Q$\mathrm{.}8.$ Two materials $($ A and $B)$ are being considered.

Material $A$ is an elasto$-$plastic material with a yield strength of $10$MPa, modulus of elasticity of $20$GPa

and an ultimate strain of $0\mathrm{.}020.$

Material B has a parabolic behavior up to failure with an ultimate strength of $60$MPa and an ultimate

strain of $0\mathrm{.}005.$

a$)$ Draw the stress$-$strain diagrams and calculate the toughness for each material.

b$)$ State whether these materials are brittle or ductile, and discuss the reason.

c$)$ A steel member of $10kg$ is to be dropped, individually, on these two materials. The specimens

are cubic with a side of $10cm.$ Calculate the heights from the top surface of the specimens just

enough to initiate fracture. Assume gravitational acceleration $\text{'}g\text{'}$ as $10\frac{m}{s^2}.$