Contents Introduction Sample x results Sample y results Elasticity and Elastic Limit Yield Point and Plasticity Ultimate Tensile Strength Stiffness Ductility Brittleness Hooke's Law Young's Modulus Conclusion Sample x graph Sample y graph Sample z graph List of references Page 2 Page 3 Page 4 Page 5 Page 5 Page 6 Page 6 Page 7 Page 7 Page 8 Page 8 Page 9 Page 11 Page 12 Page 13 Page 14

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University No. 11365048

The Tensile Test I have been provided with laboratory results from tensile tests carried out on 3 samples of materials x, y and z. My task is to use this data to determine the values of modulus of elasticity, limit of proportionality, ultimate tensile strength and other important facts about each material. I will examine the behaviour of each sample under tensile load by means of stress-v's-strain tables and graphs, then identify each material. In order to calculate the value of stress, we must first determine the cross sectional area (CSA) of each material tested. Each sample is of rectangular cross section 20mm by 1mm. CSA = 20mm x 1mm CSA (m^2) = (20x10^-3) x (1x10^-3) = 20 x 10^-6 m^2 or = 0.00002 m^2 I can now use the CSA together with the test results I have been provided with to calculate the instantaneous stress and strain values of each sample after each tensile load is applied using the following formulae: Stress (σ) = Force (F) / CSA Strain (ε) = Extension (x) / Original Length (L) As an example, I will show my calculations of the stress and strain values for the first load applied on test sample x, then I will display the remainder of my results in tables. σ = F / CSA = 1x10^3 / 20x10^-6 = 50x10^6 Pa ε (%) = (x / L) x 100 = (0.48 / 375) x 100 = 0.128% Page 2 of 15

University No. 11365048

Results for sample x length 375mm CSA of 20x10^-6 m^2 Load Applied (Kn) Extension (mm) Stress (MPa) Strain (%)

1.0 2.0 3.0 4.0 5.0 6.0 7.0 7.5 8.0 8.5 8.3 8.0 7.0 6.1

0.48 0.60 0.70 0.80 0.85 0.95 1.27 1.60 2.65 5.50 7.00 7.90 8.70 9.10

50 100 150 200 250 300 350 375 400 425 415 400 350 305

0.128 0.160 0.187 0.213 0.227 0.253 0.339 0.427 0.707 1.467 1.867 2.107 2.320 2.427

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University No. 11365048

Results for sample y Length 550mm CSA 20x10^-6 m^2 Load Applied (Kn) Extension (mm) Stress (MPa) Strain (%)

2.0 4.0 6.0 8.0 9.4 9.2 9.2 10.0 11.0 12.0 14.0 12.0 10.0 8.0

0.60 0.80 1.00 1.18 1.30 1.50 1.60 1.75 2.10 2.40 5.00 7.20 7.25 7.27

100 200 300 400 470 460 460 500 550 600 700 600 500 400

0.109 0.145 0.182 0.215 0.236 0.273 0.291 0.318 0.382 0.436 0.909 1.309 1.318 1.322

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University No. 11365048

I would now like to discuss the various important stages of the test and also some relevant mechanical properties of the materials used. This is best done by analysing dia grammatic results. Elasticity and Elastic Limit Elasticity is a physical phenomenon that some materials exhibit. These materials will deform immediately upon loading, then return to their original shape when the load is removed (Roylance, 2000). Hibbeler (2010) suggests that if a material with length x is used to support a body, then the length of the material will change in direct proportion to the force acting on it. The test results for sample materials x and y display this characteristic in the linear region between points A and B on their respective graphs. There are however some materials (e.g. cast iron and concrete) for which the elastic stage of the stress-strain curve isn't linear (Callister, Rethwisch, 2008), sample z is an example of this as there is no linear region at all. Point B on both x and y's graphs represents the Elastic Limit, beyond this stress value a permanent extension occurs and the material is no longer considered elastic (Strike, 2011). As sample z has no defining features between points 0 and E it is impossible to pinpoint an elastic limit other than at the point of destruction, which is point E. Yield Point and...