#1: Experiment Static Tensile Testing of Metallic Alloys Materials Science 104 Discussion 2A
Introduction
Tensile testing of metallic alloys is very important in determining the amount of applied force that a specimen can withstand. These tests could assist scientists in choosing the best type of material for various projects. In order to perform these tests, scientists utilize the tensile test machine which stretches out a specimen at a constant rate and also records data on factors such as the time, load strength, elongation, etc. Other concepts that are important in regards to this experiment include yield strength, ductility, elastic and plastic elongation, stress, and strain. These concepts are all very important in understanding what tensile strength is: the maximum stress that can be sustained in tension. One most note, however, that the results of tensile tests are not always completely accurate in the real world because of the controlled environment. Objective The objective of this experiment is to determine various mechanical properties of two metallic alloys: aluminum and brass. In order to determine these properties, we subject aluminum and brass rods to the tensile test machine to apply a load on the metallic alloy until the point of fracture. While this load is applied, the PLW software will be recording data such as the load and elongation so that we will be able to analyze the data during the elongation. With these data points, we will be able to then plot a stress vs. strain graph. This graph will allow us to calculate the yield strength at a 0.2% offset strain, tensile strength, ductility, and modulus of elasticity. Experimental Procedures Before placing the aluminum and brass rods into the tensile testing machine, we first need to measure the cross sectional diameter and the gage length of the specimens between the two points on the rod using calipers. Following this we then place the rod and secure it in the tensile test machine. The PLW program is then activated and a constant load is applied to the specimen. We then observe as the load cell vs. extensometer chart on the computer screen shows the specimen transitioning through elastic deformation to plastic deformation. We can visually see this occurring as the specimen becomes more deformed as time progresses. After the specimen undergoes plastic deformation for a period of time, fracture occurs and it breaks into two. The smallest cross section is then measured as is the elongated gage length between the two points. We then use the data points from the program to plot a stress vs. strain graph. This procedure is then repeated for the second metallic alloy. Results The first thing we have to do is convert the voltage readings into pounds so that we can create our stress vs. strain curve. In order to do so, we use the equation: y = -0.0017x2 + 12.098x to convert from mV lb. Once this is converted to pounds, we can then find out the stress on the metallic alloy by using the equation = F/A0. A0 is the original cross sectional area of the rod. We need to make sure to convert the area into square inches. Next, we want to find the amount of elongation that occurs in each metallic alloy. To do this, we use the equation L/L 0. The value of L (elongation) varies with time and is unique for each metallic alloy. L 0 is the original gage length of the rod. For the aluminum, L = (0.05 in/min)t. For the brass, L = (0.5 in/min)t. With these two items calculated, we are able to create our stress vs. strain graph. *Note that these calculations were performed on excel. A raw sample of the data is included at the end of this report.*
Aluminum Results:
Stress vs. Strain Graph (Aluminum)
20000 15000
Stress (psi)
10000 5000 0 0 -5000 Strain 5 10 15 20 25
We can now find the modulus of elasticity by using:
E slope
2 1 2 1
We take 1 = 0, 1 = 0 and the arbitrarily choose the other point to be 2 = 16758.5, 2 = 3.24154. Using these points, we plug it into the equation to find the modulus of elasticity which turns out to be: E = 4841.3 psi. Next, we find tensile strength which is the maximum stress that can be sustained. This is found by looking at the graph and finding where the peak of the stress is sustained at. After looking at my excel graph, I can conclude that: Tensile Strength = 18859.8 psi. The yield strength of this material is calculated by drawing at 0.0002 strain offset line with a slope of 4841.3 psi and finding where this line intersects the curve. After drawing this line, we see that the yield strength = 7649.3 psi. Below is a zoomed in picture of the line that we have drawn at a 0.0002 offset strain.
Stress vs. Strain Graph (Alum inum )
25000
20000
15000
Stress (psi)
10000
5000
0 0 -5000 Strain 1 2 3 4 5
Al
Lo (in) do(mm) Lf(in) df(mm) 1.95 7.936 2.18 6.118
This chart will allow us to see the ductility of the metallic alloy. We are able to then calculate the percentage elongation and the percentage reduction of cross sectional area using the following equations: l f lo % EL (100) lo
Ao Af % AR (100) Ao After doing the calculations, we see that the percentage elongation of the aluminum is 11.8%. The percentage reduction of area turns out to be -40.6%.
Brass Results: To complete this portion, we complete the same calculations for the brass as we did for the aluminum. We first want to find the modulus of elasticity. Choosing the points 1 = 0, 1 = 0 and 2 = 13265.7, 2 = 3.85604. The modulus of elasticity turns out to be E = 3440.2 psi. Next, we want to find the tensile strength of the brass. We look at our graph shown below and see that the maximum stress the brass can withstand occurs at 19405.4 psi therefore, Tensile Strength: 19405.4 psi.
Stress vs. Strain Graph (Brass)
25000 20000
Stress (psi)
15000 10000 5000 0 0 -5000 Strain 10 20 30 40 50 60
As mentioned above, the yield strength of this material is calculated by drawing at 0.002 strain offset line with a slope of 3440.2 psi and finding where this line intersects the curve. After drawing this line, we see that the yield strength = 13898.4 psi. Below is a zoomed in picture of the Stress vs. Strain Graph with the 0.0002 offset strain to see where it intersects in order to find the yield strength.
Stress vs. Strain Graph (Brass) 25000
20000
15000
Stress (psi)
10000
5000
0 0 -5000 Strain 2 4 6 8 10
Lastly, we can calculate the percentage elongation and percentage reduction of area by using the equations from above and the following chart:
Brass
Lo (in) do(mm) Lf(in) df(mm) 1.945 7.949 2.475 5.914
The percentage elongation is 27.2% and the percentage area reduction is -44.6%. Discussion For the aluminum alloy we determined that the modulus of elasticity is approximately 4841.3 psi. This figure represents the stiffness of the specimen and its willingness to elongate. With this value, we were then able to plot an offset strain line of 0.0002 and find the yield strength of the aluminum. Once we plotted the line on excel, we saw that it intersected the stress vs. strain curve at approximately 7649.3 psi. Although there should only be one intersection, we see from the graph that there are two due to the close nature of the line and the stress vs. strain curve. We make sure to take the first point that intersects, or overlaps the curve as our yield strength. This figure deviates from the theoretical yield strength of 7977.1 psi. The deviation in this case was quite small and could be attributed to the temperature in the room, the purity of the alloy, etc. When it came to the tensile strength, we simply found the peak of the stress vs. strain curve and saw how much force was being withstood at the moment. This figure was determined to 18859.8 psi. The theoretical value for this is approximately 17984.6748 psi. Our figure is very close to the theoretical figure. The small deviation could be due to improper experiment set up, the temperature of the room, inconsistent load force, etc. Finally, we were asked to find the ductility of the material. We found that the percentage elongation of the aluminum was 11.8% and the percentage reduction of the cross sectional area was -40.6%. This makes sense considering the fact that plastic deformation did occur, which resulted in a longer rod with a smaller cross sectional area. The table in the back of the book says that aluminum 6000 series should have a percent elongation of 30%. Ours did not display that large percentage. This could be due to the impurities that were present in the rod. For the brass alloy, we first determined the modulus of elasticity to be approximately psi. 3440.2 We then used this value as the slope of our offset strain line of 0.0002 to determine the yield strength of the material. After plotting the line, we saw that the yield strength that we calculated in this experiment was 13898.4 psi. The tensile strength of the brass was determined to be 19405.4 psi. The theoretical value for the yield strength of copper is 14503.8 psi. Our value for the yield strength was pretty close to the theoretical value. It differs because the factors mentioned above as well as additional factors such as crystalline irregularities, improper equipment set up, etc. The tensile strength, on the other hand, deviated greatly from the theoretical value of approximately 40000 psi. The only reason I could see why this occurred was either due to the properties of the brass alloy. We were not told which brass alloy the one we tested was, therefore, we aren't able to make an accurate comparison between the two. The brass also could have had different physical properties that we were not aware of. In addition, any fractures of cracks may have lessened the tensile strength by a considerable amount. Finally, when finding the ductility of the specimen, we found that the percentage elongation is 27.2% and the percentage area reduction is -44.6%. There seemed to be a lot of deviation of the brass values and the theoretical values that I researched on the internet. Ideally, I would have liked to redo this portion of the experiment if time permitted. Since we were not able to, these figures are representative of the experiment that we performed.
Conclusion This experiment allowed us to see different properties of these two metallic alloys. Although we conducted static tensile stress testing, we gained much more information about the materials than just the tensile strength. With the data points, we were able to calculate items such as the modulus of elasticity, yield strength, percentage elongation, and percentage of area. These items allowed us to see the physical properties of the specimens. This experiment also allowed us to compare the ductility and tensile strengths of the two materials. We were able to see which one was more prone to fracture and which one could withstand the most force applied. Overall, I would have to say that this experiment was a success because were able to gain more knowledge about the two specimens by putting them to the tensile strength test.
Sample Raw Data for Aluminum Strain Stress 0 0.025641026 0.051282051 0.076923077 0.102564103 0.128205128 0.179487179 0.179487179 0.205128205 0.230769231 0.256410256 0.282051282 0.307692308 0.333333333 0.358974359 0.384615385 0.41025641 0.435897436 0.461538462 0.487179487 0.512820513 0.538461538 0.564102564 0.58974359 0.615384615 0.641025641 0.666666667 0.692307692 0.717948718 0.743589744 0.769230769 0.794871795 0.820512821 0.846153846 0.871794872 0.897435897 0.923076923 -66.2769836 80.46867775 205.0934658 348.6142999 451.106698 550.4276036 673.3719581 815.1973033 964.8628653 1076.692047 1179.051275 1311.30314 1457.688349 1607.182027 1712.590343 1827.41555 1967.375956 2112.017206 2270.764922 2383.903992 2489.165533 2627.389253 2779.7097 2938.267062 3049.7011 3157.974731 3300.738107 3465.419447 3617.510192 3738.212313 3844.784531 4006.171044 4153.414762 4269.302465 4385.165884 4535.438998 4673.153449 0.948717949 0.974358974 1 1.025641026 1.051282051 1.076923077 1.102564103 1.128205128 1.153846154 1.179487179 1.205128205 1.230769231 1.256410256 1.282051282 1.307692308 1.333333333 1.358974359 1.384615385 1.41025641 1.435897436 1.461538462 1.487179487 1.512820513 1.538461538 1.564102564 1.58974359 1.615384615 1.641025641 1.666666667 1.692307692 1.717948718 1.743589744 1.769230769 1.794871795 1.820512821 1.846153846 1.871794872 4828.041159 4982.885405 5104.853291 5218.97828 5387.777387 5528.403797 5695.546236 5814.233391 5921.966651 6067.138943 6227.876396 6391.68654 6516.461452 6638.089665 6787.748891 6948.27532 7111.870341 7236.481351 7351.721267 7505.855611 7666.171473 7835.774885 7953.999301 8081.528495 8240.120757 8401.775167 8574.257248 8695.428184 8811.913257 8985.81786 9139.49079 9276.052462 9389.310517 9556.827035 9711.888802 9873.105998 9998.636165 1.897435897 1.923076923 1.948717949 1.974358974 2 2.025641026 2.051282051 2.076923077 2.102564103 2.128205128 2.153846154 2.179487179 2.205128205 2.230769231 2.256410256 2.282051282 2.307692308 2.333333333 2.358974359 2.384615385 2.41025641 2.435897436 2.461538462 2.487179487 2.512820513 2.538461538 2.564102564 2.58974359 2.615384615 2.641025641 2.666666667 2.692307692 2.717948718 2.743589744 2.769230769 2.794871795 2.820512821 10122.58802 10285.23175 10435.44014 10601.08553 10765.13277 10890.45603 11011.1102 11167.30179 11326.53969 11496.54764 11621.701 11739.10239 11895.08302 12057.19315 12222.34078 12351.95382 12456.85574 12608.00185 12771.43848 12927.11947 13045.77657 13159.78588 13304.57352 13453.94095 13609.42352 13726.39048 13829.48485 13967.93849 14107.89398 14255.49954 14366.17688 14463.00069 14585.92621 14714.96745 14850.11995 14946.85576 15040.50383
Sample Raw Data for Brass Strain 0 0.257069409 0.514138817 0.771208226 1.028277635 1.285347044 1.542416452 1.799485861 2.05655527 2.313624679 2.570694087 2.827763496 3.084832905 3.341902314 3.598971722 3.856041131 4.11311054 4.370179949 4.627249357 4.884318766 5.141388175 5.398457584 5.655526992 5.912596401 6.16966581 6.426735219 6.683804627 6.940874036 7.197943445 7.455012853 7.712082262 7.969151671 8.22622108 8.483290488 8.740359897 8.997429306 9.254498715 9.511568123 9.768637532 10.02570694 10.28277635 10.53984576 10.79691517 11.05398458 11.31105398 11.56812339 11.8251928 12.08226221 Stress -251.700311 935.0177238 2191.284604 3504.108727 4494.095453 5463.6177 6759.350717 7946.607894 9063.210527 9847.018381 10566.4393 11451.27366 12170.09063 12725.08939 13032.31996 13265.69695 13512.78094 13706.0711 13845.62591 13959.08306 14097.03885 14222.70075 14351.39674 14470.87224 14558.16426 14637.78655 14734.23601 14830.66792 14940.85434 15002.05912 15075.49552 15156.56971 15239.16083 15326.32637 15393.60223 15448.63975 15522.01419 15598.43508 15679.42915 15731.38107 15795.54993 15850.54559 15920.8095 15984.95533 16046.03935 16090.32085 16148.33924 16209.40435 12.33933162 12.59640103 12.85347044 13.11053985 13.36760925 13.62467866 13.88174807 14.13881748 14.39588689 14.6529563 14.91002571 15.16709512 15.42416452 15.68123393 15.93830334 16.19537275 16.45244216 16.70951157 16.96658098 17.22365039 17.48071979 17.7377892 17.99485861 18.25192802 18.50899743 18.76606684 19.02313625 19.28020566 19.53727506 19.79434447 20.05141388 20.30848329 20.5655527 20.82262211 21.07969152 21.33676093 21.59383033 21.85089974 22.10796915 22.36503856 22.62210797 22.87917738 23.13624679 23.3933162 23.6503856 23.90745501 24.16452442 24.42159383 16288.77841 16325.40856 16375.77086 16427.65425 16485.63553 16542.08485 16578.69739 16629.03548 16680.89393 16732.74727 16796.79434 16831.86443 16873.03068 16908.09569 16978.21869 17026.9944 17059.00099 17107.7692 17142.81855 17193.10267 17254.04666 17286.03942 17311.9369 17356.112 17395.7141 17453.58873 17494.70629 17512.97973 17544.95671 17605.85986 17642.39836 17686.54564 17721.55636 17733.73346 17785.48295 17866.14109 17884.40158 17904.18307 17977.21593 18012.20723 18041.11133 18054.80219 18080.66172 18133.8979 18182.56625 18208.41947 18217.54383 18266.2044 24.67866324 24.93573265 25.19280206 25.44987147 25.70694087 25.96401028 26.22107969 26.4781491 26.73521851 26.99228792 27.24935733 27.50642674 27.76349614 28.02056555 28.27763496 28.53470437 28.79177378 29.04884319 29.3059126 29.56298201 29.82005141 30.07712082 30.33419023 30.59125964 30.84832905 31.10539846 31.36246787 31.61953728 31.87660668 32.13367609 32.3907455 32.64781491 32.90488432 33.16195373 33.41902314 33.67609254 33.93316195 34.19023136 34.44730077 34.70437018 34.96143959 35.218509 35.47557841 35.73264781 35.98971722 36.24678663 36.50385604 36.76092545 18316.38087 18431.92049 18556.55303 18527.6774 18486.64088 18485.12094 18498.80018 18521.59812 18530.71702 18533.75662 18545.91483 18562.63191 18585.42706 18673.55897 18770.79071 18802.69093 18820.91876 18830.03243 18951.53286 18956.08857 18942.42131 18927.23503 18927.23503 18924.19773 18907.49222 18887.74866 18887.74866 18939.38409 18987.97747 19012.27246 19032.01131 19051.74942 19073.005 19080.59607 19089.70521 19086.66884 19076.04144 19066.93206 19073.005 19079.07786 19083.63247 19124.62209 19153.46471 19217.21642 19283.99557 19356.83578 19350.76615 19344.69645
37.01799486
19344.69645
37.27506427
19341.66158
37.53213368
19338.62668