Sample 1, Original Length 250 mm and 10 mm Diameter, Length after testing 250.23 mm the force used for the test was 15KN

Calculate the Stress and Strain for each of the Samples and from this and, assuming the material has remained within the elastic limit, determine their modulus of elasticity.

To calculate the stress and strain for each sample, we need to understand the formulas and concepts involved.

1. Stress (σ): It is the force applied per unit area of the material. It is calculated using the formula:

Stress = Force / Area

2. Strain (ε): It is a measure of deformation or elongation in the material. It is calculated using the formula:

Strain = Change in length / Original length

Now, let's calculate the stress and strain for each sample:

For Sample 1:
Original length (L1) = 250 mm
Change in length (ΔL1) = 250.23 mm - 250 mm = 0.23 mm
Diameter (d1) = 10 mm
Radius (r1) = d1 / 2 = 10 mm / 2 = 5 mm = 0.005 m
Force (F1) = 15 kN = 15,000 N

Area (A1) = π * r1^2 = π * (0.005 m)^2 ≈ 0.00007854 m^2

Now, calculate the stress:
Stress (σ1) = F1 / A1

Next, calculate the strain:
Strain (ε1) = ΔL1 / L1

Now, repeat the same calculations for Sample 2 (assuming you have the values for the original length, change in length, diameter, and force).

Once you have the stress and strain values for both samples, we can calculate their modulus of elasticity (E). The modulus of elasticity represents how much a material can be stretched or deformed under a given amount of stress.

The formula to calculate the modulus of elasticity is:

E = Stress / Strain

Calculate the modulus of elasticity for both samples using the stress and strain values obtained earlier.

Remember, to assume the material has remained within the elastic limit, the stress-strain relationship should be linear. If any sample has exceeded the elastic limit, this method may not be accurate in determining the modulus of elasticity.