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Chap 15 Solns-6E

# Chap 15 Solns-6E - CHAPTER 15 CHARACTERISTICS APPLICATIONS...

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CHAPTER 15 CHARACTERISTICS, APPLICATIONS, AND PROCESSING OF POLYMERS PROBLEM SOLUTIONS 15.1 From Figure 15.3, the elastic modulus is the slope in the elastic linear region of the 20 ° C curve, which is E = ∆(στρεσσ 29 ∆(στραιν 29 = 30 ΜΠα- 0 ΜΠα 9 ξ 10 -3 - 0 = 3.3 ΓΠα (483, 000 πσι 29 The value range cited in Table 15.1 is 2.24 to 3.24 GPa (325,000 to 470,000 psi). Thus, the plotted value is a little on the high side. The tensile strength corresponds to the stress at which the curve ends, which is 52 MPa (7500 psi). This value lies within the range cited in the table--48.3 to 72.4 MPa (7,000 to 10,500 psi). 15.2 The reason that it is not necessary to specify specimen gauge length when citing percent elongation for semicrystalline polymers is because, for semicrystalline polymers that experience necking, the neck normally propagates along the entire gauge length prior to fracture; thus, there is no localized necking as with metals and the magnitude of the percent elongation is independent of gauge length. 15.3 The explanation of viscoelasticity is given in Section 15.4. 15.4 This problem asks for a determination of the relaxation modulus of a viscoelastic material, which behavior is according to Equation (15.10)--i.e., σ (t) = s(0) exp - t t We want to determine σ (10) , but it is first necessary to compute τ from the data provided in the problem. Thus, 128

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τ = - t ln s(t) s(0) = - 30 s ln 0.5 MPa 3.5 MPa = 15.4 s Therefore, σ (10) = (3.5 MPa) exp - 10 s 15.4 s = 1.83 MPa Now, using Equation (15.1) E r (10) = σ(1029 ε ο = 1.83 ΜΠα 0.5 = 3.66 ΜΠα (522 πσι 29 15.5 Below is plotted the logarithm of E r (10) versus temperature. The glass-transition temperature is that temperature corresponding to the abrupt decrease in log E r (10) , which for this PMMA material is about 115 ° C. 15.6 We are asked to make schematic strain-time plots for various polystyrene materials and at several temperatures. (a) Crystalline polystyrene at 70 ° C behaves in a glassy manner (Figure 15.8, curve A ); therefore, the strain-time behavior would be as Figure 15.5(b). (b) Amorphous polystyrene at 180 ° C behaves as a viscous liquid (Figure 15.8, curve C ); therefore, the strain-time behavior will be as Figure 15.5(d). 129
(c) Crosslinked polystyrene at 180 ° C behaves as a rubbery material (Figure 15.8, curve B ); therefore, the strain-time behavior will be as Figure 15.5(c). (d) Amorphous polystyrene at 100 ° C behaves as a leathery material (Figure 15.7); therefore, the strain-time behavior will be as Figure 15.5(c). 15.7 (a) Stress relaxation tests are conducted by rapidly straining the material elastically in tension, holding the strain level constant, and then measuring the stress as a function of time. For viscoelastic creep tests, a stress (usually tensile) is applied instantaneously and maintained constant while strain is measured as a function of time.

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