ME 212 LABORATORY EXPERIMENT #2
TENSILE & COMPRESSIVE TESTING OF MATERIALS
1.INTRODUCTION & THEORY
TENSION TEST
The tension test is the most commonly used method to evaluate the mechanical properties
of metals. Its main objective is the determination of properties related to the elastic design of
machines and structures. Since the test is fully standardized and well established, one may state
that it is a rapid way of obtaining the desired mechanical characteristics of materials.
Basically, in a tension test a metallic specimen of specified dimensions according to
relevant standards is pulled under the action of uniaxial forces applied at both ends until the
specimen undergoes fracture. A typical tensile test specimen can be seen in Figure 1. The “gage
length” corresponds to the effective length of the specimen over which the elongation occurs.
Therefore, the initial length of the specimen is taken to be equal to the gage length Lg. Turkish
standards Institute (TSE) suggest a formula for the determination of gage lengths depending on
the initial cross-sectional area of the specimen, Ao :
(where K = 11,3 for relatively long bars and K = 5,65 for relatively short bars)
Figure 1. Typical Tensile Test Specimen
In tensile testing of metals and polymers, an elastic deformation to a certain limit is
observed first which is followed by a considerable plastic (permanent) deformation. The plastic
deformation ends with the total fracture of the specimen. In contrast, in ceramics and some
plastics, very little plastic deformation is observed before fracture. The first set of materials which
can be plastically deformed are called “ductile”, where as the second set of materials are called
“brittle”.
While the applied uniaxial load is continuously increasing, the elongation in the specimen
is recorded, such that at the end of the test a set of data for corresponding readings of load and
displacement values is obtained. Recalling that the engineering stress is defined to be the ratio of
the applied load to the initial cross sectional area, “
” and that the engineering strain is
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defined to be the ratio of the elongation to the initial length of the specimen, “
”, one
can plot the engineering stress-engineering strain curve. A typical stress strain curve for a ductile
material is shown in Figure 2.
Figure 2. Typical stress-strain curve for a ductile material
However, it should be taken into account that the cross-sectional area of the specimen is
continuously decreasing due to the conservation of volume principle as the sample elongates
during the test. Therefore the true value of stress during a tensile test should be defined as
“
” , taking A values to be instantaneous area values. Similarly, the engineering
equation for strain takes it as granted that the gage length does not change, which is quite
unrealistic. A better equation for the strain values is given as “
”, taking the change of
gage length into account. The engineering values for stress and strain are most of the time
appropriate for engineering purposes, which usually involve only elastic eformations, whereas the
true values of stress and strain are needed to understand the behavior of materials in a better way.
According to the fact that mild steel is the most common engineering material employed
in structures, its stress-strain curve at a first sight turns out to be more significant. Typical low
carbon steel would yield a stress-strain curve as in Figure 3, if tensile loads are applied at both
ends at room temperature.
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Figure 3. Stress-Strain Curve for typical low-carbon steel
The engineering stress-strain curve can be best interpreted by dividing it into two parts,
namely elastic and plastic portions.
(i) Elastic Range
As the specimen is loaded, first it behaves like a spring with a definite spring constant
according to the so-called Hooke’s Law:
where “E”, defined as Young’s Modulus, acts as the corresponding “spring” constant. In this
“elastic” region, the stress-strain curve is linear. The point at which the linearity ends is defined as
the yield point. In the stress-strain curve, “E” acts as the slope of the loading line in the elastic
region. Typical values of elastic moduli for some common engineering materials are listed in
Table 1. As long as the metal is loaded within the elastic region, the strains are totally recoverable
and the specimen will return to its original dimensions as the load is relaxed to zero. When the
load exceeds the corresponding yield point, the specimen undergoes gross plastic deformation,
and is permanently deformed even if the load is returned to zero afterwards.
Table 1. Elastic Moduli of some common Engineering Materials
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In the case of mild steel, one should distinguish between the upper and the lower yield
strengths (points). The maximum stress reached in the specimen prior to the onset of significant
plastic deformation is called the “upper yield strength”, whereas the “lower yield strength” is the
stress corresponding to the horizontal portion of the stress-strain curve immediately following the
beginning of plastic deformation. The oscillating character of this portion of the stress-strain curve
–usually referred to as
serrated yielding– represents temporary plastic instability, a common
characteristic of mild-steel. Beyond the lower (
serrated) yield point, the material continues
deforming as expected until fracture.
Sometimes a definite yield point as in mild-steel cannot be observed in other ductile
metals. Nevertheless an offset yield strength can be determined by drawing a parallel line to the
elastic portion of the curve, starting from the 0.2% strain level. Therefore, the offset strength of a
metal can be obtained this way, and the determined value may be employed in the calculations.
The term “toughness” associated with stress-strain curve for a given material, is defined as
the ability of the material to absorb mechanical energy until fracture. Toughness can be defined as
the strain integral of the stress-strain curve, such that:
From this definition, one may deduce that toughness is the area under the stress-strain
curve until the fracture strain. Since most of the time, the exact functional dependence of stress on
strain is unknown in the plastic zone, some approximation formulas to calculate the toughness of
brittle and ductile materials have been proposed in the literature. One of these approximating
formulas can be found in the “Tasks” section of these experiment sheets.
The ability to absorb energy solely in the elastic region is defined as “resilience”. The
calculation of “resilience” again involves the calculation of the area under the stress-strain curve
up to the yield point, thus forming a triangle with side lengths of
and
.
(ii) Plastic Range
Although extensive discussion of plastic deformation mechanisms is beyond the scope of
this laboratory session, brief information regarding the mechanisms will be given here.
As one loads the specimen beyond the yield point and then relaxes the load to zero, the
material does not recover its initial dimensions completely, instead a permanent strain is observed.
This property characterizes the induced deformation as “plastic”and the portion of the stress-strain
curve beyond the yield point is defined as the plastic “range”. Beyond the yield point, Hooke’s
Law is not applicable any more, since the stress needed to produce continued plastic deformation
increases with increasing strain in the plastic region. This phenomenon is defined as “strain-
hardening”. The maximum point in the engineering stress-strain curve corresponds to the
“ultimate tensile strength, UTS” of the material, which is at the same time the minimum necessary
stress to cause the phenomenon known as “necking”. Necking is defined as a localized decrease in
the cross-sectional area of the specimen, which results due to the imperfections which act as local
stress raisers in the material. Upon application of the UTS, all further plastic deformation is
concentrated in the “necking” region and rapid fracture follows.
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COMPRESSION TEST
Simple tensile testing usually yields sufficient data to determine the mechanical properties
of ductile materials. In those materials, the yield limits under tension and compression are
generally the same. Therefore, it is not necessary to perform the compression test on highly
ductile materials such as mild steel or most Al-alloys.
However, in some materials such as brittle and fibrous ones, the tensile strength is
considerably different from compressive strength as seen in Figure 4. Therefore it is necessary to
test them under tension and compression separately.
Figure 4. Compression and Tension stress-strain curves for (a) GCI and (b) Concrete
Brittle materials, such as cast iron and concrete, are often weak in tension because of the
presence of submicroscopic cracks and faults. However, these materials can prove to be quite
strong in compression, due to the fact that the compression test tends to increase the cross
sectional areas of specimens, preventing necking to occur. In general, the average compressive
strength to tensile strength ratio of brittle materials is around 8/1.
Wood is a commonly used engineering material showing different mechanical behavior
under tensile and compressive loadings. However, contrary to Gray Cast Iron or Concrete, it does
not show brittle characteristics under tensile loading and surprisingly, it’s considerably stronger in
tension than compression. The fact that the cell structures in the material are stronger in the
longitudinal than transverse direction is the major factor leading to this unusual mechanical
behavior of wood.
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2. TASKS
A) TENSION TEST
1. Measure initial and final sample dimensions such as lo, do, lf, df.
2. Prepare a load displacement plot from the data given to you by TA.
3. Construct both the engineering and true stress-strain curves on MS Excel.
4. Determine the following properties of the material:
a. Modulus of elasticity.
b. Yield strength, tensile strength, true tensile strength, breaking strength, true breaking
strength, and strain hardening exponent.
c. Ductility as both percentage elongation and percentage reduction in area.
d. Estimate toughness (total energy absorption capacity) by the aid of the stress-strain curve.
e. Discuss the mode of fracture by observing the fracture surface.
B) COMPRESSION TEST
1. Summarize compression testing
2. Determine compression strength of the material.
3. Determine the nature of fracture (if occurs) in the specimens.
4. Comment on why tensile and compressive strengths of some materials differ while most of
the metallic ones are similar.
REFERENCES
• William D. Callister, Jr.,
Materials science and engineering: an introduction, Wiley,
(New York:2000).
• Fenner, A.J,
Mechanical Testing of Materials, Philosophical Library,
(New York:1965).
• Foster, P.F,
The mechanical testing of metals and alloys : the theory and practice of
standardized mechanical testing, Sir I. Pitman & Sons Ltd., (London:1942).
