# GVSU EGR 250 - EGR250 Methods of Determining Grain Size (10 pages)

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**View the full content.**## EGR250 Methods of Determining Grain Size

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## EGR250 Methods of Determining Grain Size

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- Pages:
- 10
- School:
- Grand Valley State University
- Course:
- Egr 250 - Materials Science and Engineering

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1 Abstract Ten photomicrographs were taken of AA5182 aluminum with solidification rates ranging between 0 1 K s and 14 1 K s at 50X magnification The objective was to determine the effects of solidification rate on the grain size and yield strength of the aluminum Grain size calculations were performed on each photomicrograph using both the ASTM comparative chart method and the linear intercept method The resultant grain diameters were found to range from 100 m to 300 m and the size was inversely proportional to the solidification rate The yield strength of the aluminum was found using the Hall Petch equation which ranged from 75MPa to 86MPa It was determined that increasing the solidification rate increases the effective yield strength of the aluminum Introduction The properties of engineering materials depend heavily on the processes that are used to fabricate them Therefore materials can be manipulated to obtain desirable properties if one understands 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 of AA5128 aluminum were formed using a range of solidification rates to exemplify the effect of solidification rate on yield strength Photomicrographs were taken of each materials grain structure and the ASTM comparative chart method and the linear intercept method were used to determine the grain size of each material The Hall Petch equation was then used to determine the relationship between grain size and yield strength of the aluminum Experimental Procedure Ten photomicrographs were taken of AA5182 aluminum with different solidification rates at 50X magnification Aluminum AA5182 consists of 4 5 wt Mg 0 35 wt Fe 0 25 wt 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 interior grains were counted separately Since the grains on the edge represent approximately one half of a grain the number of grains on the edge are divided by two and added to the number of interior 2 grains Then the total number of grains is divided by the area of the photomicrograph to obtain the grain concentration of the photomicrograph With the grain concentrations known the ASTM grain size number and the grain size index was computed The ASTM grain size number was used to reference the approximate grain diameter of each material using a chart This method is typically referred to as the ASTM comparative chart method The mean linear intercept method was also used to determine the grain diameter of the material This method was performed by drawing four horizontal lines four vertical lines and two diagonal lines across each photomicrograph The number of grains intersected by each line was counted and the length of each line was measured Finally the average grain diameter of each material was computed based on the number of grains intersected by a line the length of the line and the magnification of the photomicrograph Results The ASTM grain size number was computed for each material using equation 1 n 1 4427 ln g i 1 1 where n the ASTM grain size number and g i 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 G E 1 4427 ln g m 8 2877 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 Table 1 for each material Note that the grain size number decreases as the solidification rate of aluminum decreases Table 1 ASTM grain size numbers and grain size index numbers are compared with data from the photomicrographs and material solidification rates 3 Area of Number Photomicrograph Area Density of Grains Solidification of Frame Rate K s Grains in2 mm2 grains in2 grains mm2 14 1 224 5 15 75 10120 14 25 0 0222 7 5 202 5 15 75 10120 12 86 0 0200 6 192 15 75 10120 12 19 0 0190 2 9 145 15 75 10120 9 21 0 0143 1 6 157 15 75 10120 9 97 0 0155 1 2 144 5 15 75 10120 9 17 0 0143 0 8 110 5 15 75 10120 7 02 0 0109 0 6 124 15 75 10120 7 87 0 0123 0 2 66 5 15 75 10120 4 22 0 0066 0 1 38 5 15 75 10120 2 44 0 0038 Grain Size Index Grain Size Number 2 79 2 64 2 57 2 16 2 28 2 16 1 77 1 94 1 04 0 25 2 83 2 68 2 61 2 20 2 32 2 20 1 81 1 98 1 08 0 29 The yield strength was calculated for each material using equation 3 the Hall Petch equation y Ky D o 3 where y the effective yield strength of the material K y a material dependant constant 300 for AA5182 aluminum D the grain diameter of the material m and o the minimum possible yield strength of the material K y for AA5182 aluminum was equivalent to the slope of the yield strength chart in appendix A The average grain diameter was calculated for each material using equation 4 D 359e 0 345 n 4 where D the average grain diameter and n the ASTM grain size number The derivation of this equation is shown in appendix A The resulting yield strengths and grain diameters are shown in Table 2 Note that the yield strengths increase as the average grain diameters decrease Also note that the grain diameter is inversely proportional to the solidification rate Table 2 Grain sizes are compared to the yield strengths of the materials 4 Solidification Rate K s 14 1 7 5 6 2 9 1 6 1 2 0 8 0 6 0 2 0 1 ASTM Grain Size Number n 2 83 2 68 2 61 2 20 2 32 2 20 1 81 1 98 1 08 0 29 Average Grain Diameter m 135 142 146 168 161 168 192 182 247 325 Yield Strength MPa 83 8 83 2 82 8 81 2 81 6 81 1 79 6 80 3 77 1 74 6 The ASTM grain size number was also calculated using the diameters found using the mean linear intercept method The grain size number was calculated using equation 5 D n 359 0 345 ln 5 where n the ASTM grain size number and D the grain diameter The derivation of this equation is shown in appendix A The resulting ASTM grain size numbers were compared to the corresponding mean grain sizes in Table 3 Table 3 also includes yield strengths which were calculated from the results of the mean linear intercept method using equation 3 Table 4 compares all of the results obtained by ASTM comparative chart method with the results obtain by the mean linear intercept method Note …

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