顯微結(jié)構(gòu)的量化處理及組織分析的教程lecturen(1)-在線瀏覽
2025-02-25 08:37本頁面
【正文】 n 2D, without accounting for their 3D nature. The next lecture will consider such conversions in situations where they are applied, but for grain size determination it should just be remembered that the true grain dimensions and distribution of sizes may be larger than that reported. In some practical situations, grain size is assessed by parison of an image with a series of standard images of microstructures. This method is rapid, but it is imprecise and not suitable for detailed quantitative analysis (being rather used for quality control in an industrial setting) and is not discussed here. Linear Intercept Method The linear intercept method is the main way used to determine the grain size of materials. The mean linear intercept is the average distance between grain boundaries along lines placed at random on the image. The mean linear intercept can be determined using: LTotalNLL? (1) where LTotal is the total length of the line, and NL is the number of boundaries crossed. A worked example of grain size determination by the linear intercept method using an artificial microstructure is given below. Worked Example 1 Figure 1 shows a simulated material microstructure, where the black lines represent grain boundaries. Figure 1 – An artificial microstructure, the black lines representing grain boundaries. Quantification of Microstructure and TextureSize from Planar Sections R Goodall, October 2022 2 Figure 2 – The linear intercept method for grain size determination Quantification of Microstructure and TextureSize from Planar Sections R Goodall, October 2022 3 The analysis proceeds as follows, using the procedures shown in Figure 2 and Table 1. 1) Draw a series of lines on the image. These lines can be spaced equally, but should be randomly placed and should be spaced sufficiently that no grain is crossed by two or more lines, in order to respect the random sampling criterion for us to be able to statistically analyse our results. See Figure 2a. 2) For the first line, identify the number of times that line crosses a grain boundary and count the total. This is shown in Figure 2b 3) Repeat for all of the lines (Figure 2c). The measurement is performed on a line by line basis as this allows each line to be treated as a measurement of the grain size. The results could be put together and treated as one sample, but in this case we would not be able to use the statistical analysis given here, and would have to estimate the error using the equations discussed later in this lecture. Either method is equally valid. 4) Measure the real length of the lines used (using the scale bar or magnification of the image). In the case of this example it is 1mm. 5) For each line, i, divide this total length by the number of grain boundaries to get the linear intercept length (Table 1, column 3). 6) These linear intercept lengths are summed, and divided by the total number of lines to get the mean linear intercept length (Table 1, column 3). 7) The difference of the linear intercept length of each line Li from the mean linear intercept length is calculated and squared (Table 1, column 4). 8) This data is then used to calculate the standard deviation of the measurements using the equation given in the lecture on statistics (Table 1, column 4). 9) From the standard deviation, the standard error can be calculated using: ? ? nsLS ? where n is our number of lines. 10) From the standard error, the 95% confidence limit can be calculated using the relevant tvalue (. from the table given in the lecture on Statistics and the result of the measurement expressed according to: ? ? ? ?LStL n 195 ?? Line Number, i No. of Grain Boundaries, NL Linear In
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