Answer to Question #101920 in Mechanics | Relativity for jude

Question

An alloy of steel has a Young's modulus of 180GPa, elastic limit of 0.002 and ultimate tensile strength of 860MPa. An alloy of aluminium has a Young's modulus of 70GPa, elastic limit of 0.004 and ultimate tensile strength of 110MPa.
a) Sketch a stress-strain graph for both of these alloys, plotting them on the same graph
b) Label significant positions on the graphs
c) Compare and contrast the mechanical properties of these alloys

Answer 1

a, b) Begin with significant points: elastic limit and Young's modulus. Take aluminum alloy as reference: its Young's modulus is 2.57 times smaller than that of steel , its elastic limit is 2 times longer, ultimate tensile strength of aluminum is 7.81 times smaller. Stress is strain times Young's modulus, therefore:

$$\sigma_s=Y_s\epsilon_s=180\cdot10^9\cdot0.002=360\cdot10^6\text{ Pa},\\ \sigma_a=Y_a\epsilon_a=70\cdot10^9\cdot0.004=280\cdot10^6\text{ Pa}.$$

Take 860 MPa as 1:

c) Since the ultimate tensile strength of aluminum (green) is lower that its yield strength, it is nonsense, so perhaps there is a mistake in elastic limit or UTS. But as we see, aluminum can elastically elongate two times longer than steel. The stress steel experiences is higher.