ASTM E112-13(2021)

Standard Test Methods for Determining Average Grain Size

SIGNIFICANCE AND USE
4.1 These test methods cover procedures for estimating and rules for expressing the average grain size of all metals consisting entirely, or principally, of a single phase. The grain size of specimens with two phases, or a phase and a constituent, can be measured using a combination of two methods, a measurement of the volume fraction of the phase and an intercept or planimetric count (see Section 17). The test methods may also be used for any structures having appearances similar to those of the metallic structures shown in the comparison charts. The three basic procedures for grain size estimation are:  
4.1.1 Comparison Procedure—The comparison procedure does not require counting of either grains, intercepts, or intersections but, as the name suggests, involves comparison of the grain structure to a series of graded images, either in the form of a wall chart, clear plastic overlays, or an eyepiece reticle. There appears to be a general bias in that comparison grain size ratings claim that the grain size is somewhat coarser (1/2 to 1 G number lower) than it actually is (see X1.3.5). Repeatability and reproducibility of comparison chart ratings are generally ±1 grain size number.  
4.1.2 Planimetric Procedure—The planimetric method involves an actual count of the number of grains within a known area. The number of grains per unit area, NA , is used to determine the ASTM grain size number, G. The precision of the method is a function of the number of grains counted. A precision of ±0.25 grain size units can be attained with a reasonable amount of effort. Results are free of bias and repeatability and reproducibility are less than ±0.5 grain size units. An accurate count does require marking off of the grains as they are counted.  
4.1.3 Intercept Procedure—The intercept method involves an actual count of the number of grains intercepted by a test line or the number of grain boundary intersections with a test line, per unit length of test line, used to calculate t...
SCOPE
1.1 These test methods cover the measurement of average grain size and include the comparison procedure, the planimetric (or Jeffries) procedure, and the intercept procedures. These test methods may also be applied to nonmetallic materials with structures having appearances similar to those of the metallic structures shown in the comparison charts. These test methods apply chiefly to single phase grain structures but they can be applied to determine the average size of a particular type of grain structure in a multiphase or multiconstituent specimen.  
1.2 These test methods are used to determine the average grain size of specimens with a unimodal distribution of grain areas, diameters, or intercept lengths. These distributions are approximately log normal. These test methods do not cover methods to characterize the nature of these distributions. Characterization of grain size in specimens with duplex grain size distributions is described in Test Methods E1181. Measurement of individual, very coarse grains in a fine grained matrix is described in Test Methods E930.  
1.3 These test methods deal only with determination of planar grain size, that is, characterization of the two-dimensional grain sections revealed by the sectioning plane. Determination of spatial grain size, that is, measurement of the size of the three-dimensional grains in the specimen volume, is beyond the scope of these test methods.  
1.4 These test methods describe techniques performed manually using either a standard series of graded chart images for the comparison method or simple templates for the manual counting methods. Utilization of semi-automatic digitizing tablets or automatic image analyzers to measure grain size is described in Test Methods E1382.  
1.5 These test methods deal only with the recommended test methods and nothing in them should be construed as defining or establishing limits of acceptability or fitness of purpose of the ma...

General Information

• Status: Published
• Publication Date: 31-Aug-2021
• ICS: 77.040.01 - Testing of metals in general
• Technical Committee: E04 - Metallography
• Drafting Committee: E04.08 - Grain Size

Relations

• Refers: ASTM E883-11(2024) - Standard Guide for Reflected–Light Photomicrography
• Effective Date: 01-Apr-2024
• Refers: ASTM E407-23 - Standard Practice for Microetching Metals and Alloys
• Effective Date: 01-Nov-2023
• Refers: ASTM E562-19e1 - Standard Test Method for Determining Volume Fraction by Systematic Manual Point Count
• Effective Date: 15-Aug-2019
• Refers: ASTM E883-11(2017) - Standard Guide for Reflected–Light Photomicrography
• Effective Date: 01-Jun-2017
• Refers: ASTM E930-99(2015) - Standard Test Methods for Estimating the Largest Grain Observed in a Metallographic Section (ALA Grain Size)
• Effective Date: 01-Oct-2015
• Refers: ASTM E7-15 - Standard Terminology Relating to Metallography
• Effective Date: 01-Jun-2015
• Refers: ASTM E407-07(2015)e1 - Standard Practice for Microetching Metals and Alloys
• Effective Date: 01-Jun-2015
• Refers: ASTM E7-14 - Standard Terminology Relating to Metallography
• Effective Date: 01-Nov-2014
• Refers: ASTM E691-13 - Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method
• Effective Date: 01-May-2013
• Refers: ASTM E691-11 - Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method
• Effective Date: 01-Nov-2011
• Refers: ASTM E562-11 - Standard Test Method for Determining Volume Fraction by Systematic Manual Point Count
• Effective Date: 01-Oct-2011
• Refers: ASTM E562-08e1 - Standard Test Method for Determining Volume Fraction by Systematic Manual Point Count
• Effective Date: 01-Oct-2011
• Refers: ASTM E883-11 - Standard Guide for Reflected–Light Photomicrography
• Effective Date: 01-May-2011
• Refers: ASTM E7-03(2009) - Standard Terminology Relating to Metallography
• Effective Date: 01-Oct-2009
• Refers: ASTM E562-08 - Standard Test Method for Determining Volume Fraction by Systematic Manual Point Count
• Effective Date: 01-Oct-2008

Overview

ASTM E112-13(2021) - Standard Test Methods for Determining Average Grain Size provides internationally recognized procedures for estimating and expressing the average grain size in metallic and certain nonmetallic materials. Developed by ASTM International, this standard is widely adopted in metallurgical laboratories and industrial quality control settings to ensure consistent, reliable grain size measurements across a range of applications. The standard describes manual measurement methods, including procedures suitable for single-phase and selected multi-phase materials, and supports both quality assurance and research in material science sectors.

Key Topics

• Scope and Applicability

  • Primarily for the measurement of average grain size in single-phase metals, but procedures may also be adapted for certain nonmetallic materials and multi-phase grain structures.
  • Applicable to microstructures with unimodal grain size distributions.

• Manual Grain Size Measurement Methods

  • Comparison Procedure: Involves visually comparing the microstructure to standardized, graded images (comparison charts or overlays). This quick visual approach is best for equiaxed grains and can be subject to minor observer bias.
  • Planimetric (Jeffries) Procedure: Involves counting the number of grains within a defined area (typically inscribed as a circle or square). This method is precise and minimizes bias; repeatability and reproducibility are generally within ±0.5 grain size units.
  • Intercept Procedure: Counts the number of grains intercepted or the number of grain boundary intersections per unit length along a test line. Precision is related to the number of intercepts measured, often offering efficiency compared to the planimetric method.

• Selection of Test Fields and Sampling

  • Emphasizes random selection of specimen areas to avoid bias.
  • Suggests measuring at least three fields per specimen for accurate averaging.
  • Recommends not estimating average grain size in heavily cold-worked material.

• Reporting and Calibration

  • Requires documentation of procedures, fields measured, and number of grains or intercepts counted.
  • Outlines calibration procedures for microscopes and comparison charts to ensure measurement accuracy.

Applications

• Metallurgical Quality Control

  • Used by manufacturers and material testing laboratories to measure grain size for production control and certification.
  • Supports the verification of product compliance with mechanical property specifications, as grain size directly affects material strength and performance.

• Materials Research and Development

  • Facilitates alloy development and process optimization by providing reliable methods to track changes in grain size resulting from mechanical or thermal treatments.

• Educational and Standardization Purposes

  • Acts as the foundational method in academic labs for teaching grain size analysis.
  • Used in the creation of new material standards and specifications in line with global trade and quality frameworks.

Related Standards

• ASTM E930: Test Methods for Estimating the Largest Grain Observed in a Metallographic Section.
• ASTM E1181: Test Methods for Characterizing Duplex (Mixed) Grain Size Distributions.
• ASTM E1382: Test Methods for Determining Average Grain Size Using Semiautomatic and Automatic Image Analysis.
• ASTM E3: Guide for Preparation of Metallographic Specimens.
• ASTM E407: Practice for Microetching Metals and Alloys.

Practical Value

Adopting ASTM E112-13(2021) ensures:

• Consistent grain size measurement across organizations.
• Improved accuracy and traceability in metallography and materials science.
• Support for global trade, as measurements align with international standards and WTO technical barriers to trade principles.

By following ASTM E112, laboratories and industries optimize their testing processes, meet regulatory requirements, and improve material performance predictability.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E112 − 13 (Reapproved 2021)
Standard Test Methods for
Determining Average Grain Size
This standard is issued under the fixed designation E112; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the U.S. Department of Defense.
INTRODUCTION
These test methods of determination of average grain size in metallic materials are primarily
measuring procedures and, because of their purely geometric basis, are independent of the metal or
alloy concerned. In fact, the basic procedures may also be used for the estimation of average grain,
crystal, or cell size in nonmetallic materials. The comparison method may be used if the structure of
the material approaches the appearance of one of the standard comparison charts. The intercept and
planimetric methods are always applicable for determining average grain size. However, the
comparison charts cannot be used for measurement of individual grains.
1. Scope 1.4 These test methods describe techniques performed
manually using either a standard series of graded chart images
1.1 These test methods cover the measurement of average
for the comparison method or simple templates for the manual
grain size and include the comparison procedure, the planim-
counting methods. Utilization of semi-automatic digitizing
etric (or Jeffries) procedure, and the intercept procedures.
tablets or automatic image analyzers to measure grain size is
These test methods may also be applied to nonmetallic
described in Test Methods E1382.
materialswithstructureshavingappearancessimilartothoseof
the metallic structures shown in the comparison charts. These
1.5 Thesetestmethodsdealonlywiththerecommendedtest
test methods apply chiefly to single phase grain structures but
methods and nothing in them should be construed as defining
theycanbeappliedtodeterminetheaveragesizeofaparticular
or establishing limits of acceptability or fitness of purpose of
type of grain structure in a multiphase or multiconstituent
the materials tested.
specimen.
1.6 The measured values are stated in SI units, which are
1.2 These test methods are used to determine the average
regarded as standard. Equivalent inch-pound values, when
grain size of specimens with a unimodal distribution of grain
listed, are in parentheses and may be approximate.
areas, diameters, or intercept lengths. These distributions are
1.7 This standard does not purport to address all of the
approximately log normal. These test methods do not cover
safety concerns, if any, associated with its use. It is the
methods to characterize the nature of these distributions.
responsibility of the user of this standard to establish appro-
Characterization of grain size in specimens with duplex grain
priate safety, health, and environmental practices and deter-
size distributions is described in Test Methods E1181. Mea-
mine the applicability of regulatory limitations prior to use.
surement of individual, very coarse grains in a fine grained
1.8 The paragraphs appear in the following order:
matrix is described in Test Methods E930.
Section Number
1.3 These test methods deal only with determination of
Scope 1
planar grain size, that is, characterization of the two-
Referenced Documents 2
Terminology 3
dimensional grain sections revealed by the sectioning plane.
Significance and Use 4
Determinationofspatialgrainsize,thatis,measurementofthe
Generalities of Application 5
sizeofthethree-dimensionalgrainsinthespecimenvolume,is
Sampling 6
Test Specimens 7
beyond the scope of these test methods.
Calibration 8
Preparation of Photomicrographs 9
Comparison Procedure 10
These test methods are under the jurisdiction of ASTM Committee E04 on
Planimetric (Jeffries) Procedure 11
Metallography and are the direct responsibility of Subcommittee E04.08 on Grain
General Intercept Procedures 12
Size.
Heyn Linear Intercept Procedure 13
Current edition approved Sept. 1, 2021. Published November 2021. Originally
Circular Intercept Procedures 14
approved in 1955. Last previous edition approved 2013 as E112–13. DOI:
Hilliard Single-Circle Procedure 14.2
10.1520/E0112-13R21.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E112 − 13 (2021)
100X magnification. To obtain the number per square milli-
Abrams Three-Circle Procedure 14.3
Statistical Analysis 15
metre at 1X, multiply by 15.50.
Specimens with Non-equiaxed Grain Shapes 16
3.2.2 grain—an individual crystal with the same atomic
Specimens Containing Two or More Phases or Constituents 17
Report 18
configuration throughout in a polycrystalline material; the
Precision and Bias 19
grain may or may not contain twinned regions within it or
Keywords 20
Annexes: sub-grains.
Basis of ASTM Grain Size Numbers Annex
3.2.3 grain boundary—a very narrow region in a polycrys-
A1
talline material corresponding to the transition from one
Equations for Conversions Among Various Grain Size Measurements Annex
A2
crystallographic orientation to another, thus separating one
Austenite Grain Size, Ferritic and Austenitic Steels Annex
adjacent grain from another; on a two-dimensional plane
A3
Fracture Grain Size Method Annex through three-dimensional polycrystalline materials, the grain
A4
edgesbetweenadjacentgrainssurroundingasinglegrainmake
Requirements for Wrought Copper and Copper-Base Alloys Annex
up the outline of the two-dimensional grains that are observed
A5
Application to Special Situations Annex in the light microscope and are measured or counted by the
A6
procedures in this test method.
Appendixes:
Results of Interlaboratory Grain Size Determinations Appendix 3.2.4 grain boundary intersection count, P—determination
X1
of the number of times a test line cuts across, or is tangent to
Referenced Adjuncts Appendix
(tangent hits are counted as one (1) intersection) grain bound-
X2
aries (triple point intersections are considered as 1- ⁄2 intersec-
1.9 This international standard was developed in accor-
tions).
dance with internationally recognized principles on standard-
3.2.5 grain intercept count, N—determinationofthenumber
ization established in the Decision on Principles for the
of times a test line cuts through individual grains on the plane
Development of International Standards, Guides and Recom-
of polish (tangent hits are considered as one half an intercep-
mendations issued by the World Trade Organization Technical
tion;testlinesthatendwithinagrainareconsideredasonehalf
Barriers to Trade (TBT) Committee.
an interception).
2. Referenced Documents
3.2.6 intercept length—the distance between two opposed,
2.1 ASTM Standards: adjacent grain boundary intersection points on a test line
E3Guide for Preparation of Metallographic Specimens segment that crosses the grain at any location due to random
E7Terminology Relating to Metallography placement of the test line.
E407Practice for Microetching Metals and Alloys
3.3 Symbols:
E562Test Method for Determining Volume Fraction by
Systematic Manual Point Count
α = matrix grains in a two phase (constituent)
E691Practice for Conducting an Interlaboratory Study to microstructure.
Determine the Precision of a Test Method A = test area.
¯
A = mean grain cross sectional area.
E883Guide for Reflected–Light Photomicrography
AI = grainelongationratiooranisotropyindexfora
E930Test Methods for Estimating the Largest Grain Ob- ℓ
longitudinally oriented plane.
served in a Metallographic Section (ALA Grain Size)
¯
d = mean planar grain diameter (Plate III).
E1181Test Methods for Characterizing Duplex Grain Sizes
¯
D = mean spatial (volumetric) grain diameter.
E1382Test Methods for Determining Average Grain Size
f = Jeffries multiplier for planimetric method.
Using Semiautomatic and Automatic Image Analysis
G = ASTM grain size number.
2.2 ASTM Adjuncts:
¯
ℓ = mean lineal intercept length.
2.2.1 For a complete adjunct list, see Appendix X2
¯
ℓ = mean lineal intercept length of the α matrix
α
phase in a two phase (constituent) microstruc-
3. Terminology
ture.
¯
3.1 Definitions—For definitions of terms used in these test
ℓ = mean lineal intercept length on a longitudi-
ℓ
methods, see Terminology E7. nally oriented surface for a non-equiaxed
grain structure.
3.2 Definitions of Terms Specific to This Standard:
¯
ℓ = mean lineal intercept length on a transversely
t
3.2.1 ASTM grain size number—the ASTM grain size
oriented surface for a non-equiaxed grain
number, G, was originally defined as:
structure.
G21
N 52 (1)
¯
AE
ℓ = mean lineal intercept length on a planar ori-
p
ented surface for a non-equiaxed grain struc-
where N is the number of grains per square inch at
AE
ture.
ℓ = baseinterceptlengthof32.00mmfordefining
the relationship between G and ℓ (and N ) for
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
L
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
macroscopically or microscopically deter-
Standards volume information, refer to the standard’s Document Summary page on
mined grain size by the intercept method.
the ASTM website.
E112 − 13 (2021)
size of specimens with two phases, or a phase and a
L = length of a test line.
constituent, can be measured using a combination of two
M = magnification used.
M = magnification used by a chart picture series. methods, a measurement of the volume fraction of the phase
b
n = number of fields measured. andaninterceptorplanimetriccount(seeSection17).Thetest
N = number of α grains intercepted by the test line
α methods may also be used for any structures having appear-
in a two phase (constituent) microstructure.
ances similar to those of the metallic structures shown in the
N = number of grains per mm at 1X.
A comparison charts. The three basic procedures for grain size
N = number of α grains per mm at 1X in a two
Aα
estimation are:
phase (constituent) microstructure.
2 4.1.1 Comparison Procedure—The comparison procedure
N = number of grains per inch at 100X.
AE
does not require counting of either grains, intercepts, or
N = N on a longitudinally oriented surface for a
Aℓ A
intersectionsbut,asthenamesuggests,involvescomparisonof
non-equiaxed grain structure.
the grain structure to a series of graded images, either in the
N = N on a transversely oriented surface for a
At A
form of a wall chart, clear plastic overlays, or an eyepiece
non-equiaxed grain structure.
reticle. There appears to be a general bias in that comparison
N = N on a planar oriented surface for a non-
Ap A
grain size ratings claim that the grain size is somewhat coarser
equiaxed grain structure.
( ⁄2 to 1 G number lower) than it actually is (see X1.3.5).
N = number of intercepts with a test line.
I
N = number of grains completely within a test
Repeatability and reproducibility of comparison chart ratings
Inside
circle.
are generally 61 grain size number.
N = numberofgrainsinterceptedbythetestcircle.
Intercepted
4.1.2 Planimetric Procedure—The planimetric method in-
N = number of intercepts per unit length of test
L
volves an actual count of the number of grains within a known
line.
area. The number of grains per unit area, N , is used to
A
N = N on a longitudinally oriented surface for a
Lℓ L
determine the ASTM grain size number, G. The precision of
non-equiaxed grain structure.
the method is a function of the number of grains counted. A
N = N on a transversely oriented surface for a
Lt L
precision of 60.25 grain size units can be attained with a
non-equiaxed grain structure.
reasonable amount of effort. Results are free of bias and
N = N on a planar oriented surface for a non-
Lp L
repeatability and reproducibility are less than 60.5 grain size
equiaxed grain structure.
units.An accurate count does require marking off of the grains
P = numberofgrainboundaryintersectionswitha
I
as they are counted.
test line.
P = number of grain boundary intersections per
4.1.3 Intercept Procedure—The intercept method involves
L
unit length of test line.
an actual count of the number of grains intercepted by a test
P = P on a longitudinally oriented surface for a
line or the number of grain boundary intersections with a test
Lℓ L
non-equiaxed grain structure.
line, per unit length of test line, used to calculate the mean
P = P on a transversely oriented surface for a
¯ ¯
Lt L
lineal intercept length, ℓ. ℓ is used to determine the ASTM
non-equiaxed grain structure.
grainsizenumber, G.Theprecisionofthemethodisafunction
P = P on a planar oriented surface for a non-
Lp L
of the number of intercepts or intersections counted. A preci-
equiaxed grain structure.
sion of better than 60.25 grain size units can be attained with
Q = correction factor for comparison chart ratings
a reasonable amount of effort. Results are free of bias;
using a non-standard magnification for micro-
repeatability and reproducibility are less than 60.5 grain size
scopically determined grain sizes.
units. Because an accurate count can be made without need of
Q = correction factor for comparison chart ratings
m
marking off intercepts or intersections, the intercept method is
using a non-standard magnification for mac-
faster than the planimetric method for the same level of
roscopically determined grain sizes.
precision.
s = standard deviation.
S = grain boundary surface area to volume ratio
V
4.2 For specimens consisting of equiaxed grains, the
for a single phase structure.
method of comparing the specimen with a standard chart is
S = grain boundary surface area to volume ratio
Vα
most convenient and is sufficiently accurate for most commer-
for a two phase (constituent) structure.
cial purposes. For higher degrees of accuracy in determining
t = students’ t multiplier for determination of the
averagegrainsize,theinterceptorplanimetricproceduresmay
confidence interval.
be used. The intercept procedure is particularly useful for
V = volume fraction of the α phase in a two phase
Vα
structures consisting of elongated grains (see Section 16).
(constituent) microstructure.
95 %CI = 95% confidence interval.
4.3 Incaseofdispute,theplanimetricprocedureshallbethe
%RA = percent relative accuracy.
referee procedure in all cases.
4.4 Noattemptshouldbemadetoestimatetheaveragegrain
4. Significance and Use
size of heavily cold-worked material. Partially recrystallized
4.1 These test methods cover procedures for estimating and
wroughtalloysandlightlytomoderatelycold-workedmaterial
rules for expressing the average grain size of all metals may be considered as consisting of non-equiaxed grains, if a
consisting entirely, or principally, of a single phase. The grain grain size measurement is necessary.
E112 − 13 (2021)
4.5 Individual grain measurements should not be made 7. Test Specimens
based on the standard comparison charts. These charts were
7.1 In general, if the grain structure is equiaxed, any
constructed to reflect the typical log-normal distribution of
specimen orientation is acceptable. However, the presence of
grain sizes that result when a plane is passed through a
an equiaxed grain structure in a wrought specimen can only be
three-dimensional array of grains. Because they show a distri-
determined by examination of a plane of polish parallel to the
bution of grain dimensions, ranging from very small to very
deformation axis.
large, depending on the relationship of the planar section and
7.2 If the grain structure on a longitudinally-oriented speci-
the three-dimensional array of grains, the charts are not
menisequiaxed,thengrainsizemeasurementsonthisplane,or
applicable to measurement of individual grains.
any other, will be equivalent within the statistical precision of
the test method. If the grain structure is not equiaxed, but
5. Generalities of Application
elongated, then grain size measurements on specimens with
5.1 It is important, in using these test methods, to recognize
different orientations will vary. In this case, the grain size
that the measurement of average grain size is not an exact
should be evaluated on at least two of the three principle
measurement. A metal structure is an aggregate of three-
planes, transverse, longitudinal, and planar (or radial and
dimensional crystals of varying sizes and shapes. Even if all
transverse for round bar) and averaged as described in Section
these crystals were identical in size and shape, the grain cross
16 to obtain the mean grain size. If directed test lines are used,
sections, produced by a random plane (surface of observation)
ratherthantestcircles,interceptcountsonnon-equiaxedgrains
through such a structure, would have a distribution of areas
in plate or sheet type specimens can be made using only two
varyingfromamaximumvaluetozero,dependinguponwhere
principle test planes, rather than all three as required for the
the plane cuts each individual crystal. Clearly, no two fields of
planimetric method.
observation can be exactly the same.
7.3 The surface to be polished should be large enough in
5.2 The size and location of grains in a microstructure are
area to permit measurement of at least five fields at the desired
normallycompletelyrandom.Nonominallyrandomprocessof
magnification. In most cases, except for thin sheet or wire
positioning a test pattern can improve this randomness, but
specimens,aminimumpolishedsurfaceareaof160mm (0.25
random processes can yield poor representation by concentrat- 2
in. ) is adequate.
ing measurements in part of a specimen. Representative
7.4 The specimen shall be sectioned, mounted (if
implies that all parts of the specimen contribute to the result,
necessary), ground, and polished according to the recom-
not, as sometimes has been presumed, that fields of average
mendedproceduresinGuideE3.Thespecimenshallbeetched
grainsizeareselected.Visualselectionoffields,orcastingout
using a reagent, such as listed in Practice E407, to delineate
of extreme measurements, may not falsify the average when
most, or all, of the grain boundaries (see also Annex A3).
done by unbiased experts, but will in all cases give a false
impression of high precision. For representative sampling, the
TABLE 1 Suggested Comparison Charts for Metallic Materials
area of the specimen is mentally divided into several equal
NOTE 1—These suggestions are based upon the customary practices in
coherent sub-areas and stage positions prespecified, which are
industry. For specimens prepared according to special techniques, the
approximately at the center of each sub-area. The stage is
appropriate comparison standards should be selected on a structural-
successively set to each of these positions and the test pattern
appearance basis in accordance with 8.2.
appliedblindly,thatis,withthelightout,theshutterclosed,or
Material Plate Number Basic Magnification
the eye turned away. No touch-up of the position so selected is
Aluminum I 100X
allowable. Only measurements made on fields chosen in this
Copper and copper-base alloys (see III or IV 75X, 100X
Annex A4)
way can be validated with respect to precision and bias.
Iron and steel:
Austenitic II or IV 100X
6. Sampling
Ferritic I 100X
Carburized IV 100X
6.1 Specimens should be selected to represent average
Stainless II 100X
conditions within a heat lot, treatment lot, or product, or to
Magnesium and magnesium-base alloys I or II 100X
Nickel and nickel-base alloys II 100X
assess variations anticipated across or along a product or
Super-strength alloys I or II 100X
component, depending on the nature of the material being
Zinc and zinc-base alloys I or II 100X
tested and the purpose of the study. Sampling location and
frequency should be based upon agreements between the
manufacturers and the users.
8. Calibration
6.2 Specimens should not be taken from areas affected by 8.1 Use a stage micrometer to determine the true linear
shearing, burning, or other processes that will alter the grain magnification for each objective, eyepiece and bellows, or
structure.
zoom setting to be used within 62%.
E112 − 13 (2021)
8.2 Use a ruler with a millimetre scale to determine the
actuallengthofstraighttestlinesorthediameteroftestcircles
used as grids.
9. Preparation of Photomicrographs
9.1 When photomicrographs are used for estimating the
average grain size, they shall be prepared in accordance with
Guide E883.
10. Comparison Procedure
10.1 The comparison procedure shall apply to completely
recrystallized materials with equiaxed grains.
10.2 When grain size estimations are made by the more
convenientcomparisonmethod,repeatedchecksbyindividuals
as well as by interlaboratory tests have shown that unless the
appearance of the standard reasonably well approaches that of
the sample, errors may occur. To minimize such errors, the
comparison charts are presented in four categories as follows:
10.2.1 Plate I—Untwinned grains (flat etch). Includes grain
1 1 1 1 1 1
size numbers 00, 0, ⁄2,1,1 ⁄2,2,2 ⁄2,3,3 ⁄2,4,4 ⁄2,5,5 ⁄2,6,
1 1 1 1
6 ⁄2,7,7 ⁄2,8,8 ⁄2,9,9 ⁄2, 10, at 100X.
10.2.2 Plate II—Twinned grains (flat etch). Includes grain
size numbers, 1, 2, 3, 4, 5, 6, 7, 8, at 100X.
FIG. 1 Example of Untwinned Grains (Flat Etch) from Plate I.
10.2.3 Plate III—Twinned grains (contrast etch). Includes
Grain Size No. 3 at 100X
nominal grain diameters of 0.200, 0.150, 0.120, 0.090, 0.070,
0.060, 0.050, 0.045, 0.035, 0.025, 0.020, 0.015, 0.010, 0.005
mm at 75X.
10.2.4 Plate IV—Austenite grains in steel (McQuaid-Ehn).
Includes grain size numbers 1, 2, 3, 4, 5, 6, 7, 8, at 100X.
10.3 Table1listsanumberofmaterialsandthecomparison
charts that are suggested for use in estimating their average
grain sizes. For example, for twinned copper and brass with a
contrast etch, use Plate III.
NOTE 1—Examples of grain-size standards from Plates I, II, III, and IV
are shown in Fig. 1, Fig. 2, Fig. 3, and Fig. 4.
10.4 The estimation of microscopically-determined grain
size should usually be made by direct comparison at the same
magnification as the appropriate chart. Accomplish this by
comparing a projected image or a photomicrograph of a
representative field of the test specimen with the photomicro-
graphs of the appropriate standard grain-size series, or with
suitablereproductionsortransparenciesofthem,andselectthe
photomicrograph which most nearly matches the image of the
testspecimenorinterpolatebetweentwostandards.Reportthis
estimated grain size as the ASTM grain size number, or grain
diameter, of the chart picture that most closely matches the
image of the test specimen or as an interpolated value between
FIG. 2 Example of Twin Grains (Flat Etch) from Plate II. Grain
two standard chart pictures.
Size No. 3 at 100X
10.5 Goodjudgmentonthepartoftheobserverisnecessary
to select the magnification to be used, the proper size of area
(number of grains), and the number and location in the
the characteristic or average grain size. It is not sufficient to
specimen of representative sections and fields for estimating
visually select what appear to be areas of average grain size.
Recommendations for choosing appropriate areas for all pro-
Plates I, II, III, and IVare available fromASTM Headquarters. OrderAdjunct: cedures have been noted in 5.2.
ADJE11201P (Plate I), ADJE11202P (Plate II), ADJE11203P (Plate III), and
10.6 Grain size estimations shall be made on three or more
ADJE11204P (Plate IV). A combination of all four plates is also available. Order
Adjunct: ADJE112PS. representative areas of each specimen section.
E112 − 13 (2021)
10.9 The use of transparencies or prints of the standards,
with the standard and the unknown placed adjacent to each
other, is to be preferred to the use of wall chart comparison
with the projected image on the microscope screen.
10.10 No particular significance should be attached to the
fact that different observers often obtain slightly different
results, provided the different results fall within the confidence
limits reasonably expected with the procedure used.
10.11 There is a possibility when an operator makes re-
peated checks on the same specimen using the comparison
methodthattheywillbeprejudicedbytheirfirstestimate.This
disadvantage can be overcome, when necessary, by changes in
magnification, through bellows extension, or objective or
eyepiece replacement between estimates (1).
10.12 Make the estimation of macroscopically-determined
grain sizes (extremely coarse) by direct comparison, at a
magnification of 1X, of the properly prepared specimen, or of
a photograph of a representative field of the specimen, with
photographs of the standard grain series shown in Plate I (for
untwinned material) and Plates II and III (for twinned mate-
rial). Since the photographs of the standard grain size series
were made at 75 and 100 diameters magnification, grain sizes
estimated in this way do not fall in the standard ASTM
FIG. 3 Example of Twin Grains (Contrast Etch) from Plate III. grain-size series and hence, preferably, should be expressed
Grain Size 0.090 mm at 75X
either as diameter of the average grain or as one of the
macro-grain size numbers listed in Table 3. For the smaller
10.7 Whenthegrainsareofasizeoutsidetherangecovered
macroscopic grain sizes, it may be preferable to use a higher
bythestandardphotographs,orwhenmagnificationsof75Xor magnification and the correction factor given in Note 3,
100X are not satisfactory, other magnifications may be em-
particularly if it is desirable to retain this method of reporting.
ployedforcomparisonbyusingtherelationshipsgiveninNote
NOTE 3—If the grain size is reported in ASTM macro-grain size
2 and Table 2. It may be noted that alternative magnifications
numbers, it is convenient to use the relationship:
are usually simple multiples of the basic magnifications.
Q 52 log M (3)
m 2
NOTE2—IfthegrainsizeisreportedinASTMnumbers,itisconvenient
to use the relationship:
56.64log M
where Q is a correction factor that is added to the apparent grain size
M
Q 52 log ~M/M ! (2)
2 b
of the specimen, when viewed at the magnification M, instead of at 1X,
to yield the true ASTM macro-grain size number. Thus, for a magnifi-
56.64log M/M
~ !
10 b
cation of 2X, the true ASTM macro-grain size number is two numbers
where Q is a correction factor that is added to the apparent micro-grain
higher (Q=+2), and for 4X, the true ASTM macro-grain size number
size of the specimen, as viewed at the magnification, M, instead of at the
is four numbers higher (Q=+4) than that of the corresponding photo-
basicmagnification, M (75Xor100X),toyieldthetrueASTMgrain-size
b
graph.
number. Thus, for a magnification of 25X, the true ASTM grain-size
number is four numbers lower than that of the corresponding photomi-
crographat100X(Q=−4).Likewise,for400X,thetrueASTMgrain-size
number is four numbers higher (Q= +4) than that of the corresponding
Transparencies of the various grain sizes in Plate I are available from ASTM
photomicrograph at 100X. Similarly, for 300X, the trueASTM grain-size
Headquarters. OrderAdjunct: ADJE112TS for the set. Transparencies of individual
number is four numbers higher than that of the corresponding photomi-
grain size groupings are available on request. OrderAdjunct: ADJE11205T (Grain
crograph at 75X.
Size 00), ADJE11206T (Grain Size 0), ADJE11207T (Grain Size 0.5),
ADJE11208T(GrainSize1.0),ADJE11209T(GrainSize1.5),ADJE11210T(Grain
10.8 The small number of grains per field at the coarse end
Size 2.0), ADJE11211T (Grain Size 2.5), ADJE11212T (Grain Sizes 3.0, 3.5, and
ofthechartseries,thatis,size00,andtheverysmallsizeofthe
4.0), ADJE11213T (Grain Sizes 4.5, 5.0, and 5.5), ADJE11214T (Grain Sizes 6.0,
grains at the fine end make accurate comparison ratings
6.5,and7.0),ADJE11215T(GrainSizes7.5,8.0,and8.5),andADJE11216T(Grain
Sizes 9.0, 9.5, and 10.0). Charts illustrating grain size numbers 00 to 10 are on 8 ⁄2
difficult.Whenthespecimengrainsizefallsateitherendofthe
by 11 in. (215.9 by 279.4 mm) film.Transparencies for Plates II, III, and IVare not
chart range, a more meaningful comparison can be made by
available.
changing the magnification so that the grain size lies closer to 5
The boldface numbers in parentheses refer to the list of references appended to
the center of the range. these test methods.
E112 − 13 (2021)
FIG. 4 Example of Austenite Grains in Steel from Plate IV. Grain
Size No. 3 at 100X
TABLE 2 Microscopically Determined Grain Size Relationships Using Plate III at Various Magnifications
NOTE 1—First line—mean grain diameter, d, in mm; in parentheses—equivalent ASTM grain size number, G.
NOTE 2—Magnification for Plate III is 75X (row 3 data).
Chart Picture Number (Plate III)
Magnification
1 2 3 4 5 6 7 8 9 10 11 121314
25X 0.015 0.030 0.045 0.060 0.075 0.105 0.135 0.150 0.180 0.210 0.270 0.360 0.451 0.600
(9.2) (7.2) (6.0) (5.2) (4.5) (3.6) (2.8) (2.5) (2.0) (1.6) (0.8) (0) (0/00) (00+)
50X 0.0075 0.015 0.0225 0.030 0.0375 0.053 0.0675 0.075 0.090 0.105 0.135 0.180 0.225 0.300
(11.2) (9.2) (8.0) (7.2) (6.5) (5.6) (4.8) (4.5) (4.0) (3.6) (2.8) (2.0) (1.4) (0.5)
75X 0.005 0.010 0.015 0.020 0.025 0.035 0.045 0.050 0.060 0.070 0.090 0.120 0.150 0.200
(12.3) (10.3) (9.2) (8.3) (7.7) (6.7) (6.0) (5.7) (5.2) (4.7) (4.0) (3.2) (2.5) (1.7)
100X 0.00375 0.0075 0.0112 0.015 0.019 0.026 0.034 0.0375 0.045 0.053 0.067 0.090 0.113 0.150
(13.2) (11.2) (10.0) (9.2) (8.5) (7.6) (6.8) (6.5) (6.0) (5.6) (4.8) (4.0) (3.4) (2.5)
200X 0.0019 0.00375 0.0056 0.0075 0.009 0.013 0.017 0.019 0.0225 0.026 0.034 0.045 0.056 0.075
(15.2) (13.2) (12.0) (11.2) (10.5) (9.6) (8.8) (8.5) (8.0) (7.6) (6.8) (6.0) (5.4) (4.5)
400X — 0.0019 0.0028 0.0038 0.0047 0.0067 0.0084 0.009 0.0012 0.0133 0.0168 0.0225 0.028 0.0375
(15.1) (14.0) (13.1) (12.5) (11.5) (10.8) (10.5) (10.0) (9.5) (8.8) (8.0) (7.3) (6.5)
500X — — 0.0022 0.003 0.00375 0.00525 0.0067 0.0075 0.009 0.010 0.0133 0.018 0.0225 0.03
(14.6) (13.7) (13.1) (12.1) (11.5) (11.1) (10.6) (10.3) (9.5) (8.7) (8.0) (7.1)
10.13 The comparison procedure shall be applicable for 10.14 The “Shepherd Fracture Grain Size Method” of judg-
estimating the prior-austenite grain size in ferritic steel after a inggrainsizefromtheappearanceofthefractureofahardened
McQuaid-Ehn test (see Annex A3, A3.2), or after the prior- tool steel (2), involves comparison of the specimen under
austenite grains have been revealed by any other means (see investigation with a set of standard fractures. It has been
Annex A3, A3.3). Make the grain-size measurement by com- found that the arbitrarily numbered fracture grain size series
paring the microscopic image, at magnification of 100X, with agree well with the correspondingly numbered ASTM grain
the standard grain size chart in Plate IV, for grains developed sizespresentedinTable4.Thiscoincidencemakesthefracture
inaMcQuaid-Ehntest(seeAnnexA3);forthemeasurementof grain sizes interchangeable with the prior-austenite grain sizes
prior-austenite grains developed by other means (see Annex
A3), measure by comparing the microscopic image with the
plate having the most nearly comparable structure observed in 6
Aphotograph of the Shepherd standard fractures can be obtained fromASTM
Plates I, II, or IV. Headquarters. Order Adjunct: ADJE011224.
E112 − 13 (2021)
TABLE 3 Macroscopic Grain Size Relationships Computed for Uniform, Randomly Oriented, Equiaxed Grains
NOTE1—MacroscopicallydeterminedgrainsizenumbersM-12.3,M-13.3,M-13.8andM-14.3correspond,respectively,tomicroscopicallydetermined
grain size numbers (G) 00, 0, 0.5 and 1.0.
¯ ¯ ¯ ¯ ¯ ¯
N Grains/UnitArea A Average Grain Area d Average Diameter ! Mean Intercept N N
Macro Grain A L
2 2 2 2 −1
Size No.
No./mm No./in. mm in. mm in. mm in. mm 100 mm
M-0 0.0008 0.50 1290.3 2.00 35.9 1.41 32.00 1.2 0.031 3.13
M-0.5 0.0011 0.71 912.4 1.41 30.2 1.19 26.91 1.0 0.037 3.72
M-1.0 0.0016 1.00 645.2 1.00 25.4 1.00 22.63 0.89 0.044 4.42
M-1.5 0.0022 1.41 456.2 0.707 21.4 0.841 19.03 0.74 0.053 5.26
M-2.0 0.0031 2.00 322.6 0.500 18.0 0.707 16.00 0.63 0.063 6.25
M-2.5 0.0044 2.83 228.1 0.354 15.1 0.595 13.45 0.53 0.074 7.43
M-3.0 0.0062 4.00 161.3 0.250 12.7 0.500 11.31 0.44 0.088 8.84
M-3.5 0.0088 5.66 114.0 0.177 10.7 0.420 9.51 0.37 0.105 10.51
M-4.0 0.0124 8.00 80.64 0.125 8.98 0.354 8.00 0.31 0.125 12.50
M-4.5 0.0175 11.31 57.02 0.0884 7.55 0.297 6.73 0.26 0.149 14.87
M-5.0 0.0248 16.00 40.32 0.0625 6.35 0.250 5.66 0.22 0.177 17.68
M-5.5 0.0351 22.63 28.51 0.0442 5.34 0.210 4.76 0.18 0.210 21.02
M-6.0 0.0496 32.00 20.16 0.0312 4.49 0.177 4.00 0.15 0.250 25.00
M-6.5 0.0701 45.26 14.26 0.0221 3.78 0.149 3.36 0.13 0.297 29.73
M-7.0 0.099 64.00 10.08 0.0156 3.17 0.125 2.83 0.11 0.354 35.36
M-7.5 0.140 90.51 7.13 0.0110 2.67 0.105 2.38 0.093 0.420 42.05
−3 −3 −3
×10 ×10 ×10
M-8.0 0.198 128.0 5.04 7.812 2.25 88.4 2.00 78.7 0.500 50.00
M-8.5 0.281 181.0 3.56 5.524 1.89 74.3 1.68 66.2 0.595 59.46
M-9.0 0.397 256.0 2.52 3.906 1.59 62.5 1.41 55.7 0.707 70.71
M-9.5 0.561 362.1 1.78 2.762 1.33 52.6 1.19 46.8 0.841 84.09
M-10.0 0.794 512.0 1.26 1.953 1.12 44.2 1.00 39.4 1.00 100.0
M-10.5 1.122 724.1 0.891 1.381 0.994 37.2 0.841 33.1 1.19 118.9
M-11.0 1.587 1024.1 0.630 0.977 0.794 31.2 0.707 27.8 1.41 141.4
M-11.5 2.245 1448.2 0.0445 0.690 0.667 26.3 0.595 23.4 1.68 168.2
M-12.0 3.175 2048.1 0.315 0.488 0.561 22.1 0.500 19.7 2.00 200.0
M-12.3 3.908 2521.6 0.256 0.397 0.506 19.9 0.451 17.7 2.22 221.9
M-12.5 4.490 2896.5 0.223 0.345 0.472 18.6 0.420 16.6 2.38 237.8
M-13.0 6.349 4096.3 0.157 0.244 0.397 15.6 0.354 13.9 2.83 282.8
M-13.3 7.817 5043.1 0.128 0.198 0.358 14.1 0.319 12.5 3.14 313.8
M-13.5 8.979 5793.0 0.111 0.173 0.334 13.1 0.297 11.7 3.36 336.4
M-13.8 11.055 7132.1 0.091 0.140 0.301 11.8 0.268 10.5 3.73 373.2
M-14.0 12.699 8192.6 0.079 0.122 0.281 11.0 0.250 9.84 4.00 400.0
M-14.3 15.634 10086.3 0.064 0.099 0.253 9.96 0.225 8.87 4.44 443.8
determined microscopically. The sizes observed microscopi- cepted is the number of grains that intercept the test circle. The
¯
cally shall be considered the primary standard, since they can average grain area, A, is the reciprocal of N , that is, 1/ N ,
A A
be determined with measuring instruments. while the mean grain diameter, d, as listed on Plate III (see
¯
10.2.3), is the square root of A. This grain diameter has no
11. Planimetric (or Jeffries’) (3) Procedure
physical significance because it represents the side of a square
¯
grain of area A, and grain cross sections are not square.
11.1 For the planimetric procedure, inscribe a circle of
knownarea(usually5000mm tosimplifythecalculations)on
11.2 To obtain an accurate count of the number of grains
a micrograph, a monitor or on the ground-glass screen of the
completely within the test circle and the number of grains
metallograph or video monitor. Select a magnification which
intersecting the circle, it is necessary to mark off the grains on
will give at least 50 grains in the field to be counted.When the
the template, for example, with a grease pencil or felt tip pen.
image is focused properly, count the number of grains within
The precision of the planimetric method is a function of the
this area.The sum of all the grains included completely within
number of grains counted (see Section 19). The number of
the known area plus one half the number of grains intersected
grains within the test circle, however, should not exceed about
by the circumference of the area gives the number of equiva-
100 as counting becomes tedious and inaccurate. Experience
lent whole grains, measured at the magnification used, within
suggests that a magnification that produces about 50 grains
thearea.IfthisnumberismultipliedbytheJeffries’multiplier,
within the test circle is about optimum as to counting accuracy
f, in the second column of Table 5 opposite the appropriate
per field. Because of the need to mark off the grains to obtain
magnification, the product will be the number of grains per
an accurate count, the planimetric method is more time
square millimetre N . Count a minimum of three fields to
A
consuming than the intercept method (see Section 12).
ensure a reasonable average. The number of grains per square
11.3 Fields should be chosen at random, without bias, as
millimetre at 1X, N , is calculated from:
A
described in 5.2. Do not attempt to choose fields that appear to
N
Intercepted
be typical. Choose the fields blindly and select them from
N 5 f SN 1 D (4)
A Inside
different locations on the plane of polish.
where f is the Jeffries’ multiplier (see Table 5), N is the 11.4 By original definition, a microscopically-determined
Inside
number of grains completely inside the test circle and N - grainsizeofNo.1has1.000grains/in. at100X,hence15.500
Inter
E112 − 13 (2021)
TABLE 4 Grain Size Relationships Computed for Uniform, Randomly Oriented, Equiaxed Grains
¯ ¯ ¯ ¯ ¯
N Grains/UnitArea A Average Grain Area d Average Diameter ! Mean Intercept N
Grain Size No. A L
2 2 2 2
G
No./in. at 100X No./mm at 1X mm µm mm µm mm µm No./mm
00 0.25 3.88 0.2581 258064 0.5080 508.0 0.4525 452.5 2.21
0 0.50 7.75 0.1290 129032 0.3592 359.2 0.3200 320.0 3.12
0.5 0.71 10.96 0.0912 91239 0.3021 302.1 0.2691 269.1 3.72
1.0 1.00 15.50 0.0645 64516 0.2540 254.0 0.2263 226.3 4.42
1.5 1.41 21.92 0.0456 45620 0.2136 213.6 0.1903 190.3 5.26
2.0 2.00 31.00 0.0323 32258 0.1796 179.6 0.1600 160.0 6.25
2.5 2.83 43.84 0.0228 22810 0.1510 151.0 0.1345 134.5 7.43
3.0 4.00 62.00 0.0161 16129 0.1270 127.0 0.1131 113.1 8.84
3.5 5.66 87.68 0.0114 11405 0.1068 106.8 0.0951 95.1 10.51
4.0 8.00 124.00 0.00806 8065 0.0898 89.8 0.0800 80.0 12.50
4.5 11.31 175.36 0.00570 5703 0.0755 75.5 0.0673 67.3 14.87
5.0 16.00 248.00 0.00403 4032 0.0635 63.5 0.0566 56.6 17.68
5.5 22.63 350.73 0.00285 2851 0.0534 53.4 0.0476 47.6 21.02
6.0 32.00 496.00 0.00202 2016 0.0449 44.9 0.0400 40.0 25.00
6.5 45.25 701.45 0.00143 1426 0.0378 37.8 0.0336 33.6 29.73
7.0 64.00 992.00 0.00101 1008 0.0318 31.8 0.0283 28.3 35.36
7.5 90.51 1402.9 0.00071 713 0.0267 26.7 0.0238 23.8 42.04
8.0 128.00 1984.0 0.00050 504 0.0225 22.5 0.0200 20.0 50.00
8.5 181.02 2805.8 0.00036 356 0.0189 18.9 0.0168 16.8 59.46
9.0 256.00 3968.0 0.00025 252 0.0159 15.9 0.0141 14.1 70.71
9.5 362.04 5611.6 0.00018 178 0.0133 13.3 0.0119 11.9 84.09
10.0 512.00 7936.0 0.00013 126 0.0112 11.2 0.0100 10.0 100.0
10.5 724.08 11223.2 0.000089 89.1 0.0094 9.4 0.0084 8.4 118.9
11.0 1024.00 15872.0 0.000063 63.0 0.0079 7.9 0.0071 7.1 141.4
11.5 1448.15 22446.4 0.000045 44.6 0.0067 6.7 0.0060 5.9 168.2
12.0 2048.00 31744.1 0.000032 31.5 0.0056 5.6 0.0050 5.0 200.0
12.5 2896.31 44892.9 0.000022 22.3 0.0047 4.7 0.0042 4.2 237.8
13.0 4096.00 63488.1 0.000016 15.8 0.0040 4.0 0.0035 3.5 282.8
13.5 5792.62 89785.8 0.000011 11.1 0.0033 3.3 0.0030 3.0 336.4
14.0 8192.00 126976.3 0.000008 7.9 0.0028 2.8 0.0025 2.5 400.0
TABLE 5 Relationship Between Magnification Used and Jeffries’ TABLE 6 Grain Size Equations Relating Measured Parameters to
Multiplier, f, for an Area of 5000 mm (a Circle of 79.8-mm the Microscopically Determined ASTM Grain Size, G
Diameter) (f = 0.0002 M )
NOTE 1—Determine the ASTM Grain Size, G, using the following
Magnification Used, M Jeffries’ Multiplier, f, to Obtain Grains/mm
equations:
1 0.0002
NOTE 2—The second and third equations are for single phase grain
10 0.02
structures.
25 0.125
50 0.5
A NOTE 3—To convert micrometres to millimetres, divide by 1000.
75 1.125
100 2.0
NOTE 4—A calculated G value of−1 corresponds to ASTM G=00.
150 4.5
Equation Units
200 8.0
250 12.5 −2
¯
G = (3.321928 log N )−2.954 N in mm
10 A A
300 18.0 −1
¯ ¯
G = (6.643856 log N )−3.288 N in mm
10 L L
500 50.0 −1
G = (6.643856 log P ) − 3.288 P in mm
10 L L
750 112.5
G = (−6.643856 log !) − 3.288 ! in mm
1000 200.0
A
At 75 diameters magnification, Jeffries’ multiplier, f, becomes unity if the area
used is 5625 mm (a circle of 84.5-mm diameter).
11.5.1 A simple way to reduce the data scatter for coarse
grained structures where high counts cannot be made, is to use
a rectangle rather than a circle, as recommended by
grains/mm at 1X. For areas other than the standard circle,
Saltykov(4). However, the counting procedure must be modi-
determine the actual number of grains per square millimetre,
fied slightly. First, it is assumed that the grains intersecting
N , and find the nearest size from Table 4. The ASTM grain
A
each of the four corners are, on average, one fourth within the
size number, G, can be calculated from N (number of grains
A
figures and three-fourths outside. These four corner grains
per mm at 1X) using (Eq 1)in Table 6.
together equal one grain within the test box.
11.5 This approach assumes that, on average, half of the
11.5.2 Ignoring the four corner grains, a count is made of
grainsintersectingthetestcirclearewithinthecirclewhilehalf
N ,thegrainscompletelywithinthebox,andof N ,
Inside Intercepted
are outside the circle. This assumption is valid for a straight
the grains intersected by the four sides of the box. Eq 4 now
line through a grain structure, but not necessarily for a curved
becomes:
line. It has been stated that as the number of grains inside the
N 5 ~M ⁄ A!~N 1 0.5 N 1 1! (5)
A Inside Intercepted
test circle decreased, bias was introduced. However, experi-
mentshaveshownnobias,butexcessivedatascatteras(n whereMisthemagnification,Aisthetestfigureareainmm
inside
+ 0.5n ) decreased below 50. and N is the number of grains per square millimeter at 1×.
intercepted A
E112 − 13 (2021)
Select the fields at random, as described in 11.3. It is recom- precision of the test methods. Additional details concerning
mendedthatenoughfieldsshouldbeevaluatedsothatatotalof grain size relationships are given in AnnexA1 and AnnexA2.
~700 grains are counted which will usually provide a 10%
¯
12.4 The mean intercept distance, ℓ, measured on a plane
relative accuracy (see Appendix X1, section X1.3.2). Experi-
section is an unbiased estimate of the mean intercept distance
ments have demonstrated that a consistent average grain size,
within the solid material in the direction, or over the range of
G, can be obtained using the Saltykov (4) rectangle method
directions, measured. The grain boundary surface area-to-
down to lower counts of (n + 0.5n +1) than with
inside intercepted
volumeratioisgivenexactlybyS =2N whenN isaveraged
v L L
the Jeffries’ (3) circular test grid.
over three directions. These relations are independent of grain
¯
11.5.3 Theaveragegrainarea, A,isthereciprocalof N and
A shape.
¯
themeangraindiameter,d,isthesquarerootof A,asdescribed
in 11.1. The ASTM grain size number, G, can be estimated 13. Heyn (5) Lineal Intercept Procedure
using the data in Table 4, or can be calculated from N using
A
13.1 Estimate the average grain size by counting (on the
Eq (1) in Table 6.
ground-glass screen, on a photomicrograph of a representative
field of the specimen, a monitor or on the specimen itself) the
12. General Intercept Procedures
number of grains intercepted by one or more straight lines
sufficientlylongtoyieldatleast50intercepts.Itisdesirableto
12.1 Intercept procedures are more convenient to use than
select a combination of test line length and magnification such
the planimetric procedure. These procedures are amenable to
that a single field will yield the required number of intercepts.
use with various types of machine aids. It is strongly recom-
One such test will nominally allow estimation of grain size to
mended that at least a manual tally counter be used with all
the nearest whole ASTM size number, at the location tested.
intercept procedures in order to prevent normal errors in
Additionallines,inapredeterminedarray,shouldbecountedto
counting and to eliminate bias which may occur when counts
obtain the precision required. The precision of grain size
appear to be running higher or lower than anticipated.
estimates by the intercept method is a function of the number
12.2 Intercept procedures are recommended particularly for
of grain interceptions counted (see Section 19). Because the
all structures that depart from the uniform equiaxed form. For
ends of straight test lines will usually lie inside grains (see
anisotropic structures, procedures are available either to make
14.3), precision will be reduced if the average count per test
separatesizeest
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