E562-11 - Método de Teste Padrão para Determinação da Fração de Volume por Contagem Manual Sistemática de Pontos

Designation E562 11 Standard Test Method for Determining Volume Fraction by Systematic Manual Point Count1 This standard is issued under the fixed designation E562 the number immediately following the designation indicates the year of original adoption or in the case of revision the year of last revision A number in parentheses indicates the year of last reapproval A superscript epsilon indicates an editorial change since the last revision or reapproval INTRODUCTION This test method may be used to determine the volume fraction of constituents in an opaque specimen using a polished planar cross section by the manual point count procedure The same measurements can be achieved using image analysis per Practice E1245 1 Scope 11 This test method describes a systematic manual point counting procedure for statistically estimating the volume fraction of an identifiable constituent or phase from sections through the microstructure by means of a point grid 12 The use of automatic image analysis to determine the volume fraction of constituents is described in Practice E1245 13 The values stated in SI units are to be regarded as standard No other units of measurement are included in this standard 14 This standard does not purport to address all of the safety concerns if any associated with its use It is the responsibility of the user of this standard to establish appro priate safety and health practices and determine the applica bility of regulatory limitations prior to use 2 Referenced Documents 21 ASTM Standards2 E3 Guide for Preparation of Metallographic Specimens E7 Terminology Relating to Metallography E407 Practice for Microetching Metals and Alloys E691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method E1245 Practice for Determining the Inclusion or Second Phase Constituent Content of Metals by Automatic Image Analysis 3 Terminology 31 DefinitionsFor definitions of terms used in this practice see Terminology E7 32 Definitions of Terms Specific to This Standard 321 point countthe total number of points in a test grid that fall within the microstructural feature of interest or on the feature boundary for the latter each test point on the boundary is one half a point 322 point fractionthe ratio usually expressed as a percentage of the point count of the phase or constituent of interest on the twodimensional image of an opaque specimen to the number of grid points which is averaged over n fields to produce an unbiased estimate of the volume fraction of the phase or constituent 323 stereologythe methods developed to obtain informa tion about the threedimensional characteristics of microstruc tures based upon measurements made on twodimensional sections through a solid material or their projection on a surface 324 test grida transparent sheet or eyepiece reticle with a regular pattern of lines or crosses that is superimposed over the microstructural image for counting microstructural features of interest 325 volume fractionthe total volume of a phase or constituent per unit volume of specimen generally expressed as a percentage 33 Symbols PT total number of points in the test grid Pi point count on the ith field PP i Pi P T 31005 percentage of grid points in the constituent observed on the ith field n number of fields counted 1 This test method is under the jurisdiction of ASTM Committee E04 on Metallography and is the direct responsibility of Subcommittee E0414 on Quanti tative Metallography Current edition approved Oct 1 2011 Published October 2011 Originally approved in 1976 Last previous edition approved in 2008 as E562 081 DOI 101520E056211 2 For referenced ASTM standards visit the ASTM website wwwastmorg or contact ASTM Customer Service at serviceastmorg For Annual Book of ASTM Standards volume information refer to the standards Document Summary page on the ASTM website Copyright ASTM International 100 Barr Harbor Drive PO Box C700 West Conshohocken PA 194282959 United States 1 Copyright by ASTM Intl all rights reserved Wed Oct 29 084132 EDT 2014 Downloadedprinted by UFSCAR Universidade Federal de Sao Carlos pursuant to License Agreement No further reproductions authorized P p 1 n i51 n Pp i5 arithmetic average of Pp i s estimate of the standard deviation s see Eq 3 in Section 10 95 CI 95 confidence interval 56ts n see Note 1 t a multiplier related to the number of fields examined and used in conjunction with the stan dard deviation of the measurements to determine the 95 CI VV volume fraction of the constituent or phase ex pressed as a percentage see Eq 5 in Section 10 RA relative accuracy a measure of the statistical precision 95 CIP p 100 NOTE 1Table 1 gives the appropriate multiplying factors t for any number of fields measured 4 Summary of Test Method 41 A clear plastic test grid or eyepiece reticle with a regular array of test points is superimposed over the image or a projection of the image produced by a light microscope scanning electron microscope or micrograph and the number of test points falling within the phase or constituent of interest are counted and divided by the total number of grid points yielding a point fraction usually expressed as a percentage for that field The average point fraction for n measured fields gives an estimate of the volume fraction of the constituent This method is applicable only to bulk opaque planar sections viewed with reflected light or electrons 5 Significance and Use 51 This test method is based upon the stereological prin ciple that a grid with a number of regularly arrayed points when systematically placed over an image of a two dimensional section through the microstructure can provide after a representative number of placements on different fields an unbiased statistical estimation of the volume fraction of an identifiable constituent or phase 1 2 33 52 This test method has been described 4 as being superior to other manual methods with regard to effort bias and simplicity 53 Any number of clearly distinguishable constituents or phases within a microstructure or macrostructure can be counted using the method Thus the method can be applied to any type of solid material from which adequate two dimensional sections can be prepared and observed 54 A condensed stepbystep guide for using the method is given in Annex A1 6 Apparatus 61 Test Grid consisting of a specified number of equally spaced points formed by the intersection of very thin lines Two common types of grids circular or square array are shown in Fig 1 611 The test grid can be in the form of a transparent sheet that is superimposed upon the viewing screen for the measure ment 612 Eyepiece Reticle may be used to superimpose a test grid upon the image 62 Light Microscope or other suitable device with a viewing screen at least 100 mm 125 mm preferably with graduated x and y stage translation controls should be used to image the microstructure 63 Scanning Electron Microscope may also be used to image the microstructure however relief due to polishing or heavy etching must be minimized or bias will be introduced as a result of deviation from a true twodimensional section through the microstructure 64 Micrographs of properly prepared opaque specimens taken with any suitable imaging device may be used provided the fields are selected without bias and in sufficient quantity to properly sample the microstructure 641 The applicable point counting grid shall only be applied once to each micrograph Point counting measurements should be completed on different fields of view and therefore different micrographs Repeated point count measurements on an individual micrograph is not allowed 642 The magnification of the micrograph should be as high as needed to adequately resolve the microstructure without resulting in adjacent grid points overlaying a single constituent feature 7 Sample Selection 71 Samples selected for measurement of the phase or constituent should be representative of the general microstructure or of the microstructure at a specified location within a lot heat or part 72 A description of the sample locations should be included as a part of the results 73 Any orientation of the prepared section that is whether longitudinal or transverse can be used However it should be recorded since it may have an effect upon the precision obtained 3 The boldface numbers in parentheses refer to the list of references at the end of this standard TABLE 1 95 Confidence Interval Multipliers No of Fields n t No of Fields n t 5 2776 19 2101 6 2571 20 2093 7 2447 21 2086 8 2365 22 2080 9 2306 23 2074 10 2262 24 2069 11 2228 25 2064 12 2201 26 2060 13 2179 27 2056 14 2160 28 2052 15 2145 29 2048 16 2131 30 2045 17 2120 40 2020 18 2110 60 2000 1960 E562 11 2 Copyright by ASTM Intl all rights reserved Wed Oct 29 084132 EDT 2014 Downloadedprinted by UFSCAR Universidade Federal de Sao Carlos pursuant to License Agreement No further reproductions authorized 74 If the sample microstructure contains gradients or inho mogeneities for example banding then the section should contain or show the gradient or inhomogeneity 8 Sample Preparation 81 The twodimensional sections should be prepared using standard metallographic ceramographic or other polishing procedures such as described in Methods E3 82 Smearing or other distortions of the phases or constitu ents during preparation of the section or sections should be minimized because they tend to introduce an unknown bias into the statistical volume fraction estimate 83 Etching of the sections as described in Test Methods E407 should be as shallow that is light as possible because deviations from a planar twodimensional section will cause a bias toward over estimation of the volume fraction 84 Stain or coloringtype etchants are preferable to those that cause attack of one or more of the constituents or phases 85 Description of the etchant and etching procedure should be included in the report 86 If etching is used to provide contrast or distinguishabil ity of constituents then the volume fraction estimates should be obtained as a function of etching time to check the significance of any bias introduced 9 Procedure 91 Principle 911 An array of points formed by a grid of lines or curves is superimposed upon a magnified image that is a field of view of a metallographic specimen 912 The number of points falling within the microstruc tural constituent of interest is counted and averaged for a selected number of fields 913 This average number of points expressed as a percent age of the total number of points in the array PT is an unbiased statistical estimation of the volume percent of the microstructural constituent of interest 914 A condensed stepbystep description of the procedure is provided in Annex A1 92 Grid Selection 921 The grid should consist of equally spaced points formed by the intersection of fine lines Diagrams of two possible grids one with a circular pattern and one with a square pattern which are recommended for use are shown in Fig 1 922 Determine the number of points that is the grid size PT from a visual estimate of the area fraction occupied by the constituent of interest Table 2 provides guidelines for this selection The values in Table 2 do not correspond to theoreti cal constraints but by using these values empirical observa tions have shown that the method is optimized for a given precision 9221 The user may choose to employ a 100 point grid over the entire range of volume fractions The use of 100point grid facilitates easy volume percent calculations the use of Circular Grid Square Grid NOTE 1The entire 24 points can be used or the outer 16 or the inner 8 points FIG 1 Examples of Possible Grid Configurations That Can Be Utilized TABLE 2 Guidelines for Grid Size SelectionA NOTE 1A grid size selection which gives a significant number of fields having no grid points on the constituent of interest should be avoided Visual Area Fraction Estimate Expressed as a Percentage Grid Size Number of Points PT 2 to 5 100 5 to 10 49 10 to 20 25 20 16 A These guidelines represent an optimum for efficiency for the time spent counting and for the statistical information obtained per grid placement E562 11 3 Copyright by ASTM Intl all rights reserved Wed Oct 29 084132 EDT 2014 Downloadedprinted by UFSCAR Universidade Federal de Sao Carlos pursuant to License Agreement No further reproductions authorized only one overlay or eyepiece reticle for all volume percent determinations may save both time and money 9222 For constituents present in amount of less than 2 a 400point grid may be used 923 Superimpose the grid in the form of a transparency upon a ground glass screen on which the section image is projected 924 A grid in the form of an eyepiece reticle may also be used 925 If the constituent areas form a regular or periodic pattern on the section image avoid the use of a grid having a similar pattern 93 Magnification Selection 931 Select the magnification so that it is as high as needed to clearly resolve the microstructure without causing adjacent grid points to fall over the same constituent feature 932 As a guideline choose a magnification that gives an average constituent size that is approximately one half of the grid spacing 933 As the magnification is increased the field area decreases and the fieldtofield variability increases thus requiring a greater number of fields to obtain the same degree of measurement precision 94 Counting 941 Count and record for each field the number of points falling on the constituent of interest 942 Count any points falling on the constituent boundary as one half 943 In order to minimize bias any point that is doubtful as to whether it is inside or outside of the constituent boundary should be counted as one half 944 PPi 5 Pi 3100 PT 1 945 The values of PPi are used to calculate P p and standard deviation s 95 Selection of the Number of Fields 951 The number of fields or images to measure depends on the desired degree of precision for the measurement Table 3 gives a guide to the number of fields or images to be counted as a function of PT the selected relative accuracy statistical precision and the magnitude of the volume fraction 96 Selection of the Array of Fields 961 Use a uniformly spaced array of fields to obtain the estimated value Pp and the estimated standard deviation s 962 If gradients or inhomogeneities are present then a uniform spacing of fields may introduce a bias into the estimate If another method of field selection is used for example random then describe it in the report 963 When the microstructure shows a certain periodicity of distribution of the constituent or phase being measured any coincidence of the points of the grid and the structure must be avoided This can be achieved by using either a circular grid or a square grid placed at an angle to the microstructural periodicity 97 Grid Positioning Over FieldsMake grid positioning of each field without viewing the microstructure to eliminate any possibility of operator bias This can be accomplished by moving the x and y stage mechanism a fixed amount while shifting to the next field without looking at the microstructure 98 Improving Measurement PrecisionIt is recommended that the user attempt to sample more of the microstructure either by multiple specimens or by completely repeating the metallographic preparation on the same sample when the precision for a single set of data is not acceptable see Section 11 10 Calculation of the Volume Percentage Estimate and Relative Accuracy 101 The average percentage of grid points on the features of interest provides an unbiased statistical estimator for the volume percentage within the three dimensional microstruc ture The value of the multiplier t can be found in Table 1 Thus the average P p the standard deviation estimator s and the 95 confidence interval 95 CI should be calculated and recorded for each set of fields The equations for calculat ing these values are as follows TABLE 3 Prediction of the Number of Fields n to be Observed as a Function of the Desired Relative Accuracy and of the Estimated Magnitude of the Volume Fraction of the Constituent Amount of volume fraction Vv in percent 33 Relative Accuracy 20 Relative Accuracy 10 Relative Accuracy Number of fields n for a grid of PT Number of fields n for a grid of PT Number of fields n for a grid of PT 16 points 25 points 49 points 100 points 16 points 25 points 49 points 100 points 16 points 25 points 49 points 100 points 2 110 75 35 20 310 200 105 50 1250 800 410 200 5 50 30 15 8 125 80 40 20 500 320 165 80 10 25 15 10 4 65 40 20 10 250 160 85 40 20 15 10 5 4 30 20 10 5 125 80 40 20 NOTE 1The given values in the table above are based on the formula nS 4 E 2 3PTD S 1002Vv VV D where E 001 RA and VV is expressed in E562 11 4 Copyright by ASTM Intl all rights reserved Wed Oct 29 084132 EDT 2014 Downloadedprinted by UFSCAR Universidade Federal de Sao Carlos pursuant to License Agreement No further reproductions authorized P p 5 1 n i51 n Pp i 2 s 5F 1 n 2 1 i51 n Pp i 2 P p 2G 12 3 95 CI 5 t 3 s n 4 102 The volume percentage estimate is given as Vv 5 P p 695 CI 5 103 An estimate of the relative accuracy associated with the estimate can be obtained as RA 5 95 CI P p 3100 6 1031 Estimates for the number of fields required to obtain a relative accuracy of 10 20 or 33 with different volume percentages and grid sizes are provided in Table 3 These values were calculated under the assumption that the features have a random distribution upon the metallographic section 104 The relative accuracy reported should always be calculated from the sample data and should not be taken from Table 3 11 Improving the Volume Fraction Estimate 111 If additional fields are measured to reduce the relative accuracy then the following rule gives an excellent guideline To reduce the RA by 50 then a total of four times the original number of fields should be measured 112 When additional fields are selected on the same section they should not overlap the initial set but may fit between fields of the initial set and should also form a systematic sampling array 113 As an example if a 6 by 5 array of fields was used to obtain the initial set then by halving the spacing and measur ing the intermediate field positions a total of four times the number of fields can be measured Hence 120 total fields would be measured by halving the spacing in both x and y directions and measuring the intermediate positions to form a 12 by 10 array This additional effort should reduce the confidence interval and thus the RA by approximately 50 114 Where additional fields are measured on the same section the average P p the standard deviation estimate s the 95 confidence interval 95 CI and the relative accuracy RA should be calculated using the increased total number of fields as a single data set 115 If additional sections are prepared from the same sample by completely repeating the sample preparation or if additional samples are prepared then the same procedure should be used for each section and the data recorded and reported separately A grand average can be calculated by taking the average of the set means in this case If no sample heterogeneity is indicated that is the confidence intervals about the mean of each set overlap then the 95 CI can be calculated from the standard deviation obtained using the data from all of the sets that is pooling the data and calculating a mean standard deviation and 95 CI 116 Where the 95 CI do not overlap for the different sets then a statistically significant difference between samples or sections may be present In this case more rigorous statistical significance tests should be considered 12 Report 121 Report the following information 1211 Raw data note when n 30 the reporting of raw data is optional however the raw data shall be available for review when requested 1212 Estimated volume P p 6 95 CI 1213 Standard deviation 1214 relative accuracy calculated value not one esti mated from Table 2 1215 Number of fields per metallographic section 1216 Number of sections 1217 Sample description and preparation including etchant if used 1218 Section orientation 1219 Magnification 12110 Grid description 12111 Field array description and spacing and 12112 List of volume estimates for each metallographic section 6 95 CI 13 Effort Required 131 A reasonable estimate for the time required to perform the manual point count on 30 fields for a single type of microstructural feature is 30 min This time estimate can probably be decreased to 15 min after some experience and familiarity with the point counting procedure and the micro structure analyzed are obtained 14 Precision and Bias4 141 The systematic point count technique is the most efficient manual technique for development of an unbiased estimate of the volume fraction of an identifiable constituent or phase 142 The presence of periodicity structural gradients or inhomogeneities in the section can influence the precision and accuracy of the volume fraction estimate Guidelines are given in 74 925 962 963 115 and 116 143 The quality of the sample preparation can influence precision and accuracy of the volume fraction estimate Guide lines are given in Section 8 144 The point density of the grid used to make the volume fraction estimate can influence the efficiency precision and relative accuracy of the volume fraction estimate Guidelines are given in 92 145 The magnification employed in the point count can influence precision and relative accuracy Guidelines are given in 93 4 Supporting data have been filed at ASTM International Headquarters and may be obtained by requesting Research Report RRE041003 E562 11 5 Copyright by ASTM Intl all rights reserved Wed Oct 29 084132 EDT 2014 Downloadedprinted by UFSCAR Universidade Federal de Sao Carlos pursuant to License Agreement No further reproductions authorized 146 The counting of grid points at a constituent boundary particularly when doubt exists as to their exact location presents an opportunity for bias in the estimate of the volume fraction Guidelines are given in 942 and 943 147 The number of fields measured the method of field selection and their spacing will influence the precision and relative accuracy of the volume fraction estimate Guidelines are given in 95 and 96 148 The precision of a given measurement of the volume fraction is determined by calculation of the standard deviation 95 confidence interval and relative accuracy as described in Section 10 149 If a greater degree of precision and relative accuracy is required follow the guidelines in Section 11 1410 Results from a roundrobin interlaboratory program 5 where three micrographs with different constituent volume fractions were point counted using two different grids 25 and 100 points by 33 different operators were analyzed4 in accordance with Practice E691 to develop repeatability and reproducibility standard deviations and 95 confidence limits see Table 4 For the same number of random grid placements 10 on each micrograph the repeatability and reproducibility standard deviations and 95 confidence intervals increased with increasing P p for measurements with the 25 point test grid but were essentially constant for the 100 point test grid Note that the interlaboratory relative accuracies which are much poorer than those for the individual operators improve as P p increases and as the grid point density PT increases The 100 point grid with four times the number of grid points decreased the relative accuracies by about 21 to 51 as P p increased Micrographs A to C ANNEX Mandatory Information A1 PROCEDURE FOR SYSTEMATIC MANUAL POINT COUNT A11 Visually estimate area percent of constituent or feature of interest on metallographic section A12 Using Table 3 select grid size PT A13 Superimpose the grid upon the microscope viewing screen and select magnification such that the size of the features of interest are approximately one half of the spacing between grid points A14 Select a statistical precision RA for example 10 20 or 33 desired for the measurement Note that the RA is defined as follows RA 5 95 CI P p 3100 A15 Using Table 3 obtain an estimate of the number of fields n required to obtain the desired degree of precision NOTE A11A minimum of 30 fields must be measured in order to calculate the 95 confidence interval using the equation given in A112 A16 Determine the spacing between fields that will form a systematic equally spaced array covering a majority of the sample area without overlap A161 For example on a 10 mm 15 mm specimen area where 40 fields are indicated from Table 3 a 5 by 8 array of fields at 15 mm intervals might be used A17 Determine the number of turns required on the stage translation knobs to move the stage from one field position to the next Do not observe the image while translating to a new field to avoid bias in positioning the grid A18 Count and record the number of grid points Pi falling within the features of interest NOTE A12Any point that falls on the boundary should be counted as one half To avoid bias questionable points should be counted as one half A19 Calculate the average of points per field P p and its standard deviation s NOTE A13A hand calculator with a key can be used to calculate these quantities TABLE 4 Results of Interlaboratory Point Counting RoundRobin5 Micrograph P p Repeatability Std Dev Reproducibility Std Dev Repeatability 95 CI Reproducibility 95 CI Repeatability RA Reproducibility RA 25 Point Test Grid A 99 53 53 148 148 1495 1495 B 178 66 69 186 194 1045 1090 C 270 88 94 247 262 915 970 100 Point Test Grid A 93 39 39 110 110 1183 1183 B 159 34 40 94 112 591 704 C 251 39 43 109 121 434 482 E562 11 6 Copyright by ASTM Intl all rights reserved Wed Oct 29 084132 EDT 2014 Downloadedprinted by UFSCAR Universidade Federal de Sao Carlos pursuant to License Agreement No further reproductions authorized A110 The average percentage of points is P p 5 1 n i51 n Pp i 5 1 n i51 n Pi PT 3100 A111 The standard deviation estimate is s 5F 1 n 2 1 i51 n Pp i 2 P p 2G 12 A112 The 95 confidence interval for P p is 95 CI 5 ts n REFERENCES 1 DeHoff R T and Rhines F N eds Quantitative Microscopy McGrawHill Book Co New York NY 1968 2 Underwood E E Quantitative Stereology AddisonWesley Publish ing Co Reading MA 1970 3 Howard R T and Cohen M Quantitative Metallography by PointCounting and Lineal Analysis Transactions AIME Vol 172 1947 pp 413426 4 Hilliard J E and Cahn J W An Evaluation of Procedures in Quantitative Metallography for VolumeFraction Analysis Transac tions AIME Vol 221 1961 pp 344352 5 Abrams H Practical Applications of Quantitative Metallography Stereology and Quantitative Metallography ASTM STP 504 ASTM Philadelphia PA 1972 pp 138182 ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentioned in this standard Users of this standard are expressly advised that determination of the validity of any such patent rights and the risk of infringement of such rights are entirely their own responsibility This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years and if not revised either reapproved or withdrawn Your comments are invited either for revision of this standard or for additional standards and should be addressed to ASTM International Headquarters Your comments will receive careful consideration at a meeting of the responsible technical committee which you may attend If you feel that your comments have not received a fair hearing you should make your views known to the ASTM Committee on Standards at the address shown below This standard is copyrighted by ASTM International 100 Barr Harbor Drive PO Box C700 West Conshohocken PA 194282959 United States Individual reprints single or multiple copies of this standard may be obtained by contacting ASTM at the above address or at 6108329585 phone 6108329555 fax or serviceastmorg email or through the ASTM website wwwastmorg Permission rights to photocopy the standard may also be secured from the ASTM website wwwastmorg COPYRIGHT E562 11 7 Copyright by ASTM Intl all rights reserved Wed Oct 29 084132 EDT 2014 Downloadedprinted by UFSCAR Universidade Federal de Sao Carlos pursuant to License Agreement No further reproductions authorized