Mechanical Behavior of Materials
17
Fig.
2.3
Tensile diagram for a mild
steel.
If the load is removed, the specimen returns to its original length and shape, which is known as elas- tic behavior.
Strain increases faster than stress at all points on the curve beyond point A. Point B is known as the
elastic limit; after this point, any continued stress results in permanent, or inelastic, deformation The stress resistance of the material decreases after the peak of the curve, and this point is also
known as the yield point Y of the material. For soft and ductile materials, the exact position on the
stress strain curve where yielding occurs may not be easily determined because the slope of the straight portion of the curve decreases slowly. Therefore,
Y is usually determined as the point on the stress strain curve that is offset by a strain of 0.002 or 0.2 elongation.
If the specimen continues to elongate further under an increasing load beyond point Y, a domain curve begins in which the growth of strain is faster than that of stress. Plastic forming of metal is performed in
this domain. If the specimen is released from stress between point Y and point the curve follows a
straight line downward and parallel to the original slope
Fig.
2.4.
As
the load and engineering stress increase further, the curve eventually reaches a maximum point and then begins to decrease. The maximum engineering stress is called tensile strength or ultimate tensile
Fig.
2.4
Schematic illustration of
loading
and
unloading
tensile test specimen.
18
Mechanical Behavior
of
Materials
A,
strength of the material.
UTS
2.1 1
If
the specimen is loaded beyond its ultimate tensile strength, it begins to “neck,” or “neck down.” The cross-sectional area of the specimen is no longer uniform along a gauge length but is smaller in the neck-
ing region. As the test progresses, the engineering stress drops further and the specimen finally fractures at the point F. The engineering stress at fracture is known as the breaking or fracture stress.
The ratio of stress to strain in the elastic region is known as the modulus
of
elasticity
or Young’s modulus and is expressed by:
e 2.12
The modulus of elasticity is essentially a measure of the stiffness of the material.
2.3 DUCTILITY
Ductility is an important mechanical property because it is a measure of the degree of plastic deformation that can be sustained before fracture. Ductility may be expressed as either percent elongation or percent
reduction in area.
Elongation can be defined as:
Reduction can be defined as: 2.13
2.14 where:
=
length at the fracture. This length is measured between original gauge marks after the pieces of
=
the original sample gauge length;
=
cross-sectional area at the fracture;
A ,
=
original sample gauge cross-sectional area. the broken specimen are placed together;
Knowledge of the ductility of a particular material is important because it specifies the degree of allowable deformation during forming operations. Gauge length is usually determined by inscribing gauge
marks on the sample prior to testing and measuring the distance between them, before and after elonga- tion has occurred. Because elongation is always declared as a percentage, the original gauge must be
recorded. Fifty millimeters two inches is the standard gauge length for strip tensile specimens and this is how the data are generally recorded. The reduction in area
is declared as a percentage decrease in the orig- inal cross-sectional area and, like percent age elongation,
it
is measured after the sample fractures. The
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.
