Mechanical Behavior of Materials
19
elongation is more a measure of the strain leading to the onset of necking than a measure of the strain at final fracture in a uniaxial tensile specimen. A better measure of the strain at final fracture is the
percentage reduction in area. The relationship between the elongation and reduction of area is different for some groups of metals,
as shown in Fig. 2.5.
Stainless steels and Alloys
Low
carbon steels cold rolled
Aluminum alloys
10
20 30
40
50
70
Reduction of area
Fig. 2.5
Relationship between elongation and reduction
of
area Elongation ranges approximately between
10 and 60 for most materials, and values between 20 and 90 are typical for reduction of area. Thermoplastics and super-plastic materials, of course, exhibit much
higher ductility, aand brittle materials have little or no ductility.
2.4 TRUE STRESS
AND TRUE STRAIN
In the solution of technical problems in the processes of sheet-metal forming, theoretical stress and strain do not have as crucial a significance as do true stress and true strain. True stress and true strain are much
more important.
It
is
apparent that, since stress is defined as the ratio of force
to
area, true stress may be defined as:
F
2.15
A
where:
A
=
the instantaneous cross-section area. As long as there is uniform elongation, true stress
can be expressed using the value for engineer- ing stress
.
Assuming that volume at plastic deformation is constant: this equation is in effect only to point the relationship between true and nominal stress may be defined as follows:
- -
In Fig. 2.6 is shown a nominal engineering curve and the true stress and strain for medium carbon
F A
A
steel.
20 Mechanical Behavior of Materials
I I
I
Strain e
Fig. 2.6
Diagram of nominal and true stress.
Because the strains at the yield point Yare very small, the difference between the true and engineer-
ing yield stress is negligible for metals. This is because the difference in the cross- sectional areas A , and A
at yielding is very small. However, the difference in the cross-sectional area A , and A , A A, above point Y is always greater, so the difference between the true and nominal stress is significant k
Because of the relationship, the given curve showing the true stress is known as the “hardening curve” of a metal.
PART
MANUFACTURING PROCESSES
This part discusses the methods that are most used for sheet metal forming. The text is presented in five chapters, which deal, in detail, with: shearing, punching and blanking, bending, deep drawing, and various
forming processes stretching, nosing, expanding, flanging, flexible die forming, and spinning. Special attention is given to the mechanism of processes, estimation of forces, clearances, minimum bend radius,
and other important factors in sheet-metal forming processes. Detailed analytical mathematical transfor- mations are not included, but the final formulas derived from them, which are necessary in practical appli-
cations, are included.
3.1
Mechanics of Shearing
SHEARING PROCESS
3.1 MECHANICS OF SHEARING
The shearing process involves the cutting of flat material forms, such as sheets and plates. The cutting may be done by different types of blades or cutters in special machines driven by mechanical, hydraulic, or
pneumatic power. Generally the operations consist of holding the stock rigidly, while it is severed by the force of an upper blade as it moves down past the stationary lower blade.
During the shearing process, three phases may be noted: In phase I, because of the action of the cut- ting force
the stress on the material is lower than the yield stress This phase is that of elastic
deformation Fig. 3.1. To prevent the movement of material during the cutting operation, the material is held by the material holder at force
In phase the stress on the material is higher than the yield stress
but lower than the UTS. This phase is that of plastic deformation In phase
the stress on the material is equal to the shearing stress
=
The material begins to part not at the leading edge, but at the appearance of the first crack or breakage in the material. Fracture of the material occurs in this phase.
The amount of penetration of the upper blade into the material is governed by the ductility and thick- ness of the work material. If the material is thicker and more brittle, the first crack will appear earlier, so
there is earlier disjunction of the material. The sheared edge is relatively smooth where the blade pene-
trates, with a considerably rougher texture along the torn portion.
3.2 SHEARING FORCES
Knowledge of the forces and the power involved in shearing operations is important, and they may be cal- culated according to the edge types of the cutters. There are three types of cutters:
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