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Laboratory 1: Tensile testing

Mechanical metallurgy laboratory 431303 1

T. Udomphol

LLaabboorraattoorryy 11

Tensile Testing

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Objectives

Students are required to understand the principle of a uniaxial tensile testing andgain their practices on operating the tensile testing machine.

Students are able to explain load-extension and stress-strain relationships. To evaluate the values of ultimate tensile strength, yield strength, % elongation,

fracture strain and Youngs Modulus of the selected metals when subjected to

uniaxial tensile loading.

Students can explain deformation and fracture characteristics of different materialssuch as aluminium, steels or brass when subjected to uniaxial tensile loading.

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1. Literature Review

1.1 Stress and strain relationship

Uniaxial tensile test is known as a basic engineering test to achieve ultimate strength, yield

strength and ductility of interested materials. These important parameters are useful for the selection

of engineering materials for any applications required. A standard specimen is prepared in a round or

a square section along the gauge length as shown in figures 1 a) and b) respectively, depending on the

standard used. Both ends of the specimens should have sufficient length and a surface condition such

that they are firmly gripped during testing. The initial gauge length Lo

is standardized (in several

countries) and varies with the diameter (Do) or the cross-sectional area (A

o) of the specimen as listed

in table 1. This is because if the gauge length is too long, the % elongation might be underestimated

in this case. Any heat treatments should be applied on to the specimen prior to machining to produce

the final specimen readily for testing. This has been done to prevent surface oxide scales that might

act as stress concentration which might subsequently affect the final tensile properties due to

premature failure. There might be some exceptions, for examples, surface hardening or surface

coating on the materials. These processes should be employed after specimen machining in order to

obtain the tensile properties results which include the actual specimen surface conditions.

Figure 1: Standard tensile specimens

Type specimen United State (ASTM) Great Britain Germany

Sheet )/( oo AL 4.5 5.65 11.3

Rod )/( oo DL 4.0 5.0 10.0

Table 1: Dimensional relationships of tensile specimens used in various countries.

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When a specimen is subjected to a tensile loading, the metal will undergo elastic and plastic

deformation. Initially, the metal will elastically deform giving a linear relationship of load and

extension. These two parameters are then used for the calculation of the engineering stress and

engineering strain to give a relationship as illustrated in figure 2 using equations 1 and 2 as follow

oA

P= (1)

oo

of

L

L

L

LL =

= (2)

where is the engineering stress

is the engineering strain

P is the external tensile load

Ao

is the original cross-sectional area of the specimen

Lo

is the original length of the specimen

Lf

is the final length of the specimen

During elastic deformation, the engineering stress-strain relationship follows the Hooks Law

and the slope of the curve indicates the Youngs modulus (E)

=E (3)

If the tensile loading continues, yielding occurs at the beginning of plastic deformation. The

yield stress, y, can be obtained by dividing the load at yielding (Py) by the original cross-sectional

area of the specimen (Ao) as shown in equation 4.

o

y

yA

P= (4)

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Figure 2: Stress-strain relationship under uniaxial tensile loading

The yield point can be observed directly from the load-extension curve of the BCC metals

such as iron and steel or in polycrystalline titanium and molybdenum, and especially low carbon

steels, see figure 3 a). The yield point elongation phenomenon shows the upper yield point followed

by a sudden reduction in the stress or load till reaching the lower yield point. At the yield point

elongation, the specimen continues to extend without a significant change in the stress level. Load

increment is then followed with increasing strain. This yield point phenomenon is associated with a

small amount of interstitial or substitutional atoms. This is for example in the case of low-carbon

steels, which have small atoms of carbon and nitrogen present as impurities. When the dislocations

are pinned by these solute atoms, the stress is raised in order to overcome the breakaway stress

required for the pulling of dislocation line from the solute atoms. This dislocation pinning is related

to the upper yield point as indicated in figure 3 a). If the dislocation line is free from the solute

atoms, the stress required to move the dislocations then suddenly drops, which is associated with the

lower yield point. Furthermore, it was found that the degree of the yield point effect is affected by the

amounts of the solute atoms and is also influenced by the interaction energy between the solute atoms

and the dislocations.

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Aluminium on the other hand having a FCC crystal structure does not show the definite yield

point in comparison to those of the BCC structure materials, but shows a smooth engineering stress-

strain curve. The yield strength therefore has to be calculated from the load at 0.2% strain divided by

the original cross-sectional area as follows

o

yA

P %2.0%2.0 = ...(5)

Note: the yield strength values can also be obtained at 0.5 and 1.0% strain.

The determination of the yield strength at 0.2% offset or 0.2% strain can be carried out by

drawing a straight line parallel to the slope of the stress-strain curve in the linear section, having an

intersection on the x-axis at a strain equal to 0.002 as illustrated in figure 3 b). An interception

between the 0.2% offset line and the stress-strain curve represents the yield strength at 0.2% offset or

0.2% strain.

Figure 3: a) Comparative stress-strain relationships of low carbon steel and aluminium alloy and b)

the determination of the yield strength at 0.2% offset.

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Beyond yielding, continuous loading leads to an increase in the stress required to

permanently deform the specimen as shown in the engineering stress-strain curve. At this stage, the

specimen is strain hardened or work hardened. The degree of strain hardening depends on the nature

of the deformed materials, crystal structure and chemical composition, which affects the dislocation

motion. FCC structure materials having a high number of operating slip systems can easily slip and

create a high density of dislocations. Tangling of these dislocations requires higher stress to

uniformly and plastically deform the specimen, therefore resulting in strain hardening.

If the load is continuously applied, the stress-strain curve will reach the maximum point,

which is the ultimate tensile strength (UTS, TS

). At this point, the specimen can withstand the

highest stress before necking takes place. This can be observed by a local reduction in the cross-

sectional area of the specimen generally observed in the centre of the gauge length as illustrated in

figure 4. After necking, plastic deformation is not uniform and the stress decreases accordingly until

fracture. The fracture strength (fracture

) can be calculated from the load at fracture divided by the

original cross-sectional area,Ao, as expressed in equation 6.

o

fracture

fracture

A

P= (6)

Figure 4: Necking of a tensile specimen occurring prior to fracture

Tensile ductility of the specimen can be represented as % elongation or % reduction in area

as expressed in the equations given below

100%

=

oL

LElongation (7)

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100100%0

=

=A

A

A

AARA

o

fo(8)

where Af is the cross-sectional area of specimen at fracture.

The fracture strain of the specimen can be obtained by drawing a straight line starting at the

fracture point of the stress-strain curve parallel to the slope in the linear relation. The interception of

the parallel line at the x axis indicates the fracture strain of the specimen being tested.

1.2 Fracture characteristics of the tested specimens

Metals with good ductility normally exhibit a so-called cup and cone fracture observed on

either halves of a broken specimen as illustrated in figure 5. Necking starts when the stress-strain

curve has passed the maximum point where plastic deformation is no longer uniform. Across the

necking area within the specimen gauge length (normally located in the middle), microvoids are

formed, enlarged and then merged to each other as the load is increased. This creates a crack having a

plane perpendicular to the applied tensile stress. Just before the specimen breaks, the shear plane of

approximately 45o

to the tensile axis is formed along the peripheral of the specimen. This shear plane

then joins with the former crack to generate the cup and cone fracture as demonstrated in figure 5.

The rough or fibrous fracture surfaces appear in grey by naked eyes. Under SEM, copious amounts of

microvoids are observed as depicted in figure 6. This type of fracture surface signifies high energy

absorption during the fracture process due to large amount of plastic deformation taking place, also

indicating good tensile ductility.

For brittle metals or metals that failed at relatively low temperatures, the fracture surfaces

usually appear bright and consist of flat areas of brittle facets when examined under SEM as

illustrated in figure 7. In some cases, clusters of these brittle facets are visible when the grain size of

the metal is sufficiently large. The energy absorption is quite small in this case which indicates

relatively low tensile ductility due to limited amount of plastic deformation.

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Figure 5: Cup and cone fracture [3]

Figure 6: Ductile fracture surface (Ductile metals) Figure 7: Brittle fracture surface (Brittle metals)

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2. Materials and equipment

2.1 Tensile specimens

2.2 Micrometer or vernia calipers

2.3 Universal testing machine

3. Experimental procedure

3.1 The specimens provided are made of aluminium, steel and brass. Measure and record

specimen dimensions (diameter and gauge length) in a table provided for the calculation of

the engineering stress and engineering strain. Marking the location of the gauge length along

the parallel length of each specimen for subsequent observation of necking and strain

measurement.

3.2 Fit the specimen on to the universal Testing Machine (UTM) and carry on testing. Record

load and extension for the construction of stress-strain curve of each tested specimen.

3.3 Calculate Youngs modulus, yield strength, ultimate tensile strength, fracture strain and %

elongation of each specimen and record on the provided table.

3.4 Analyze the fracture surfaces of broken specimens and sketch and describe the results

3.5 Discuss the experimental results and give conclusions.

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4. Results

Details Aluminium Steel Brass

Diameter (mm)

Width (mm)

Thickness (mm)

Cross-sectional area (mm2)

Gauge length (mm)

Youngs modulus (GPa)

Load at yield point (N)

Yield strength (MPa)

Maximum load (N)

Ultimate tensile strength (MPa)

% Elongation

Fracture strain

Work hardening exponent (n)

Fracture mode

Fracture surfaces

(Sketch)

Table 2: Experimental data for tensile testing.

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Engineering stress-strain curve of aluminium

Describe the engineering stress-strain curve

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Engineering stress-strain curve of steel


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Engineering stress-strain curve of brass


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5. Discussion

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6. Conclusions

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7. Questions

7.1 What is work hardening exponent (n)? How is this value related to the ability of metal to be

mechanically formed?

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7.2 If the tensile specimen is not cylindrical rod shaped but a flat rectangular plate, how do you

expect necking to occur in this type of specimen?

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M h i l t ll l b t 431303 17

7.3 Both yield strength and ultimate tensile strength exhibit the ability of a material to withstand

a certain level of load. Which parameter do you prefer to use as a design parameter for a

proper selection of materials for structural applications? Explain

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8. References

8.1 Hashemi, S. Foundations of materials science and engineering, 2006, 4th

edition, McGraw-

Hill, ISBN 007-125690-3.

8.2 Dieter, G.E.,Mechanical metallurgy, 1988, SI metric edition, McGraw-Hill, ISBN 0-07-

100406-8.

8.3 W.D. Callister, Fundamental of materials science and engineering/an interactive e. text,

2001, John Willey & Sons, Inc., New York, ISBN 0-471-39551-x.

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