Which of the statements below are accurate regarding the stress-strain behavior of polymers: This question has more than one correct answer) O a. Strain softening happens in elastomers where the deformation gradually leads to a decrease in stress under constant strain rate O b. As temperature is reduced, the necking behavior of plastic tensile bars completely disappears C. The slope of the stress-strain curve for totally elastic and brittle polymers is always positive

Please answer in proper units

1. Explain in 1-3 bullets how as a practicing engineer you determine the yield strength of a thermoplastic polymer from a tensile stress-strain curve. 2. Explain what is happening at the yield strength for a thermoplastic polymer from a physical standpoint in 1-3 bullets. (e.g. what are the atoms or polymer chains doing?)

Molecular weight data for some polymer are tabulated here. Compute (a) the number-average molecular weight, (b) the weight-average molecular weight. (c) If it is known that this material's degree of polymerization is 710, which one of the polymers listed in Table 14.3 is this polymer? Why? Molecular Weight Range g/mol 15,000-30,000 Xi Wi 0.04 0.01 30,000-45,000 0.07 0.04 45,000-60,000 0.16 0.11 60,000-75,000 0.26 0.24 75,000-90,000 0.24 0.27 90,000 105,000 0.12 0.16 105,000-120,000 0.08 0.12 120,000-135,000 0.03 0.05

An unknown polymer sample was found to have the following molecular weight distribution: Molecular weight range Xi Wi 8,000 – 20,000 0.05 0.02 20,000 – 32,000 0.15 0.08 32,000 – 44,000 0.21 0.17 44,000 – 56,000 0.28 0.29 56,000 – 68,000 0.18 0.23 68,000 – 80,000 0.10 0.16 80,000 - 92,000 0.03 0.05 What would the weight average molecular weight of the sample be if, we had filtered the monomer mixture with a 44 kDa dialysis tubing before preparation? (Hint: a dialysis tubing of a known molecular weight, only keeps molecules larger than that size)

Prove that the Poisson's ratio of an isotropic, homogeneous material must be between -1 ≤ v≤0.5. (Hint: use the relationships between elastic constants and assume that all constants are positive). What does it mean for a material to have a Poisson's ratio of v = 0.5? How about v = -1? Give an example of materials (or metamaterials) that reach these values.

The σ - ε diagram for elastic fibers is shown. (Figure 1) Figure 385 σ(MPa) 77 < 1 of 1 €(mm/mm) 1 2 2.25