Laboratory Module 9 - Materials Science and Engineering | EGR 250, Lab Reports of Materials science

Download Laboratory Module 9 - Materials Science and Engineering | EGR 250 and more Lab Reports Materials science in PDF only on Docsity! Comparison of the ASTM Comparative Chart Method and the Mean Line Intercept Method in Determining the Effect of Solidification Rate on the Yield Strength of AA5182 By Brad Peirson School of Engineering Grand Valley State University Laboratory Module 9 EGR 250 – Materials Science and Engineering Section 1 Instructor: Dr. P.N. Anyalebechi July 12, 2005 1 Abstract The purpose of this laboratory was to determine the effect of cooling rate on the yield strength of metals. The sample photomicrographs provided were of a single AA5182 sample cooled at various rates. Each photomicrograph was taken with polarized light at 50x magnification. First the photomicrographs were examined using the ASTM comparative chart method. Then each photomicrograph was examined using the mean line intercept method. The ASTM grain size was calculated for each photomicrograph using the results of both methods. The Hall-Petch Equation was then used to determine the yield strength of the metal at the points where the photomicrographs were taken. There were some slight discrepancies in the results using the different methods but both the ASTM comparative chart and the mean line intercept method show the same trends in the yield strength of the sample at the various cooling rates. Both methods show that as the cooling rate of the metal decreases the yield strength also decreases. Introduction The average size of the grains in a given metal sample is a critical value. Using the Hall-Petch equation the grain size can be used to determine the yield strength of a material. Before the Hall-Petch equation can be utilized the grain size must be determined. There are many ways that this can be accomplished. The simplest would be to calculate the area of each individual grain and determine their individual diameters. The average of these diameters would provide a very accurate average grain size diameter. The downfall is that this method would be extremely time consuming and prone to human error at nearly every stage of the analysis. A more appropriate method of determining the grain size is by a method known as the mean line intercept method. This method involves dissecting the photomicrograph with multiple lines and counting the number of grains intersected by each line [2]. The ultimate goal of this method is to determine the grain size index. The following equation is used to find this value: 4 Table 1: Average grain diameter for each of the common ASTM grain sizes [1] ASTM Grain Size Grain Diameter (µm) 0 359 1 254 2 180 3 127 4 90 5 64 6 45 7 32 8 22.4 9 15.9 10 11.2 11 7.94 12 5.61 13 3.97 14 2.81 Experimental Procedure Ten polarized light photomicrographs were obtained from the instructor. The material in the photomicrographs was known to be AA5182 – O-Temper. Each of the photomicrographs was known to be taken at 50x magnification. The number of grains contained in each of the photomicrographs was counted. Those grains that contacted the outer border of the photomicrograph were counted as ½ grain. These counts are shown in Table 2. The area of each of the photomicrographs was identical and is also recorded in Table 2. Next the grain size index was calculated. Prior to using equation (1) to calculate the index the measurement required adjusting to fit the format for the equation. In order to use equation (1) the magnification has to be 100x. Equation (2) accounts for the adjustment from any magnification, 50x in this laboratory. The corrected grain size indices are listed in Table 2. Equation (5) was used to adjust the magnification to 1x in order to calculate the ASTM grain size. This adjustment was then substituted into equation (3) to calculate the 5 ASTM grain size. Once the ASTM grain size was calculated it was used to determine the average grain diameter for each of the separate cooling rates. Equation (6) was then used to calculate the yield strength of the different solidification rates. K and σy are were first found for this material using Figure 1 and used in all subsequent calculations involving equation (6). These yield strengths are shown in Table 3. Once the ASTM comparative chart method procedure was completed the mean line intercept method of grain size determination was performed. For this portion of the laboratory a total of ten lines were drawn on each of the ten photomicrographs: four vertical, four horizontal and two diagonal. The number of grains intersected by each line was counted. Those grains that contacted the outer border of the photomicrograph were counted as ½ grains. After the grains were counted the average grain size for each photomicrograph was calculated. This was done by dividing the length of each line by the number of grains it intersected. This value was divided by 50 to adjust for the 50x magnification of the photomicrographs. A simple statistical analysis was performed on the ten separate values (one for each line) for each photomicrograph. The results are given in Table 4. The average grain diameters calculated in Table 4 were used to find the ASTM grain sizes for the ten photomicrographs. The ASTM grain sizes were estimated using Table 1. Finally, equation 5 was used to calculate the yield strength of the material in each of the ten photomicrographs. Experimental Results The results of the first portion of the ASTM comparative chart method are given in Table 2. Figures 2 and 3 show grain size index versus average solidification rate and ASTM grain size versus average solidification rate respectively. Figure 2 shows that for these ten solidification rates the grain size index decreases as the solidification rate increases. Figure 3 shows a similar trend in the ASTM grain size. The trend in Figure 2 demonstrates that a large grain size index translates to a greater number of grains and 6 thus a smaller grain size. Figure 3 seems to demonstrate the convention that a larger ASTM grain size translates to smaller grains via a fast solidification rate. Table 2: Data obtained from 10 polarized light photomicrographs of AA5182 samples taken at 50x magnification using the ASTM comparative chart method Table 3 was created using equation 5. This table shows the relationships between ASTM grain size number, grain diameter and yield strength. The data in Table 3 is represented graphically in Figures 4 and 5. These figures show that a lower solidification rate leads to a larger average grain size. The figures also show that a lower solidification rate leads to a lower yield strength. This suggests that as the grain size increases the yield strength of a metal decreases. 0.0000 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 14.1 7.5 6.0 2.9 1.6 1.2 0.8 0.6 0.2 0.1 Average Solidification Rate (K/s) G ra in S iz e In d ex Figure 2: Comparison of the average solidification rate and the grain size index of ten samples of AA5182 Average Solidification Rate (K/s) # Grains Observed Area of Photomicrograph (in2) Area of Photomicrograph (mm2) Area Density (grains/in2) Area Density (grains/mm2) Corrected Area Density (grains/in2 @ 100x) Corrected Area Density (grains/mm2 @ 1x) Grain Size Index ASTM # 14.1 184.5 19.25 8652 9.5844 0.0213 2.3961 53.3114 2.7364 2.2607 7.5 169.5 19.25 8652 8.8052 0.0196 2.2013 48.9771 2.6140 2.1384 6.0 130.5 19.25 8652 6.7792 0.0151 1.6948 37.7080 2.2368 1.7611 2.9 121.5 19.25 8652 6.3117 0.0140 1.5779 35.1075 2.1337 1.6580 1.6 113 19.25 8652 5.8701 0.0131 1.4675 32.6514 2.0291 1.5534 1.2 103 19.25 8652 5.3506 0.0119 1.3377 29.7619 1.8954 1.4197 0.8 79 19.25 8652 4.1039 0.0091 1.0260 22.8271 1.5127 1.0370 0.6 70.5 19.25 8652 3.6623 0.0081 0.9156 20.3710 1.3484 0.8728 0.2 52 19.25 8652 2.7013 0.0060 0.6753 15.0254 0.9093 0.4337 0.1 34.5 19.25 8652 1.7922 0.0040 0.4481 9.9688 0.3174 -0.1583 9 Table 4: Results of the mean line intercept method for ten samples of AA5182 Average Solidification Rate (K/s) Mean Average Grain Size (mm) Standard Deviation Average Grain Size (mm) Max Average Grain Size (mm) Min Average Grain Size (mm) Range Average Grain Sizes (mm) ASTM Grain Size Yield Strength (MPa) 14.1 0.1302 0.0271 0.1920 0.1018 0.0902 2.8 83.8884 7.5 0.1209 0.0162 0.1400 0.0958 0.0442 3.1 84.901 6.0 0.1329 0.0145 0.1461 0.1018 0.0443 2.6 83.6178 2.9 0.1424 0.0106 0.1527 0.1212 0.0316 2.4 82.7075 1.6 0.1552 0.0223 0.1920 0.1288 0.0633 2.6 81.6232 1.2 0.1760 0.0263 0.2060 0.1373 0.0687 2.1 80.1194 0.8 0.1968 0.0290 0.2585 0.1585 0.1000 1.7 78.8565 0.6 0.1981 0.0285 0.2400 0.1585 0.0815 1.6 78.7828 0.2 0.2359 0.0448 0.3055 0.1585 0.1470 1.4 76.9566 0.1 0.3972 0.1037 0.5760 0.2585 0.3175 - 72.3623 There appears to be one exception to the previous trends in the data set given in Table 4. However, overall the aforementioned trends appear to present in this data set. It appears as if a decreasing solidification rate increases the average grain size and decreases the yield strength. 65 70 75 80 85 90 14.1 7.5 6 2.9 1.6 1.2 0.8 0.6 0.2 0.1 Average Solidifcation Rate (K/s) Y ie ld S tr e n g th ( M P a ) Figure 6: Comparison of the yield strength and average solidification rate of ten AA5182 samples via the mean line intercept method 10 0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 14.1 7.5 6 2.9 1.6 1.2 0.8 0.6 0.2 0.1 Average Solidification Rate (K/s) M e a n A v e ra g e G ra in S iz e ( m m ) Figure 7: Comparison of the average grain size and solidification rate of ten AA5182 samples via the mean line intercept method The final data comparison was performed between the two test methods. The comparison shows that the trend in the yield strength does exist in both data sets. Figure 8 shows that the yield strengths found using the mean line intercept method are generally higher than those found using the ASTM comparative chart method. Though this discrepancy exists both sets of yield strengths decrease as the solidification rates decrease. Table 5: Comparison of the yield strengths calculated using both the ASTM comparative chart method and the mean line intercept method Average Solidification Rate (K/s) Yield Strength – Comparative Chart Method (MPa) Yield Strength – Mean Linear Intercept Method (MPa) 14.1 80.9433 83.8884 7.5 80.4394 84.9010 6.0 78.9513 83.6178 2.9 78.5613 82.7075 1.6 78.1725 81.6232 1.2 77.6859 80.1194 0.8 76.3536 78.8565 0.6 75.8084 78.7828 0.2 74.4247 76.9566 0.1 72.7185 72.3623 11 65.0000 70.0000 75.0000 80.0000 85.0000 90.0000 14 .1 7. 5 6. 0 2. 9 1. 6 1. 2 0. 8 0. 6 0. 2 0. 1 Average Solidification Rate (K/s) Y ie ld S tr e n g th ( M P a ) ASTM MLI Figure 8: Graphical comparison of yield strengths of ten samples of AA5182 -0.5000 0.0000 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 14 .1 7. 5 6 2. 9 1. 6 1. 2 0. 8 0. 6 0. 2 0. 1 Average Solidificaiton Rate (K/s) A S T M G ra in S iz e ASTM MLI Figure 9: Graphical comparison of ASTM Grain Size of ten samples of AA5182