lab 3tensile eng

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Laboratory 3: Tensile testing

Mechanical metallurgy laboratory 431303 1

T. Udomphol

L Laabboor r aat t oor r y y 33

Tensile Testing

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Objectives

• Students are required to understand the principle of a uniaxial tensile testing and

gain their practices on operating the tensile testing machine to achieve the required

tensile properties.

• Students are able to explain load-extension and stress-strain relationships and

represent them in graphical forms.

• 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 materials

such as aluminium, steels or brass when subjected to uniaxial tensile loading.





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Figure 1: Standard tensile specimens

Type specimen United State (ASTM) Great Britain Germany

Sheet )/( oo A L 4.5 5.65 11.3

Rod )/( oo D L 4.0 5.0 10.0

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

The equipment used for tensile testing ranges from simple devices to complicated controlled

systems. The so-called universal testing machines are commonly used, which are driven by

mechanical screw or hydraulic systems. Figure 2 a) illustrates a relatively simple screw-driven

machine using large two screws to apply the load whereas figure 2 b) shows a hydraulic testing

machine using the pressure of oil in a piston for load supply. These types of machines can be used not

only for tension, but also for compression, bending and torsion tests. A more modernized closed-loop

servo-hydraulic machine provides variations of load, strain, or testing machine motion (stroke) using a

combination of actuator rod and piston. Most of the machines used nowadays are linked to a

computer-controlled system in which the load and extension data can be graphically displayed

together with the calculations of stress and strain.

General techniques utilized for measuring loads and displacements employs sensors

providing electrical signals. Load cells are used for measuring the load applied while strain gauges are

used for strain measurement. A Change in a linear dimension is proportional to the change in

electrical voltage of the strain gauge attached on to the specimen.





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Figure 2: Schematics showing a) a screw driven machine and b) a hydraulic testing machine[3].

1.2 Stress and strain relationship

When a specimen is subjected to an external 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 3 using equations 1 and 2 as follows

o A

P =σ (1)

oo

o f

L

L

L

L L ∆=

−=ε (2)

where σ is the engineering stress

ε is the engineering strain

P is the external axial tensile load

Ao

is the original cross-sectional area of the specimen

Lo

is the original length of the specimen

L f

is the final length of the specimen

The unit of the engineering stress is Pascal (Pa) or N/m2

according to the SI Metric Unit

whereas the unit of psi (pound per square inch) can also be used.





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1.2.1 Youngs modulus, E

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

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

ε

σ

= E (3)

Youngs modulus is of importance where deflection of materials is critical for the required

engineering applications. This is for examples: deflection in structural beams is considered to be

crucial for the design in engineering components or structures such as bridges, building, ships, etc.

The applications of tennis racket and golf club also require specific values of spring constants or

Youngs modulus values.

Figure 3: Stress-strain relationship under uniaxial tensile loading





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1.2.2 Yield strength, σy

By considering the stress-strain curve beyond the elastic portion, if the tensile loading

continues, yielding occurs at the beginning of plastic deformation. The yield stress, σ y, can be

obtained by dividing the load at yielding ( P y) by the original cross-sectional area of the specimen ( A

o)

as shown in equation 4.

o

y

y A

P =σ (4)

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 4 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.

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 y A

P %2.0

%2.0=σ

...(5)





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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. However offset at different values can also be made depending on specific uses: for

instance; at 0.1 or 0.5% offset. The yield strength of soft materials exhibiting no linear portion to

their stress-strain curve such as soft copper or gray cast iron can be defined as the stress at the

corresponding total strain, for example, ε = 0005.

The yield strength, which indicates the onset of plastic deformation, is considered to be vital

for engineering structural or component designs where safety factors are normally used as shown in

equation 6. For instance, if the allowable working strength σ w= 500 MPa to be employed with a

safety factor of 1.8, the material with a yield strength of 900 MPa should be selected. It should be

noted that the yield strength value can also be replaced by the ultimate tensile strength, σ TS , for

engineering designs.

Safety factors are based on several considerations; the accuracy of the applied loads used in

the structural or components, estimation of deterioration, and the consequences of failed structures

(loss of life, financial, economical loss, etc.) Generally, buildings require a safety factor of 2, which

is rather low since the load calculation has been well understood. Automobiles has safety factor of 2

while pressure vessels utilize safety factors of 3-4.

Factor Safety Factor Safety

TS y

w

σ σ

σ ,= (6)





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Figure 4: a) Comparative stress-strain relationships of low carbon steel and aluminium alloy and b)

the determination of the yield strength at 0.2% offset.

1.2.3 Ultimate Tensile Strength, σTS

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, σ 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 5.





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o

TS A

P max=σ (6)

1.2.4 Fracture Strength, σf

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

fracture. The fracture strength (σ fracture

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

original cross-sectional area, Ao, as expressed in equation 7.

o

fracture

fracture A

P =σ (7)

1.2.5 Fracture Strain, εf

Figure 5: Necking of a tensile specimen occurring prior to fracture

1.2.6 Tensile ductility

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

as expressed in the equations given below





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100% ×∆

=

o L

L Elongation (8)

100100%0×

∆

=×

−

= A

A

A

A A

RAo

f o

(9)

where A f

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.

1.2.7 Work hardening exponent, n

Furthermore, material behavior beyond the elastic region where stress-strain relationship is

no loner linear (uniform plastic deformation) can be shown as a power law expression as follows

n K ε σ = (10)

Where σ is the true stress

ε is the true strain

n is the strain-hardening exponent

K is the strength coefficient

The strain-hardening exponent values, n, of most metals range between 0.1-0.5, which can be

estimated from a slope of a log true stress-log true strain plot up to the maximum load as shown in

figure 5. Equation 10 can then be written as follows

K n logloglog += ε σ (11)

Y = mX + C (12)





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KK

While n is the slope (m) and the K value indicates the value of the true stress at the true strain

equal to unity as illustrated in figure 6. High value of the strain-hardening exponent indicates an

ability of a metal to be readily plastically deformed under applied stresses. This is also corresponding

with a large area under the stress-strain curve up to the maximum load. This power law expression

has been modified variably according to materials of interest especially for steels and stainless steels.

Figure 6: Slope of log true stress- log true strain curve up to the ultimate tensile strength indicating

the work hardening exponent (n value) [3]

1.2.8 Modulus of Resilence, UR

Apart from tensile parameters mentioned previously, analysis of the area under the stress-strain curve can give informative material behavior and properties. By considering the area under the

stress-strain curve in the elastic region (triangular area) as illustrated in figure 7, this area represents

the stored elastic energy or resilence. The latter is the ability of the materials to store elastic energy

which is measured as a modulus of resilence, U R

, as follows

E

U ooo R

22

12

σ

ε σ == (13)





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The significance of this parameter is considered by looking at the application of mechanical

springs which requires high yield stress and low Youngs modulus. For example, high carbon spring

steel has the modulus of resilence of 2250 kPa while that of medium carbon steel is only 232 kPa.

1.2.9 Tensile toughness, UT

Tensile toughness, U T , can be considered as the area under the entire stress-strain curve which

indicates the ability of the material to absorb energy in the plastic region. In other words, tensile

toughness is the ability of the material to withstand the external applied forces without experiencing

failure. Engineering applications that requires high tensile toughness is for example gear, chains and

crane hooks, etc. The tensile toughness can be estimated from an expression as follows

f uo

f uT or U ε

σ σ

ε σ

2

+≈ (14)

Fig 7: Area under the stress-strain curve of high carbon spring steel and structural steel [2].

1.3 Fracture characteristics of the tested specimens

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

observed on either halves of a broken specimen as illustrated in figure 8. 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





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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 8. The rough or fibrous fracture surfaces appear in grey by naked eyes. Under

SEM, copious amounts of microvoids are observed as depicted in figure 9. 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. Metals such as aluminium and copper

normally exhibit ductile fracture behavior due to a high number of slip systems available for plastic

deformation.

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 10. 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 prior to failure.

Figure 8: Cup and cone fracture [4]





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Figure 9: Ductile fracture surface (Ductile metals) Figure 10: Brittle fracture surface (Brittle metals)

In summary, tensile properties should be considered as important design parameters for the

selection of engineering materials for their desired application. Engineers have played a significant

role in that they should be able to analyze and understand material behavior and properties through

these mechanical testing parameters. Table 2 lists tensile properties of various engineering materials.

Table 2

Tensile properties of metals [2]





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2. Materials and equipment

2.1 Tensile specimens

2.2 Micrometer or vernia calipers

2.3 Universal testing machine

2.4 Stereoscope

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, %

elongation and % area of reduction of each specimen and record on the provided table.

3.4 Analyze the fracture surfaces of broken specimens using stereoscope, 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

% Area of reduction

Fracture strain

Work hardening exponent (n)

Fracture mode

Fracture surfaces

(Sketch)

Table 3: 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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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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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 Norman E. Dowling, Mechanical Behavior of Materials, Prentice-Hall International, 1993.

8.4 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

lab 3tensile eng

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