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Midterm_practice - Materials Science and Engineering 644 Structure and properties of composite materials Midterm Exam Instructions February 9 2004

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Unformatted text preview: Materials Science and Engineering 644 Structure and properties of composite materials Midterm Exam Instructions: February 9, 2004 Enter your 4 digit course code here: _____________ You have approximately 50 minutes to complete this exam. Answer all 6 questions. Write your answers in the spaces provided. You may use your one-sided sheet of personal notes and a calculator. The point values for each question are given below. Good luck! 1: 2: 3: 4: 5: 6: __/10 __/10 __/30 __/10 __/10 __/30 TOTAL: ______/100 1/7 MSE 644 Midterm Feb. 9, 2004 1. Properties of Matrix Materials (10 points) Composite materials provide improvement over inherently poor matrix properties. State the relevant properties next to each matrix below. Make sure your answers are complete. Answer: CERAMIC METAL POLYMER 2. Relative properties of a metal matrix and ceramic fiber (10 points) Sketch on the stress-strain plot below the relative tensile response of an aluminum matrix and an alumina fiber. On your plot, be sure to indicate the relative differences in elastic modulus, strength, and ductility. Answer: page 2 / 7pages total MSE 644 Midterm Feb. 9, 2004 3. Conditions for a lightweight, buckling-resistant rod (30 points) Consider a rod having a circular cross section of radius r. The rod length l must equal 1m and when loaded axially with a force F = 100 N, the rod must not buckle. The buckling force for a circular rod of length l is p 3 Er 4 Fbuckle = 16 l 2 (a) Using the above information, derive an expression for the minimum radius r required to satisfy the buckling condition mentioned above. Your answer should be stated in terms of Young's modulus E and any other necessary parameters. Answer to part (a): rmin = (b) Derive an expression for the weight of a beam that will satisfy the deflection condition mentioned in part (a). Express your answer in terms of the density, r, and E, as well as other necessary parameters. Answer to part (b): weight = page 3 / 7pages total MSE 644 Midterm Feb. 9, 2004 Problem 3 cont'd (c) Label on the diagram below the specific point(s) at which the rod will have minimum weight and still satisfy the buckling requirement. Answer to part (c): 4. Infiltration Pressure (10 points) The pressure to infiltrate a preform of continuous, unidirectional glass fibers is 100 Pa, when the spacing from fiber-to-fiber center is 40 mm and the fiber radius is 10 mm. Based on this information, determine the pressure necessary to infiltrate a similar preform with having 35% volume fraction of the same glass fibers. Answer: page 4 / 7pages total MSE 644 Midterm Feb. 9, 2004 5. Stress-strain behavior for a CMC (10 points) Provide qualitative sketches of the tensile stress strain curves for the following: (1) monolithic lithium alumino silicate (LAS) matrix (2) LAS reinforced with unidirectional SiC fibers (3) LAS with the same volume fraction of SiC fibers, but in a 0/90 layup (4) LAS with the same volume fraction of SiC fibers, but in a 3D braid. Put all curves on the plot below. There is no need to indicate numerical values of stress or strain. However, make sure that your answer reflects proper relative trends in elastic moduli, tensile strength, and ductility. Answer: page 5 / 7pages total MSE 644 Midterm Feb. 9, 2004 6. Optimal Properties in a layered composite (30 points) You are considering a layered composite material comprised of alternating layers of aluminum and alumina. The relevant constituent properties are: Aluminum E = 69 GPa k = 222 W/m-K Alumina E = 380 GPa k = 39 W/m-K Note that the thermal conductivity k relates the heat flux q (in W/m2) parallel to a temperature gradient dT/dx (in K/m) according to: dT q = -k dx (a) Draw on the plot below an estimate of the elastic modulus of the composite parallel to the layers, as a function of volume fraction of alumina. Answer to part (a): (b) Determine the numerical range of volume fraction of alumina over which the elastic modulus of the composite parallel to the layers is greater than 160 GPa. Answer to part (b): page 6 / 7pages total MSE 644 Midterm Feb. 9, 2004 Question 6 continued... (c) Draw on the plot below an estimate of the composite thermal conductivity perpendicular to the layers, as a function of volume fraction of alumina. Answer to part (c): kcomposite (W/m-K) 200 150 100 50 0 0 0.2 0.4 0.6 0.8 1 volume fraction alumina, v(Al2O 3) (d) Determine the numerical range of volume fraction of alumina over which the thermal conductivity of the composite perpendicular to the layers is greater than 92 W/m-K. Answer to part (d): END OF EXAM page 7 / 7pages total ...
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This note was uploaded on 07/17/2008 for the course MSE 644 taught by Professor Anderson during the Winter '05 term at Ohio State.

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