Question

The graph below shows the stress vs. strain curves for thredifferent materials(A, 8, & c) obtained from a tensile test 3001 A 275 250 225 200 175 150 125 100 75 50 x-Break 25 0.00 0.01 002 0.03 004 005 0.06 007 0.08 0.09 0.10 Strain Using the curves above: a) Estimate the Young's Modulus for materials A, B, and C b) Estimate the yield strength and tensile strength (if any) of materials A, B, and C c) Using what you know about the mechanical behaviour, identify materials A, B, and C as either metal, ceramic or polymer.

Answer 1

a) According to Hook's law, the stress is proportional to strain. The proportionality constant is Young's modulus. Hookes law gives the linear relationship between stress and strain this in the graph given above, we look only in the linear regime to estimate the Young's modulus.

E = stress/ strain.

Therefore greater is the value of stress for given value of strain, Young's modulus E will the higher. Which means, higher is the slope in the graph, higher is the Young's Modulus. In the graph above, E_A>E_B>E_C

b) Yeild point is the point in the strain-stress curve above which the elastic behavious of the material cease to exist and the plastic behaviour starts. If the material is deformed beyondthe yeild point , the material cannot be brought back to its original point when the stress applied is removed i.e it wont be elastic, it will be deformed permanently(plastic behaviour).

Yeild strength of B(at 225Mpa) > Yeild strength of C (at 25Mpa) . There is no yeild point for A

** Tips: Yeild point is the point at which the straight line ends and hooke's law is no longer valid.

ii) Tensile strength is the ability of the material to withstand maximum stress without break down. The point from which the curve starts going downward is the point to calculate tensile strength. There is no tensile strength for A and B, whereas material C has a tensile strength at 25Mpa.

c) Metal is highly elastic . Take for example gold, it can be shaped into any form withput permanently damaging it. Therefore material A is metal. Ceramic tend to get fractured before getting any plastic deformation can take place so material C is ceramic whose yeild point and tensile strength are same. Polymer elasticity lies between metala and Ceramic. In polymer plastic deformation takes place after some point unlike metal however it will not get easily fractured like ceramic. Therefore material B is polymer.