VV mm3 mm3 Sum of volumes of structural features divided by total test Volume fraction. N Number of features, NL mm Number of interceptions of features divided by total test Lineal density. line length, PA mm 2 Number of point features divided by total test area. LA mm mm Sum of lengths of linear features divided by total test area Perimeter total. NA mm 2 Number of interceptions of features divided by total test Areal density. PV mm 3 Number of points per test volume, LV mm mm3 Length of features per test volume. NV mm Number of features per test volume Volumetric. mm Mean linear interception distance LL NL, mm Mean area intercept AA NA. mm Mean particle surface area SV NV, mm Mean particle volume VV NV. Note Fractional parameters are expressed per unit length area or volume. These measurements are made manually with the aid of templates outlining a fixed field area. systems of straight or curved lines of known length or a number of systematically spaced points. The simple counting measurements PP PL NL PA and NA are most important and are easily. made These measurements are useful by themselves and can be utilized to derive other. important relationships These measurements can also be made using semiautomatic or automatic. image analyzers, Volume Fraction, One of the simplest and most useful measurements is the point count described in ASTM E 562 used to. estimate volume fractions of microstructural constituents While other manual procedures can be. employed the point count is most efficient it gives the best accuracy with minimum effort To perform. this test a clear plastic grid with a number of systematically spaced points usually crosses are employed. where the point is the intersection of the arms typically 9 16 25 49 64 or 100 is placed on a. micrograph on a projection screen or inserted as an eyepiece reticle The number of points lying on the. phase or constituent of interest is counted and divided by the total number of grid points Points lying on a. boundary are counted as half points This procedure is repeated on a number of fields selected without. bias without looking at the image, The point fraction PP is given by. PP P PT Eq 1, where P is the number of grid points lying inside the feature of interest plus one half the number of. grid points lying on particle boundaries and PT is the total number of grid points Studies have shown that. the point fraction is equal to the area fraction AA and volume fraction VV of the second phase particles. PP AA VV Eq 2, The volume fraction can also be estimated by dividing the total length of linear elements of a test pattern. lying within the phase by the total length of the test pattern The lineal fraction LL is also equal to the. parameters in Eq 2 Point counting is always performed on the minor phases where VV 0 5 The amount. of the major matrix phase can be determined by difference. The fields measured should be selected at locations over the entire polished surface not confined to a. small portion of the specimen surface The field measurements should be averaged and the standard. deviation can be used to assess the relative accuracy of the measurement as described in ASTM E 562. In general the number of points on the grid should be increased as the volume fraction of the feature of. interest decreases One study suggested that the optimum number of grid test points is 3 VV Hence for. volume fractions of 0 5 50 and 0 01 1 the optimum numbers of grid points are 6 and 300. respectively If the structure is heterogeneous measurement accuracy is improved by using a low point. density grid and increasing the number of fields measured. Figure 1 demonstrates the point counting procedure and shows a synthetic microstructure consisting of 24. circular particles each 6 mm in diameter within a field area of 12 100 mm2 The total area of the circular. particles is 678 6 mm2 which is an area fraction of 0 056 5 6 A square grid pattern has been drawn. over this field producing 100 intersection points Four of these intersections are completely within the. particles and four lie on the particle interface The number of hits is therefore 4 4 6 Thus PP is. or 0 06 6 which agrees very closely with the theoretically calculated area fraction The area. fraction AA is equal to the volume fraction VV as long as the sectioning plane intersects the structural. features at random, Fig 1 Synthetic microstructure of uniformly shaped. identical size spherical particles in a matrix phase. Test area is 12 100 mm2 Test lines ten horizontal, and ten vertical are 110 mm long. Number per Unit Area, The count of the number of particles within a given measurement area NA is a useful microstructural. parameter and is used in other calculations Referring again to Fig 1 there are 24 particles in the. measurement area 12 100 mm2 Hence the number of particles per unit area NA is 0 00198 mm 2 The. average area of the particles can be calculated by dividing the volume fraction VV by NA. A VV NA Eq 3, This yields an average area A of 28 23 mm2 which agrees well with the calculated area of a 6 mm. diameter particle of 28 27 mm2, Counting of the number of intersections of a line of known length with particle or grain features PL or. the number of interceptions of particles or grains by a line of known length NL provides two very useful. microstructural parameters For space filling grain structures single phase PL NL while for two phase. structures PL 2NL this may differ by one count in actual cases. Grain Structure Measurements For single phase grain structures it is usually easier to count the. grain boundary intersections with a line of known length This is the basis of the Heyn intercept grain. size procedure described in ASTM E 112 For most work a circular test grid composed of three. concentric circles with a total line length of 500 mm is preferred Grain size is defined by the mean lineal. intercept length l, l 1 PL 1 NL Eq 4, This equation must be modified as described later for two phase structures To calculate the ASTM grain. size number l can be used, PL measurements can be utilized to define the surface area per unit volume SV and the length per unit. area LA of grain boundaries, SV 2PL Eq 5, LA 2 PL Eq 6. For single phase structures PL and NL are equal and either measurement can be used For two phase. structures it is best to measure PL to determine the phase boundary surface area per unit volume or. phase boundary length per unit area, Grain Size, Perhaps the most common quantitative microstructural measurement is that of the grain size of metals and. alloys Numerous procedures have been developed to estimate grain size these procedures are. summarized in detail in ASTM E 112 and illustrated in Several types of grain sizes can be measured. ferrite grain size austenite grain size and prior austenite grain size Each type presents particular. problems associated with revealing these boundaries so that an accurate rating can be obtained To. complicate matters a variety of parameters are utilized to define grain size. Average grain diameter d, Average grain area A, Number of grains per unit area NA. Average intercept length l, Number of grains intercepted by a line of fixed length. Number of grains per unit volume NV, Average grain volume V. These parameters can be related to the ASTM grain size number G. The ASTM grain size scale was established using the Imperial system of units but no difficulty is. introduced by metric measurements The ASTM grain size equation is. n 2G 1 Eq 12, where n is the number of grains per square inch at 100 Multiplication of n by 15 5 gives the number of. grains per square millimeter at 1 NA, Planimetric Method The oldest procedure for measuring the grain size of metals is the planimetric. method A circle of known size generally 79 8 mm diameter 5000 mm2 area is drawn on a. photomicrograph or used as a template on a projection screen The number of grains completely within. the circle n1 and the number of grains intersecting the circle n2 are counted For accurate counts the. grains must be marked off as they are counted which makes this method slow The number of grains per. square millimeter at 1 NA is determined, NA f n1 n2 2 Eq 13. where f is the magnification squared divided by 5000 the circle area The average grain area A in. square millimeters is, A 1 NA Eq 14, and the average grain diameter d in millimeters is. d A 1 2 1 NA 1 2 Eq 15, The ASTM grain size G can be found by using the tables in ASTM E 112 or by the following equation. G 3 322 log NA 2 95 Eq 16, Figure 2 illustrates the planimetric method Expressing grain size in terms of d is being discouraged by. ASTM Committee E 4 on Metallography because the calculation implies that grain cross sections are. square which they are not, Fig 2 Example of grain size measurement by the. planimetric method Micrograph at 100 of an, austenitic manganese steel that was solution. annealed at 1040 C 1900 F and aged at 620 C, 1150 F to decorate the grain boundaries with fine. pearlite The circle has a diameter of 79 8 mm for, an area of 5000 mm2 A count is made to determine. the number of grains completely within the circle, 44 and the number intersecting the circle 25 The. planimetric multiplier for 100 is 2 The number of, grains per square millimeter at 1 is 2 44 25 2. 113 The ASTM grain size G is 3 322 log 113, 2 95 3 87 round to 3 9 or 4. The intercept method is faster than the planimetric method because the micrograph or template does. not require marking to obtain an accurate count ASTM E 112 recommends use of a template consisting. of three concentric circles with a total line length of 500 mm template available from ASTM The. template is placed over the grain structure without bias and the number of grain boundary intersections. P or the number of grains intercepted N is counted Dividing P or N by the true line length L gives PL. or NL which are identical N or P can differ slightly due to tangent hits for a single phase grain structure. It is usually easier to count grain boundary intersections for single phase structures If a grain boundary is. tangent to the line it is counted as of an intersection If a triple point line junction is intersected it is. counted as 1 or 2 The latter is preferred because the small diameter of the inner circle introduces a. slight bias to the measurement that is offset by weighing triple line intersections as 2 hits. The mean lineal intercept length l determined as shown in Eq 4 is a measure of ASTM grain size It is. smaller than d because the test lines do not intersect each grain at its maximum breath The ASTM grain. size G can be determined by use of the tables in ASTM E 112 or can be calculated. G 6 644 log l 3 288 Eq 17, where l is in millimeters Figure 3 shows the intercept method for a single phase alloy. Fig 3 Example of grain size measurement using the intercept. method The three concentric circles have diameters of 79 5. 47 8 and 31 8 mm for a total line length of 500 mm The. magnification of this micrograph is 500 and hence the true. line length is 1 mm A count of the number of grain boundary. intersections several are not well delineated by the nital etch a. common problem in such ratings especially if automated. devices are used revealed 60 grain boundary intersections and. 7 triple line junction intersections Hence P 7 1 5 60. 70 5 and PL 70 5 1 mm 70 5 mm Therefore l 1 PL, 0 0142 mm The ASTM grain size number can be evaluated. using Eq 17 G 6 6457 log 0 0142 3 298 8 98 round to. Nonequiaxed grain structures require measurements on the three principle planes the longitudinal. planar and transverse For such structures the intercept method is preferred but the test grid should. consist of a number of straight parallel test lines of known length rather than circles Because the ends of. the straight lines generally end within grains these interceptions are counted as half hits Three mutually. perpendicular orientations are evaluated using grain interception counts. NLl parallel to the grain elongation longitudinal plane. NLt perpendicular to the grain elongation through thickness direction transverse plane. NLP perpendicular to the grain elongation across width planar surface. The average NL value is obtained from the cube root of the product of the three directional NL values G is. determined by reference to the tables in ASTM E 112 or by use of Eq 17 l is the reciprocal of NL Eq 4. Two Phase Grain Structures The grain size of a particular phase in a two phase structure requires. determination of the volume fraction of the phase of interest such as by point counting The minor phase. second phase is point counted and the volume fraction of the major phase matrix phase is determined. by difference, Next a circular test grid is applied to the microstructure without bias and the number of grains of the. phase of interest intercepted by the test line N is counted The mean lineal intercept length of the alpha. grains l is determined by, l VV L M N Eq 18, where L is the line length and M is the magnification The ASTM grain size number can be determined. from the tables in ASTM E 112 or by use of Eq 17 The method is shown in Fig 4. Fig 4 Example of grain size measurement for a two, phase alloy using point counting and intercept. counting Micrograph at 500 of a specimen of, alloy Ti 6Al 2Sn 4Zr 2Mo that was forged at 955 C. Measurement of Microstructure QUANTIFYING MICROSTRUCTURAL PARAMETERS has received considerable attention in recent years and success in developing procedures and using such data to develop structure property relationships has been achieved Chart methods for rating microstructures have been used for many years to evaluate microstructures chiefly for conformance to specifications At this time

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