顯微結(jié)構(gòu)的量化處理及組織分析的教程lecturen(1)(參考版)
2025-01-11 08:37本頁面
【正文】 its “diameter”. Most of these can be performed by hand or, increasingly, using automated image analysis software. Some of these account in different ways for the fact that the shape of the particles may not be spherical (it may be anisotropic). Caliper Diameter / Feret Diameter These measures are the shortest distance between two straight parallel lines that are tangent to the object of interest’s surface. Normally a direction would need to be specified (. horizontal or vertical in the image) for the direction in which the measurement is taken, as this will vary for nonspherical particles. Length / Breadth Normally the length would be the largest Feret diameter (of all the angles possible around an object). The breadth would be the Feret diameter at 90176。 181。m) = 181。m with 95% confidence limits by treating each of the lines as a separate measurement. If we wanted to estimate the expected error before doing this experiment, or if we decided to take all the measurements together and needed to estimate the error, we can use Eqn. (8). In worked example 1, we had 231 intercepts (we can assume that the number of grains examined, n is equal to the number of grain boundary intercepts) in a total line length of 10 mm, giving a mean linear intercept length of 181。 20% 42 Table 3 – Number of grains needing to be measured in order to achieve various estimated relative errors of volume fraction in linear intercept method, determined from Eqn. (8). A similar equation can be used for the standard error in the ASTM grain size number, g: ? ?ngS ? (9) Note that in both of these equations the error will decrease as the root of the number of grains measured. That is, the reductions in error on taking further measurements decrease as the total number of measurements gets larger, in line with the statistical principles discussed before. 3 R L Higginson and C M Sellars, Worked Examples in Quantitative Metallography, (2022) Maney, London Quantification of Microstructure and TextureSize from Planar Sections R Goodall, October 2022 9 Worked Example 3 In worked example 1, we measured the mean grain size of the example microstructure to be 177。 5% 676 177。m Table 2 – The calculation of grain size and second phase region size using the linear intercept method Experimental Planning Just as for the measurements of volume fraction discussed previously, equations have been developed to allow the rapid estimation of the error likely in measurements of the grain size, depending on the number of grains that are analysed. The relative standard errors (standard errors as a percentage of the measured values) in measurements of grain size are given by3: ? ? ? ?nNNSLLS LL ?? (8) where n is the number of grains counted. These can be used with the values of t(95, n1) given in the lecture on statistics to determine 95% confidence limits expected for the result. Values of the number of grains that must be counted for a given accuracy are given in Table 3. Relative Error 95% CL No. of grains, n 177。m) 1 1 4 25 2 0 0 33 3 2 29 4 1 2 32 5 2 4 29 6 4 32 7 0 2 28 8 0 0 31 9 2 33 10 0 3 29 pP = )(InterLL = 181。 the ratio between the largest and the smallest grain size when it is measured along three orthogonal directions. The closer this value is to 1 the more equaixed are the grains. In order to determine this parameter, polished sections should be prepared along at least 2 orthogonal directions in the sample. Lines are then placed at right angles on images taken from these surfaces, and used to determine L1, L2 and L3. Figure 3
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