Metal forming is a branch of engineering that deals with the manufacturing
of metal products and parts by plastic deformation. Industry employs metal
forming techniques extensively because they are economic and reliable.
But the significant technological and economical aspects of these techniques
require the correct estimation of at least the following process parameters:
- the power and motivation forces needed for the deformation
- the distribution of internal stresses in the workpiece
- the mechanical characteristics of the final product.
For this, a sound background in the mechanics of the plastic flow is
essential. The main purpose of the text is to provide this background.
The textbook is primarily for the beginner who knows the principles
of mathematics and mechanics but who has had no previous experience with
plastic flow phenomena except, perhaps, for a first course on manufacturing
engineering. Typical readers are senior students or new engineers. To meet
their needs and to make this textbook a useful reference for them, all
basic concepts and analytical procedures are presented in a rigorous manner
but without excessive detail.
The elementary nature of this textbook notwithstanding, its educational
objectives are not very modest. First, the text should show how to estimate:
- the total power and the motivation forces required of a metal-forming
- the average mechanical properties of the final product.
Second, it should provide the mechanical background needed to review
and apply with ease the results of research papers on bulk-forming processes.
Many of these papers derive their results from energy considerations, which
is the approach used here.
Third, it should be an adequate basis for subsequent studies of more
advanced topics that show, among others, how to estimate the distribution
of internal stresses and mechanical characteristics of the final product.
Last, the text should facilitate in-depth investigations of new metal-forming
processes, should the reader wish - or need - to do so.
Traditional textbooks on the theory of plasticity for engineers view
the mechanics of plastic flow as a natural extension of the mechanics of
solids. As such, the focus is on strains, stresses and the criterion for
plastic yield, which differentiates plastic flow from elastic deformation.
In contrast, the subject of plastic flow is approached here in the established
tradition of classical texts that introduce senior undergraduate students
to the mechanics of fluids and fluid-like flows. The focus is thus on velocities,
strain rates and power requirements. On this basis, the internal stresses,
flow rules and yield criteria are left out for presentation in a second
course on the mechanics of plastic flow. Also left out for a more advanced
course are the mathematical and computational aspects of computer-based
numerical schemes such as UBET (Upper-Bound Elemental Technique) and FEM
(Finite-Element Method). With these omissions, the alternative approach
used in this text appears to be simpler and thus more suitable for a first
course on the mechanics of metal forming.
The presentation starts in Chapter I with a review of the principal
modes of shaping metals by plastic deformation: forging, drawing, extrusion
and rolling. These classes of bulk (massive) forming processes define the
book's main field of application, though the topics discussed are equally
relevant in many other metal forming contexts, such as deep drawing, which
is a sheet-metal forming process.
Chapter 2 is concerned with the kinematics of plastic flow. It builds
the theoretical base and provides the analytical tools needed to describe
plastic-flow phenomena. The flow is characterized in terms of the motion
of the particles involved or by means of a velocity field.
Chapter 3 shows how to calculate the deformation rates from the velocity
field. As these rates play a major role throughout the text, subsequent
chapters use almost exclusively the velocity field description. In light
of this, we take time toward the end of the chapter to explain how to derive
the velocity fields from the stream functions.
Power consumption is the subject of Chapter 4, which shows how to calculate
the net power of external forces, the internal power of deformation, and
the shear and frictional power losses. These are the main terms of the
balance-of-power equation, the single most important elementary tool that
we use to estimate the external power needed to successfully form sound
With Chapter 5 we leave the realm of concepts and principles universally
applicable to all materials. From there on, the text focuses on the flow
of metals in their plastic state. To succeed, some simple assumptions are
made concerning the macroscopic behaviour of metals when loaded beyond
their elastic range. Ideal materials which meet these assumptions are called
Mises materials. In the first half of Chapter 5 we outline the necessary
assumptions and their range of applicability. In the second half, we apply
the general principles of the mechanics of deformable bodies to the flow
of Mises materials and derive important consequences for the mechanics
of metal forming.
The last chapter, Chapter 6, expands on the Mises model and shows how
to account for the hardening that is often observed when a metal is being
No metallurgical aspects are examined here, their importance notwithstanding.
This should not detract from understanding the material presented in the
text. Though, naturally, the broader the reader's metallurgical background,
the easier it should be for him or her to appreciate the usefulness of
analyzing the mechanical aspects of metal forming processes.
Note also that there are no full, detailed studies of metal forming
operations. This textbook simply provides the mechanical background needed
to review with ease the relevant literature. Processes such as indentation,
open- and closed-die forging, drawing and extrusion with conical dies,
rolling, spinning, and machining, have all been researched extensively-a
wealth of analyses can be found in the references at the end of each chapter.
Finally, note the choice of examples and end of chapter problems. We
have selected known metal forming analyses and adapted them for the needs
of this text without attributing them to one author or another. Also, only
rarely did we include references to the original publications. We believe
these practices best meet the intent of our textbook: to be an introduction
rather than a definitive treatise on the mechanics of metal forming.
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