Homework 10

Homework 10 - MSE 230 HW10(due 04/08 04/09 Spring 2010 This...

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Unformatted text preview: MSE 230 HW10 (due 04/08, 04/09) Spring 2010 This assignment covers polymers and composites over two weeks. It is due in recitation the week after the exam, so that you do not have a homework assignment due the week of the exam. 1. In order to get an idea of the size and number of “macromolecules” that constitute polymers: (a) Calculate the length of individual polyethylene molecules having molecular weight of 10,000, 100,000 and 1,000,000 g/mol if the molecules were straightened as in Fig. 14.5(b) so the carbon atoms all lie in a plane (i.e., straight end-to-end length not including the zigzagging). The carbon-carbon bond length is 0.155 nm and the tetrahedral bond angle is 109°. (b) Polyethylene has a density of ~1 g/cm3. Calculate the number of molecules in 1 cm3 of polyethylene having the three molecular weights in part (a). 2. The table shows the molecular weight data measured for a particular polytertrafluoroethylene (Teflon). (a) Plot histograms for the molecular weight distribution on a number basis (Number fraction of molecules) and on a weight basis (Weight fraction of molecules). (b) Calculate the number-average molecular weight and the weight-average molecular weight. (c) If the price of the polymer were proportional to its “molecular weight,” which of these averages would be better to use if you were the buyer versus the seller. Explain. 3. Sketch the repeat unit structure and explain briefly the rank order of the melting temperatures of the following thermoplastics in terms of intermolecular bonding energy. Molecular Weight Range (g/mol) 10,000 – 20,000 20,000 – 30,000 30,000 – 40,000 40,000 – 50,000 50,000 – 60,000 60,000 – 70,000 70,000 – 80,000 80,000 – 90,000 xi 0.03 0.09 0.15 0.25 0.22 0.14 0.08 0.04 wi 0.01 0.04 0.11 0.23 0.24 0.18 0.12 0.07 Polymer Polyethylene Polypropylene Polyvinylchloride Polytetrafluoroethylene TM (° C) 137 175 212 327 4. (a) Why does the elastic modulus value for individual polymers (Table 15.1) vary so much compared to those for individual metals and ceramics? (b) What is the structural origin of the 3 to 5 times higher elastic modulus in HDPE compared to LDPE? (c) Briefly explain how and why the yield strength of a semi-crystalline polymer depends on each of the following: (i) molecular weight, (ii) degree of crystallinity, (iii) deformation by drawing. 5. Bungee cords are sized to the jumper to stretch to a strain of about 3 (300%). Lower strains would create g-forces on the jumper that are too high (decelerate too fast) and higher strains would reduce the safety factor (fracture stress/stress in the cord at the max strain). For an elastomer exhibiting the stress-strain behavior shown in Fig. 15.1C: (a) Calculate the diameter of cord for a strain of 3 with a 75-kg jumper; approximate E as linear up to ε = 3. (b) Estimate the safety factor for this case. Physics: By equating the gravitational potential energy of the jumper at a height equal to the maximum length of the cord (mgLf) and the strain energy stored in the stretched cord 2 mg (ε + 1) (Eε2A0L0/2), the design equation for the cord size is, A0 = . E ε2 € 6. A PMMA washer is compressed under the head of a steel bolt to a strain of 0.005. Assuming this strain is applied instantaneously and held constant with time and the temperature of the system is 60°C, use Fig. 15.27 to estimate the stress in the washer at (a) 0.001 h, (b) 1 h, (c) 1 day, and (d) 1 month (assume 30 days). (e) Comment briefly on the implications of these results. 7. For a composite block of continuous, uniaxially aligned E-glass fibers having Ef = 72 GPa (Table 16.4) and an epoxy matrix having density = 1.2 g/cm3 and Em = 3.4 GPa: (a) Calculate the elastic modulus of the composite for loading parallel to the fibers, Elongitudinal, if the volume fraction of fibers is 0.25. (b) Calculate the volume fraction of fibers necessary for the modulus transverse to the fibers, Etransverse, to be equal to the longitudinal modulus calculated in part (a). (c) Calculate the specific stiffness of the composite for longitudinal loading and compare it to the specific stiffness of steel and of aluminum. Cite the source of the properties data you use. 8. Consider carbon fiber-epoxy matrix composites in sheet form. Use the property values for carbon fibers (middle of the ranges given) in Table 16.4. (a) Calculate and plot Ecomposite versus Vf (0 to 1) for uniaxially aligned fibers in the longitudinal (Elongitudinal) and transverse (Etransverse) directions in the plane of the sheet. Calculate the upper limit of the fiber volume fraction (hint: closest packing of circular cylinders) and make the Ecomposite versus Vf lines dotted above this limit. (b) For discontinuous fibers oriented randomly in the plane of the sheet, the factor K in Eqn. 16.20 is 0.38 and, due to packing interference, the practical upper limit for Vf is 0.35. Graph Erandom on the same plot as in part (a). (c) For this limiting fiber volume fraction (Vf = 0.35), calculate the specific stiffness for in-plane, uniaxial loading of the discontinuous, randomly oriented fiber composite and the uniaxially aligned fiber composite in both the longitudinal and transverse directions. (d) Compare the three values for specific stiffness in uniaxial loading you calculated in part (c) with the corresponding values for specific stiffness in bending, which is E1/3/ρ for bending a sheet or panel. Compare these values to those (axial loading and bending) for bulk steel and aluminum. Organize the values in a table to make the comparison clear and comment on the significance of the results. (e) Regardless of fiber volume fraction, what advantage does the randomly oriented, discontinuous fiber composite have over the uniaxially oriented fiber composite. ...
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This note was uploaded on 11/11/2010 for the course MSE 230 taught by Professor Trice during the Spring '08 term at Purdue.

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