$2.$ A rectangular steel specimen with a cross$-$sectional area of $20$ mm $\backslash$times $10$ mm and an initial gauge length of $100$mm is subjected to a uniaxial tensile test until fracture. The following data are recorded during the test:

Load corresponding to the $0\mathrm{.}2\%$ offset yield point: $30$kN

Maximum load: $50$kN

Load at fracture: $45$kN

Gauge length after fracture: $112$mm

Cross$-$sectional dimensions after fracture: $18$mm$\backslash$times $9$mm

Young's Modulus, E$=210$GPa

Poisson's ratio,

u $=0\mathrm{.}3$

Using the data provided, calculate the following properties of the material:

Stress at yield, maximum, and fracture

b$.$ Strain at yield, maximum, and fracture

c$.$ Young's Modulus of the material

d$.$ Deformation of the specimen at maximum load

e$.$ Poisson's ratio and its validation with lateral strain measurements

f$.$ Yield strength

g$.$ Ultimate tensile strength $($UTS$)$

h$.$ Fracture strength

i$.\%$ Elongation

j$.\%$ Reduction in Area $($RA$)$

k$.$ Elastic strain at maximum load

l$.$ Plastic strain at maximum load

Explain the stress$-$strain curve for a ductile material during a uniaxial tensile test. What are the key regions, and what do they signify about the material's behavior?