PARAPHRASING

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Summary :

In this experiment four materials were tested to find their modulus of elasticity , yield strength , tensile strength ,fracture of stress and the elongation percentage . These materials were steel , brass , aluminium and copper. All results are presented in table 1.0.The strongest material was steel .Aluminium was the weakest metal among the other materials and the values compared were relatively close to the values provided in chapter 6 of the book ”Materials Science and Engineering an Introduction “.

Introduction :

The tensile test is the test most commonly used to indicate the strength and ductility of a material and, often, it is on tensile testing results that the engineer bases his/her design.

In this test a prepared testpiece is held in a suitable device and subjected to a gradually increasing uniaxial load, until failure occurs. During the test, observations of the applied load for appropriate extensions (usually measured via an extensometer) are recorded, frequently in graphical form as a plot of load vs. extension (elongation). The load-deflection characteristics are dependent on the specimen size. Thus, to minimise these geometric factors, load and extension are normalised to engineering stress and engineering strain respectively. It should be noted that the central portion of the testpiece length is reduced in cross sectional area to ensure that yielding and fracture occur in a region where the stresses are not affected by the gripping devices. The transition from the ends to the reduced section is made by an adequate fillet to avoid stress-concentrations caused by an abrupt change of section. This is particularly important for brittle materials which would fracture at a poorly prepared fillet rather than in the central gauge length, as is required in all tensile tests.

Theory :

Stress-strain plot is slightly different between materials and this would lead to a variety of modulus of elasticity , Yield strength and tensile strength values .

Aim :

To calculate Young’s Modulus, Stress, Strain and Elongation for four metals which are: Mild Steel (Grade 250), Aluminium 6061, Copper (C12200) and Brass (C380).

Procedure:

· Record the dimensions and all information of each of the metal test piece.

· Place metal piece into the Universal Testing Machine.

· Use load extension data to create a stress vs. strain graph for the material.

· Calculate young’s modulus, yield strength, ultimate tensile strength, fracture stress and percentage of elongation.

RESULTS:

1- Mild steel:

Area = 10*2.95×10-6 m2 , initial length = 25 mm, Max Length = 10.74872 mm

Stress, load= 7088.28 N, .·. σ = 240.28 MPa

Strain =, L = 0.03228 mm, .·. ε= 1.29×10-3

.·. E = , .·. E = 186.26 GPa

YS = , yield load= 8878.177 N,

.·. YS = 300.95 MPa

Ultimate Tensile Strength, UTS = , max load= 11.11858×103KN,

.·. UTS= 376.9 MPa

Fracture Stress = , load= 4233.288 N, .·. Fracture Stress = 143.5 MPa

% elongation, δ = , .·. δ = 42.99 % =43%

Toughness = from graph 1.0 , .·. T = 131.65 Mpa

Resilience = , .·. Resilience = 243 kpa

2- Aluminium 6061 :

Area = 10*2.95×10-6 m2 , initial length = 25 mm, Max Length = 4.11199 mm

Stress , F = 3942.067 N, .·. σ = 133.62 MPa

Strain = , , .·. ε = 0.0177

E = , .·. E = 7.54 GPa

YS = , yield load = 3971.444 N, .·. YS = 134.62 MPa

Ultimate Tensile Strength, UTS = , max load= 3.978×103 KN,

.·. UTS= 134.84 MPa

Fracture Stress = , load= 86.656 N, .·. Fracture Stress = 2.937 MPa

% elongation, δ = , .·. δ = 16.44 %

Toughness = from graph 2.0, .·. T = 35.40 Mpa

Resilience = , .·. Resilience = 1201 kpa

3- Copper:

Area = 10.3*3×10-6 m2 , initial length = 25 mm, Max Length = 11.0361 mm

Stress , F = 7332.15 N, .·. σ = 237.28 MPa

Strain = , , .·. ε = 0.208

E = , .·. E = 1.140 GPa

YS = , yield load = 7330.55 N, .·. YS = 237.23 MPa

Ultimate Tensile Strength, UTS = , max load= 7.33331×103 KN,

.·. UTS= 237.23 MPa

Fracture Stress = , load= 3311.45 N, .·. Fracture Stress = 107.166 MPa

% elongation, δ = , .·. δ = 44.14 %

Toughness = from graph 3.0 , .·. T = 103.8 Mpa

Resilience = , .·. Resilience = 24683 kpa

4- Brass:

Area = 10*2.95×10-6 m2 , initial length = 25 mm, Max Length = 14.21716 mm

Stress , F = 10646.7 N, .·. σ = 360.9 MPa

Strain = , , .·. ε = 0.448

E = , .·. E = 0.805 GPa

YS = , yield load = 10647.3 N, .·. YS = 360.92 MPa

Ultimate Tensile Strength, UTS = , max load= 10.71058×103 KN,

.·. UTS= 363.07 MPa

Fracture Stress = , load= 5183.832 N, .·. Fracture Stress = 175.72 MPa

% elongation, δ = , .·. δ = 56.8 %

Toughness = from graph 4.0 , .·. T = 127.5 Mpa

Resilience = , .·. Resilience = 80908 kpa

Table 1.0 Calculated results for the three tested specimens:

Test piece

and

Composition

E

[GPa]

YS

[MPa]

UTS

[MPa]

Fracture

Stress

[MPa]

Elongati

on

[%]

Fracture

Appearance

1. Mild Steel (Grade 250)

186.26

300.95

376.9

143.5

43 %

2. Aluminium 6061

7.54

134.62

134.84

2.937

16.44 %

3. Copper (C12200)

1.140

237.32

237.323

107.166

44.14 %

4. Brass (C380)

0.805

360.92

363.07

175.72

56.8 %

Graph 10: Copper – Stress vs Strain (Whole Curve)

Graph 2.0: Mild Steel – Stress vs Strain (Whole Curve)

Graph 2.1: Mild Steel – Stress vs Strain (Elastic)

Graph 3.0: Aluminium – Stress vs Strain (Whole Curve)

Graph 3.1: Aluminium – Stress vs Strain (Elastic)

Graph 4.0: Brass – Stress vs Strain (Whole Curve)

Graph4.1: Brass – Stress vs Strain (Elastic)

Discussion:

Mild steel, Aluminium, Copper and Brass are stretched by the testing machine and as expected fractured in the centre. The machine recorded load extension data which was graphed and transformed into a stress and strain graph using the equations to calculate. Calculations made in order to determine young’s modulus, yield strength, ultimate tensile strength, fracture stress and percentage elongation of the material.

Toughness is determined by how much energy a material can absorb before breaking. Resilience is the capacity to absorb energy when deformed elastically. Lower young’s modulus and the greater tensile strength is greater resilience as it can see from the equation.

Aluminium has very little ductility, which can break quickly, this lead to the area under its stress – strain curve to be lower than other materials. Tensile strength is determining the amount of strain in the material before starting to neck itself. Higher tensile strength has high in toughness. Ultimately strength and ductility is required for a tough material.

Issues that could contribute to uncertainties in the experimental measurement and error in the results are approximated to some extent from the testing machine. Error due to results of equations being rounded then reused as powers in later equations. All engineering materials are not exactly the same and each sample of material have slightly different mechanical properties.

Conclusion:

After testing the specimens Mild Steel, Aluminium, Copper and Brass calculations was computed to determine stress, strain, young’s modulus, % of elongation, toughness, resilience, fracture stress, and ultimate tensile strength. All results are presented in Table 1.0. According to the calculation, Mild Steel found to be the strongest material among the other tested specimens with approximately 43 % elongation and the ultimate tensile strength of 376.9 Mpa. Copper was ductile stretching with elongation of 44.14 %, but it was weaker than mild steel and brass. Brass was relatively strong as well; the ultimate tensile strength was 363.07 Mpa and had 56.8 % of elongation. Aluminium was the weakest metal as its ultimate tensile strength was 134.84 Mpa and 16.44 %. The values computed were relatively close to the values provided in chapter 6 of the book “Materials Science and Engineering an Introduction”.

References

William D. Callister, Jr. Seventh Edition, 2007, Materials Science and Engineering An Introduction, John Wiley Inc.

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Aluminium 6061 2.0000000000000029E-5 1.2250000000000002E-2 2.2620000000000012E-2 3.1660000000000001E-2 3.985000000000001E-2 4.6490000000000004E-2 5.2440000000000001E-2 5.8430000000000003E-2 6.5620000000000012E-2 7.4490000000000098E-2 8.6560000000000067E-2 0.10255 0.12157000000000008 0.14437 0.17136000000000001 0.20066999999999999 0.23223000000000016 0.26708000000000032 0.30098000000000047 0.32291000000000047 0.36589000000000033 0.43673000000000001 0.45778000000000002 0.45991000000000032 0.48822000000000032 0.55366000000000004 0.63437000000000066 0.63634000000000079 0.64982000000000095 0.65492000000000095 0.66161000000000092 0.74272000000000094 0.82685000000000064 0.87425000000000064 0.87928000000000062 0.91405000000000003 0.91673000000000004 0.91787000000000063 0.97924000000000067 1.0659099999999975 1.1319399999999977 1.14653 1.19164 1.2272199999999998 1.2308999999999988 1.2345999999999975 1.23651 1.23881 1.2991699999999988 1.37964 1.46031 1.52057 1.5807199999999999 1.5870500000000001 1.5864500000000001 1.5905199999999999 1.5984500000000001 1.60575 1.6958199999999999 1.7725500000000001 1.8631800000000001 1.9565100000000013 1.9842000000000013 1.98159 1.9866400000000013 1.9903200000000001 2.0321999999999987 2.0876700000000001 2.1673400000000012 2.2335400000000001 2.3019499999999962 2.3693200000000001 2.3716099999999956 2.3710899999999961 2.37303 2.4063300000000001 2.4704999999999977 2.4884900000000001 2.4955099999999977 2.4967099999999967 2.5012699999999977 2.5004599999999977 2.5025300000000001 2.5037200000000026 2.5282100000000001 2.5967599999999962 2.6631300000000055 2.7400200000000012 2.8049300000000001 2.8769599999999955 2.9543599999999977 3.0311999999999997 3.12297 3.1896900000000001 3.2396099999999977 3.29637 3.3158799999999942 3.3235700000000001 3.3244699999999967 3.3421999999999987 3.3839399999999999 3.4150999999999967 3.4350999999999976 3.71468 4.4476300000000002 1011.67526 1859.8989399999998 2614.8098 3282.4932000000022 3808.7095300000001 4297.8456600000054 4742.7740700000004 5178.9240500000005 5589.9198400000005 5957.0315500000006 6271.3220700000065 6534.58133 6754.9686100000008 6940.7084599999998 7096.8975100000007 7231.6351500000001 7349.9062700000004 7454.1051700000044 7540.0811400000002 7614.8781200000003 7591.0788799999991 7757.93552 7834.4929200000024 7790.9830199999997 7856.55141 8056.1310100000001 8107.5659400000004 8140.9952000000003 8237.6369799999848 8338.1867399999846 8283.5957400000007 8313.8671499999818 8370.7800500000048 8588.4118099999851 8602.7455300000001 8648.7087600000068 8627.6641500000005 8600.1625700000004 8606.5417500000149 8832.7512100000004 8831.0337100000088 8890.1898299999848 8987.0095299999848 8950.1434600000157 9012.5629299999819 9108.003969999987 9082.3709999999719 9209.4764099999848 9116.6773400000002 9016.2295100000028 9263.2010600000049 9104.1496399999851 9331.9112100000002 9240.40049 9469.8107199999849 9501.1755799999846 9562.1108999999851 9228.47271 9417.072239999985 9404.1135900000008 9398.6982100000005 9528.6056399999761 9404.3281699999843 9526.4071199999798 9557.704929999989 9642.6549599999871 9687.0955799999847 9528.4259299999721 9637.1492700000108 9741.6749600000003 9769.2292900000029 9788.4160299999839 9667.1086500000001 9694.780109999987 9733.67929 9735.2430200000108 9767.655729999984 9766.6794100000006 9799.0965799999849 9932.6267800000005 9733.6927100000048 9809.3891099999819 9887.9939299999842 9928.6794700000009 9958.2034300000068 9988.7099899999848 9890.2434100000119 9908.5092500000028 9926.8519899999719 9939.4556899999698 9990.559819999984 9881.463649999987 9867.7459400000007 9770.7769299999818 9767.3231400000004 9755.7771199999843 10050.80937999999 9995.3475600000002 9954.0495900000005 9943.8089099999761 9680.5992700000006 9612.2252900000003 5466.9789999999994

Strain

Stress (N)

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