Young's Modulus Experiment: Measuring Elasticity of Everyday Materials, Study notes of Materials science

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Young's Modulus Experiment

ENGR45 – Materials Science Laboratory

Chad Philip Johnson

Submitted: March 14

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Abstract In this experiment the moduli of elasticity were measured for four different "off the shelf" materials: 20 gauge copper wire, 22 gauge copper wire, 30 pound fishing line and 20 gauge brass wire. The methods and techniques employed in determining these values required only a small testing apparatus, the tested materials in various wire gauges, a set of weights to apply force, and somewhat crude measurement tools—very little was needed in the way of precise equipment or specialized machinery. As such, these experimental results should only be considered to be general estimates of the true values of the modulus of elasticity constants for the tested materials and not necessarily representative of the true materials in their pure forms. In the cases where the accepted values were available, comparisons were made with the experimental values to assess the degree of success or failure of the experimental process and/or to draw attention to the discrepancies that exist in common items purchased through everyday hardware stores when compared to the pure materials. Table 1 summarizes the results of the experiment and shows an extremely large discrepancy between experimental and expected values. Table 1. Experimental results and comparisons with accepted values Material Modulus of Elasticity (GPa) Accepted Value (GPa) Percent Difference (%) 20 Gauge Copper Wire 6.063 110 94. 22 Gauge Copper Wire 7.904 110 92. 30lb Monofilament Fishing Line

0. 266 N/A N/A

20 Gauge Brass Wire 10.567 97 89. Procedure A device dubbed the "Young's Modulus Apparatus" was assembled for the purposes of this experiement and used for the testing of each material. The device is simple in that it allows a test wire to be anchored in two places within a metal chasis that sits approximately 1.5 meters off the ground. This arrangement allows weights to be applied to the bottom tip of the test wire by way of a weight bearing mechanism while the top portion is secured in place. At the point where the lower anchor point is located there exists a leveling device with an adjustment knob that can be used to make measurements with 1x10-5^ m accuracy for the change of wire length which is obtained as additional

Results For 20 gauge copper wire the following experimental results produced a Young's Modulus constant of 6063 MPa, or 6.063 GPa. When compared to the accepted value this represents a percent difference of 94.5%. As the shown in Figure 1 the sample was never taken past the elastic region. Figure 1. Elastic Region for 20 Gauge Copper Wire. For 22 gauge copper wire a slightly different experimental value was found: 7904 MPa or 7.904 GPa. This represents a percent difference of 92.8%. This sample was taken past its elastic region into the plastic region, as shown by Figure 2 on the following page. The first five data points were used to determine the value for the modulus of elasticity since the graph became non-linear starting approximately with the fifth data point (see Figure 3, next page). The 30lb monofilament fishing line proved to be the most ductile by showing greater increases in strain for smaller applied stresses (see Figure 4, page 6). The Young's modulus constant was found to be 266 MPa (or 0.266 GPa), a value which could not be compared to a known value. Like the first copper sample this material was not taken into the plastic region and maintained a consistent linear relationship when all of its data points were plotted. This result is expected since fishing line is designed to handle large variations in load without breaking. 0.0000 0.0020 0.0040 0.0060 0.0080 0.0100 0.0120 0.0140 0.0160 0.0180 0.0200 0.

f(x) = 6063.12x + 0 Copper Wire (20 Gauge)

Elastic Region

Strain (l/l) Stress (MPa)

Figure 2. Entering the plastic deformation region for 22 gauge copper wire. Figure 3. The elastic region for 22 gauge copper wire represented by the first five data points. 0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.0350 0.0400 0.0450 0.

Copper Wire (22 Gauge)

Plastic Deformation

Strain (l/l) Stress (MPa) 0.0000 0.0020 0.0040 0.0060 0.0080 0.0100 0.0120 0.

f(x) = 7903.53x - 0 Copper Wire (22 Gauge)

Elastic Region

Strain (l/l) Stress (MPa)

Finally, the 20 gauge brass had a modulus of elasticity value of 10567 MPa or 10.567 GPa. This also differed greatly from the accepted value and produced a percent difference of 89.1%. Like the 2 0 gauge copper sample, the 2 0 gauge brass sample was never taken past its elastic region. The relationship of stress versus strain for this sample can be seen in Figure 5 (previous page). Conclusion As the experiment results clearly show, the samples of copper and brass obtained at the local hardware store differ enormously from the known and accepted values for pure samples. The values are so different that a verification of the mathematical techniques used in this experiment to obtain them is required. However, provided no errors exist in these calculations then this experiment proves that wildly varying properties exist in "off the shelf" materials: when a person buys copper or brass from an inexpensive and convenient source he or she is oftentimes receiving something that is quite different and, as far as tensile strength is concerned, completely unrecognizable.