Figure shown below is the engineering stress$-$strain curve for a plain steel. The

Determine:

$(1)$ Ultimate tensile strength

$(2)$ Yield strength

$(3)$ Modulus of elasticity

$(4)$ Modulus of resilience

$(5)$ Ductility

$(6)$ How does stress strain curve change when strain and temperature increase?

$(7)$ You're asked to select a material for an application that requires high impact strength at $50$C$.$ Two candidates, an aluminum alloy and $1040$ steel, have similar and adequate impact strength at room temperature. Which one do you suggest for this application $($i$.$e$.$ use at $-50$C$)?$

$(8)$ Identify the preferred slip systems in FCC$,$ BCC and HCP metals.

$(9)$ Explain why HCP metals are typically brittle than FCC and BCC$?$ How do you think the ductility of BCT $($body centered tetragonal$)$ crystals would compare with BCC and FCC crystals?

$(10)$ A single Crystal of zinc is oriented for a tensile test such that the normal to its slip plane makes an angle of $65$ with an applied stress. Three possible slip direction make angles of $30$ and $78`$ with the applied stress. Which of these slip directions is most favored?

$(11)$ Nanostructured metals usually have low ductility. Explain why in terms of mechanical behavior and deformation mechanism.