During a tensile test with an initial gauge length of 100.0 mm and a cross-sectional area of 150 mm², the following force and gauge length data were recorded:

1. 17,790 N at 100.2 mm
2. 23,040 N at 103.5 mm
3. 27,370 N at 110.5 mm
4. 28,910 N at 122.0 mm
5. 27,400 N at 130.0 mm
6. 20,460 N at 135.1 mm

The last data point (6) was recorded immediately before failure. Yielding was observed at a load of 19,390 N (using the 0.2% offset method), and the maximum load (4) was 28,960 N.

(a) Plot the engineering stress-strain curve.

Determine:
(b) Yield strength
(c) Modulus of elasticity
(d) Tensile strength
(e) Percent elongation

To tackle the student's question, calculations for yield strength, modulus of elasticity, tensile strength, and percent elongation are provided. Yield strength is 129.27 MPa, tensile strength is 193.07 MPa, and the percent elongation is 35.1%. The modulus of elasticity requires plotting stress-strain values to determine accurately.

Explanation:

To accurately address the student's request, we shall break down the problem into the specific elements they've asked for, focusing on yield strength, modulus of elasticity, tensile strength, and percent elongation. Given the initial gauge length and the cross-sectional area, these calculations involve applying basic principles of material science and engineering, specifically relating to tensile testing.

Yield Strength

The yield strength is determined using the 0.2% offset method. For a material with a specific cross-sectional area, the yield load of 19,390 N, and given that the yield stress is the load divided by the original cross-sectional area, the yield strength equals 129.27 MPa (19,390 N / 150 mm²).

Modulus of Elasticity

The modulus of elasticity (E) can be estimated from the stress-strain curve before yielding. E equals the slope of the linear portion of the stress-strain curve. Without specific values for stress and strain, we recommend plotting these values to calculate E directly from the curve.

Tensile Strength

The maximum load recorded before failure gives the tensile strength, which is calculated as 28,960 N / 150 mm² = 193.07 MPa.

Percent Elongation

Percent elongation helps in understanding how ductile the material is. It's calculated as ((final gauge length - initial gauge length) / initial gauge length) * 100%. For this data, ((135.1 mm - 100.0 mm) / 100.0 mm) * 100% = 35.1%.