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Unformatted text preview: Bending Beam Test Experimental Procedure The goal of this experiment is to calculate the modulus of elasticity for three materials (1018 steel, 3003 aluminum, and a graphite epoxy composite). To do this, we measured the displacement of a sample of each material when a force acted on it. First, the thickness and width of each sample was measured using a caliper (see Figure 1). Next, the distance from outside one support pin to the outside of the other support pin was measured. The average diameter of a support pin was subtracted from this to calculate the length between bending points (see Figure 2). Now, for each sample, the sample was placed on the bending jig and then a base plate was set on top of it (see #2 and #3 on Figure 2). The bezel screw was then turned to calibrate the displacement gauge to zero. Various weights were then placed on the beam, starting with low weights and gradually increasing, and the corresponding displacements were recorded. A plot was made for each sample of the load versus displacement data. Finally, the modulus of elasticity of each sample was calculated by Equation 1: Calculating elastic modulus from bending beam test where L is the length between bending points, m is the slope of the load versus displacement graph, d is the thickness and b is the width of the sample. b d Figure 1. The width (b) and thickness (d) of each sample were measured. P S Figure 2. The length of support (L) was calculated by subtracting (P) from (S) since both pins had the same diameter in our case. Results The length between the bending points (L) was found to be 5.855 inches (148.7 mm) by subtracting the diameter of a support pin (length P in Figure 2 – 0.125 inches) from the distance between the outside pins (length S in Figure 2 ‐‐ 5.980 inches). For the steel sample, the width (b) was 0.976 inches (24.8 mm) and the thickness (d) was 0.059 inches (1.50 mm). Now we will use Equation 2 and the values recorded during the experiment to create Table 1 and Graph 1. Equation 2: Calculating force of weight on beam Mass of weights (g) Weight, F (N) 100 0.981 200 1.96 300 2.94 400 3.92 500 4.90 600 5.89 800 7.85 Table 1: Data from experiment with steal Displacement (inches) 0.002 0.004 0.006 0.008 0.010 0.012 0.016 Displacement (mm) 0.051 0.102 0.152 0.203 0.254 0.305 0.406 Graph 1: Plotted data from bending test with steal The slope of the graph is m = 19.3. Using this and Equation 1, the elastic modulus is calculated to be 1.60 x 105 N/mm2 = 1.60 x 1011 N/m2 = 160 GPa. References have this value to be 205 GPa. The most likely cause for this error is that the base plate and masses were not centered directly above the shaft of the displacement gauge. For the aluminum 3003 sample, the width (b) was 0.986 inches (25.0 mm) and the thickness (d) was 0.060 inches (1.52 mm). The following data was collected in the experiment. Mass of weights (g) Weight, F (N) Displacement (inches) Displacement (mm) 100 0.981 0.004 0.102 200 1.96 0.0085 0.216 300 2.94 0.013 0.330 400 3.92 0.018 0.457 500 4.90 0.0215 0.546 700 6.87 0.030 0.762 Table 2: Data from experiment with aluminum Graph 2: Plotted data from bending test with aluminum The slope of the graph is m = 8.92. From this, the elastic modulus is calculated to be 7.02 x 104 N/mm2 = 7.02 x 1010 N/m2 = 70.2 GPa. References have this value to be 68.9 GPa. For the graphite epoxy composite sample, the width (b) was 0.987 inches (25.1 mm) and the thickness (d) was 0.056 inches (1.42 mm). The following data was collected in the experiment. Mass of weights (g) Weight, F (N) Displacement (inches) 100 0.981 0.004 200 1.96 0.007 300 2.94 0.010 500 4.90 0.017 600 5.89 0.021 700 6.87 0.024 Table 3: Data from experiment with graphite epoxy composite Displacement (mm) 0.102 0.178 0.254 0.432 0.533 0.610 Graph 3: Plotted data from bending test with graphite epoxy composite The slope of the graph is m = 11.4. From this, the elastic modulus is calculated to be 1.10 x 105 N/mm2 = 1.10 x 1011 N/m2 = 110 GPa. Without knowing the exact composition of the composite, there is no reference to compare this value to. 6061 Aluminum and A36 Steel Tensile Test Experimental Procedure The objective of this test was to determine the yield strength, elastic modulus, tensile strength, percent area reduction, and percent elongation of two different specimens. The two specimens were A36 Steel and 6061 Aluminum cylinders with threaded ends as shown in Figure 1. D= 12.9 mm L0=51.1 mm Figure 1. Illustration of the two specimens used according to ASTM E8. The average diameters (D) of the two specimens were determined using a dial caliper. Next, the gauge length (L0) was stamped and measured on the specimens. The specimens were then loaded into the tensile test machine using threaded wedge blocks similar to Figure 2. Figure 2. Threaded wedge blocks for uniaxial tension test. The wedge shape is used to ensure the specimen is loaded in uniaxial tension to minimize bending moments that would not be accounted for in the stress calculations. Once loaded in the machine an extensometer was attached to the specimens, which were loaded at a constant crosshead displacement rate. The strain and corresponding loads were recorded during the test. After fracture the gauge length indentations were measured again to determine the percent elongations. The percent elongation is calculated with Equation 1, where L1 and L0 are the final and initial gauge lengths respectively. Equation 1. Percent elongation after fracture. The minimum diameter was also measured after fracture to calculate the percent reduction in area. The percent reduction in area is calculated with Equation 2, where A1 and A0 are the final and initial areas respectively. Equation 2. Percent reduction in area after fracture. Results The dimensions in Figure 1, along with initial and final areas are given in Table 1 with units of length in mm and area in mm2. Table 1. Steel and Aluminum test specimen dimensions in units of mm or mm2. Initial Final Diameter (D0) Diameter (D1) A36 Steel 6061 Aluminum 12.9 12.9 7.82 8.33 Initial Area (A0) 130.7 130.7 Final Extensometer Initial Gauge Final Gauge Area (A1) Gauge Length Length (L0) Length (L1) 48.0 54.5 25.4 25.4 51.1 51.1 69.7 64.4 The two samples were loaded at a constant crosshead displacement rate of 5.08 mm/s. The tensile test machine provided data measurements for time, load and strain. The strain data was collected with the extensometer up to a strain of about 0.1 or 10% to prevent damaging the sensor. This strain is referred to as engineering strain. The engineering stress (load divided by initial area) was calculated for both samples to determine the Young’s modulus, tensile strength and yield strength using the .002 strain offset method. The plot of engineering stress and engineering strain for the samples is shown in Figure 3 and Figure 4. 500 400 σy=348 MPa Engineering Stress (MPa) 300
Young's Modulus E=218.7 GPa 200 100
.002 Offset 0 0 0.02 0.04 0.06 0.08 0.1 Engineering Strain (mm/mm)
Figure 3. A36 Steel engineering stress‐strain curve using the extensometer. 300 240 σy=202 MPa Engineering Stress (MPa) 180 120 Young's Modulus E=60.3 GPa 60
.002 Offset 0 0 0.02 0.04 0.06 0.08 0.1 Engineering Strain (mm/mm)
Figure 4. 6061 Aluminum engineering stress‐strain curve using the extensometer. The Young’s or elastic modulus was calculated by first isolating the initial linear section of the stress‐ strain curve and calculating its slope. The slope of the linear region is the Young’s modulus. The yield strength of the two materials was calculated using the .002 strain offset method. The .002 method involves offsetting the linear region of the stress‐strain curve by a strain of .002. The point where the offset line intersects the stress‐strain curve is the yield strength. This offset line is illustrated in Figure 3 and Figure 4. The final property calculated was tensile strength. The tensile strength is simply the maximum engineering stress or maximum force per initial cross‐sectional area. To find the maximum force, the force versus crosshead displacement was plotted for each of the materials (see Figure 5 and Figure 6) and the maximum force was found from them. The dip in these curves near the peak is most likely caused by the machine stopping to remove the extensometer. However, this does not affect the tensile strength calculation because the only value of importance is the maximum force applied. 70000 56000 Max Force=65,498 N Force (N) 42000 28000 14000 0 0 5 10 15 20 25 Crosshead Displacement (mm) Figure 5. A36 Steel force versus crosshead displacement. 40000 30000 Max Force=35,988 N Force (N) 20000 10000 0 0 4 8 12 16 Crosshead Displacement (mm)
Figure 6. 6061 Aluminum force versus crosshead displacement. The Young’s modulus, yield strength and tensile strength for the two samples are summarized in Table 2 below. Generally accepted reference values are provided in italics with aluminum assumed to be 6061 T6. Table 2. Young's modulus, yield strength and tensile strength for the two samples. Young's Modulus (GPa) A36 Steel 6061 Aluminum 219 (207) 60 (69) Yield Strength (MPa) 348 (220‐250) 202 (276) Tensile Strength (MPa) 505 (400‐500) 277 (310) The last two material properties measured were percent area reduction and percent elongation at failure using Equation 1 and Equation 2. These two calculations are a measurement of the ductility of the material. The values for area reduction and elongation percentages are summarized in Table 3 with length units of mm and area units of mm2. Table 3. Percent area reduction and percent elongation for the two samples in units of mm or mm2 for length and area respectively. Initial Area (A0) A36 Steel 6061 Aluminum 130.7 130.7 % Area Final Reduction Area (A1) 48.0 54.5 63.3% 58.3% Initial Gauge Final Gauge % Elongation Length (L1 ) (ΔL) Length (L0) 51.1 51.1 69.7 64.4 36.4% 26.0% ...
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- Fall '08