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14 - Finite Element Analysis
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 219-241
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Summary
Lately, the most important advancement in metal forming analysis has been the development and application of finite element analysis (FEA), i.e., use of the computerized finite element method (FEM). Recent progress in FEA, together with increasingly powerful computers, has permitted increased use of such numerical modeling. Hence, today it is possible to FEM-simulate the metal forming processes at various design stages.
When a FEM model has been made for a particular forming application, the load requirement, velocity, strain rate, strain and stress fields, etc., can easily be obtained for the considered process. Therefore, the current trend is toward increased application of FEA for process simulation and optimization. For practical applications, the modeling techniques must, of course, describe experimental observations quantitatively with sufficient accuracy.
After an introduction to modeling techniques in general in metal forming, this chapter will focus on the application of FEM modeling as a practical tool to investigate the process conditions in forming operations. An overview of some commonly applied FEM codes will be given. Afterwards, it will be shown how the two- and three-dimensional versions of the DEFORM™ FEM program can be used to FEM-model metal forming.
Some examples will be presented where the DEFORM FEM code is used for deformation analysis in practical metal forming cases like plane strain compression and cylinder compression. Finally, a case will be presented where the complex conditions in extrusion welding are investigated by means of FEA. There is work being done to create corresponding models using QFORM. The DEFORM and QFORM models will be available at www.cambridge.org/valberg.
8 - Flow Stress Data
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 115-126
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The flow stress of a material is indeed an important parameter in metal forming. To create a good FEM model of a forming process, for example, it is required that one be able to specify the flow stress of the workpiece material with good accuracy.
Because of this, the main processing parameters affecting the flow stress of commonly used metals and their alloys will be considered in this chapter, as regards both cold and hot forming applications. When the flow stress has been measured, so one knows how the processing parameters affect the flow stress, it is common to search for an equation that can describe the actual flow stress dependence well. When one has arrived at such an equation, one says that one has obtained a good material model for the material. It is also common to call the material model the constitutive equation for the actual metal. Commonly applied procedures to determine constitutive equations for metals will be described and material models for some commonly used metals will be reviewed in this chapter.
The Flow Stress
In Fig. 7.8(b), flow stress curves were shown as they commonly appear for a metal at room temperature. As depicted in this figure, the true flow stress often increases with increasing strain when the metal is tested at room temperature.
If we consider metals, at cold, warm, and hot forming temperatures, a number of parameters can affect flow stress, not only strain.
17 - FEA of Forging
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 285-319
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In this chapter, two rather different cases of forging will be considered, the first one being cold backward cup extrusion, and the second one, hot closed-die forging. During FEA, a large number of analysis results can be achieved when realistic models of the forming operations have been made. These two cases demonstrate some important results achieved this way.
Cold Forging by Backward Cup Extrusion
As explained in Sec. 2.2.3, hollow cups of metal are commonly manufactured from cylindrical workpieces, called slugs, by use of backward cup extrusion. Even though this process is called extrusion, it is often classified as a forging process and will be so considered in the following.
Let us now analyze the backward cup extrusion process visualized in the FEM model in Fig. 17.1. Only one half of the workpiece and the dies was modeled, because there is rotational symmetry around the y-axis. The mirroring option of the program, however, was used to visualize the full longitudinal cross section of the forming process as shown in Fig. 17.1. In this figure, (a) shows the initial die and workpiece configuration, (b) shows an intermediate stage of forming, and (c) shows the final thick-bottomed cup at the end of forming.
The FEM model mimics an industrial cold-forging process, where a soft-annealed slug of the alloy AA 6082 was given the cup shape shown in Fig. 17.1(c). The tooling consisted of a moving punch and a stationary container.
Index
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 453-465
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6 - Deformations from the Velocity Field
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 84-91
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It may be useful to know the velocity field for a metal forming process, as will be shown in the forthcoming sections. If the velocity field is known, a number of deformation parameters can, in principle, be deduced from it. This is realized if one considers the definitions of the different strain and strain-rate components in Sec. 4.2.1 and Sec. 4.3.3.
Let us first explain what is meant by a velocity field. The term refers to the distribution of velocities, at a given moment of forming, within a workpiece, and the evolution of them with time, from beginning to end of the forming process.
The usefulness of determining the velocity will first be shown for the simple case of homogeneous slab compression. It will be shown how a simple velocity field can be determined, which gives an adequate description of the overall deformational behavior of the slab. Then it will be shown how different strain and strain-rate components can be deduced from this velocity field. In the last problem at the end of this chapter, a complex velocity field that incorporates the effect of bulging in cylinder compression, is dealt with.
Stationary and Nonstationary Velocity Fields
Metal forming processes are commonly classified in two groups, stationary processes and nonstationary processes, dependent on whether there is a constant velocity field or the field changes with time throughout the forming operation.
19 - FEA of Extrusion
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 347-364
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Extrusion as a metal forming process has previously been dealt with in Sec. 2.2.5 and Ch. 18. In Ch. 12, commonly used experimental grid pattern techniques were described, and it was shown that such techniques are required in order to be able to describe the deformations occurring in forward and backward extrusion. The treatment showed that metal flow and deformational behavior in the extrusion processes are indeed complex.
It will now be shown how simple axisymmetric aluminum extrusion can be modeled by FEA, with respect to both forward and backward extrusion. A comparison of results obtained by means of simulation models with corresponding results from experimental grid pattern analysis confirms that these simulations describe the real metal flow in extrusion with good accuracy. Finally, the FEM models are used to show some differences in deformation characteristics in forward and backward extrusion.
Forward Extrusion of Aluminum
Forward Extrusion Divided into Subprocesses
A new concept has been proposed to explain the complex metal flow phenomena taking place in the unlubricated forward extrusion process, as applied for hot extrusion of Al and Al alloys. The concept is based on considering the process to be partitioned into four subprocesses. Then, by FEA, it is possible to model and to analyze each of the four different subprocesses by individual FEM models, which each describe particularly well the different deformation phenomena encountered in the forward extrusion process.
Frontmatter
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp i-iv
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22 - Drawing of Wire, Profiles, and Tubes
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 395-413
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Wiredrawing was described briefly in Ch. 2.2.6 as a metal forming process in which a wire is reduced in thickness by pulling it through a drawing die shaped as a conical channel. It was also mentioned that drawing can be performed for profiled cross sections also, not only round ones. In addition to this, hollow products like tubes can be manufactured by drawing.
Drawing processes are attractive in that they are cold forming processes, use a stiff die with rather small reduction. Because of this, the forming load on the die is small. Therefore, the dimensional stability is better than if the product were made by alternative processes, like extrusion or rolling. To improve the dimensional accuracy of the cross section of rolled or extruded products, they are sometimes given a final calibration draw before final use.
In this chapter, various practical aspects of wiredrawing will first be considered. It will be shown how a thin wire is manufactured by drawing down a thick wire in many steps in a drawing machine. Typical dies used in order to reduce the diameter of the wire will then be described.
It was early figured out that the drawing force is an important parameter in drawing, because higher friction contributes to increase in the required drawing force. A methodology was therefore developed, that allowed friction to be measured directly, using a longitudinally split drawing die. The measuring principle used for this purpose will be described.
15 - FEA of Technological Tests
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 242-267
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Use of FEM analysis for the study of the mechanics of some important technological test methods will be treated in this chapter. Detailed knowledge of the deforming conditions in such tests is crucial when they are to be used to collect precise material data, such as, for example, flow stress data for a particular alloy.
Tensile testing of round specimens is first considered. FEA predicts nonuniform deformation across the thinnest neck in the specimen, and experimental grid pattern analysis confirms this; the largest deformation occurs at the center of the neck. Thus, in reality one assumption in Bridgman's correction analysis fails. Because of this, for metals exhibiting strain hardening, it can be shown that in tensile testing it is appropriate to perform a larger correction of the flow stress than that proposed by Bridgman.
Cylinder compression testing is then subjected to an in-depth analysis. First, it is shown how experimental grid pattern analysis, supported by inverse FEM modeling, can be used for finding an approximate friction value in the compression test. Thereafter, FEA is used to map internal deformations inside cylinders being compressed with friction, so that overfolding of the side of the cylinder occurs.
After this, the friction effects on the compression load are investigated using FEA. It is shown that friction effects are reduced as the cylinder height is increased.
2 - Important Metal Forming Processes
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 18-33
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Although there are many different metal forming processes, in this chapter only some of the most important processes will be described. A more complete overview of metal forming processes is given elsewhere. A classification system that is useful for those who are not experienced metal formers will also be described.
Classification System for Metal Forming Processes
In Fig. 1.9, a sketch was shown in which the primary metal forming processes were organized among various common manufacturing methods. In Fig. 2.1, we have expanded the metal forming region downward, thus including the most significant metal forming processes. As seen from this figure, the processes at the lowest level of the diagram are commonly described by the name of the product created by that particular forming process.
Figure 2.1 also shows the important distinction between bulk-metal forming and sheet-metal forming. Bulk-metal forming is the shaping of bodies with concentrated mass, i.e., where the dimensions in each of the three orthogonal directions x, y, and z of the body are of similar size. Sheet-metal forming, on the other hand, is the forming of bodies with initial large extensions in two directions and small extension in the third direction, such as in a piece of sheet metal or a steel plate.
As mentioned before, sheet-metal forming is quite different from bulk-metal forming. In sheet-metal forming, a relatively thin, wide sheet is formed against a die. In this case, it is impossible to keep the workpiece inside a configuration of closed dies.
4 - Theory
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 53-76
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Because metal forming produces elastic and plastic deformations in the workpiece material and elastic deformations in the dies, an in-depth study of the metal forming process will require the determination of stresses and strains in the workpiece and the tooling. In addition, one needs to know some basic topics from the theory of elasticity and plasticity. In this chapter, a short introduction to this theory is therefore given. Because of the rather shallow treatment here, readers who are unfamiliar with this theory are referred to other textbooks for a more profound study.
Stresses
During metal forming the workpiece is deformed plastically by forces transferred from the die to the workpiece. A successful forming operation requires that there be plastic deformations in the workpiece, so that it changes shape permanently and conforms to the geometry of the die, while the die remains in the elastic state. If the die material becomes plasticized, the situation is one of overloading of the tooling, and the die geometry will gradually change because of the excessive forming loads. This means that the correct geometry of the formed component no longer can be maintained, so to continue appropriate metal forming, the dies must be replaced by new dies that can work the material while remaining in the elastic state.
The Stress Concept
Stress is defined as force per unit of area and refers to a particular point in a material.
7 - Technological Tests and Physical Simulation
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 92-114
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In order to model metal forming processes either by theoretical models or by FEM modeling, as already shown in Ch. 3, it is required, for instance, to know the flow stress of the metal that is formed, and the actual friction between the die and the workpiece. To obtain such data, a number of different test methods have been developed over the years, by which it is possible to bring a specimen of the actual material, usually of small size, into a plastic state, and during plastic deformation of it measure the required deformation force, concurrently as the size of deformations subjected to the specimen is measured. Tests of this kind are called technological tests and are commonly run on small specimens of the material, often in advanced equipment especially designed for the purpose. In this chapter, the most common technological tests for measurement of flow stress and ductility of metallic materials are discussed. The main focus will be on the tensile test and the compression test. The basic mechanics of these technological tests, and how to determine stresses and strains during the tests, will be reviewed.
Physical Simulation of Metal Forming
Some industrial metal forming processes – as for instance rolling, extrusion, and forging – are commonly run in large industrial equipment, where the possibilities of experimentation is limited. Most commonly the machinery lacks sensors to allow accurate recording of relevant process parameters. Moreover, running of full-scale experiments in big industrial equipment is expensive.
16 - Forging
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 268-284
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The classification system for metal forming processes shown in Fig. 2.1 partitions the forging processes into three different groups: open-die forging, closed-die forging, and impact extrusion. In reality, open-die forging consists of a number of different subprocesses, in each of which considerable parts of the workpiece are formed freely, without full contact with the dies; see, for instance, cogging, as shown in Fig. 2.2(c). Closed-die forging, on the other hand, refers to forging between dies, where at the end of forging, either the entire workpiece is confined in a closed space between the dies, or an amount of excess material is used, which flows out of the flash gap; see Fig. 2.3(b). When flash is formed, the process is most commonly called closed-die forging. When there is no flash, the process is called precision forging, flashless forging, or zero-loss forging. Impact extrusion, such as forward and backward cup extrusion, is also described in Ch. 2; see Fig. 2.4. Both are commonly classified as forging processes. In addition, many more exotic forging processes have been developed over the years.
In this chapter, some practical aspects of importance in closed-die forging processes will be considered. First, the concept of forgeability will be discussed. Then the implications of this concept for forging practice will be dealt with, such as selection of forging temperature and possible shapes of forgings. A common classification system for forged components will also be presented. After this, commonly used design principles in multistep forging processes will be discussed.
Applied Metal Forming
- Including FEM Analysis
- Henry S. Valberg
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- 31 March 2010
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Applied Metal Forming: Including FEM Analysis describes metal forming theory and how experimental techniques can be used to study any metal forming operation with great accuracy. For each primary class of processes, such as forging, rolling, extrusion, wiredrawing, and sheet-metal forming, it explains how FEA (Finite Element Analysis) can be applied with great precision to characterize the forming condition and in this way optimize the processes. FEA has made it possible to build very realistic FEM-models of any metal forming process, including complex three-dimensional forming operations, in which complex products are shaped by complex dies. Thus, using FEA it is now possible to visualize any metal forming process and to study strain, stresses, and other forming conditions inside the parts being manufactured as they develop throughout the process.
Preface
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp vii-viii
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Finite element analysis (FEA) has currently been developed into an efficient, user-friendly tool for investigation of metal forming processes. At the same time, cheap, efficient computers have been developed that allow simulation of metal forming to be done by use of the finite element method (FEM), within reasonable times. This recent development is, as this book will show, about to revolutionize the art of metal forming.
This technology has made it possible to build realistic FEM models of perhaps any metal forming process, including complex three-dimensional forming operations, in which complex products are shaped by means of complex dies. Thus, by FEA, it is now possible to visualize any metal forming process on the computer screen and to study strain, stress, and other important forming conditions inside the workpiece, as they develop throughout the duration of the process. Because of this, FEA has also become an important industrial tool in connection with development and design of new metal forming processes.
However, in spite of this development, there is still need for classical theory as a tool for providing knowledge about forming. For a person to be able to utilize the new FEA technology and to evaluate the results obtained in FEA, it is required that he or she have deep insight into the theory of metal forming.
In order to establish correct FEM models, it is still required to investigate metal forming by means of experiments performed in the laboratory or on industrial equipment.
24 - Sheet-Metal Forming
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 435-452
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As pointed out previously in Ch. 2, sheet-metal forming differs a lot from bulk-metal forming in that the stress condition in a sheet-metal forming operation usually is characterized by tensile stress, whereas most commonly in bulk-metal forming there is compressive stress. Because of this, necking and fracturing of the workpiece material is a much larger problem in sheet-metal forming than in bulk-metal forming. A useful tool for optimization of sheet-metal forming processes, so that they can be conducted without problems due to necking or fracture, is circle grid analysis. The principles applied in circle grid analysis will therefore be described in this chapter. After this, some technological test methods applied in order to test the formability of sheet metals will be described: plane strain stretching, biaxial stretching, and the Erichsen test.
The principles used when forming-limit diagrams (FLDs) are made will be explained. It will also be shown how such diagrams and circle grid analysis can be used in order to optimize the deformation conditions in a typical industrial sheet-metal forming operation.
Elastic springback is a phenomenon of great importance in sheet-metal forming. Commonly the cross section of the sheet does not become fully plasticized in such processes. In bending, the midlayer of the sheet will deform elastically only, and will therefore cause elastic springback in the material when the forming load is removed.
Sheet metals used for forming are commonly anisotropic, i.e., they have different properties in different directions.
Contents
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp v-vi
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12 - Experimental Metal Flow Analysis
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 181-203
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In this chapter, the principles of metal flow analysis will be discussed, with particular emphasis on use of stripe or line patterns, made of contrast material, to map metal flow in hot aluminum extrusion. Emphasis will also be on use of ring patterns on the surface of workpieces to trace friction-dependent metal flow against die surfaces.
Grid Pattern Techniques Used to Trace Metal Flow
Grid pattern analysis was developed as a tool for understanding different metal flow phenomena encountered in metal forming processes. In the beginning, it was common to use model materials, such as Plasticine or clays, to imitate metal flow. These model materials have deformation characteristics similar to metals, and thus can be used to reproduce the real metal flow conditions with good similarity, when chosen appropriately. Such materials require only low loads in forming, and therefore their flow could be studied visually through glass plates in order to determine the main factors affecting metal flow. Grid patterns were also added on the surface of the model materials, or to their interior, to study material flow, as for metals.
Typical flow-related defects were observed to occur on various occasions; for instance, pipe formation can appear in the rear end of an extrusion. That some of these defects are related to the nature of the metal flow in the process was discovered through the use of grid pattern techniques.
10 - Friction and Friction Models
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 139-158
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In metal forming, friction is a crucial factor that determines whether an industrial process can be run with acceptable, economic result. In many forming applications, the actual friction conditions are not sufficiently known. In spite of much research on that important topic, there is still lack of knowledge and need for continued research.
This chapter will first explain why friction is so important in metal forming. Then the two most-applied friction models will be presented, and the characteristic of each model will be explained and discussed. Afterwards the most common lubrication mechanisms that may be present in the interface between die and workpiece will be described. Moreover, it will be explained how relevant metal forming friction data can be measured by the ring compression test. Finally, it will be shown how in situ friction measurements can be performed inside a die during the course of forming, using pins inserted into holes drilled into the tooling.
Friction Effects in Metal Forming
The friction phenomenon in metal forming is of great importance. There are various reasons for this:
Forming loads and stresses transferred to the dies depend on friction and can be reduced by use of appropriate lubricants.
The surface quality of the formed workpiece depends on the lubricant used. If there is lubricant breakdown during forming, the product may obtain bad surface quality (for instance, scoring).
Wear of the dies can be reduced if lubricant films are applied, which provide reduced friction, or even full or partial separation, between the die and the workpiece during forming.
18 - Extrusion
- Henry S. Valberg, Norwegian University of Science and Technology, Trondheim
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- Applied Metal Forming
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- 31 March 2010, pp 320-346
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As previously described in Ch. 2, extrusion is done by placing a piece of metal of good formability, called a billet, in a hardened steel container. In direct extrusion, a ram is then pushed from the back end of the container, so the billet is forced against a die placed at the other end of the container. The die has a hole in its middle, and as the billet is pushed forward, the front part of it starts to flow into the hole, and then out into the space at the exit side of the hole. Here it appears as a continuous extrusion with cross section approximately that of the hole. The longitudinal shape obtained in this process is generally called an extruded profile, or an extrudate. This metal forming technique is hence used to manufacture products with constant cross-sectional shape along their length, either as massive or hollow profiles, or as rod, tube, wire, or strip.
Because the flow stress is reduced when metals are heated, and workability also most commonly increases, extrusion is usually conducted as hot forming. Extrusion can either be done as forward (direct) or backward (indirect) extrusion; see Ch. 2.2.5. In forward extrusion, the material is pushed through the container and the die by means of the ram, whereas in backward extrusion, the die is placed in front of the hollow ram, whereafter the die is pushed into the billet.