Chapter 2, Problem 35P

The modulus of elasticity (E ) is a measure of a material’s resistance to deformation: the larger the modulus, the stiffer the material. During fabrication of a ceramic material from a powder form, pores were generated that affect the strength of the material. The magnitude of elasticity is related to volume fraction porosity P by

$E=304\left(1-1.9P+0.9P^2\right)$. (2.76)

(a) If a porous sample of silicon nitride has a modulus of elasticity of $E=209$ GPa. obtain the quadratic equation for volume fraction porosity P. (b) Solve the quadratic equation found in part (a) using both the methods of completing the square and the quadratic formula.

(c) Repeat parts (a) and (h) to find the volume fraction porosity of a silicon nitride sample with a modulus of elasticity of 25 GPa.