Dec 2006 Final apsc278

# Dec 2006 Final apsc278 - Applied Science 278 December Exam...

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Applied Science 278 December Exam - 2006 1 THE UNIVERSITY OF BRITISH COLUMBIA Department of Materials Engineering APPLIED SCIENCE 278 Engineering Materials FINAL EXAMINATION, December, 2006 This is a Closed Book Examination. The use of calculators containing stored information of relevance to this course is forbidden. Time: 2.5 hours Answer 4 of 5 questions. Only 4 questions will be marked. Each question is worth 25 marks. The complete exam is 10 pages in length. Some useful formulae, material data and phase diagrams are given on the last 5 pages of the exam. The use of sketches or schematic diagrams is encouraged wherever these will aid in solving or discussing a problem. Marks Question #1 1 a) An aluminum alloy which is presently being used in a commercial airliner has a yield stress of 450MPa, a tensile stress of 550 MPa, an elastic modulus of 70 GPa and a Poisson ratio of 0.3. Given a member which has a circular cross-section with a diameter = 8.75 mm : (2) i) what is the maximum tensile load that may be applied without causing plastic deformation ? (2) ii) what is the maximum tensile load the member can support ? (3) iii) if the original length of the component is 350 mm, what would the length of the component be just prior to the onset of plastic deformation ? (3) iv) what would be the change in diameter of the component just prior to the onset of plastic deformation ? (3) b) calculate the atomic packing factor for the FCC unit cell assuming the atoms to be hard spheres. (4) c) Prove that the true stress is related to the engineering stress in a tensile test is given by: ( ) ε σ + = 1 T Under what conditions can this equation not be used. (3) d) A brass alloy to be used for a spring application must have a modulus of resilience of at least 1.4 MPa. What must be its minimum yield stress ? Given: E = 100 GPa, ν = 0.3. E A G E R K E E N E R.C O M

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Applied Science 278 December Exam - 2006 2 (5) e) the combination of slip plane and slip direction defines what is know as the slip system. For face-centred cubic materials, the slip plane is the ( ) 111 which has 3 possible slip directions, i.e. [ ] 10 1 , [ ] 01 1 and [ ] 1 1 0 i. in the x-y-z reference frame, sketch this slip plane and the associated slip directions ii. using a 2-dimensional sketch, show the hard sphere representation of this plane Question #2 (5) a) A cylindrical aluminum alloy 2024-T6 bar with a very gentle radius of curvature (for the transition from the grip to the gauge section) is subjected to repeated compression-tension stress cycling along its axis. If the load amplitude is 18 000 N, compute the minimum allowable diameter to ensure that fatigue failure will not occur. Assume a factor of safety of 2.0 (3) b) If the sample described in part a) had been machined with the geometry shown below, predict the number of cycles to failure (in this case, assume no factor of safety) , Given: applied load = 7.5 kN, thickness = 5 mm, w = 20 mm, h = 10, r = 1 mm Figure 1 – stress concentration factor for geometry shown.
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Dec 2006 Final apsc278 - Applied Science 278 December Exam...

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