$($a$)$ Define a slip system.

$($b$)$ Do all metals have the same slip system? Why or why not?

$($a$)$ What is the approximate ductility $(\%$EL$)$ of a brass that has a yield strength of $345$MPa$(50,000)?$

$($b$)$ What is the approximate Brinell hardness of a $1040$ steel having a yield strength of $620$MPa$(90,000)?$

A cylindrical rod of $1040$ steel originally $11\mathrm{.}4$ mm $(0\mathrm{.}45$ in $.)$ in diameter is to be cold worked by drawing; the

circular cross section will be maintained during deformation. A cold$-$worked tensile strength in excess of $825$

MPa $(120,000)$ and a ductility of at least $12\%$ EL are desired. Furthermore, the final diameter must be $8\mathrm{.}9$ mm

$(0\mathrm{.}35$ in$.).$ Explain how this may be accomplished.

A specimen of a $4340$ steel alloy with a plane strain fracture toughness of $54\mathrm{.}8$MPa$\sqrt[\phantom{2}]{m}(50k\frac{s}{\sqrt[\phantom{2}]{in.}})$ is

exposed to a stress of $1030$MPa$(150,000).$ Will this specimen experience fracture if the largest surface

crack is $0\mathrm{.}5$ mm $(0\mathrm{.}02$ in $.)$ long? Why or why not? Assume that the parameter $Y$ has a value of $1\mathrm{.}0.$

The fatigue data for a brass alloy are given as follows:

$($a$)$ Make an S$-$N plot $($stress amplitude versus logarithm of cycles to failure$)$ using these data.

$($b$)$ Determine the fatigue strength at $4{10}^6$ cycles.

$($c$)$ Determine the fatigue life for $120$ MPa $.$