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METU

METALLURGICAL AND MATERIALS ENGINEERING DEPARTMENT

Met E 206

MATERIALS LABORATORY

EXPERIMENT 1

Prof. Dr. Rıza GÜRBÜZ

Res. Assist. Erkan Aşık (Room: B-105)

TENSION TEST

INTRODUCTION

Mechanical testing plays an important role in evaluating fundamental properties of

engineering materials as well as in developing new materials and in controlling the quality of

materials for use in design and construction. If a material is to be used as part of an

engineering structure that will be subjected to a load, it is important to know that the material

is strong enough and rigid enough to withstand the loads that it will experience in service. As

a result engineers have developed a number of experimental techniques for mechanical

testing of engineering materials subjected to tension, compression, bending or torsion

loading.

The most common type of test used to measure the mechanical properties of a

material is the Tension Test. Tension test is widely used to provide basic design information

on the strength of materials and is an acceptance test for the specification of materials. The

major parameters that describe the stress-strain curve obtained during the tension test are the

tensile strength (UTS), yield strength or yield point (σy), elastic modulus (E), percent

elongation (%ΔL) and percent reduction in area (%RA). In addition, toughness (UT),

resilience (UR), Poisson’s ratio () can also be calculated by the use of this testing technique.

Generally, round cross section is preferred in tensile testing; however, rectangular

specimens can also be used. Specimen used is approximately uniform over a gage length (the

length within which elongation measurements are done) with wider sections at the grip

positions. This, so called “dog bone” shape is preferred to confine the deformation to the

narrow section (gage length).

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Fig. 1. (a) A standard round tensile test specimen, (b) Screw-driven tensile test machine.

Fig. 1 (a) shows a round tensile test specimen which is machined from the material to

be tested in the desired orientation according to standard ASTM-E8. Fig. 1 (b) is schematic

view of a screw-driven tensile test machine equipped with an extensometer to precisely

measure extension of the specimen.

During tension test, increase in load is recorded with the change in the gage length of

the sample as pulling proceeds. The change in specimen gage length can be measured from

either the change in actuator position (stroke or overall change in length) or a sensor attached

to the sample (called an extensometer). The instantenous load, on the other hand, is measured

by an electronic device called a load cell.

Tensile test machines can be divided in to two categories according to creation of load

on the specimen.

Electromechanical (Screw Driven) Testing Machine: Electromechanical machines

are composed of a variable-speed electric motor which transmits movement to the crosshead

by a screw system made up of two screws (according to the capacity of the machine there can

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also be one or four screws as well). Motion of the crosshead loads the sample in tension or in

compression. Speed of the crosshead can be adjusted by variying the speed of the motor. In

modern universal electromechanical machines, there is a microprocessor-based closed-loop

servo system which can accurately control the speed of the crosshead.

Hydraulic Testing Machine: Hydraulic testing machines are based on action of a

piston. There can be either a single or dual-acting piston; however, most static hydraulic

testing machines have a single acting piston. In a manually operated machine, the operator

adjusts the rate of loading by controlling the pressure which moves the crosshead. In modern,

universal type testing machines, the speed of the crosshead can be adjusted by a

microprocessor based closed loop system which accuraletly controls the pressure.

Electromechanical machines are usually preferred since they have a wider range of

test speeds and longer crosshead displacements. However, hydraulic test machines are more

cost-effective for generating higher forces. Dynamic type hydraulic universal testing

machines are more sophisticated and they can be used to conduct fatigue tests.

Tension test is conducted by applying load to the specimen until it fractures. During

the test, the load required to make a certain elongation on the material is recorded. A load-

elongation curve is plotted by an x-y recorder, so that the tensile behavior of the material can

be obtained. In a modern system, load and elongation data are recorded to a computer by

software. An engineering stress-strain curve can be constructed from this load-elongation

curve or data by making the required calculations. Then the mechanical parameters that we

search for can be found by studying on this curve.

Load and elongation of a specimen are depended to material properties as well as

geometry (size) of the specimen. This raises an urge to normalize load and elongation with

respect to geometry so that it will be material’s property. This is done by normalizing load to

engineering stress and elongation to engineering strain. Engineering stress is obtained by

dividing the load by the original area of the cross section of the specimen, (1) and

engineering stain is calculated by dividing the change in length to original length, (2). The

unit of stress is Pa; however, MPa (106

Pa) is generally preferred and strain is a unitless

parameter.

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= P / Ao (1)

e = l / lo (2)

A typical load versus elongation curve for a ductile metal is shown in Fig 2 (a). It can

be seen that by normalizing the curve, Fig. 2 (b), converting load to stress and elongation to

strain, the shape of the curve does not change but it becomes independent of the geometry.

Fig. 2. Typical behavior of a ductile metal, (a) Load vs. Elongation curve,

(b) Stress vs. Strain curve.

Deformation of a material under load is divided in to two categories, namely; elastic

deformation and plastic deformation. Elastic deformation is recordable and it is temporary

since deformation occurs by stretching of atomic bonds under tensile load. When load is

removed, the material returns to its original shape and dimensions. On the other hand, plastic

deformation includes slipping of atomic planes on one another, breaking bonds and

rebonding, so it is not recoverable. The change in shape and dimensions are permanent. It

must not be misunderstood that, the name, “Plastic deformation” means the material is

plastic. All materials show elastic deformation but some exhibits both elastic and plastic

deformation. Generally, ceramics and glass only deforms elastically, on the other hand metals

and polymers deform both elastically and plastically.

(a)

(b)

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Stress strain curves show limits and characteristics of these two deformation modes

and it is crucial for engineers to know the stress level where plastic deformation starts in

order to design components. A typical engineering stress engineering strain diagram is shown

in Fig. 3. The change in the specimen shape is also shown on the curve. The typical stress

strain diagram for a ductile metal exhibits three different regions corresponding to elastic,

uniform plastic and non uniform plastic deformations. Most of the tensile properties can

directly be determined from this curve.

Fig. 3. Stress-Strain curve of a typical ductile metal, showing different deformation regions

and parameters which can be calculated from the diagram.

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Elastic Deformation Region: The part of the stress-strain curve up to the yielding

point. Elastic deformation is recoverable. In the elastic region, stress and strain are related to

each other linearly.

= E e (3)

The linearity constant E is called the elastic modulus which is specific for each type

of material. GPa (109

Pa) is the standard unit for elastic modulus.

Plastic Deformation Region: The part of the stress-strain diagram after the yielding

point. At the yielding point, measurable amount of plastic deformation starts. Plastic

deformation is permanent. It should not be confused that, in plastic region not only plastic

deformation occurs but also the specimen keeps deforming elastically. Elastic deformation in

this region still obeys Hooke’s law. At the maximum point of the stress-strain diagram

(UTS), neck formation is observed on the test specimen.

(Ultimate) Tensile Strength is the maximum stress that the material can support.

UTS = Pmax / Ao (4)

Because the tensile strength is easy to determine and is a quite reproducible property,

it is useful for the purposes of specifications and for quality control of a product. Extensive

empirical correlations between tensile strength and properties such as hardness and fatigue

strength are often quite useful. For brittle materials, the tensile strength is a valid criterion for

design.

Yield Strength is the stress level at which measurable plastic deformation starts. The

beginning of first recognizable plastic deformation is called yielding. It is an important

parameter in design.

The stress at which plastic deformation or yielding is observed to begin depends on

the sensitivity of the strain measurements. With most materials there is a gradual transition

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from elastic to plastic behavior, and the point at which plastic deformation begins is hard to

define with precision. Various criteria for the initiation of yielding are used depending on the

sensitivity of the strain measurements and the intended use of the data. 0.2% off-set method

is a commonly used method to determine the yield strength. y(0.2%) is found by drawing a

parallel line to the elastic region and the point at which this line intersects with the stress-

strain curve is set as the yielding point. An illustration of 0.2% off-set method is shown in the

Fig. 4 (a). In addition, some materials like low-C steel, exhibit a yielding behavior called

yield point phenomenon. Materials yielding with this phenomenon exhibit a definite drop in

the stress followed by a plateau region where stress fluctuates with increasing strain. This

definite behavior is the start of yielding, Fig. 4 (b). Upper and lower parts of fluctuation are

called upper yield strength (σu

y) and lower yield strength (σly).

Fig. 4. Determination of yield point, (a) typical material,

(b) material exhibiting yield point phenomenon.

Ductility is the degree of plastic deformation that a material can withstand before

fracture. A material that experiences very little or no plastic deformation upon fracture is

termed brittle.

In general, measurements of ductility are of interest in three ways:

1. To indicate the extent to which a metal can be deformed without fracture in

metalworking operations such as rolling and extrusion.

2. To indicate to the designer, in a general way, the ability of the metal to flow

plastically before fracture.

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3. To serve as an indicator of changes in impurity level or processing conditions.

Ductility measurements may be specified to assess material quality even though no

direct relationship exists between the ductility measurement and performance in

service.

Ductility can be expressed either in terms of percent elongation (%Δl) or percent

reduction in area (%RA);

%Δl = [(lf - lo) / lo] x 100 (5)

%RA = [(Ao - Af) / Ao] x 100 (6)

Resilience is the capacity of a material to absorb energy when it is deformed

elastically. It is defined as the area under the stress strain curve up yield point. Since the

deformation is linear, resilience (UR) can be calculated by;

UR= σy2

/ 2E (7)

Toughness is a measure of energy required to cause fracture. A brittle material has a

low toughness. Engineers almost always want to use tough materials in applications.

Toughness (UT) is calculated from the area under the stress strain curve. This area gives the

energy per unit volume of the material and has a unit of J/m3.

Poisson’s Ratio is the lateral contraction per unit breadth divided by the longitudinal

extension per unit length.

= - (d / do) / (l / lo) (8)

Poisson’s ratio is an elastic property and is different for each material. For plastic

deformation, on the other hand, Poisson’s ratio is not a materials property and is equal to 0.5

for all materials.

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True Stress and True Strain: Engineering stress and engineering strain is converted

to true stress and true strain to predict how a material will behave under other forms of

loading and to see the real behavior of the material especially after necking. In engineering

stress-strain diagrams, it seems like the metal gets weaker after necking. However, this is not

the actual case. When instantaneous diameter is measured from the specimen and

instantaneous stress is calculated, it is seen that true stress is much higher than the stress

calculated by initial diameter. True stress and true strain can be calculated from engineering

stress and engineering strain diagrams in the uniform plastic deformation region. On the other

hand, after necking there is no straight way of converting engineering values other than

measuring instantaneous diameter. Fig. 5 show engineering and true stress strain diagrams of

a typical ductile material. For the elastic deformation, true values are very close to

engineering values.

Conversion of engineering values starts by assuming that there is no volume change

in the material;

Ai li = Ao lo (9)

Than true stress (σT) is derived as;

σT =Pi / Ai (10)

where;

Ai= Ao lo / li (11)

and

li = l + lo (12)

By using (11) and (12) in (10)

σT = Pi (l + lo) / ( Ao lo) (13)

σT = σ (1 + e) (14)

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True strain (ε) is defined as the sum of all the instantaneous engineering strains and is

driven as;

d(ε)=dl / l (15)

The true strain is then

∫

(16)

ε=ln(li / lo) (17)

By combining (12) with (17)

ε=ln(1 + e) (18)

Fig. 5. Comparison of engineering and true stress-strain curves.

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For some metals and alloys the region of the true stress–strain curve from the onset of plastic

deformation to the point at which necking begins may be approximated by

σT = K εn (19)

Where K (strength index) and n (strain hardening exponent) are constant which change from

material to material.

PROCEDURE

Before the test

1. Put gage marks on the specimen

2. Measure the initial gage length and diameter

3. Determine the testing speed (i.e either elongation rate or loading rate) in

accordance with the test standard and make the necessary adjustments on

testing machine accordingly.

Conduct the test until fracture

Keep the testing speed constant during the whole test. Make a few

measurements for the instantaneous gage length and gage diameter after yielding and after

necking.

After the test

1. Measure the final gage length and diameter. The diameter should be

measured from the neck.

2. Measure hardness of the specimen and check if the empirical relation

UTS=3.45 HB is true for plain-C steels.

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ASSIGNMENTS

1. Tabulate the data obtained during the test.

2. Plot the load versus elongation curve with computer software. Make scales

for both x and y axis. Label the known values.

3. Plot the engineering stress-strain curve with computer software. Make scales

for both x and y axis. Label the known values.

4. Calculate the strength parameters;

a. Yield stress (0.2 % off-set), y [MPa]

b. Young’s modulus, E [GPa]

c. Ultimate tensile strength, UTS [MPa]

d. Fracture Stress, F [MPa]

5. Calculate the critical strains;

a. Yield strain, ey

b. Strain at onset of neck (Maximum uniform strain), eu

c. Fracture strain, ef

6. Calculate the ductility parameters;

a. Percent elongation, %∆L

b. Percent reduction in area, %RA

7. Calculate the energy parameters

a. Resilience, UR; the elastic energy in J/m3.

b. Toughness, UT; the total energy absorbed by the specimen in J/m3.

PS: Do not forget MPa to J/m3 conversion derivation

8. Calculate the Poisson’s ratio assuming volume is constant during elastic

deformation.

9. Relate Brinell hardness of the specimen with its UTS.

10. Derive the true stress-true strain equations. Draw true stress vs. true strain

diagram. Draw log σT vs log ε. Find the constants of the equation; σT =K εn

.

11. Tabulate your results.