May 2021 Volume 3

cannot be neglected. The elastic recovery or “springback,” as it is often called, plays a critical role in controlling the geometry of the object. (1) The area under the elastic curve is the work done or one-half of the strain ene elastic deformation is fully recoverable after force is removed. In bulk formin elevated temperature, the elastic deformation is negligible when compared to the deformation. By ignoring the elastic deformation in finite element modelin equations are simplified and the chance of convergence is improved. In cold an the other hand, the elastic def rmation cannot be ne lected. The elastic recovery it is often called, plays a critical role in controlling the geometry of the object. 1 = 1 [ 1 − ( 2 + 3 )], 2 = 1 [ 2 − ( 3 + 1 )] and 3 = 1 [ 3 − ( 1 + 2 )] σ region is proportional to the applied force in factors E and ν, where E is Young’s property that measures the stiffness of the object, and ν is Poisson’s ratio, equal by the longitudinal strain. This relationship of the stresses and strains is expresse as shown in Eq. (1).

FORGING RESEARCH

Selection of a particular forming process is largely dependent on the product to be formed. Once the specifications of the product (for example, the material grade and formability, dimensions, geometries and precisions, as well as the property requirements) are thoroughly evaluated, the type of metal forming process, equipment and working temperature can be determined. Meanwhile, the economic analysis, which is in many circumstances one of the most important deciding factors, is conducted. Considerations of material utilization, order quantities and manufacturing costs are taken seriously. Material cost is the single largest portion of the overall costs in manufacturing a product, ranging from 30% to 50%. Forming a desired shape that as closely follows the final profile of the product as possible can substantially increase material utilization and reduce material waste and subsequent machining costs; on the other hand, small machining stock and tight tolerances can cause higher forming costs, more frequent tool changes and more scraps. Each forming process has its own minimum order quantity below which adopting it is no longer economical because of the costs of production organization, labor, tooling, fixture, equipment. etc. After the order quantity is determined, the lot size (the number of parts to be made in eachmachine setup) needs to be decided. A small lot size provides customers a short lead time and small inventory, but at a cost of more setups andmore scraps to the suppliers.The benefits of the selected metal forming process can be maximized only when all the aspects of the process are thoroughly evaluated and balanced. 4. Brief Introduction to Fundamental Forming Theories 4.1 Elastic and plastic deformation The primary objective in the study of metal forming is to find out how a metal behaves under force – defining the relationship of the stresses and strains. For the relationship to be useful, it must be mathematically and quantitatively explained. That is what elasticity and plasticity are all about. Most metals and steels are isotropic materials. They display a linear relationship between the applied force F and the deformation D , or between the stress (force per unit area) σ and the strain (displacement per unit length) ɛ in the elastic region, as shown in Figure 7. The displacement in this region is proportional to the applied force in factors E and ν , where E is Young’s modulus, a material property that measures the stiffness of the object, and ν is Poisson’s ratio, equal to the lateral strain by the longitudinal strain. This relationship of the stresses and strains is expressed by Hooke’s Law, as shown in Eq. (1). The area under the elastic curve is the work done or one-half of the strain energy U . Usually, the elastic deformation is fully recoverable after force is removed. In bulk forming, especially at an elevated temperature, the elastic deformation is negligible when compared to the much larger plastic deformation. By ignoring the elastic deformation in finite element modeling, the constitutive equations are simplified and the chance of convergence is improved. In cold and sheet forming, on the other hand, the elastic deformation

Plastic

Elastic

E

U

σ

Plastic

Elastic

Figure 7. Elastic deformation Plastic deformation occurs in a region created by yielding beyond the elastic region to the ultimate strengthwhennecking occurs, as shown in Figure 8. From micrometallurgy it is generally accepted that, based on the dislocation and slip-line theory, plastic deformation involves the breaking of a limited number of atomic bonds by the movement of dislocations, which is in response to an applied shear stress. In plastic deformation, there is also a relationship between stresses and strains similar to Hooke’s Law for elastic deformation. The relationship, however, is much more complex because plastic deformation is nonlinear, load history-dependent and permanent. Furthermore, in anisotropic sheet metal forming, the relationship is different in each direction. In the subsequent sections of this article, the development of the relationship between stresses and plastic strains is described. It is noted that in a large plastic deformation, the true flow curve (the green dash line in Figure 8) is believed to more accurately describe the stress and strain relationship. It uses the actual cross-section area at any given moment to calculate the true strain, so the stress increases continuously even after necking. Figure 7. Elastic deformation Plastic deformation occurs in a region created by yielding beyond the elastic region to the ultimate strength when necking occurs, as shown in Figure 8. From micrometallurgy it is generally accepted that, based on the dislocation and slip-line theory, plastic deform tion involves t e breaking of a limited number of atomic bon s by the movement of dislocations, which is in response to an applied shear stress. In plastic deformation, there is also a relationship between stresses and strains similar to Hooke’s Law for elastic deformation. The relationship, however, is much more complex because plastic deformation is nonlinear, load history-dependent and permanent. Furthermore, in anisotropic sheet metal forming, the relationship is different in each direction. In the subsequent sections of this article, the development of the r lationship between stresses and plastic strains is described. It is noted that in a large plastic deformation, the true flow curve (the green dash line in Figure 8) is believed to more accurately describe the stress and strain relationship. It uses the actual cross-section area at any given moment to calculate the true strain, so the stress increases continuously even after necking. Metal forming region Ultimate strength σ u Fracture X σ Yield point True flow curve Figure 7. Ela t c deformation Plastic defo mation occu s a region created by yielding beyond the lastic region to the ultima strength when necki g ccurs, as shown in Figure 8. Fr m icrometallurgy it is generally accept that, ba ed on the dislocati n and slip-line theory, plastic deformation involves the breaking of limited number of atomic bonds by the movement of dislocations, which is in response to an appli shear stress. In plastic deformation, there is also a relationship between stresses and strains similar Hooke’s Law for elastic deformati . The relationship, however, is much more complex becau plastic deformation is nonlinear, load history-dependent and permanent. Furthermore, in anisotrop sheet metal forming, the relationship is different in each direction. In the subsequent sections of this article, the development of the relationship between stresses a plastic strains is escribed. It is noted that n a large plastic deformation, the true flow curve (the gre dash line in Figure 8) is believed to more accurately describe the stress and strain relationship. It us the actual cross-section area at any given moment to calculate the true strain, so the stress increas continuously even after necking. E U

Ultimate strength σ u

σ

Fracture

True flow curve

Elastic region

Yield point

Permanent deformation

X

Elastic recovery

ε

ε p

ε e Metal forming region

Figure 8. Plastic deformation region

Elastic region

Permanent deformation

Elastic recovery

8

ε

ε p

ε e

Figure 8. Plastic deformation region Figure 8. Plastic deformation region

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FIA MAGAZINE | MAY 2021