A.0 Test Questions 337 Part Il(68%) 1.(4%)Name two main advantages of high-modulus carbon fiber compared to high-strength carbon fiber. 2.(4%)A piezoresistive material exhibits a gage factor of 22.The gage factor is defined as the fractional change in resistance per unit strain.A piece of this material has a resistance of 461.What is its resistance when the strain is 4.5%? 3.(4%)A unidirectional continuous fiber composite contains fibers of modu- lus 3.4GPa.The fiber volume fraction is 57%.The modulus of the matrix is 0.12 GPa.Assuming that the bonding between the fiber and the matrix is per- fect,calculate the modulus of the composite in the longitudinal direction(i.e., in the fiber direction). 4.(4%)In relation to carbon materials,the inhibition factor of a treated carbon is defined as the ratio of the oxidation rate of untreated carbon to the oxidation rate of the treated carbon.The oxidation rates are 9.9%/min for the untreated carbon and 2.8%/min for the treated carbon.Calculate the inhibition factor. 5.(4%)The rate r of a thermally activated process relates to the activation energy Q of the process by the equation r=Ae-Q/RT where T is the temperature in K(not in C),R is the gas constant (a universal constant equal to 8.314 J/(mol K))and A is just a proportionality constant.The rate at temperature Ti is ri and the rate at temperature T2 is r2.Derive an expression for Q in terms of T1,T2,r and r2. 6.(4%)Using a graph,define the plastic viscosity and the apparent viscosity. 7.(4%) T=n, T=Toeioot, Y=Yoei(t-6) In the above equations that pertain to viscoelastic behavior,r is the shear stress,y is the shear strain,and n is the viscosity.Derive the equation Inl GVa, where G is the shear modulus. 8.(4%)Using a graph of stress versus strain,explain the phenomenon of pseu- doplasticity. 9.(4%)A brittle material is much stronger under compression than under ten- sion.Explain the scientific origin of this phenomenon.A.0 Test Questions 337 Part II (68%) 1. (4%) Name two main advantages of high-modulus carbon fiber compared to high-strength carbon fiber. 2. (4%) A piezoresistive material exhibits a gage factor of 22. The gage factor is defined as the fractional change in resistance per unit strain. A piece of this material has a resistance of 46Ω. What is its resistance when the strain is 4.5%? 3. (4%) A unidirectional continuous fiber composite contains fibers of modu￾lus 3.4GPa. The fiber volume fraction is 57%. The modulus of the matrix is 0.12GPa. Assuming that the bonding between the fiber and the matrix is per￾fect, calculate the modulus of the composite in the longitudinal direction (i.e., in the fiber direction). 4. (4%) In relation to carbon materials, the inhibition factor of a treated carbon is defined as the ratio of the oxidation rate of untreated carbon to the oxidation rate of the treated carbon. The oxidation rates are 9.9%/min for the untreated carbon and 2.8%/min for the treated carbon. Calculate the inhibition factor. 5. (4%) The rate r of a thermally activated process relates to the activation energy Q of the process by the equation r = Ae−Q/RT where T is the temperature in K (not in °C), R is the gas constant (a universal constant equal to 8.314J/(molK)) and A is just a proportionality constant. The rate at temperature T1 is r1 and the rate at temperature T2 is r2. Derive an expression for Q in terms of T1, T2, r1 and r2. 6. (4%) Using a graph, define the plastic viscosity and the apparent viscosity. 7. (4%) τ = η, τ = τoeiωt , γ = γoei(ωt−δ) In the above equations that pertain to viscoelastic behavior, τ is the shear stress,γ is the shear strain, and η is the viscosity. Derive the equation |η| = |G|/ω , where G is the shear modulus. 8. (4%) Using a graph of stress versus strain, explain the phenomenon of pseu￾doplasticity. 9. (4%) A brittle material is much stronger under compression than under ten￾sion. Explain the scientific origin of this phenomenon