TENSILE TESTING PRACTICAL

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Ts’epo Mputsoe

215024596

TENSILE TESTING PRACTICAL

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Summary

Material have different properties all varying form mechanical to chemical properties. Taking special interest in mechanical properties alone, we can physically test and quantify such properties. The properties vary from how brittle or ductile a material is to how much energy it can absorb before it breaks. The experiment employs this physical approach in testing for mechanical properties of metals and attempting to quantify these properties so that it provides a platform in which different material strengths can be compared against each other.

List of Contents

Aim of practical ... 2

Introduction ... 2

Stress (𝜎) ... 2

Strain (𝜀) ... 2

Elastic modulus (E) ... 2

Yield Strength ... 3 Tensile strength ... 3 Elongation (ductility) ... 3 Resilience ... 3 Toughness ... 3 Results ... 4 Raw Data ... 4 Processed Data ... 4

Interpretation and Discussion of Results ... 5

Ductility ... 5

Plasticity ... 6

Yield Stress ... 6

Worst Case graph ... 7

Tensile Strength ... 7 Modulus of resilience ... 7 Modulus of Toughness ... 8 Conclusion ... 8 Appendix ... 9 Bibliography ... 9

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Aim of practical

To determine mechanical properties for a material from a stress strain test.

Introduction

Materials behave differently when exposed to mechanical loads. To quantify these properties

and enable comparison between materials, standard quotients and integrals have been

derived. The functions are explained as follows:

Stress (𝜎)

This is just a quantification of the load per unit area of the material with quotient:

𝜎 =

𝐹_𝐴

[1]

Where: F= Load applied

A= Area on which the load is subjected

Strain (𝜀)

A material under loading will experience a deformation. Strain is a measure of the amount of

deformation an object experiences. [1]

𝜀 =

𝑙𝑒𝑥𝑡𝑒𝑛𝑑𝑒𝑑_𝐿 −𝐿𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙

𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙

Where: 𝐿

𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙

is the original length of the specimen

𝑙

𝑒𝑥𝑡𝑒𝑛𝑑𝑒𝑑

is the extended length of the specimen

Elastic modulus (E)

This is a measure of the proportionality between the stress and the stress on a specimen. The ratio is calculated:

E

=

∆𝜎

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Yield Strength

A specimen under loading will experience a constant ratio of strain due to stress until a limit is

reached where the material becomes permanently deformed and does not display elastic

properties. [1] This is the yielding point of the material and the strain that causes it is called the

yield stress and thus the yield strength of the material.

Tensile strength

After the specimen has reached yield strength, it will continue to experience strain without any increase in the stress. This will continue until it has yielded and will experience strain hardening which is an increase in both the stress and the strain but does not follow the proportionate relationship of the first stage. It will continue to display these properties until it reaches the ultimate tensile strength after which the material will begin necking. [1]

Elongation (ductility)

Necking continues until the material ultimately fractures. The elongation is thus, the stress at the fracture point.

Resilience

In the proportional limits of the stress to strain, work is done by the load on the specimen. This implies therefore, that energy is tranferred to the specimen and is related to the strains of the specimen. This energy is comprehended in terms of the energy density of the specimen which is the amount of strain energy per unit volume of the material. The totality of the strain energy density in the limits of proportionality is then referred to as the resilience of the specimen. [1]

Toughness

The toughness is the total amount of strain energy the material can absorb just before it fractures. This is therefore the total amount of energy within and beyond the proportional limit until the fracture point.

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Results

Raw Data

Force (kN) Guage Length(mm) 0 100 15.7 100.03 31.4 100.07 39.2 100.66 55 103.29 62.8 106.58 90 109.57 100 111.18 96 112.5

Processed Data

Guage Length(m) Extension (m) Stress Strain 0.1 0 0 0 0.10003 3E-05 163541666.7 0.0003 0.10007 7E-05 327083333.3 0.0007 0.10066 0.00066 408333333.3 0.0066 0.10329 0.00329 572916666.7 0.0329 0.10658 0.00658 654166666.7 0.0658 0.10957 0.00957 937500000 0.0957 0.11118 0.01118 1041666667 0.1118 0.1125 0.0125 1000000000 0.125

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Interpretation and Discussion of Results

Ductility

The data produces a standard stress strain curve particular with ductile materials. To quantify

the ductility of the material, it will be expressed as a percentage so that it is easily

comprehensible. This is achieved by expressing the strain at fracture point as a percentage.

Percentage elongation= (𝜀

𝑓

× 100)

= 0.215× 100%

= 21.5%

0 200000000 400000000 600000000 800000000 1E+09 1.2E+09 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Str es s (Pa ) Strain (m/m)

Graph of Stress versus Strain

Stress versus strain graph OFFSET

Strain at fracture Ultimate Tensile Strength Poly. (Stress versus strain graph) Linear (OFFSET)

Linear (Strain at fracture) Linear (Ultimate Tensile Strength)

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This implies that the material elongated by 21.5% of its original length which is a considerable

extension in length and hence a fitting justification to the affirmation that it is a ductile

material.

Plasticity

It is also a largely plastically deformable material up to stresses of about 600MN where the

material starts to yield. The modulus of elasticity is approximated to be 21GPa.

These figures are obtained from the stress strain graph where the modulus of elasticity is

obtained through the 0.2% offset method. Notice however that four of the six initial data points

that build up the graph fall off the best fit line.

Estimation of the elastic region therefore exploits only two of the six possible data points. That

is only 33% of the possible data. It is therefore highly inaccurate with an uncertainty value of

77%. The modulus of elasticity could therefore be anything between 37.17GPa to 16.17GPa.

That is a huge deviation of 21GPa which is 100% of approximated value itself.

The spreadsheet however feeds back an R

2

_{value of 0.9563 which is reasonably close to 1. Take}

then, nothing away from the precision of the best fit line. The large discrepancy is only in the

initial values of the graph with a 100% alignment with the remaining data points.

Yield Stress

The approximated yield stress is definitely affected by the inaccuracy in the starting values. The

inaccuracy however is not as large as that in the plasticity of the material. To quantify the inaccuracy of the yield stress, we analyze the worst case graph which is represented in diagram. The worst case graph does not consider the standard graphs that display mechanical properties and only the precision in the number of data points covered by the graph. That is to say, the worst case graph optimizes the number of data points covered by best fit curve.

The Worst case graph feeds back a yield stress value of about 664MPa while the best fit approximation was 600MPa. This is a deviation of only 10.7%.

The deviation in itself is practically a lot less than 10.7% due to the impossibility of the shape of the graph. The worst case graph in in violation of the standard, observed behavior of metals. It suggests that the material experiences increasing strain under a reducing amount of stress after it has yielded and yet consequently to that, reaches another stage where it undergoes strain hardening. There is no material that displays such properties and thus is simply due to the inaccuracy of the set of data in the beginning stages of the graph.

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Worst Case graph

Tensile Strength

The best fit graph reflects an ultimate tensile strength of 1.04 GPa while the worst case graph feeds back a value of l.06 GPa. There is thus a discrepancy of just 1.2% in the two values. This goes to emphasize the accuracy of the final half of the graph as observed from the exceptional alignment of the best fit curve with the last portion of the data values on the graph.

Modulus of resilience

The modulus of resilience is calculated as the area of the graph in the proportional region. To calculate this, the trapezoidal formula was used in a spreadsheet to calculate the area. The area was therefore determined to be 8.83MJ/m3_{. The material can therefore absorb an approximation of 8.83MJ/m}3_before

it deforms permanently.

The figure is not precisely 8.83MJ/m3_{. It could be understated considering that the system would not be}

closed to interaction with the environment if it so happens that the material is exposed to loading of the stated amount of density. Energy could be lost as thermal heat to the environment during the

interaction and hence more energy may be loaded onto the material before it permanently deforms.

R² = 0.9216 0 200000000 400000000 600000000 800000000 1E+09 1.2E+09 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Stra in Stress

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Modulus of Toughness

As opposed to the modulus of resilience, the modulus of toughness encompasses the totality of the area of the stress strain graph. A similar approach to that which was employed in calculating the modulus of resilience was used to calculate the modulus of toughness. That is to say, the trapezoidal method was used to calculate the total area. It was approximated to be 48.6 MJ/m3_{. This implies that the material}

may absorb energy densities of up to 48.6 MJ/m3 _{before it fractures.}

Conclusion

The material that was tested to have properties:

 Elastic Modulus:

21GPa

 Yield Strength: 600MPa

 Tensile Strength: 1.04 GPa

 Elongation:

21.5%

 Resilience: 8.83MJ/m3

 Toughness: 48.6 MJ/m3

The material is then identified to be a stainless steel alloy. This is because of the extensively elastic properties and yet incredible tensile strength. The stainless steel has been enriched with properties that allow it to be shapeable and yet strong enough to resist stress.

Stainless steel alloy properties vary greater and therefore it is hard to find a metal alloy with properties that are exactly in line with the properties observed from the specimen.

It would have aided in identifying the metal if the metal was tested for composition and the dominant compositor identified. It is a close to impossible task attempting to identify a non- pure specimen from mechanical properties alone as mechanical properties are not necessarily generic to a single type of material. The properties vary greatly due to factors such as wear and slight impurities embedded in the material. The experiment is therefore inconclusive in terms of identifying the metal but nonetheless is a very accurate experiment in terms of investigating mechanical properties alone.

Despite the large variation in the initial set of data points that build up the graph, it revealed to be highly accurate on the determination of the:

 Yield stress

 Tensile Stress

 Toughness

 Resilience

The inaccuracy was reflected extensively in the determination of the modulus of elasticity alone and is only one of the six properties that were subject to investigation. All in all therefore, the experiment is highly accurate and precise.

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Appendix

Forc e (kN) Guage Length(m m) Guage Length( m) Extensi on (m)

Stress Strain Derivat ive Area(mm^2) Integra l Summ ation 0 100 0.1 0 0 0 96 0 15.7 100.03 0.10003 3E-05 16354 1666.7 0.000 3 Area(m^2) 24531. 25 31.4 100.07 0.10007 7E-05 32708 3333.3 0.000 7 0.000096 65416. 66667 39.2 100.66 0.10066 0.0006 6 40833 3333.3 0.006 6 Yield Strength 12045 83.333 55 103.29 0.10329 0.0032 9 57291 6666.7 0.032 9 600MN 75338 54.167 88283 85.417 62.8 106.58 0.10658 0.0065 8 65416 6666.7 0.065 8 Tensile Strength 10761 041.67 90 109.57 0.10957 0.0095 7 93750 0000 0.095 7 1041666666 .67Pa 14015 625 100 111.18 0.11118 0.0111 8 10416 66667 0.111 8 Stress At Fracture Point 83854 16.667 96 112.5 0.1125 0.0125 10000 00000 0.125 0.125 66000 00 48590 468.75 0 0.002 240000 00000 60000 0000 0.027 0 0.125 6 10000 00000 0.125 10716 66667 0.115 0 0.115 1 s

Bibliography

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