yornen:

Problem #$1[25$ Points$]$

Given the properties above for the carbon fiber and polyimide matrix,

$($a$)[5$ Pts$]$ Find the fiber volume fraction of a continuously reinforced$-$unidirectional lamina whose longitudinal modulus $(E_1)$ is $30$ times the matrix modulus $(E_1=30Em).$

$($b$)8Pts$ Determine the density $($ Pc $),$ the transverse $(E_2$ or $E{T}^2)$ modulus, the shear modulus $(G_{12}),$ and the major Poisson's ratio $(V_{12})$ of the composite for the volume fraction obtained above. Use appropriate models and state which model was used in your answer.

$($c$)[12$ Pts$]$ What is the cost of the lamina $($in $\frac{\text{\$}}{K}g)$ at the above volume fraction? $($Hint: Add up the cost of the fiber and the matrix per Kg of the composite. Mind the difference between weight and volume fraction$).$