BS 7590-1992 Method for statistically estimating the volume fraction of phases and constituents by systematic manual point counting with a grid《通过系统人工格点计数统计估算相位和成分的体积分数方法》.pdf

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1、BS 7590 : 1992 BRITISH STANDARD | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | N NO O C CO OP PY YI IN NG G I IN N A AN NY Y F FO OR RM M W WI IT TH HO OU UT T W WR RI IT TT TE EN N P PE ER RM MI IS SS SI IO ON N F FR

2、 RO OM M B BS SI I Method for Statistically estimating the volume fraction of phases and constituents by systematic manual point counting with a gridBS 7590 : 1992 This British Standard, having been prepared under the direction of the Iron and Steel Standards Policy Committee, was published under th

3、e authority of the Standards Board and comes into effect on 15 October 1992 BSI 1992 The following BSI references relate to the work on this standard: Committee reference ISM/72 Draft for comment 91/37958 DC ISBN 0 580 21089 8 Amendments issued since publication Amd. No. Date T ext affected Committe

4、es responsible for this British Standard The preparation of this British Standard was entrusted by the Iron and Steel Standards Policy Committee (ISM/-) to T echnical Committee ISM/72, upon which the following body was represented: British Steel Industry1 BS 7590 : 1992 Contents Page Committees resp

5、onsible Inside front cover Foreword 2 Method 1 Scope 3 2 Informative references 3 3 Principle 3 4 Symbols 3 5 Apparatus 3 6 T est samples 6 7 Procedure 6 8 Calculation of the volume fraction ofa-phase V v , the 95 % confidence interval CI and the relative error 8 9 Improving the volume fraction esti

6、mate 9 10 T est report 9 Annex A (informative) Worksheet for the determination of volume fraction by systematic manual point count 10 Tables 1 Guidelines for grid size selection (total number of points on a grid) for visually estimated area fractions 6 2 Number of fields (n) for a relative error of

7、33 % for a given volume fraction and grid size 7 3 Number of fields (n) for a relative error of 20 % for a given volume fraction and grid size 7 4 Number of fields (n) for a relative error of 10 % for a given volume fraction and grid size 7 5 Number of fields (n) for a relative error of 5 % for a gi

8、ven volume fraction and grid size 8 6 Multipliers for calculation of 95 % confidence interval 8 Figures 1 Examples of circular grid configurations 4 2 Examples of square grid configurations 5 List of references Inside back coverBS 7590 : 1992 2 1) Annex A is also separately available from BSI. Forew

9、ord This British Standard has been prepared under the direction of the Iron and Steel Standards Policy Committee. It is related to ISO 9042 : 1988, published by the International Organization for Standardization (ISO). Compared with ISO 9042, tables 2 to 6 of this British Standard are more comprehen

10、sive and their relationship to the procedure given in clause 7 is clearer; the requirements for the test report in clause 10 are more readily achieved. Annex A includes a worksheet describing a step-by-step procedure designed to assist in the use of this British Standard. 1) It has been assumed in t

11、he drafting of this British Standard that the execution of its provisions is entrusted to appropriately qualified and experienced personnel. This British Standard calls for the use of substances and/or procedures that may be injurious to health if adequate precautions are not taken. It refers only t

12、o technical suitability and does not absolve the user from legal obligations relating to health and safety at any stage. Compliance with a British Standard does not of itself confer immunity from legal obligations.3 BS 7590 : 1992 Method 1 Scope This British Standard describes a method for statistic

13、ally estimating the volume fraction of clearly defined constituents or phases in the microstructure of a steel on a metallographically prepared section using a systematic manual point counting technique. 2 Informative references This British Standard refers to other publications that provide informa

14、tion or guidance. Editions of these publications current at the time of issue of this standard are listed on the inside back cover , but reference should be made to the latest editions. 3 Principle 3.1 The method is based on the statistical principle that, when a regular array of points is systemati

15、cally placed over a two-dimensional section through a uniform microstructure, the proportion of points which fall within a randomly distributed second phase or constituent, designated a-phase, in the structure is equal both to the area fraction of the second phase in a random planar section through

16、the microstructure and to the volume fraction of the second phase. This mathematical relationship can be summarized as follows: V v = = = (1) V a V A a A P a P where V v is the volume fraction of thea-phase in a three-dimensional sample; V a is the volume of thea-phase in the three-dimensional sampl

17、e; V is the total volume of the three-dimensional sample; A a is the area of thea-phase in a random planar section; A is the total area of the random planar section; P a is the number of points falling in thea-phase in a random planar section; P is the total number of points laid down in the random

18、planar section. 3.2 The method consists of superimposing a point grid over a number of different representative fields on the microstructure, counting the number of points included in the constituent or phase, and then calculating the volume fraction of the phase. A predetermined number of fields ha

19、ve to be examined to obtain particular specified levels of precision. 3.3 Any number of clearly identifiable phases or constituents can be counted at the same time using the method. 4 Symbols n Number of fields examined, i.e. number of grid placements P T T otal number of points in the grid P i Poin

20、t count on ith field, i.e. number of grid points falling on the constituent of interest in the ith field P p(i) Proportion of grid points in the constituent of interest on the ith field expressed as a percentage of the total number of points in the grid P p(i) = 3 100 (2) P i P T P p Mean of P p(i)

21、P p = P p(i) (3) 1 n 1 n s Estimate of standard deviation (s) s = (4) 2 1 n21 1 n (P p(i) 2 P p ) CI 95 % confidence interval CI = (5) 2s n 5 Apparatus 5.1 A microscope or other suitable means of observation with either: a) a viewing screen; or b) a monocular or binocular eyepiece. NOTE. The microsc

22、ope should preferably have a stage with graduated X and Y translation controls. 5.2 A test grid which consists of a specified number of equally and regularly spaced points formed by the intersection of very thin lines. NOTE 1. The grid may be a suitably marked transparency which is superimposed onto

23、 the viewing screen of the microscope or on photomicrographs. The grid may also be an eyepiece graticule which is placed in the eyepiece of the microscope. NOTE 2. An error can arise from the accuracy of detection of the intersection point within a phase (see 7.6.2). Thus it is recommended that grid

24、 lines should be as fine as possible to improve the sharpness of the intersection point. NOTE 3. The grids may be constructed by the user or obtained commercially. Examples of different types of grid pattern and size (circular or square array) are shown in figures 1 and 2. It is useful to have a ran

25、ge of grids available consisting of 1, 4, 12, 16, 25 and 100 intersecting points.BS 7590 : 1992 4 Figure 1. Examples of circular grid configurations5 BS 7590 : 1992 Figure 2. Examples of square grid configurationsBS 7590 : 1992 6 6 T est samples 6.1 Sampling procedure Ensure that the sample is repre

26、sentative of the microstructure for which the constituent or phase is to be measured. Unless otherwise specified by the customer , ensure that the plane of sectioning is transverse in order to generate a random microstructure. The position of sampling, the number of samples and the surface area to b

27、e examined shall be: a) specified in the product standard; or b) decided by the laboratory conducting the test; or c) agreed between customer and supplier . 6.2 Preparation of test samples Prepare the samples in accordance with standard metallographic techniques. T ake care during the preparation to

28、 avoid any alteration of the microstructure (smearing, distortion or overheating). NOTE. Metallographic preparation in accordance with ASTM E3-801 is considered acceptable. 6.3 Revealing the constituent or phase Etch the sample as necessary to reveal the constituent or phase to be measured. NOTE 1.

29、Etching should be as shallow as possible while still clearly revealing the constituent. This is to avoid errors due to deviating from a two-dimensional section. Stain or colour type etchants are preferable to avoid such errors. NOTE 2. Etchant, etching technique and time can have an influence on the

30、 estimated volume fraction and it may be necessary to check these prior to the test. 7 Procedure 7.1 General Superimpose on a magnified image of the microstructure a regular array of points formed by a grid of fine intersecting straight lines or curves. Count and average, for a predetermined number

31、of fields, the number of points falling within the microstructural constituent of interest. This average, expressed as a percentage of the total grid points, is a statistical estimate of the volume percentage of the constituent. NOTE 1. Grid size, magnification and the number of fields observed (see

32、 7.2, 7.3 and 7.4) are mutually dependent and this should be recognized in their selection to achieve the desired precision. NOTE 2. A worksheet similar to that shown in annex A may be useful in following the procedure. The worksheet includes a condensed step-by-step guide of the procedure. 7.2 Grid

33、 selection Make an initial visual estimation of the area fraction of the constituent followed by selection of the grid size P T (total number of points in the grid). NOTE. T able 1 provides a guideline for the selection of a grid size which represents optimum efficiency for time spent counting. T ab

34、le 1. Guidelines for grid size selection (total number of points on a grid) for visually estimated area fractions Visual estimate of area fraction Recommended grid size P T (number of points on grid) 2 % to 5 % 100 5%t o10% 4 9 10 % to 20 % 25 20% #16 NOTE 1. A grid size which gives a significant nu

35、mber of fields with no grid points in the constituent of interest should be avoided. NOTE 2. These guidelines represent optimum efficiency for time spent counting. 7.3 Magnification selection Place the selected grid on the image of the microstructure. Ensure that the magnification selected is as hig

36、h as possible without causing two adjacent grid points to fall on the same constituent feature. NOTE. A magnification should be selected which gives an average constituent size which is approximately one-half of the grid spacing. 7.4 Selection of the number of fields observed If 30 fields or more ar

37、e available for examination, examine a minimum of 30 fields to provide acceptable statistical precision. NOTE. The degree of precision obtained depends on the number of fields examined. Tables 2, 3, 4 and 5 give a guideline to the number of fields to be examined (grid placements) as a function of th

38、e degree of precision required, and the visually estimated volume fraction of constituent, for different grid sizes. If less than 30 fields are available for examination, take the appropriate multiplier from table 6 and use it in equation (5) (see 8.3) instead of the multiplier 2 for the calculation

39、 of CI, the 95 % confidence interval. 7.5 Array of fields observed 7.5.1 When the number of fields examined, n, has been defined, determine the spacing of those fields to form a regular distribution on the surface of the sample, without overlapping of the fields. 7.5.2 In the case where a structure

40、shows a non-uniform distribution of the constituent being counted (e.g. banding) avoid any coincidence of the alignment of the grid and structure by use of a circular grid or by placing a square array of points at an angle to the image of the inhomogeneous microstructure. NOTE. This avoids operator

41、bias in field selection. 7.5.3 Move from one field to the next without viewing the microstructure and base the movement only on the predetermined array spacing.7 BS 7590 : 1992 Table 2. Number of fields (n) for a relative error of 33 % for a given volume fraction and grid size 1) Estimate of volume

42、fraction % Grid size (P T ) for relative error 33 % 1 point 4 points 12 points 16 points 25 points 49 points 100 points 2 1836 459 153 115 73 38 18 5 735 184 61 46 30 15 7 10 367 92 31 23 15 8 4 20 183 46 15 11 7 4 2 30 122 31 10 8 5 3 2 50 74 19 6 5 3 2 1 1) See note to 7.4. Table 3. Number of fiel

43、ds (n) for a relative error of 20 % for a given volume fraction and grid size 1) Estimate of volume fraction % Grid size (P T ) for relative error 20 % 1 point 4 points 12 points 16 points 25 points 49 points 100 points 2 5000 1250 415 312 200 102 50 5 2000 500 165 125 80 40 20 10 1000 250 83 62 40

44、20 10 20 500 125 41 31 20 10 5 30 300 75 25 19 12 6 3 50 200 50 16 13 8 4 2 1) See note to 7.4. Table 4. Number of fields (n) for a relative error of 10 % for a given volume fraction and grid size 1) Estimate of volume fraction % Grid size (P T ) for relative error 20 % 1 point 4 points 12 points 16

45、 points 25 points 49 points 100 points 2 20000 5000 1650 1250 800 410 200 5 8000 2000 665 500 320 165 80 10 4000 1000 335 250 160 85 40 20 2000 500 165 125 80 40 20 30 1500 350 110 85 55 27 13 50 800 200 65 50 32 16 8 1) See note to 7.4.BS 7590 : 1992 8 Table 5. Number of fields (n) for a relative e

46、rror of 5 % for a given volume fraction and grid size Estimate of volume fraction % Grid size (P T ) for relative error 20 % 1 point 4 points 12 points 16 points 25 points 49 points 100 points 2 80000 20000 6666 5000 3200 1632 800 5 32000 8000 2666 2000 1280 653 320 10 16000 4000 1333 1000 640 326 1

47、60 20 8000 2000 666 500 320 163 80 30 5333 1333 444 333 213 109 53 50 3222 800 266 200 128 65 32 1) See note to 7.4. T able 6. Multipliers for calculation of 95 % confidence interval Number of fields examined (n) Multiplier (for substitution in equation (5) 5 2.57 7 2.36 9 2.26 11 2.2 13 2.16 15 2.1

48、3 20 2.09 25 2.06 29 2.04 7.6 Counting 7.6.1 Count and record for each field the number of grid points falling on the constituent of interest, P i . 7.6.2 Count any point falling on the constituent boundary as one-half. 7.6.3 Divide the number of grid points falling on the constituent of interest, P

49、 i , by the total number of points in the grid, P T , and express, as a percentage to give the volume fraction percentage of the constituent of interest, P p(i) , for that field. P p(i) = 3 100 (2) P i P T 7.6.4 Use the value P p(i) to represent a single result with counts obtained in a similar manner in other fields. Calculate from these results the volume fraction ofa-phase V v , the standard deviation s and the confidence interval CI. 8 Calculation of the volume fraction of a-phase V v , the 95 % confidence interval CI and the relative error 8.1 Calculate the aver