For iron, $C_{11}=237G\frac{N}{m^2},C_{12}=141G\frac{N}{m^2},$ and $C_{44}=116G\frac{N}{m^2}.$

D$.$ Determine $E_{[100]},E_{[110]},E_{[121]}$ and $E_{[111]}$ of Fe$.$

b$.$ Suppose a polycrystalline Fe wire is composed of grains with either $[100],[110],$ or $[111]$ crystal directions lying

along the wire axis. If all three orientations are present in equal amounts, what is $E$ for the wire? $($State your

assumptions.$)$

c$.$ The polycrystalline elastic modulus of Fe is $209G\frac{N}{m^2}.$ How does this compare with the modulus estimated in

part $($b$)?$

d$.$ By changing the processing conditions, a different kind of texture can be produced in Fe wire; $70\%$ of the grains are

oriented so that a direction is aligned with the wire axis and the remaining $30\%$ are evenly split between

and directions lying along this axis. What is the modulus along the wire axis for this case?

Is $E$ transverse to the wire axis different from the modulus along the axis for the situations pertaining to parts $($b$)$

and $($d$)?$ Explain your reasoning.