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GVSU EGR 250 - EGR250 Methods of Determining Grain Size

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1AbstractTen photomicrographs were taken of AA5182 aluminum with solidification rates rangingbetween 0.1°K/s and 14.1°K/s at 50X magnification. The objective was to determine the effectsof solidification rate on the grain size and yield strength of the aluminum. Grain sizecalculations were performed on each photomicrograph using both the ASTM comparative chartmethod and the linear intercept method. The resultant grain diameters were found to range from100µm to 300µm and the size was inversely proportional to the solidification rate. The yieldstrength of the aluminum was found using the Hall-Petch equation which ranged from 75MPa to86MPa. It was determined that increasing the solidification rate increases the effective yieldstrength of the aluminum.IntroductionThe properties of engineering materials depend heavily on the processes that are used tofabricate them. Therefore, materials can be manipulated to obtain desirable properties if oneunderstands the relationship between the process and the resultant microstructure of the material.In this case, the relationship between grain size and yield strength was studied. Ten samples ofAA5128 aluminum were formed using a range of solidification rates to exemplify the effect ofsolidification rate on yield strength. Photomicrographs were taken of each materials grainstructure and the ASTM comparative chart method and the linear intercept method were used todetermine the grain size of each material. The Hall-Petch equation was then used to determinethe relationship between grain size and yield strength of the aluminum.Experimental Procedure Ten photomicrographs were taken of AA5182 aluminum with different solidificationrates at 50X magnification. Aluminum AA5182 consists of 4-5 wt. % Mg, 0.35 wt. % Fe, 0.25wt. % Zn, 0.2-0.5 wt. % Mn, 0.2 wt. % Si, and the balance is Al. The number of grains along the edge of each photomicrograph and the number of interiorgrains were counted separately. Since the grains on the edge represent approximately one-half ofa grain, the number of grains on the edge are divided by two and added to the number of interior2grains. Then the total number of grains is divided by the area of the photomicrograph to obtainthe grain concentration of the photomicrograph. With the grain concentrations known, theASTM grain size number and the grain size index was computed. The ASTM grain size numberwas used to reference the approximate grain diameter of each material using a chart. Thismethod is typically referred to as the ASTM comparative chart method.The mean linear intercept method was also used to determine the grain diameter of thematerial. This method was performed by drawing four horizontal lines, four vertical lines andtwo diagonal lines across each photomicrograph. The number of grains intersected by each linewas counted and the length of each line was measured. Finally, the average grain diameter ofeach material was computed based on the number of grains intersected by a line, the length of theline and the magnification of the photomicrograph.ResultsThe ASTM grain size number was computed for each material using equation 1:1ln4427.1 ign(1)where n = the ASTM grain size number and gi = the grain concentration of the photomicrograph(grains/in2). The derivation of this equation is shown in appendix A.The grain size index was computed for each material using equation 2:2877.8ln4427.1 mEgG(2)where GE = the grain size index and gm = the grain concentration of the photomicrograph(grains/mm2). The derivation of this equation is shown in appendix A.The resulting grain size index numbers and ASTM grain size numbers are shown in Table1 for each material. Note that the grain size number decreases as the solidification rate ofaluminum decreases.Table 1: ASTM grain size numbers and grain size index numbers are compared with data from thephotomicrographs and material solidification rates.3SolidificationRate (°K/s)NumberofGrainsArea ofPhotomicrographFrameArea Density of GrainsGrainSizeIndexGrainSizeNumberin2mm2grains/in2grains/mm214.1 224.5 15.75 10120 14.25 0.0222 2.79 2.837.5 202.5 15.75 10120 12.86 0.0200 2.64 2.686 192 15.75 10120 12.19 0.0190 2.57 2.612.9 145 15.75 10120 9.21 0.0143 2.16 2.201.6 157 15.75 10120 9.97 0.0155 2.28 2.321.2 144.5 15.75 10120 9.17 0.0143 2.16 2.200.8 110.5 15.75 10120 7.02 0.0109 1.77 1.810.6 124 15.75 10120 7.87 0.0123 1.94 1.980.2 66.5 15.75 10120 4.22 0.0066 1.04 1.080.1 38.5 15.75 10120 2.44 0.0038 0.25 0.29The yield strength was calculated for each material using equation 3 (the Hall-Petchequation):oyyDK(3)where y = the effective yield strength of the material,yK = a material dependant constant(300 for AA5182 aluminum),D = the grain diameter of the material (µm), and o = theminimum possible yield strength of the material. yKfor AA5182 aluminum was equivalent tothe slope of the yield strength chart in appendix A.The average grain diameter was calculated for each material using equation 4: neD345.0359(4)where D = the average grain diameter and n = the ASTM grain size number. The derivation ofthis equation is shown in appendix A.The resulting yield strengths and grain diameters are shown in Table 2. Note that theyield strengths increase as the average grain diameters decrease. Also note that the graindiameter is inversely proportional to the solidification rate.Table 2: Grain sizes are compared to the yield strengths of the materials4SolidificationRate (°K/s)ASTM GrainSize Number, nAverage GrainDiameter, µmYield Strength(MPa)14.1 2.83 135 83.87.5 2.68 142 83.26 2.61 146 82.82.9 2.20 168 81.21.6 2.32 161 81.61.2 2.20 168 81.10.8 1.81 192 79.60.6 1.98 182 80.30.2 1.08 247 77.10.1 0.29 325 74.6The ASTM grain size number was also calculated using the diameters found using themean linear intercept method. The grain size number was calculated using equation 5:345.0359lnDn(5)where n = the ASTM grain size number and D = the grain diameter. The derivation of thisequation is shown in appendix A.The resulting ASTM grain size numbers were compared to the corresponding mean grainsizes in Table 3. Table 3 also includes yield strengths which were calculated from the results ofthe mean linear intercept method using equation 3.Table 4 compares all of the results obtained by ASTM


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