Question

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S. Draw a possible stress strain graph for a material with a yield stress of 300 MPa, an elastic modulus of 200 GPa, a UTS of 450 MPa and a ductility of 20%. Calculate the elastic strain at the point where the material starts to plastically deform. 6. A nylon rope with an elastic modulus of 3 GPa is placed under a force of 17.5 kN. The cross-sectional area of the rope is 250 mm2. If the rope is 150 cm long and stretches 5 cm under this loading, determine whether the cable has exceeded its elastic limit. 7. A bicycle crankshaft is to be designed. It will have a length of 25 cm and the design loading (including safety factors) is 3500 N. Assume that the pedal can be modelled as a rectangular singly-supported cantilever with a cross-sectional height of 3 cm and width of 1 cm. Find the bending stress applied to the crankshaft (see lectures on beam design) and determine whether (a) aluminium alloy (ay 500 MPa) and (b) carbon fibre reinforced polymer (oy 800 MPa) would be suitable 8. A 15 cm long section of titanium alloy (E 115 GPa) is placed under a tensile stress of 1 GPa. This takes the alloy beyond its yield point and it plastically deforms, stretching to 15.4cm under load. Calculate the final length of the section when the force is removed 9. The figure below shows a stress-strain graph for a cold-worked Al/Cu alloy. Find the following properties of that alloy: (a) The 0.2% proof stress (b) The stress at which the alloy will begin to permanently deform (c) The maximum strain that should be applied during cold working of the material (d) The strain in the material immediately before fracture (e) The strain in the material after it has fractured 750 750 500 500 250 0.5 Strain (%) 1.0 CD 250 10 15 20 Strain (%)

Answer 1

E = J/epsilon: if T = 100 M pa: epsilon = 100/200 times 10^3 = 0.4 times 10^-3 if sigma = 200 Mpa: epsilon = 1 times 10^-3 E = 3 Gpa = 3 times 10^3 Mpa: F = 17 . 5 KN: A = 250 mm^2: L = 150 cm Delta L = 5 cm: so epsilon = Delta c/L = 5/150 = 0.03 stress sigma = F/A = 17 . 5 times 10^3/250 = 70 M pa T/q = 70/0.03 = 2333.33 Mpa < E (3000 Mpa) so yes material has exceeded its elastic limit