Introduction to ASTM
Standards for Metallography
George F. Vander Voort
Director, Research & Technology
Buehler Ltd.
Lake Bluff, Illinois USA
Creating an ASTM Standard
• Each of the more than 130 ASTM committees can create
standards (of various types) on their subject of interest.
• Committee E-4 on Metallography writes test methods
standards, so the committee need not be “balanced” between
people representing producers and purchasers.
• A standard is created when a need is shown to exist and a
task group can be formed with enough people with the
needed expertise to write a draft
• The draft is balloted in the task group until all agree that it
is acceptable to go to Subcommittee ballot
• After it passes subcommittee ballot, it must pass a
committee ballot, and then a society ballot.
ASTM Standards – Upkeep Process
• Every ASTM standard must be reviewed every 5 years
• A task group is assigned to review the standard
• It decides if the standard is acceptable as written, if
technology has changed and it must be modified, or that the
standard is of no value and can be made obsolete
• For any of the above actions, a ballot is required. If it is to
be revised, a task group is given the job to make the
necessary changes. The revised draft must go through ballots
within the task group, the subcommittee, the committee and
the society
• If it is to be withdrawn or re-approved as is, this decision
must be balloted, but it is a simple ballot usually
ASTM Metallography Standards
• Terminology (E7)
• Specimen Preparation (E3, E340, E407, E768,
E1558, E1920, E2015)
• Macrostructural Evaluation (E381, E1180)
• Light Microscopy (E883, E1951)
• Quantitative Metallography (E45, E112, E562,
E930, E1077, E1122, E1181, E1245, E1268, E1382,
E2109)
• XRD, SEM, TEM (E81, E82, E766, E963, E975,
E986, E2142)
• Microindentation Hardness Testing (E384)
E-4 Standards for Quantitative Metallography
• Inclusion rating
• Grain Size
• Volume Fraction
• Characterization of Second Phases
• Case Depth/Decarburization
• Degree of Banding
E-4 Standards for Quantitative Metallography
Determine for the method defined its
Precision and Bias
(accuracy usually cannot be determined)
Using Interlaboratory Test Programs,
Commonly called “round robins”
Quantitative Metallography
Numerical measurements of microstructural features
1. Surface Gradients
Standard metrology methods
2. Matrix Microstructures
Stereological Measurements
Metrology Measurements
STEREOLOGY
Extrapolation of measurements made on
a two-dimensional sectioning plane to
determine the three-dimensional
characteristics of the microstructure
Measurements may be 0-, 1-, or 2dimensional (i.e., points, lines, areas)
STEREOLOGY
Matrix Microstructural Measurements
• Planar (flat) Surface Images
• Non-planar (curved) Surface Images
• Projected Images
Planar Surface Images
Flat, polished and etched surfaces
require no additional corrections and
are the simplest to employ. Surface
relief in preparation must be
minimized and etching depth must be
minimal.
Non-Planar Surface Images
SEM images of fractures depict the rough
surface as being flat. However, the surfaces
are not flat but exhibit hills and valleys that
vary with the fracture mode and
mechanism. The measurements must be
corrected by determining the surface
roughness by, for example, using vertical
sections. Otherwise, all measurements are
biased.
Projected Images
Images created using transmitted light or
electrons (as in TEM thin foils) sense the
structure within a volume of material.
Hence, measurements reflect data in
volume and the results must be corrected
knowing the thickness or depth of the
image plane. If not, biased data will be
obtained.
Statistical Analysis
• Mean (average)
• Standard Deviation
• 95% Confidence Interval
• % Relative Accuracy
• Tests to evaluate the significance of
differences between mean values
Statistical Analysis
Statistical precision of the data is
mainly a function of the number of
measurements made. This is why
image analysis can produce
significantly better data than
manual procedures.
Statistical Analysis
Mean (Average)
∑ Xi
X = ———
N
Xi are the individual values and
N is the number of measurements
Statistical Analysis
Standard Deviation – distribution of the
individual values around the mean
∑ ( xi – x)2 1/2
S = [ —————— ]
N-1
Statistical Analysis
95% Confidence Interval
ts
95% CI = ———
(N)1/2
t is the Students’ t value for a 95% CI and for
N-1 degrees of freedom
Statistical Analysis
% Relative Accuracy
95% CI
%RA = ———— x 100
X
10% RA is a good target, especially for manual
measurements, but is difficult to achieve when
the volume fraction is <2%, even with image
analysis equipment.
Accuracy vs. Precision
To determine the accuracy of a
measurement, we must know the true value
by some reference method. For
microstructural measurements, we never
know the true value by any independent
referee method. Therefore, we can only
assess the precision of our measurements in
terms of the scatter around the mean value.
Specimen Preparation
Image analyzers require correctly
prepared specimens - better quality
than for manual measurements.
You cannot measure what cannot be seen!
Stereological Symbols
P = Point
L = Line
A = Area (planar)
S = Surface (curved)
V = Volume
N = Number
Symbols can be combined, e.g., VV, NA, LA, SV
The following slide shows a
synthetic microstructure
consisting of 30 spherical
particles with three different
diameters to illustrate
certain measurements
Volume Fraction – A Measure of
the Concentration of a Second
Phase Constituent
∑ Vα
VV = ————
VT
But, there is no simple way to directly measure
the volume per unit volume of a constituent!
Volume fraction can be assessed
from the area fraction, linear
fraction or point fraction, that is VV = AA = LL = PP
For manual measurements, PP is the easiest
method and most efficient (i.e., best
precision for a given amount of work)
Areal Analysis – Area Fraction
Earliest measurement procedure, used
with minerals. Can only be done
manually on structures that are coarse
and consist of simple geometric shapes.
The method is very precise for a given
field, but too time consuming to measure
a large number of fields.
∑ AAα
AA = ———
AT
1
1
1
2
3
3
2
2
4
4
5
5
6
7
6
3
8
4
7
8
5
11
10
9
9
6
10
12
13
14
Calculate the Area Fraction, AA
Calculate the area of each spherical particle
(circular in cross section) based on a diameter
measurement and a count of the number of
each size particle. We will assume that the
image is at 500X magnification. The
diameters of the three circular particles
are:12.6, 21.6 and 34 µm. The areas of the
circular particles are: 124.69, 366.44 and
907.92 µm2. The test area measures 512 by
380 µm or 194560 µm2.
Calculate the Area Fraction, AA
[(6x907.92) + (10x366.44) + (14x124.69)]
AA = —————————————————
(512 x 380)
AA = 0.056 = 5.6%
Point Fraction – Point Counting
ASTM E 562
Superimpose a grid composed of points over
the microstructure. In practice, points are hard
to see, so we use crosses or intersecting vertical
and horizontal test lines. The intersection is the
“point”. The point must be in the constituent to
be a “hit”. If it is a tangent “hit”, count it as
one-half. Calculate PP by:
∑ Pα
PP = ——
PT
Point Counting Grids
The optimum number of “points” in a point
counting grid is a function of the volume
fraction to be measured and is determined from
the equation, P = 3/VV, where the volume
fraction is a fraction, not a percentage. So, as
VV decreases from 0.5 (50%) to 0.01 (1%), P
varies from 6 to 300.
The following 100-point grid is convenient to
use as each “hit” is 1%.
Use of the Point-Counting Grid
The grid consists of ten horizontal and
vertical lines, yielding 100 points (the
intersection points of the lines). This is
superimposed over the microstructure and
the image is scanned, usually from upper
left to the lower right, while noting the
number of points that are inside the
constituent of interest, and those on phase
boundaries (weighed as one-half a “hit”).
This is repeated for N fields. Then, the point
fraction is calculated and is an estimate of
the volume fraction.
1
2
3
5
4
7
Calculation of PP
In this example there were 7“hits” where
the “points” were inside the constituent of
interest, and no tangent hits. So, the point
fraction is calculated as:
7
PP = ——— = 0.07 = 7%
100
To obtain good data, more fields must be evaluated.
Image Analysis vs. Manual
For manual work, to obtain the best
precision, point count more fields as the
field-to-field variability has a greater
influence on precision than the precision in
measuring a single field. The adage is “do
more, less well” – that is, put less effort into
measuring each field and do more fields.
For IA work, all of the pixels in the field are
used. Thus, the precision per field is higher,
but the time per field is very small. Hence,
even if N is the same, the %RA is better.
Intersections Per Unit Length, PL
PL is a measure of the number of point
intersections with phase or grain
boundaries per unit length of test line. It
is calculated from:
∑ Pα
PL = ————
LT
Pα is the number of intersections and LT is the true
line length (line length/magnification)
Intersections/Unit Length, PL
To illustrate this calculation, let us
superimpose a series of horizontal test
lines, such as used in the lineal analysis,
over the synthetic microstructure.
Intersections/Unit Length, PL
The point intersections are indicated in
the next slide.
3
2
5
4
6
1
7
9
8
11
10
13
12
14
15
16
17
18
20
19
22
23
21
24
25
26
28
30
29
32
27
31
34
33
35
Intersections/Unit Length, PL
In the example, Pα is 35. If each of
the 10 lines is 256 mm long, and
the magnification is 500X, then,
LT is 5.12 mm, and
35
PL = ——— = 6.84 mm-1
5.12
Interceptions Per Unit Length, NL
NL is a measure of the number of
interceptions with phase or grain
particles per unit length of test line. It is
calculated from:
∑ Nα
NL = ————
LT
Nα is the number of interceptions and LT is the
true line length (line length/magnification)
Interceptions/Unit Length, NL
To illustrate this calculation, let us
superimpose a series of horizontal test
lines, such as used in the lineal analysis,
over the synthetic microstructure.
Interceptions/Unit Length, NL
The particle interceptions are indicated
in the next slide.
2
3
1
6
5
4
7.5
7
8.5
10
9.5
10.5
11.5
12.5
13.5
14.5
15.5
17.5
16.5
Interceptions/Unit Length, NL
In the example, Nα is 17.5. If each
of the 10 lines is 256 mm long,
and the magnification is 500X,
then, LT is 5.12 mm, and
17.5
NL = ——— = 3.42 mm-1
5.12
Number Per Unit Area, NA
The number of particles per unit area,
NA, is a measure of the quantity of
particles, that is the number density.
NA is related to the number per unit
volume, NV, which can only be
determined by serial sectioning. It is
determined by:
∑ Nα
NA = ————
AT
Number Per Unit Area, NA
To illustrate the determination of NA, let
us count the number of particles in our
synthetic microstructure and then divide
by the test area. The synthetic
microstructure with 30 particles is shown
in the next slide.
Number Per Unit Area, NA
The test area measures 256 x 190 mm and
the magnification is 500X. Therefore, NA
is given by 30 particles divided by the
true test area:
30
NA = ————————— = 154.2 mm-2
(256/500)x(190/500)
Average Particle Area, A
The average particle size, as measured by
the area, can be determined from a ration
of the field measurements, AA and NA,
without use of individual particle area
measurements from:
AA
A = ——
NA
Average Particle Area, A
The area fraction was determined
previously by areal analysis, lineal
analysis and point counting, that is, AA,
LL and PP. Of these, the AA value is the
most precise. NA was also determined. So,
the average cross-sectional area of the
particles is:
0.056
A = ——— = 0.0003632 = 363.2 µm2
154.2
Average Particle Area, A
Using image analysis, we can measure the
area of each particle, add all the areas, and
divide by the number of particles. As we
have particles with a perfect circular crosssection, we can measure the diameter and
calculate the area of each particle. Then,
sum the areas and divide by the number of
particles. The average area is:
∑ Aαi
A = —————
Nα
Average Particle Area, A
10857.6
A = ——— = 361.9 µm2
30
Comparison of Average Areas
Average area based on the area fraction divided
by the number per unit area = 363.2 µm2
Average area based on actual measurements
was 361.9 µm2
363.2 ≅ 361.9
Mean Center-to-Center Spacing, σ
The mean spacing between particle
centers, in all directions, is given simply
by the reciprocal of NL:
1
σ = ⎯⎯
NL
Mean Center-to-Center Spacing, σ
In the case of our synthetic
microstructure, NL was determined as
3.42 interceptions per mm. So, σ is:
1
σ = ⎯ = 0.2924 mm = 292.4 µm
3.42
Mean Edge-to-Edge Spacing, λ
The mean edge-to-edge spacing between
particles, known as the mean free path, is a
good structure-sensitive parameter. λ is
calculated from:
1 - AA
λ = ⎯⎯⎯⎯
NL
Mean Edge-to-Edge Spacing, λ
In the case of our synthetic microstructure,
AA and NL were determined. So, λ is:
1 – 0.056
λ = —⎯⎯⎯ = 0.276 mm = 276µm
3.42
The MFP is a very structure-sensitive parameter used in
ASTM E 1245 to characterize second-phase particles
Degree of Orientation, Ω
(PL)⊥ - (PL)||
Ω = ——————
(PL)⊥ + 0.571(PL)||
Usually expressed as a percentage (%)
Used in ASTM E 1268 to assess the degree of banding or
orientation in structures viewed on a longitudinal plane
Interlamellar Spacing
1
σr = ——
NL
σr
σt = ——
2
Where σr is the mean random spacing
and σt is the mean true spacing.
Measure NL with random test lines, such as with a circle,
rather than directed test line (perpendicular to lamellae)
Grain Size Measurement
Types of Grain Sizes
• Non-twinned(ferrite, BCC metals, Al)
• Twinned FCC Metals (austenite, Cu, Ni)
• Prior-Austenite
(Parent Phase in Q&T Steels)
Grain Size Measurements
• Number of Grains/inch2 at 100X: G
• Number of Grains/mm2 at 1X: NA
• Average Grain Area, µm2 : A
• Average Grain Diameter, µm: d
• Mean Lineal Intercept Length, µm: l
Grain Size Measurement Methods
Comparison Chart Ratings
Shepherd Fracture Grain Size Ratings
Jeffries Planimetric Grain Size
Heyn/Hilliard/Abrams Intercept Grain Size
Snyder-Graff Intercept Grain Size
2D to 3D Grain Size distribution Methods
Definition of ASTM Grain Size
n = 2 G-1
n = number of grains/in2 at 100X
G = ASTM Grain Size Number
ASTM Grain Size, G
G
n
G
n
1
1
6
32
2
2
7
64
3
4
8
128
4
8
9
256
5
16
10
512
ASTM Standards for Grain Size
ASTM E 112: For equiaxed, singlephase grain structures
ASTM E 930: For grain structures
with an occasional very large grain
ASTM E 1181: For characterizing
duplex grain structures
ASTM E 1382: For image analysis
measurements of grain size, any type
Comparison Chart Ratings
Look at a properly etched microstructure,
using the same magnification as the chart, and
pick out the chart picture closest in size to the
test specimen. If the grain structure is very
fine, raise the magnification, pick out the
closest chart picture and correct for the
difference in magnification according to:
G = Chart G + Q
Q = 6.64Log10(M/Mb)
where M is the magnification used and
Mb is the chart magnification
Jeffries Planimetric Method
n1 = number of grains completely inside the
test circle
n2 = number of grains intercepting the
circle
NA = f[ n1 + (n2/2)]
f = Jeffries multiplier
f = magnification2/circle area
Jeffries Planimetric Method
1
Average Grain Area = A = ——
NA
G = (-3.322LogA) – 2.955
n1 = 68 and n2 = 41
Jeffries Planimetric Method - Example
For the preceding micrograph,
n1 = 68 and n2 = 41
And
2
M2
100
f = —— = ——— = 0.497
A
20106.2
Jeffries Planimetric Method - Example
NA = f[n1 + (n2/2)]
NA = (0.497)[68 + (41/2)]
NA = 44.02 mm-2
Jeffries Planimetric Method - Example
1
A = —— = 0.0227 mm2
NA
d = (A)1/2
G = 2.5
Jeffries Planimetric Method - Example
This is an austenitic Mn steel, solution annealed and aged to
precipitate a pearlitic phase on the grain boundaries (at 100X).
There are 43 grains within the circle (n1) and there are 25 grains
intersecting the circle (n2). The test circle’s area is 0.5 mm2 at 1X.
Jeffries Planimetric Method - Example
NA = f[n1 + (n2/2)]
f = [(1002)/5000]
NA = 2[43 + (25/2)] = 111 mm-2
G = [3.22Log10(111)] – 2.954 = 3.8
(Of course, more than one field should be measured to get
good statistical results)
Heyn/Hilliard/Abrams Intercept Method
N = number of grains intercepted
P = number of grain boundary intersections
N
NL = ——
LT
P
PL = ——
LT
where LT is the true test line length
Heyn/Hilliard/Abrams Intercept Method
Apply a test line over the microstructure
and count the number of grains intercepted
or the number of grain boundary
intersections (easier for a single-phase grain
structure). After you count N or P, divide
that number by the true line length to get
NL or PL.
Intercept Counts (N)
1/2
1
1
1
1
1/2
1
The test line intercepted 5 whole grains and the line ends fell
in two grains. These are weighted as ½ an interception. So the
total is 6 intercepts (N=6).
Intersection Counts (P)
1
1
1
1
1
1
The test line has intersected 6 grain boundaries. The ends
within the grains are not important in intercept counting.
So, P=6 for the intercept count.
Heyn/Hilliard/Abrams Intercept Method
1
1 = ——
Mean Lineal Intercept, l = —
NL P L
G = [6.644Log10(NL or PL)] – 3.288
G = [-6.644Log10(l)] – 3.288
Note: Units are in mm-1 (for NL and PL) or mm (for l)
Heyn/Hilliard/Abrams Intercept Method
If the grain structure is not equiaxed, but
shows some distortion of the grain shape, use
straight test lines at various angles, or simply
horizontal and vertical with respect to the
deformation axis of the specimen.
Alternatively, you can use test circles, such as
the ASTM three-circle grid (three concentric
circles with a line length of 500 mm). This
test pattern averages the anisotropy.
Heyn/Hilliard/Abrams Intercept Method
Example of three concentric test circles
for point counting.
To illustrate intercept counting, note that there are 41, 25 and 20 grains
intercepted (N) by the three concentric circles.
Intercept Counting Example
LT = 11.4 mm
N = 41 + 25 + 20 = 86
86 = 7.54 mm-1
NL = ——
11.4
1 = 0.133 mm
l = ——
7.54
G = [-6.644Log10(0.133)] – 3.288 = 2.5
Intercept Grain Size Example – Single Phase
This is a 100X micrograph of 304 stainless steel etched electrolytically with
60% HNO3 (0.6 V dc, 120 s, Pt cathode) to suppress etching of the twin
boundaries. The three circles have a total circumference of 500 mm. A count
of the grain boundary intersections yielded 75 (P=75).
Intercept Grain Size Example – Single Phase
75
PL = ——— = 15 mm-1
500/100
1 = 0.067 mm
l = ——
15
G = [-6.644Log10(0.067)] – 3.288 = 4.5
Intercept Method for Two-Constituents
Nα = Number of α grains intercepted
LT = Test line length/Magnification
VVα = Volume fraction of the α phase
VVα(LT)
lα = ———
Nα
Intercept Method for Two-Constituents
This 500X micrograph of Ti-6242 was alpha/beta forged and alpha/beta annealed,
then etched with Kroll’s reagent. The circumference of the three circles is 500 mm.
Point counting revealed an alpha phase volume fraction of 0.485 (48.5%). 76 alpha
grains were intercepted by the three circles.
Intercept Method for Two-Constituents
(0.485)(500/500)
lα = ———————— = 0.006382 mm
76
G = [-6.644Log10(0.006382)] – 3.288 = 11.3
Particle Size Measurement
Six ways to measure particles on a polished cross section.
Particle Size Measurement
Volumetric Diameter, dV
Diameter of a sphere with the same
volume as the particle
π
V=—d
6
V
3
Particle Size Measurement
Feret’s Diameter, dF
Mean distance between pairs of
parallel tangents to the projected
outline of the particle
Particle Size Measurement
Projected Area Diameter, dA
Diameter of a circle with the same
area as the projected area of the
particle.
π d 2
A=—
4 A
Particle Size Measurement
Perimeter Diameter, dP
Diameter of a circle with perimeter
length the same as the projected outline
of the particle
P = π dP
Shape Descriptors
SPHERICAL
Global shaped
(Circular on a cross section
through the particle)
Shape Descriptors
ACICULAR
Needle-like in three dimensions
Shape Descriptors
FLAKY
Irregular plate-like shape
Shape Descriptors
DENDRITIC
Branched,
Tree-like in three dimensions
Shape Descriptors
LENTICULAR
Lens-like shape
Shape Descriptors
FIBROUS
Regular or irregular
Tread-like shape
Shape Descriptors
ANGULAR
Sharp edged or
Roughly polyhedral shaped
Shape Descriptors
GRANULAR
Approximately equidimensional
Irregularly shaped
Shape Descriptors
IRREGULAR
Lacking any symmetry
Shape Factors
Elongation Ratio or
Anisotropy Ratio
Length
AR = ———
Width
Shape Factors
Sphericity (Roundness)
4πA
S = ———
P2
S = 1 for a circular feature; S < 1 for other shapes
Sometimes this equation is
reversed
Perimeter – Sensitive to
Magnification
Try to use shape factors that do not
require a perimeter measurement,
especially when the particles are
small (<30 pixels/particle)
Perimeter-Free Shape Factor
Measure the maximum Feret’s diameter,
dFmax, and calculate the area of the circle
with that diameter.
dFmax 2
AF = π(———)
2
AF
SFPF = —————
Ameasured
Degree of Nodularity of Graphite
100(∑Ai with SF ≥ 0.6)
% Nod. = ——————————
∑Ai
Ai is the area of a graphite particle
Variations in Graphite Shape
Nodular Iron
Flake Gray Cast Iron
Magnification bars are
all 100 µm long
Compacted
Graphite Cast Iron
Shape Factors - Example
Histogram of sphericity shape factors for two flake gray iron specimens, a
compacted graphite specimen and a nodular graphite specimen.
ASTM E 1245
A Stereological Procedure to Characterize
Discrete Second-Phase Particles
Uses field and feature-specific measurements.
While the measurements employ stereological
parameters, they may be made on only one plane,
for example, the longitudinal. If the threedimensional values are desired, then additional test
planes must be assessed.
ASTM E 1245
Measure or calculate:
Area Fraction, usually in %
Number per mm2, NA
Average Length in µm
Average Area in µm2
Mean Free Path in µm
ASTM E 1245
Area fractions of inclusions on three parallel planes, same
specimens, of Alloy 718.
ASTM E 1245
Number per sq. mm of inclusions on three parallel planes, same
specimens, for Alloy 718.
ASTM E 1245
Average area of inclusions on three parallel planes, same
specimens, for Alloy 718
ASTM E 1245
Mean free path of the inclusions on three parallel planes, same
specimens, for Alloy 718.
ASTM E 1245
Sulfide area fractions on 12 specimens taken along an as-cast bar of 303
stainless steel, at the mid-radius location.
ASTM E 1245
Sulfide number per sq. mm taken at 12 locations along an as-cast bar
of 303 stainless steel at the mid-radius location.
ASTM E 1245
Average area of sulfides taken at 12 locations along an as-cast bar of 303
stainless steel, at the mid-radius location.
ASTM E 1245
Mean free path for sulfides at 12 locations along an as-cast bar of 303
stainless steel, at the mid-radius location.
ASTM E 1245
Distribution of area fractions of the sulfides for 106 bars of wrought 303
stainless steel, at the mid-radius location, longitudinal plane.
ASTM E 1245
Distribution of number per sq. mm of sulfides for 106 bars of wrought 303
stainless steel, at the mid-radius location, longitudinal plane.
ASTM E 1245
Distribution of average area of sulfides for 106 bars of wrought 303
stainless steel, at the mid-radius location, longitudinal plane.
ASTM E 1245
Plot of sulfide length vs. area measurements for each of 106 wrought
bar specimens in wrought 303 stainless steel.
Point Counting Inclusions
Point counting of inclusions is tedious and imprecise. This work used 100
fields measured with a 100-point grid, but the 95% confidence limits are
poor, typical for volume fractions below 2%.
Lineal Analysis of Inclusions
A Hurlbut counter was used (one hour per specimen) to measure the lineal
fraction of inclusions. Again, the precision of the measurements is poor.
Image Analysis Inclusion Measurement
Image analysis measurement of the inclusions using 1080 fields (grouped in 12 sets
of 90) gave better precision in less time than the manual measurements.
Image Analysis Inclusion Measurement
Inclusions measured by image analysis using different magnifications (field
sizes) shows the influence of the number of fields on the mean value.
Image Analysis Inclusion Measurement
The relative accuracy of the inclusion volume fractions improved with
increasing number of fields measured and is poorest for the highest
magnification (small field size increases field-to-field variability).
Image Analysis Inclusion Measurement
The relative accuracy of the inclusion area fractions improved (decreased) as
the area measured increased.