Strain Analysis for Different Shape Factors in Indentation Processes

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1 Strain Analysis for Different Shape Factors in Indentation Processes Marta María MARÍN, Beatriz DE AGUSTINA, Ana María CAMACHO, Miguel Ángel SEBASTIÁN Department of Manufacturing Engineering, National Distance University of Spain (UNED) E Madrid, Spain ABSTRACT Nowadays competitiveness is a fundamental requirement for manufacturing processes. Metal forming processes are one important group among them and trends in technology are often emerging. In order to improve conventional technologies in compression processes such us open die forging or even closed die forging, indentation processes are being studied. These processes change mechanical and geometrical properties of the parts, without loss of material similarly to other metal forming operations. However indentation processes present some characteristics that make them especially interesting. Thus, if forging between flat parallel platens and indentation processes are compared, it is observed that forces required to carry out indentation ones are lower. As a result powerless machines can be used to deform the volume of work. Although indentation processes have been traditionally used to determine the hardness of a material, in this work the capability of indentation processes to locally deform a workpiece is studied. A wide variety of parameters such as friction, material properties or the geometry of the piece and the punch can strongly affect to the properties of the final part and to the specific operation conditions during the process. In this case, it has been chosen as a relevant factor the geometry of workpiece by means of the shape factor. The indentation process has been studied assuming ideal conditions consisting of plane strain ones. Friction between the workpiece and the punch has been neglected assuming that a good lubrication has been realized. Different cases have been analyzed by the Finite Element Method, obtaining strain distributions for different values of shape factor. All cases have been solved for a strain hardened material. This work shows that, for the same material and keeping constant the rest of parameters of the process, a change of the geometry can cause different values of the distorted area in the workpiece. The main goal of this study is to determine the area affected by strain considering basically geometrical factors. Keywords: Indentation Process, Plain Strain, Finite Element Method, Shape factor. 1. INTRODUCTION The compression processes are those metal forging operations where plastic deformation of a workpiece occurs by the application of compressive forces [2], [6], [8]. The workpiece suffers a complex stress strains state. This state can often gives negative or positive important consequences in the properties of the workpiece. As a general rule, compressive stresses are beneficial so compression processes are interesting from this point of view. Indentation processes have been widely used as a method for estimating material hardening. The degree of strain hardening of the material depends on the penetration of the punch [9], [10], [13]. In this work, indentation process will be considered as a manufacturing process [3], [12]. Another particularity is that the dimension of the punch will remain constant while the dimensions of the workpiece are changed, opposite to other studies where the geometry of the punch is analyzed [11]. Indentation processes can be used for producing parts of excellent mechanical properties with minimum waste of material. If the indentation process is compared with other compression processes it is observed that the result of the force to carry out each operation is lower. In this sense, it is an interesting advantage because it allows us to choose powerless equipments. The approached problem has been studied assuming ideal conditions such as plain strain ones [1], [4]. Different cases have been analyzed according to different geometrical values of the workpiece. The workpiece is considered as a rectangular billet. This work has been analyzed by the Finite Elements Method (FEM). This numerical technique allows defining complex geometries and boundary conditions and also a more realistic material response. 2. METHODOLOGY Parameters At first, a rectangular geometry of the punch is considered, where B is the width. The problem presents symmetry, therefore a half of the punch is considered (see Figure 1). This dimension remains constant throughout the whole study.

2 hi hf r % 100 (3) hi where h i and h f are the height of the workpiece initial and final respectively. 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. Table 1. Shape factors for different values of n n w/h 3B/B 5B/2B 7B/3B 9B/4B 11B/5B Figure 1. Geometry of punch and billet Similarly, the workpiece is considered a rectangular billet but its dimensions (w, h, width and height respectively) change throughout the analysis. These geometrical parameters are obtained as follows: w = B + 2 x = B + 2 n B =B ( 1+ 2 n) (1) h = x = n B (2) Its width is the width of the punch, B, plus an additional value, 2 x; and the height of the billet is considered equal to this additional value. The value x will always be considered as a multiple of the width of the punch, where n is a variable whose value changes from 1 until 5. The value n is varied in order to solve the different cases. From now on the ratio w/h is used in order to quantify the influence of the geometry of the billet and it will be called the shape factor. As it can be observed in the Figure 1, the problem presents symmetry, and this allows considering a half of the original workpiece and punch in the model in order to simplify the calculations (see Figure 2). Afterwards, several types of geometries of the workpiece have been studied. Keeping the height of the billet constant, and varying the width of the billet while the parameter n is gradually increased it is possible to obtain the geometrical values of Table 2, where the different cases to be analyzed are sum up. Table 2. Cases of study h = B h = 2B h = 3B h = 4B h = 5B Taking into account that in the finite element modeling only a half of the problem is considered, the values corresponding to width and height of the billet are represented as a half in the finite element analysis. 3. FINITE ELEMENT MODEL Material The billet has been modeled with an aluminum alloy. The type of material is considered as a strain hardened one. A linear behaviour of strain hardening is assumed for the material. Common mechanical properties of the material are in Table 3. Table 3. Mechanical properties of the material Figure 2. Symmetry and parameters of the problem analyzed by FEM for n = 1. In the different cases, the friction at the punch-workpiece interface is considered null and the reduction in height applied is 5%, defined as: Elastic Plastic E (Pa) ,33 Y (Pa) , Finite Element Software This study has been done using the Finite Element Method (FEM) [8]. A general purpose software of implicit methodology (ABAQUS/Standard) [5] has been used. The element type of the mesh is CPE4R and consists of a continuous, plain strain, linear interpolation and reduced integration element.

3 Mesh of the billet The size of the elements in the mesh has been chosen proportionally to the height of the billet. Figure 3 shows the mesh of some particular cases, where both height and width increase from one to another. In this work, it has been chosen a workpiece where B is given the value 1. Friction model A Coulomb friction model is assumed by the Finite Element Software. As a first approach, a frictionless problem has been assumed for all the cases, simulating a well lubricated process. 4. RESULTS 3B-B The first variable analyzed is the maximum strain obtained in each particular problem. This value is always reached in the contact area between the edge of the punch and the surface of the piece. Figure 4 presents the maximum strains for the cases whose shape factors are indicated in Table 1. As it is shown, maximum strain is produced when the shape factor is 3, that is, when the height is B. As it is observed the strain decreases when the height increases until reaching the height 3B. In this moment, the strain increases with the height. 5B-2B 7B-3B Figure 4. Maximum strains for different shape factors 9B-4B The maximum strain is produced in the case 3B-B. In Figure 5 strain diagrams are obtained by FEM in this case. Considering this value, a minimum strain has been specified (10% of this value) as the strain limits for analyzing the affected areas in all the cases. 11B-5B Figure 3. Meshes of the billet for different shape factors Figure 5. Case of maximum strain (3B-B)

4 Figure 6 represents the diagrams of strains for the differents cases of the Table 1. As it can be observed, in the case of height B the strains affect to all the height of the workpiece. It is observed how the strains are generated in an angle of 45º, more or less. However, in the other cases this doesn t occur. This height (directly related to the strain area) increases with the height of the workpiece in a smaller proportion, without reaching the entire height of the workpiece, as it can be seen in the Figure 7. 3B-B 5B-2B Figure 7. Percentage of affected height by strain in the strain area 7B-3B Once these previous problems have been simulated and the strain diagrams evaluated, the case of height 3B has been chosen for a more exhaustive study. The following results have been obtained with a height of the workpiece of 3B, whereas their width has been changed. Figure 8 represents the evolution of strain affected area when width changes. In all the cases, the areas have been divided into B 2 to obtain adimensional results. 9B-4B Figure 8. Strain affected areas in function of the width for a 3B height 11B-5B Figure 6. Strains for the different cases of Table 1 The trend of the curve indicates that a slight increase of area is achieved up to the width of 3B, where a minimum is observed again. Calculating the areas for the cases of Table 2, and comparing the results it can be obtained the following figure.

5 Lastly, when h 3B the behavior is different. Initially, it shows a decrease of the area with the width although for the highest values of width the affected area seems to be constant. 6. REFERENCES Figure 9. Areas of all the studied cases The first curve (where height is equal to B) has a constant behavior and it seems to be independent of the width because it can be appreciated that there is not change of area when increasing the width of the workpiece. The next two curves (corresponding to the heights 2B and 3B) have a similar trend: the higher the width, the higher the strained area. Moreover, it is observed that the areas of height B are higher than those of height 2B but for the highest widths (9B and 11B) where these areas become identical. On the other hand, the rest of graphs (4B and 5B) have a contrary behavior because when the width of the piece increases the areas decrease. In general, when the width increases an approximately constant behavior is observed. 5. CONCLUSIONS In this work, it has been carried out a study of the area affected by the strain in indentation processes under plain strain conditions and without friction. In this study the area has been related with the dimensions of the workpiece by means of the shape factor. Once known this area, it allows us to know where maximum strains are produced. In this sense, it is important to obtain as much information as possible of what occurs in the process. A numerical method of analysis such as the Finite Element Method has allowed studying the influence of geometrical variables in the process. The results have shown that the maximum strain is reached when the height of the workpiece is the same as dimension of the punch. Its behaviour with regard to the height of workpiece presents a point of inflection when the height is three times superior to the dimension of the punch. With the increase of height of the workpiece an increase of strain area is carried out. The height of this area increases with the height of the workpiece but in a smaller proportion as the height of the piece increases. The obtained results where the height has been kept constant and the width of the piece has been varied show three types of behavior. If h = B (where h and B are height of the workpiece and width of the punch respectively), a constant trend is observed. On the contrary, if h 3B, the higher the width, the higher the area affected by the strain. [1] A.M. Camacho, M.M. Marín, J.R. Gil, C. González, Parametric study of compression processes in plane conditions by FEM, Proceedings of Advances in Materials Processing and Technologies, 2006, pp [2] A.M. Camacho, M.M. Marín, L. Sevilla, M.A. Sebastián, Analysis of Axisymmetrical Compression Processes by the Finite Element Method, Proceedings of the 9th International Conference on Numerical Methods in Industrial Forming Processes, 2007, pp [3] A.M. Camacho, C. Vallellano, M.A. Sebastián, J. García-Lomas, Análisis mediante el MEF de los efectos de la geometría del extremo del punzón en procesos de forja localizada-incremental, Anales de Ingeniería Mecánica, Vol. 2, 2008, pp [4] B. Avitzur, Metal Forming: Processes and Analysis, McGraw-Hill, [5] D. Hibbit, B. Karlsson and P. Sorensen, ABAQUS v6.6 User s Manuals, [6] F. Martín, A.M. Camacho, M. Marín, L. Sevilla, Parametrization of analytical and numerical methods in plane strain forging, Proceedings of the 1st Manufacturing Engineering Society International Conference CISIF-MESIC, 2005, pp [7] G.W. Rowe, Principles of Industrial Metalworking Processes, Edward Arnold, [8] G.W Rowe, C.E.N Sturgess, P Hartley, I. Pillinger, Finite-element plasticity and metalforming analysis, Cambridge University Press, [9] K.K. Tho, S. Swaddiwudhipong, J. Hua, Z.S. Liu. Numerical simulation of indentation with size effect, Materials Science and Engineering, Vol. 421, 2006, pp [10] L.M. Farrissey, P.E. McHugh, Determination of elastic and plastic material properties using indentation: development of method and application to a thin surface coating, Materials Science and Engineering, Vol. 399, 2005, pp [11] M. Beghini, L. Bertini, V. Fontanari, Evaluation of the stress-strain curve of metallic materials by spherical indentation, International Journal of Solids and Structures, Vol. 43, 2006, pp [12] M.A. Sebastián, A.M. Camacho, Geometrical study and basis for the analysis of localized-incremental forging processes by FEM, 2nd International Conference on New Forming Technology, Bremen, [13] X. Chen, J. Yan, A. Karlsson, On the determination of residual stress and mechanical properties by indentation, Materials Science and Engineering, Vol. 416, 2006, pp