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, 20051Abstract 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:2 32+=EGm (1) where m = number of grains per mm2 at a magnification of 1x, GE = grain size index. This equation assumes that the photomicrograph was taken at 1x magnification. The area must also be expressed in mm2. The following equation can be used to adjust the number of grains observed for any magnification: mgMm21= (2) where M = magnification of the photomicrogaph and gm = number of grains per area in mm2. Another common method for determining the grain size is the ASTM comparative chart method. This method results in an ASTM grain size number for the photomicrograph. The ASTM grain size number for a given photomicrograph can be found using: 12−=n (3) where  = the number of grains observed in an area of 1 in2 on a photomicrograph taken at a magnification of 100 times (100x), and n = the ASTM grain size number [1]. This number can then be translated into an average grain diameter via 100010024.25212×=−nd (4) where d = the average grain diameter in µm. This equation also makes assumptions about the photomicrograph. In this case it is expected that the photomicrograph was taken at 1x magnification and the area is in mm2. Equation 4 can be used to adjust the values to the required magnification.3 igM2100= (5) where M = magnification of the photmicrograph and gi = number of grains per area in in2. Once the average grain diameter is known the yield strength of the material can be determined per the Hall-Petch equation: dKy+=0σσ (6) where σy = yield strength of the material and d = the diameter of the material. K and σy are constant values for a given material. The constants K and σ0 can be solved for the given metal using a chart similar to that shown in Figure 1. By choosing two points on the curve for the material in question two equivalent expressions can be set up and solved. This will give K and σ0 for the material. Once these constants are known only the average grain diameter of the material is necessary to determine its yield strength. Therefore if care is taken during the ASTM comparative chart and mean line intercept stages calculating the corresponding yield strengths is a rather systematic process. Figure 1: Effect of grain size on the yield strength of aluminum alloys 5182 and 5754 [1]4Table 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 the5ASTM 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).