The document describes the process and results of a tension test, which is used to determine the mechanical properties of materials. In a tension test, standardized specimen grips are pulled apart in a testing machine while measuring the applied force and deformation. The data collected - stress, strain, ultimate strength, and ductility - are used to analyze a material's elasticity, plasticity, hardness, and failure point. Tension tests provide information about a material's behavior and suitability for engineering applications.

1. Instructor
Yasser M Siddiqi

2. Materials Characterization
 The American Society for Testing and Materials
(ASTM) specifies test procedures for determining the
various properties of a material.
 These descriptions are guidelines used by
experimentalists to obtain reproducible results for
material properties.

3. Tension Test
 In the tension test, standard specimen are placed in a
tension-test machine, where they are gripped at each
end and pulled in the axial direction.
 Figure 1 shows two types of standard geometry: a
specimen with a rectangular cross-section and
specimen with a circular cross-section.

4. Tension test machine and
specimens. Fig 1

5.  Two marks are made in the central region, separated
by a gage length Lo.
 The deformation δ is movement of the two marks.
 For metals, such as aluminum or steel, ASTM
recommends a gage length Lo = 2 in. and diameter do =
0.5 in.
 The normal strain ε is the deformation δ divided by Lo.

6.  The tightness of the grip, the symmetry of the grip,
friction, and other local effects are assumed and are
observed to die out rapidly with the increase in
distance from the ends.
 This dissipation of local effects is further facilitated by
the gradual change in the cross-section.
 The specimen is designed so that its central region is
in a uniform state of axial stress.

7.  The normal stress is calculated by dividing the applied
force P by the area of cross section Ao, which can be
found from the specimen’s width or diameter.
 The tension test may be conducted by controlling the
force P and measuring the corresponding deformation
δ.
 Alternatively, we may control the deformation δ by the
movement of the grips and measuring the
corresponding force P.

8.  The values of force P and deformation δ are recorded,
from which normal stress σ and normal strain ε are
calculated.
 As the force is applied, initially a straight line (OA) is
obtained.
 The end of this linear region is called the proportional
limit.
 For some metals, the stress may then decrease slightly
(the region AB), before increasing once again.

9. Stress-Strain Curve
Fig. 2.

10.  The largest stress (point D on the curve) is called the
ultimate stress.
 In a force-controlled experiment, the specimen will
suddenly break at the ultimate stress.
 In a displacement-controlled experiment we will see a
decrease in stress (region DE).
 The stress at breaking point E is called fracture or
rupture stress.

11. Elastic and Plastic regions
 If we load the specimen up to any point along line OA-
or even a bit beyond- and then start unloading, we find
that we retrace the stress-strain curve and return to
point O.
 In this elastic region, the material regains its original
shape when the applied force is removed.
 If we start unloading only after reaching point
C, however, then we will come down the straight line
FC, which will be parallel to line OA.

12.  At point F, the stress is zero, but the strain is nonzero.
C this lies in the plastic region of the stress-strain
curve, in which the material is deformed permanently,
and the permanent strain at point F is the plastic
strain.
 The region in which the material deforms permanently
is called plastic region.
 The total strain at point C is sum of the plastic strain
(OF) and an additional elastic strain (FG).

13.  The point demarcating the elastic from the plastic
region is called the yield point.
 The stress at yield point is called the yield stress.
 In practice, the yield point may lie anywhere in the
region AB, although for most metals it is close to the
proportional limit. For many materials it may not even
be clearly defined.

14.  It should be emphasized that elastic and linear are two
distinct material descriptions.
 Figure 3 shows the stress-strain curve for a soft rubber
that can stretch several times its original length and
still return to its original geometry.
 Soft rubber is thus elastic but nonlinear material.

15. Examples of nonlinear and brittle
materials. (a) Soft rubber. (b) Glass.
Fig. 3.

16. Ductile and brittle materials
 Ductile materials, such as aluminum and copper, can
undergo large plastic deformations before fracture.
 Soft rubber can undergo large deformations but it is
not a ductile material.
 Glass, on the other hand, is brittle: it exhibits little or
no plastic deformation.
 A material’s ductility is usually described as percent
elongation before rupture.

17.  The elongation values of 17% for aluminum and 35%
for copper before rupture reflect the large plastic
strains these materials undergo before
rupture, although they show small elastic deformation
as well.
 A ductile material usually yields when the maximum
shear stress exceeds the yield shear stress.
 A brittle material usually ruptures when the maximum
tensile normal stress exceeds the ultimate tensile
stress.

18. Hard and Soft materials
 A material hardness is its resistance to scratches and
indentation.
 In Rockwell test, the most common hardness test, a
hard indenter of standard shape is pressed into the
material using a specified load.
 The depth of indentation is measured and assigned a
numerical scale for comparing hardness of different
materials.

19.  A soft material can be made harder by gradually
increasing its yield point by strain hardening.
 As we have seen, at point C in Figure 2 the material has
a permanent deformation even after unloading.
 If the material now is reloaded, point C becomes the
new yield point, as additional plastic strain will be
observed only after stress exceeds this point.

20.  Strain hardening is used, for example, to make
aluminum pots and pans more durable.
 In the manufacturing process, known as deep drawing,
the aluminum undergoes large plastic deformation.
 Of course, as the yield point increases, the remaining
plastic deformation before fracture decreases, so the
material becomes more brittle.

21. True stress and true strain
 We noted that stress decreases with increasing strain
between the ultimate stress and rupture (region DE in
Figure 2).
 However, this decrease is seen only if we plot Cauchy’s
stress versus engineering strain.
 Cauchy’s stress is the load P divided by the original
undeformed cross-sectional area.
 An alternative is to plot true stress versus true strain,
calculated using the actual, deformed cross-section
and length.

22.  In such a plot, the stress in region DE continues to
increase with increasing strain and just as in region
BD.
 Past ultimate stress a specimen also undergoes a
sudden decrease in cross-sectional area called necking.
 Fig. 4.

23. Questions ??