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1. A composite material is subjected to a uniform increase in temperature. How would one obtain an estimate of the interfacial, debonding stress in the case of a suspension of spherical inclusions in a continuous matrix phase?
2. A two material composite medium has one continuous phase and the other phases are of discrete inclusions. Which shape of inclusions—spheres, fibers, or platelets—would give the greatest and the least values for the effective thermal conductivity and thermal expansion coefficient? Take the composite material as being macroscopically isotropic.
3. Consider a dilute suspension of spherical inclusions in a continuous matrix phase. Using the solution for the effective bulk modulus, under dilute conditions, obtain the solution for the effective coefficient of thermal expansion.
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4. Use the composite spheres model to predict the effective bulk modulus for a void containing foam type material. What model would you use to obtain the effective shear modulus for a foam? Do these models account for bending of the cell walls? If not, how would you account for such effects?
5. Take an idealized fiber material as being elastic-perfectly plastic. In an aligned fiber system, take the matrix phase as elastic. What would be the macroscopic stress-strain characteristics of the composite, regarding a state of uniaxial tension in the direction of the fibers?
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