taking into account these results the punch may be positioned more efficiently. In future works this indentation process will be analyzed under different conditions. Regarding, the influence of the geometrical parameters on variables such as the contact distributions should be studied. It is thought that having a good knowledge with regard to all these factors it will be possible to improve the efficiency of this process.

6. REFERENCES

Camacho, A.M.; Marin, M.; Sevilla, L. & Sebastian, M.A. (2007). Analysis of axisymmetrical compression processes by the finite element method, Proceedings of the 9th International Conference on Numerical Methods in Industrial Forming Processes, J.M.A. Cesar de Sa; A.D. Santos (Ed.), pp.1011-1016, ISBN 978-0-7354-0416-8, Oporto, June 2007, Portugal.

Camacho, A.M.; Marin, M.; Domingo, R. & Gonzalez, C. (2006a). Analysis of open die flat forging processes in plane strain conditions by FEM, Proceedings of the 17th International DAAAM Symposium "Intelligent Manufacturing & Automation: focus on mechtronics and robotics", Katalinic, B. (Ed.), pp. 75-76, ISBN 3-901509-57-7, Vienna, November, 2006, Austria.

Camacho, A.M.; Marin, M.; Rubio, E.M. & Sebastian, M.A. (2006b). Analysis of upsetting processes by the Finite Element Method, DAAAM International Scientific Book 2006, Katalonic, B. (Ed.), 93-100, Austria, ISBN 3-901509-47-X.

Camacho, A.M.; Vallellano, C.; Sebastian, M.A. & Garcia-Lomas, J. (2008). Analisis mediante el MEF de los efectos de la geometria del extremo del punzon en procesos de forja localizada-incremental. Anales de Ingenieria Mecanica, Vol. 2, pp. 279-285.

Hibbitt, D.; Karlsson, B. & Sorensen, P. (2007), ABAQUS v6.7, User's Manuals, Providence (RI).

Kucharski, S. & Mroz, Z. (2007). Identification of yield stress and plastic hardening parameters from a spherical indentation test. International Journal of Mechanical Sciences, Vol. 49, pp. 1238-1250.

Minh-Quy, L. (2008). A computational study on the instrumented sharp indentations with dual indenters. International Journal of Solids and Structures, Vol. 45, pp. 2818-2835.

Sebastian, M.A. & Camacho, A.M. (2007). Geometrical study and basis for the analysis of localized-incremental forging processes by FEM, Proceedings of the 2nd ICNFT: 2nd International Conference on New Forming Technology, Vollersten, F.; Yuan, S. (Ed.), pp. 295-304, ISBN 978-3933762-22-1, Bremen, September 2007, Germany.

Tab. 1. First group of cases: shape factors for different values
of n

 n

 1 2 3 4 5

w/h 3B/B 5B/2B 7B/3B 9B/4B 11B/5B

Tab. 2. Second group of cases

h = B; 2B; 3B; 4B; 5B

w = 3B; 5B; 7B; 9B; 11B