following data was obtained from a tensile test of steel. The test specimen was 15mm in diameter and 50 mm in length
Load (kN) /Elongation(mm)
5 /0.005
10 /0.015
30 /0.048
50 /0.084
60 /0.102
64.5 /0.109
67/ 0.119
68 /0.137
69/ 0.160
70 /0.229
72 /0.300
76 /0.424
84 /0.668
92 /0.965
100 /1.288
112 /2.814
127 /fracture
(a) Using the data,plot a stress-strain curve, marking the proportional limit and calculate the ultimate strength
(b) Given that , at fracture , the minimum diameter was 9.5 mm, calculate the reduction in cross-sectional area, expressing the answer as a percentage of the original cross-sectional area.
To plot the stress-strain curve, we need to calculate the stress and strain values first.
(a) Stress is calculated by dividing the load by the cross-sectional area, and strain is calculated by dividing the elongation by the original length.
To calculate the stress:
- Convert the diameter of the specimen to radius by dividing by 2: 15 mm / 2 = 7.5 mm = 0.0075 m
- Calculate the cross-sectional area: A = πr² = π(0.0075²) m²
- Convert the load from kN to N: 5 kN = 5000 N
- Calculate the stress: σ = F/A = 5000 N / (π(0.0075²) m²)
Repeat this process for each data point to get all the stress values.
To calculate the strain:
- Calculate the change in length for each elongation value by subtracting the initial elongation of 0.005 mm.
- Divide the change in length by the original length (50 mm) to get the strain. Multiply by 0.001 to convert mm to m.
Repeat this process for each data point to get all the strain values.
Once you have the stress and strain values, plot stress on the y-axis and strain on the x-axis. Mark the proportional limit as the point where the stress and strain linearity ends.
To calculate the ultimate strength, find the maximum stress value from the stress-strain curve.
(b) To calculate the reduction in cross-sectional area at fracture as a percentage of the original cross-sectional area:
- Calculate the area of the minimum diameter: A_fracture = π(0.0095²) m²
- Calculate the reduction in cross-sectional area: ΔA = A - A_fracture
- Calculate the percentage reduction: (ΔA / A) * 100%
By following these steps, you can plot the stress-strain curve, mark the proportional limit, and calculate the ultimate strength. Additionally, you can calculate the reduction in cross-sectional area at fracture as a percentage of the original cross-sectional area.