As described in connection with eq. 4-24, the deformations imposed on a material in a general complex deformation condition can be described uniquely by the specification of the numerical values of six different strain components. An alternative simpler approach is to quantify deformations by means of the effective strain value; see eq. 4-38. This strain parameter can be considered the “resultant” strain that takes into account the effect of all different strain components.

In an industrial metal forming process, however, the conditions are complex. It is not straightforward to quantify either the different strain components or the effective strain value. To consider the total deformation imposed on a workpiece in such industrial processes, some simplified, less scientific deformation measures are therefore commonly used. Such common measures, which characterize the size of the deformations imposed on a workpiece in a forming process, are, for instance, the area reduction, or the reduction ratio. By means of the numerical value of these parameters, it is possible to compare the size of the overall deformation in different cases of forming. Some simple deformation measures applied in industry will be defined and discussed in this chapter.

Area Reduction in Stationary Metal Forming Processes

Let us first consider total deformations subjected to the workpiece in some stationary metal forming processes like stretching, drawing, extrusion, and rolling. Sketches of these processes are shown in Fig. 5.1. The workpiece has initial diameter d0 and cross-sectional area A0.

In connection with the discussion of technological tests in Ch. 7, it was stated that the tensile test specimen after some degree of stretching tends to become unstable, due to the onset of necking. With further stretching, there is neck growth in the specimen, and finally a fracture is formed in the neck, so that the specimen breaks into two pieces.

When compression testing was discussed, it was stated that for ductile metals, larger strains can in general be obtained in this test than in tensile testing, because neck formation is avoided in compression. But also in the compression test there are limitations on how much the specimen can be deformed. This is because various cracking phenomena may occur, especially when low-ductility materials are tested.

In metal forming, it is a common problem that the material of the workpiece breaks down during forming, in a manner like that for materials subjected to technological tests. In this chapter, different phenomena that cause material failure during metal forming operations will be discussed, with special emphasis on failure due to necking, tensile stress cracking, and shear cracking.

Formability and Workability

Formability and workability are terms that refer to the property of a material with regard to its ability to be shaped in metal forming without breakdown during the forming operation.

It is important – as shown in the preceding chapters – to be able to predict the deformations and the metal flow in metal forming with sufficient accuracy. The importance of knowing such factors as the pressure against the die and the required forming load was early recognized by the metal former. Much work was therefore done to develop theoretical models that could be used to predict these parameters, so that they could be estimated with sufficient accuracy before a new process was set up. The theoretical models established for this purpose showed that the forming load depended on such factors as die geometry and friction, for instance, and in hot forming also on the forming speed. With the development of theoretical methods, it also became possible to calculate the effect of each factor on the forming load.

There are a number of theoretical methods that can be used for analyzing metal forming processes; see Table 13.1. In the following sections, they will be described, except for the slip line field and the finite difference methods, which have been described elsewhere. The information that can be obtained by the different methods is specified in Table 13.1. Additional written material that describes the application of the slip line theory for analysis of metal forming and compares it with corresponding analysis by FEA is available at www.cambridge.org/valberg.

The Uniform Energy Method

The uniform energy method is the simplest method.

When the author of this book was a small child, Wistreich performed extensive experimental work in which he studied steel and copper wiredrawing. In this connection, he applied longitudinally split dies and measured both the drawing force and the die-splitting force in the drawing operation. From the measured data, he calculated the mean contact stresses on the die wall, by means of the formulas presented in the Sec. 22.5. From the contact stresses, he finally determined the mean coefficient of friction for the various drawing geometries used in his investigation. In the following, more details about Wistreich's copper wiredrawing experiments will be presented. In addition, some of his experiments will be reproduced in FEA to characterize the mechanics of these approximately 50-year-old experiments. As will be shown, the mechanics of wiredrawing are complex and are changed a lot when the drawing geometry is altered by changing the parameter Δ and the reduction of area in the die.

In Wistreich's experiments, the die geometry was varied by varying two parameters: the cone angle and the reduction of area in the die. A large number of experiments were run, and many different die geometries were tested. The die half cone angle was varied from ≈3° up to ≈15.5°, and the reduction of area correspondingly from 0.05 to 0.45. Nine of Wistreich's experiments were later reproduced by FEA, and an additional case corresponding to normal drawing will be considered here.

Finite element analysis (FEA) has been developed during the last decades as a very useful tool for analysis of metal forming processes. Progress in development of cheap and efficient computer technology, and the implementation of the finite element method (FEM) into user-friendly, window-based programs, has brought this technology forward. One can state that this development has more or less revolutionized the art of metal forming analysis.

In this chapter, it is demonstrated how 3D FEA can be applied for the analysis of a particular metal forming operation, namely, plane strain compression. To show how well such analysis describes the actual conditions in metal forming, it is used to model and to reproduce a series of experiments conducted on an aluminum alloy in the laboratory. In the experiments, an advanced grid pattern technique was used to characterize the real metal flow occurring in this deformation process.

The Plane Strain Compression Test

The plane strain compression test is conducted as either a cold- or a hot-forming test. Although thermal effects are generally negligible in cold forming, they are important in hot forming. So to gain good accuracy, thermal effects must be included in hot-forming models. The flow stress of the workpiece material is an important parameter used in the FEM model. This parameter is very different in cold and in hot forming, as discussed in Ch. 8. Whereas flow stress is not significantly influenced by temperature in cold forming, in hot forming it depends strongly on temperature.

The energy consumed in a metal forming operation, as, for instance, in a forging stroke, is mainly transformed into heat, which leads to temperature rise in the die and the workpiece. In heavy metal forming equipment, a lot of energy is supplied to the workpiece this way, and there can be substantial global and local heating effects in the workpiece material.

In many metal forming applications, there are limits on how high the temperature of the workpiece can rise before one experiences problems such as reduced or unacceptable product quality. This is, for instance, the case in aluminum extrusion, where the maximum temperature of the metal near the outlet from the die should not exceed a certain critical temperature. In this process, material defects, such as surface cracking due to hot tearing of the material, start to appear when this critical temperature is exceeded, and a usable profile can no longer be manufactured. This phenomenon is explained and discussed in this chapter.

In addition, it is shown how one can quantify different thermal effects in a metal forming process, such as heating due to plastic deformation inside the workpiece, and heating due to friction over its surface. When the workpiece has higher temperature than the dies, there is cooling against the dies, and the physics required to calculate the cooling is shown for a simple two-dimensional case.

Metal forming is one manufacturing method among many. In order to manufacture a machine component, such as a wheel suspension arm for a car, one can choose metal forming, casting, or machining as the shaping method. These three shaping methods can be considered competing processes. The method chosen will usually be the one that provides a product, with proper function and properties, at the lowest cost. In this chapter, characteristics of these three shaping methods will be described, with special emphasis on metal forming, when used to create the intended shape of a component through plastic deformations of an initial workpiece of simple shape.

Definition of Metal Forming

Metal forming refers to shaping of metallic materials by means of plastic deformation. The term plastic deformation describes permanent shape change, in contrast to elastic deformation. An elastic deformation disappears when the load is removed. Many industrial materials are shaped into useful products by plastic deformation. Clay is a material that is shaped by plastic deformation before it is fired to become a final useful solid ceramic material. In addition, polymer materials are commonly shaped in melted condition by means of plastic deformation. But in this book, the treatment is confined to plastic deformation of metals.

A more comprehensive definition of metal forming is the technology used for shaping metal alloys into useful products by forming processes such as rolling, forging, extrusion, drawing, and sheet-metal forming.