-
Image Analysis Measurements of Duplex Grain Structures George F.
Vander Voort* and John J. FrieP *Metal Physics Research, Carpenter
Technology Corp., Reading, PA 19612; and ~Princeton Gamma-Tech,
Princeton, NJ 08540
Several types of duplex grain size distributions in five
different alloys were evaluated using image analysis. Most of the
grain structures contained annealing twins. Those with straight
interfaces could be recognized and deleted from the image, leaving
only grain boundaries. One specimen exhibited curved twin
boundaries, caused by deformation, and they could not be
discriminated by the system as currently programmed. Grain areas
were measured and grouped according to their relationship to the
ASTM grain size scale. An area-weighted histogram was shown to be
excellent for revealing the nature of the distribution, while a
numerical-frequency histogram was insensitive. The intersection of
these two curves separated only one of the four bimodal
distributions. A deconvolution approach, using the area-weighted
curve only, should be evaluated. An arithmetic grain area
classification approach using 25 classes based on the data range,
to split the two grain area populations based upon the intersection
of the number percent and area per- cent curves, worked well for
two of the four specimens. Image analysis detection of grains
results in a small portion of the image (about 6-12%) assigned to
the grain boundaries. In manual measurement methods, the area
occupied by the grain boundaries is not con- sidered, and it does
not influence measurements. Thus, compared to manual methods, image
analysis undersizes grains slightly producing a relatively small
positive bias in the grain size number, which could be ignored,but
can be eliminated or reduced.
INTRODUCTION
The measurement of grain size is one of the oldest and most
important in metal- lurgy because of the influence of grain size on
properties and behavior. Manufactur- ers seek to control the grain
size within cer- tain limits, chosen based on the specific
properties required. Measurement is re- quired to verify control.
Likewise, in struc- ture-property studies or in failure analysis
work, grain size measurements are required.
Grain size determinations are made on a polished section cut
from the material at appropriate locations. The grain size is
de-
fined in terms of sections through the grains, i.e., a planar
grain size. Most com- monly, grain size is determined by the
comparison method, i.e., by comparing the etched structure to a
graded series of grain structures and selecting the closest picture
number or an intermediate value. This method is fast but not as
precise or repeatable as actual measurement meth- ods. The
comparison method is used in quality control work for heat
clearance. In many instances, the grain size requirement is simply
that it be "fine grained." This re- quires an ASTM grain size of 5
or finer (i.e., G->5).
In the production of certain materials, it 293
Elsevier Science Publishing Co., Inc., 1992 MATERIALS
CHARACTERIZATION 29:293-312 (1992)
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294 G. F. Vander Voort and J. J. Friel
is necessary to control the grain size more tightly and,
therefore, greater measure- ment precision is required. There are
three basic measurement methods [1] for grain size. The oldest
measurement method is the planimetric method developed by Jef-
fries et al. [2, 3] based on earlier work by Sauveur [4]. In this
method, the number of grains per unit area, NA, is determined which
can be directly related to the ASTM grain size number.
The Jeffries planimetric method is slow when done manually
because it requires marking of the grains to obtain an accurate
count. The intercept method, introduced by Heyn [5] and improved by
Hilliard [6, 7] and Abrams [8], is easier to employ man- ually and,
hence, is the method of choice for manual work. In this method, the
grain size is measured in terms of an average dis- tance
intersecting the grains in random fashion. The "mean lineal
intercept length," L3, is not a maximum grain di- ameter. Rather,
it is the average of all pos- sible distances across each
grain.
The third method, the "triple-point count" method, was suggested
by Smith [9] based on Euler's Law. In this method, all of the
triple-point grain junctions within a known area are counted. From
this, the number of grains per unit area can be de- termined. To
obtain an accurate count, the triple points must be marked, in the
same manner as grains are marked in the pla- nimetric method. This
method, however, is rarely used.
The previous three measurement meth- ods - the planimetric,
intercept, and tri- ple-point count methods--are based on
measurements of two-, one-, and zero-di- mensional features. All
describe the grain size in planar terms, not spatial, three-di-
mensional terms. Direct determination of the spatial grain size is
extremely difficult and is rarely performed.
If the grain structure is equiaxed in all directions, then the
planar grain size is di- rectly proportional to the spatial grain
size. In this case, the mean lineal intercept length, L3, is a
simple function of the mean true volumetric grain size, D, and NA
is a
simple function of the number of grains per unit volume, Nv
[1].
When the grain structure is not equiaxed but elongated,
determination of the planar grain size is more difficult. The
grains must be measured on at least two principal planes, the
longitudinal and transverse, e.g., using directed test lines
parallel to the principal orientations. Results are then av- eraged
to obtain L3.
Starting with Desch [10] in 1919, a num- ber of researchers have
used liquid metal embrittlement to completely disintegrate a
specimen intergranularly. Such studies have demonstrated that the
grains exhibit a range of sizes and shapes. Grain volumes are
statistically approximated by a log-nor- mal distribution [11].
Serial sectioning [12- 18], although extremely tedious, repre-
sents another approach for performing spatial grain size analysis,
and these stud- ies also confirmed the log-normal distri- bution of
grain volumes.
Planar grain size is far easier to deter- mine than spatial
grain size. In most grain size analysis work, the grains conform to
a single log-normal distribution. Some studies have claimed that
other special dis- tribution functions gave a better fit to the
data; however, the log-normal distribution gives a reasonably good
fit, and it is easier to deal with than these special functions.
Grain structures with unimodal grain size distributions are
commonly measured using the methods described in ASTM El12 [19],
i.e., the chart comparison method, the Jeffries planimetric method,
and the Heyn-Hill iard-Abrams intercept method. These methods do
not describe the distribution of grain sizes as observed on the
plane of polish. Rather, they pro- duce an arithmetic numerical
average value, in terms of the ASTM grain size number, G, the mean
lineal intercept, L3, or the number of grains per unit area,
NA.
There are situations where the grain structure does not exhibit
a unimodal grain size distribution. Indeed, there are in- stances
where bimodal (duplex) distribu- tions arise, e.g., in partially
recrystallized specimens [1, 20, 21]. A number of types
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Image Analysis of Duplex Grain Structures 295
of bimodal distributions have been ob- served. ASTM El181 [22]
has classified these types as random:
isolated coarse grains in a fine-grained matrix (ALA)
extremely wide distribution of grain sizes
two distinct grain sizes, randomly dis- tributed (bimodal
condition)
and topologically varying:
variations in size across a product necklace structure banded
structures of alternate size
ASTM EllS1 describes manual methods for rating the grain size of
specimens with duplex grain size distributions. At the time it as
introduced, image analysis proce- dures for unimodal distribution
specimens had not been standardized. Also, many specimens with
duplex grain structures are face-centered cubic and exhibit
annealing twins, which presents another problem. Grain size
analysis of twinned austenite grains, whether done manually or
auto- matically, must separate grain boundaries from twin
boundaries, i.e., twin bounda- ries are ignored.
However, progress in discrimination be- tween twin boundaries
and grain bound- aries by image analysis is being made [23, 24]
using an artificial intelligence (AI) ap- proach. Twin boundaries
are frequently straight lines, or two or more parallel lines, that
may run partly or completely across a grain. Twins may also exhibit
a stepped appearance. The AI approach looks for straight, parallel
lines in the structure, and, after removal from the image, it con-
siders if the resulting feature looks like a grain from a geometric
viewpoint.
A duplex grain size distribution can be best evaluated by
measuring grain inter- cept lengths, grain diameters or grain areas
and plotting a frequency histogram of the measurements. The term
grain diameter is ill defined, however, and there is no direct link
between measured diameters and the ASTM Grain size number. For
example, one could measure diameters taken in a
number of orientations, calculate the av- erage for each grain,
and repeat this for many grains. Or, one could measure a Fer- et's
diameter (maximum or minimum), or other statistical diameters, for
a large num- ber of grains. Frequency histograms would show whether
the structure was unimodal or bimodal in each case, but the data
can- not be used to determine the mean ASTM grain size number of
the unimodal distri- bution, or of each portion of a bimodal
distribution.
Grain intercept lengths could be mea- sured for each grain.
Because the structure may not be perfectly equiaxed, intercept
lengths for each grain must be assessed using several orientations,
at least three. For any grain, a large number of intercept lengths
can be measured. Hence, when this is done for a large number of
grains, an enormous amount of data is generated. Also, because
modern image analyzers are software-based systems, intercept length
measurements are not as simple to perform as was the case with
older, hardware- based systems.
Measurement of individual grain areas on the planar surface is
much easier to do by image analysis than by manual methods and has
the decided advantage that grain areas can be used to generate ASTM
grain size numbers. Because the average grain area, A, is the
reciprocal of NA, and the ASTM grain size number G is an exponen-
tial function of NA, A can be related to G. Accordingly, regression
analysis of G and A data from Ell2, as shown in ASTM E1382 [25],
produces the following equation:
G = [-3.3223 Log A] - 2.955 (1)
where the grain area is in mm 2. Using this equation, the
average grain area, or the in- dividual grain areas, can be
converted to an equivalent ASTM grain size number G.
EXPERIMENTAL PROCEDURE
Seven 8 x 10in. micrographs of five dif- ferent alloys depicting
various types of du-
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296 G. F. Vander Voort and J. J. Friel
Fro. 1. Examples of the duplex grain structure microstructures:
(a) carbon steel, nital etch; (b) INCONEL 718, as rolled, 20% HNO3
in water, 2V dc, 2 minutes, Pt cathode; (c) experimental modified
625 alloy, as forged, acetic glyceregia etch; (d) Pyromet 31,
solution annealed and aged, glyceregia etch; and, (e) SCF-19, warm
worked and annealed (900C-h, water quenched), 60% HNO3 in water, 1V
dc, 1 minute, stainless steel cathode.
plex grain size distributions were ana- lyzed. Figure l(a) shows
the microstruc- ture of a carbon steel specimen. Note that there
are three very large ferrite grains near the center of the
micrograph (the one large grain near the edge intersected the
frame
border after digitization). The matrix grain size is of much
finer size. This is an ex- ample of a random duplex type with iso-
lated coarse grains in a fine-grained matrix. Two micrographs of
INCONEL (INCO- NEL is a registered trademark of INCO A1-
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Image Analysis of Duplex Grain Structures 297
loys International, Huntington, WV) alloy 718 (the specimen was
used in a round robin conducted by R. K. Wilson of Inco Alloys
International) were used in this study. Some of the large grains
contained faint twins and some grains etched very darkly because of
lack of recrystallization. Figure l(b) shows one of these micro-
graphs. A micrograph of an as-forged modified alloy 625
(experimental alloy) was also employed, Fig. 1(c), where the fine
grains are recrystallized and contained twins. This is a
necklace-type duplex grain structure. Two micrographs of a solution
annealed specimen of Pyromet (Pyromet is a registered trademark of
Carpenter Tech- nology Corporation, Reading, PA) 31 were used. As
Fig. l(d) shows, nearly all of the grains exhibit twins. This is an
example of a wide-range, random duplex condition. The last
micrograph chosen was that of a warm-worked, partially
recrystallized SCF 19 (SCF 19 is a registered trademark of Car-
penter Technology Corp., Reading, PA) drill collar alloy. As Fig.
l(e) shows, this is a necklace-type structure with small re-
crystallized twinned grains. The larger grains exhibit twins, many
of which are curved because of the deformation pro- cess. Some
recrystallized fine grains are present along twins in the very
large grains.
The images were digitized using the IM- AGIST (IMAGIST is a
registered trademark of Princeton Gamma-Tech, Princeton, NJ) image
analyzer made by Princeton Gamma-Tech. This system was chosen to
test its ability to recognize twins and re- move them from the
grain structure [23, 24]. Annealing twins were not present in the
carbon steel specimen with its ferritic grain structure, and they
were only lightly revealed by the etchant in the alloy 718
specimen. The twins were of classic form in the Pyromet 31 specimen
and were pres- ent in certain grains in the Mod. 625 and the SCF-19
specimens. Figure 2(a,b) shows two of these structure before and
after dig- itization, image cleaning, and twin re- moval (where
appropriate). The twins were effectively removed from the Pyro-
met 31 [Fig. 2(a)], the INCONEL 718, and the mod. alloy 625
specimens. However, for the SCF 19 specimen, the twins were not
fully removed because of their curva- ture [Fig. 2(b)]. Hence,
grain size analysis results will not be reported for this
specimen.
After the grain structures were digitized, cleaned, enhanced,
and the twins were re- moved (when present), the grain areas were
measured. Additional measurements of each grain, such as their
average di- ameter, maximum diameter, perimeter, etc., were made
but are not reported.
The grain areas were grouped in histo- gram fashion based on the
relationship be- tween grain area and the ASTM grain size number,
as defined in Table 1. The grain size distribution was plotted as a
function of the grain size number using a number percent basis and
an area percent basis, as suggested by Peyroutou and Honnorat [26].
The area-weighted grain size distri- bution can be calculated in
two ways. The first approach is to multiply the number of
Table 1 Classifying Grain Areas by ASTM G
ASTM #.m 2 grain size number Range of grain Mean grain % (G)
areas area
15 2.8-5.6 3.9 14 5.6-11.1 7.9 13 11.1-22.3 15.8 12 22.3-44.6
31.5 11 44.6-89.1 63 10 89.1-178 126 9 178-356 252 8 356-713 504 7
713-1430 1010 6 1430-2850 2020 5 2850-5700 4030 4 5700-11,400 8060
3 11,400-22,800 16,100 2 22,800-45,600 32,300 1 45,600-91,200
64,500 0 91,200-182,400 129,000
00 182,400-364,800 258,100
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FIc. 2. Examples of screen images of (a, top) Pyromet 31 before
(left) and after (right) image processing and twin removal, which
was quite successful, compared to screen images of the SCF-19 (b,
bottom) before (left) and after (right) image processing and twin
removal, which had limited success due to the curvature of the twin
boundaries.
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Imay, e Analysis of Duplex Grain Structures 299
grains in each size class by the mean grain area for each class.
The method is fast but becomes inaccurate as the number of grains
decreases. In the other approach, the actual areas of each grain in
each class are summed and used for the area per class. This can be
easily done with a spreadsheet when the measured grain areas are
sorted in either ascending or de- scending order.
Next, the h istogrammed data can be sep- arated into two
distinct populations, which we will call " f ine" and "coarse." G
can be calculated based on the average area of all of the grains,
which would be incorrect; or G can be calculated for the "f ine"
and "coarse" populat ions based on the average grain areas for each
populat ion using the histogram data. Naturally, as the number of
grains in a populat ion decreases, there will be a greater
difference between G de- termined using the average area of the ac-
tual grain areas and G based on the use of the mean grain area per
class approach. Likewise, in the determination of the area percent
of the fine and coarse populations, we will obtain differences.
Hence, it is best to use the actual grain areas for all calcu-
lations involving grain areas.
RESULTS
The nontwinned carbon steel specimen is an example of a random
type of duplex condition with isolated coarse grains within a
fine-grained matrix. The grains were equiaxed (determined by
viewing on a longitudinal plane) and recrystallized. The grain area
measurements (Table 2) can be broken into two distinct populations.
Three grains (the fourth large grain inter- sected the frame border
and was not in- cluded in the analysis) of very large size,
equivalent to ASTM 2 and 1, make up the coarse population, while
the remaining 7177 grains make up the fine population. The number
percent of these three coarse grains is only 0.04%, while the area
percent is 7.58%.
Figure 3 shows number percent and area
Table 2 Data for Carbon Steel Micrograph
Number Area ASTM Number percent Area per class percent
G grains per class (p~m 2) per class
14 0 0. 0 0 13 409 5.70 7413.55 0.58 12 1195 16.64 38,667.32
3.03 11 1681 23 .41 110,034.82 8.63 10 1794 24.99 228,555.06 17.92
9 1365 19 .01 335,885.02 26.34 8 561 7.81 269,453.89 21.13 7 145
2.02 135,985.39 10.66 6 26 0.36 49,439.78 3.68 5 1 0.01 3,263.36
0.26 4 0 0 0 0 3 0 0 0 0 2 2 0.03 48,111.44 3.77 1 1 0.01 48,548.96
3.81 0 0 0 0 0
7180 1,275,358.6
Number % of Grains 30
25
20
15
10
5
0 ~ i = i 0 1 2 3
Area % of Grains 3O
4 5 6 10
ASTM Gra in S i ze Number
. . - - - - - -No. %
11 12 13 14
,!
0 1 2 3 4 6 6 7 8 9 10 11 12 13 14
ASTM Gra in S i ze Number
FIG. 3. Number-weighted (top) and area-weighted (bottom)
histograms of the grain areas converted to their equivalent ASTM
grain size number for the car- bon steel specimen. Note that the
area-weighted his- togram clearly reveals two distinct grain size
populations.
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300 G. F. Vander Voort and J. J. Friel
percent histograms. The equivalent ASTM grain size number, based
on the grain area, is plotted on the x axis. Because grain size is
defined in an exponential fashion as
NA = 2 c 1 (2)
where G is the ASTM grain size number and NA is the number of
grains per square inch at x 100 magnification, this is actually a
semi-log plot. The log of the mean grain area is a linear function
of G.The plots would be identical in appearance if the x axis was a
logarithmic scale of the mean grain areas as shown in Table 1. Such
plots are useful because it is well known that grain area
measurements exhibit distribu- tions very close to a log-normal
distribu- tion. When the areas are scaled in a loga- rithmic
manner, rather than in linear fash- ion, the histogram curve for a
unimodal distribution will be bell shaped, i.e., Gaussian.
Figure 3 demonstrates the value of an area fraction size
distribution (area per- cent) over a numerical frequency size dis-
tribution (number percent). The area frac- tion distribution
clearly shows that there are two separate grain size populations,
in agreement with the micrograph in Fig. l(a). The numerical
frequency distribution shows only a single distribution curve, be-
cause 0.04% will not be visible on the Y axis. The value of an
area-weighted distri- bution plot is well known [27, 28] for such
purposes. The area percent histogram should be constructed by
adding up all of the grain areas in each class, particularly when
the number of grains per class is low.
Figure 4 shows the number percent and area percent distribution
curves superim- posed on the same plot. Note that the number
percent curve is shifted to the right (finer grain size direction)
of the area per- cent curve. For this type of duplex condi- tion
with two distinct populations, the in- tersection of the number
percent and area percent curves is not useful for separating the
populations. However, because the area percent plot reaches zero at
G = 4, the two distributions should be broken at this location.
Figure 5 shows two Gaussian
Percent of Grains 30
26
Area %-~. ....-----No. % 20
lo \
5
0 1 2 3 4 5 6 7 9 10 11 12 13 14
ASTM Grain Size Number
F~G. 4. The histograms in Fig. 3 have been super- imposed to
demonstrate the differences between the two plots.
curves fitted to the two grain populations. Once the two
populations have been di-
vided, the grain size of each population can be determined. The
grain size can be computed from the actual grain area mea-
surements. The total area of the large grains was 96,660.4~m 2. For
the determi- nation of the area percent of the coarse grains, use
the actual grain areas rather than the area per class computed from
the mean area per class and the number per class. By using the
actual grain areas, the total area of the three coarse grains is
96,660.4l~m 2, while the total area of the 7177 fine grains is
1,178,698.2p~m 2. Hence, 7.58% of the grain areas are coarse, and
92.42% are fine.
Next, the average grain area for the coarse and fine grains was
computed fol- lowed by the ASTM grain size number using eq. (1).
This yielded 32,220.1p, m 2 (G
Area % of Grainn 30
25
20
15
10
5
o i [I l l, I1, II, 1 2 3 4 5 6 7 e 9 10 11 12 13 14
ASTM Grain Size Number
I - . , . o ..... i
FIG. 5. Two separate Gaussian curves have been plot- ted for the
two grain size populations for the carbon steel specimen.
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Image Analysis Of Duplex Grain Structures 301
= 2.00) and 164.21xm 2 (G = 9.62) for the coarse- and
fine-grained regions. The av- erage area for all grains would be
177.61xm 2, which would correspond to an ASTM grain size of 9.50.
However, this value should not be used to represent the grain size
of the specimen because it im- plies that the distribution is
unimodal.
Table 3 shows the grain size histogram data for the two INCONEL
alloy 718 mi- crographs. Figure 6 shows the number per- cent and
area percent histograms. The number percent histogram reveals a
slight tail at low grain size numbers but other- wise gives no
indication of a duplex con- dition. The area percent histogram,
how- ever, clearly reveals a bimodal condition.
Figure 7 shows the two histograms su- per imposed on the same
axis. Again, the number percent histogram is shifted to- ward the
finer grain sizes. The two histo- gram curves intersect at ASTM 9.
We will consider all of the grains of 9 or finer as the "f ine"
populat ion and all those of 8 or coarser as the "coarse"
population, i.e., breaking the area percent histogram at 356#,m 2.
Figure 8 shows two Gaussian curves fitted in this manner, which
appear to be quite satisfactory.
Table 3 Data for Inconel 718 Micrograph
Number Area per Area ASTM Number percent class percent
G grains per class (}xrn 2) per class
15 0 0. 0. 0. 14 3 0.33 32.64 0.02 13 39 4.26 704.52 0.50 12 196
21.42 6669.19 4.72 11 277 30.27 18,072.36 12.79 10 254 27.76
30,738.75 21.76 9 92 10.05 21,818.99 15.44 8 26 2.84 12,528.51 8.87
7 16 1.75 17,210.03 12.18 6 8 0.87 15,596.01 11.04 5 3 0.33
11,675.26 8.26 4 1 0.11 6227.53 4.41 3 0 0 0 0
915 141,273.7
Number % of Grains 35f
30
25
20
15
10
,.------No. %
0 ~ ~ . . . . 2 3 4 5 6 7 8 9 10 11 12 13 14 15
ASTM Grain Size Number
Ares % of Grains 25
0 2 3 4 5 e 7 8 9 10 11 12 13 14 15
ASTM Grain Size Number
FIG. 6. Number-weighted (top) and area-weighted (bottom)
histograms of the grain areas converted to their equivalent ASTM
grain size number for the IN- CONEL 718 specimen (two micrographs
used). Note that the area-weighted histogram reveals two over-
lapping grain size populations.
Using this break, there are 861 grains with a total area of
78,036.51xm 2 in the "f ine" region and 54 grains with a total area
of 63,237.3~xm 2 in the "coarse" region. Hence, 55.24% of the
grains are in the "f ine" region with an average area of 90.6lxmR(G
= 10.48) and 44.76% of the grains are in the "coarse" region with
an average area of 1171.1txm 2 (G = 6.78).
Percent of Grains
2 3 4 5 6 7 8 9 10 I t 12 13 14 15
ASTM Grain Size Number
FIG. 7. The histograms in Fig. 6 have been super- imposed to
demonstrate the differences between the two plots.
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302
Area % of Grains 26
20 i ] ~ , , ~ ~ 1 0 1 5 5 Break at 356 sq. ~m ~
0 ' 3 4 5 7 8 9 10 11 12 13 14 16
ASTM ~rain Size Number
I ....... Fine Coarse - - All Greine i
FIG. 8. The intersection point at ASTM 9, shown in Fig. 7, has
been used to separate the two grain size populations. Two Gaussian
curves have been fitted to these populations.
Table 4 shows the data for the two mi- crographs of Pyromet 31.
This is an ex- ample of a random, wide-range type du- plex
structure. The grain structure is rather coarse, and the two
micrographs provided only 323 grains for measurement. A greater
number of measurements would be desir- able. Figure 9 shows plots
of the number percent and area percent of the grains as a function
of G, the ASTM grain size num- ber. The number percent plot shows a
slight left-hand tail at low grain size num- bers. The area percent
plot shows a non- Gaussian distribution similar to that for the
alloy 718 micrographs (Fig. 6) but not as pronounced.
Table 4 Data for Pyromet 31 Micrograph
Number Area ASTM Number percent Area per class percent
G grains per class (pom 2) per class
9 0 0 0 0 8 2 0.62 896.16 0.04 7 30 9.29 32,569.9 1.41 6 75
23.22 161,813.45 6.98 5 89 27.55 359,501.34 15.52 4 74 22.91
591,747.59 25.54 3 43 13.31 667,011.25 28.79 2 6 1.86 173,659.57
7.50 1 3 0.93 185,743.77 8.02 0 1 0.31 143,722.1 6.20
00 0 0 0 0
323 2,316,665.1
G. F. Vander Voort and J. J. Friel
Number % of Graine 30
25
2O
15
10
ooo , ;M3, S Grain Size Number
....----No. %
7 8 9
Area % of Grains
lO
30;
25
2O
16
10
5
0 00 0 tAS2TM 3 4 6 e 7 8 9 to
Grain Size Number
FIG. 9. Number-weighted (top) and area-weighted (bottom)
histograms of the grain areas converted to their equivalent ASTM
grain size number for the Py- romet 31 specimen (two micrographs
used). Note that the area-weighted histogram reveals two
overlapping grain size populations.
Figure 10 shows these two graphs plot- ted on the same axes. As
before, the num- ber percent curve is shifted towards the right,
i.e., toward the fine-grained end. The two curves intersect at ASTM
4. Hence, grains of ASTM 3 and below (areas
-
Area % of Grains
;;[ !~-.~ Break at 11400 sq. /~m 2oi 15
o L , , _ 00 0 1 2 3 4 5 6 7 8 9 10
ASTM Gra in S ize Number
I Fio, c ..... --A,,Gr=ne I
Fie. 11. The intersection point at ASTM 4, shown in Fig. 10, has
been used to separate the two grain size populations. Two curves
have been fitted to these populations, but the result appears to
place too many grains in the "coarse" category.
p laced in the " f ine" popu la t ion . F igure 11 shows Gauss
ian curves f i tted to each of these two popu la t ions .
The resul ts shown in Fig. 11 d id not ad- equate ly fit the two
popu la t ions . The "coarse" gra ins appeared to be excessive.
Hence, the data were inspected visual ly . Because there was a gap
in the gra in area data round 18,000/~m 2 (about G = 2.8), w i th
in the gra ins c lassed as G = 3 (G of 3.5-2.5, i .e., gra in areas
f rom 11,400 to 22,800bLm2), this va lue was used to sepa- rate the
two popu la t ions . In the ASTM G = 3 class, there were 43 grains,
of wh ich 9 were larger in area than 18,000~m 2. Fig- ure 12 shows
the Gauss ian curves p lo t ted for the "coarse" and " f ine" popu
la t ions us ing this separat ion . If one compares
Area % of Grains 30r
00 0 1 2 3 4 5 S 7 8 9 10
ASTM Gra in S ize Number
I Fine Coarse - - All Grains
FIG. 12. Inspection of the grain area data indicated that the
break between the two populations was at 18,000bLm 2, about ASTM
2.8. Note that the curves fit- ted to the "fine" and "coarse"
populations seem to be more reasonable than those shown in Fig.
11.
303
Figs. 11 and 12, it is apparent that 18,000p, m 2 was a better b
reak po int be- tween the two popu la t ions than 11,400tzm 2.
The effect of the shift f rom 11,400 to 18,000p, m 2 as the
breakpo in t is substant ia l . If one cons iders l l ,400p, m 2
first (Fig. 11), there wou ld be 270 gra ins in the " f ine" popu
la t ion w i th an average area of 4246.4~m 2 (G = 4.92) and 49.49%
of the surface area. There wou ld be 53 gra ins in the "coarse"
popu la t ion wi th an average area of 22,078.1~m 2 (G = 2.55) and
50.51% of the surface area.
By shi f t ing the break po in t to 18,000~,m 2 (with in the G =
3 class), 34 of the ASTM 3 gra ins are now in the " f ine" popu la
t ion for a total of 304 " f ine" gra ins w i th an av- erage area
of 5377.2~m 2 (G = 4.58) and 70.56% of the surface area. On ly 19
gra ins remain in the "coarse" popu la t ion (only 9 from the G = 3
class, rather than 43), and their average area was 35,894.4#,m 2 (G
= 1.85) cover ing 29.44% of the surface area. These d i f ferences
are substant ia l and show how critical se lect ion of the break po
int is.
Table 5 shows the gra in size data for the
Table 5 Data for Modified 625 Micrograph
Number Area per Area ASTM Number percent class percent
G grains per class (~m 2) per class
14 0 0 0 0 13 26 8.93 487.77 0.16 12 38 13.06 1179.35 0.39 11 45
15.46 2690.38 0.89 10 53 18.21 6573.97 2.18 9 43 14.78 11,196.93
3.71 8 33 11.34 16,609.97 5.51 7 18 6.19 18,803.57 6.23 6 16 5.50
32,771.18 10.86 5 10 3.44 39,471.03 13.08 4 2 0.69 17,720.52 5.87 3
5 1.72 78,344.42 25.97 2 1 0.34 27,397.08 9.08 1 1 0.34 48,405.7
16.05 0 0 0 0 0
291 301,651.8
-
304 G. F. Vander Voort and J. J. Friel
experimental modified alloy 625 that ex- hibited a necklace type
duplex condition. Only 291 grains were measured, which is really a
bit low for such an analysis. Figure 13 shows the number percent
and area per- cent histograms as functions of the ASTM grain size
number. In this case, the number percent plot shows a substantial
left-side tail to the distribution, the most pro- nounced of the
four specimens. Note also that the area percent histogram is the
only one with higher percentages in the coarse- grained region,
which is consistent with the number percent histogram. Note also
the uneveness of the area percent histo- gram in the coarse-grained
region. This may be due to the limited number of grains measured,
or the distribution may be more complex than bimodal.
Number % of Grains 20
m .....----No. %
0 i , i i i
O0 0 1 2 3 4 5 6 7 6 9 10 11 12 13 14
ASTM Grain Size Number Area % of Qrain$
30
25
20
15
to
5
0 O0 0 I 2 3 4 5 6 7 8 9 10 11 12 13 14
ASTM Gra in S i ze Number
FIG. 13. Number-weighted (top) and area-weighted (bottom)
histograms of the grain areas converted to their equivalent ASTM
grain size number for the mod- ified 625 specimen, which had a
"necklace" type du- plex condition. Note that both histograms
reveal a non-Gaussian grain size population. The area- weighted
histogram reveals a more complex condition than observed
previously. This may be due partly to the need for additional grain
area measurements (only 291 grains were measured) for this type of
structure.
Percent of Grains .^
oo 0 1 2 3 4 s 6 7 s 9 10 11 12 13 14
ASTM Gra in S i ze Number
FIG. 14. The histograms in Fig. 13 have been super- imposed to
demonstrate the differences between the two plots. Note the
intersection point at ASTM 7.
Figure 14 shows the number percent and area percent histograms
plotted on the same axes. This produced a pronounced "saddle" at
the intersection point (G = 7). As a first try, all grains of G = 6
and coarser were placed in the "coarse" population, i.e., grains
>1430~m 2 in area. The plot (Fig. 15) is not a good fit to the
data. Next, all grains of G = 5 and coarser were placed in the
"coarse" population, i.e., grains >2850~m 2 area. This plot
(Fig. 16) is also a poor fit to the data. As a third attempt, all
grains of G = 4 and coarser were placed in the "coarse" population,
i.e., grains ~5700~m 2 in area. Figure 17 shows the data fit, which
appears to be reasonably good.
As might be expected, the shift in the break point from 1430~m 2
(G = 6) to 5700p, m 2 (G = 4) produces a substantial
Area % of Grains
25
20 Break a t 1430 sq~ p,m
10
O0 0 1 2 3 4 5 e 7 8 9 10 11 12 13 14
ASTM Gra in S i ze Number
..... Fine Coarse - - All Grains i
FIG. 15. The intersection point at ASTM 7, shown in Fig. 14, has
been used to separate the two grain size populations. Two curves
have been fitted to these populations, but the result appears to
place too many grains in the "coarse" category.
-
hnage Analysis of Duplex Grain Structures
Area % of Grains 30~
25 '
2
1
1
Area % of Grains
305
00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
ASTM Grain Size Number
I Fine C . . . . . - - All Grains /
FIG. 16. The intersection point was moved to ASTM 5, and the two
populations were again separated. The results are better, but it
still looks like too many grains are in the "coarse"
population.
O0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
ASTM Grain Size Number
Fine Coarse - - All Grain8
FIG. 1V. The intersection point was moved to ASTM 4 and the two
populations were again separated. This looks but neither curve
could be claimed to be Gaussian.
change in the analysis results. For the 1430p, m 2 break point,
there are 256 "f ine" grains with an average area of 224.8p, m 2 (G
= 9.17) and a surface area of 19.08%. There are 35 grains in the
"coarse" population with an average area of 6974.7~m 2 (G = 4.21)
covering 80.92% of the area.
For the 2850#,m 2 break point, there are 272 "f ine" grains with
an average area of 332.0Dm 2 (G = 8.60) covering 29.94% of the
area. There are 19 grains in the "coarse" population with an
average area of 11,123. lp, m 2 (G = 3.54) covering 70.06% of the
area.
For the 5700Dm 2 breakpoint, there are 282 "f ine" grains with
an average area of 460.2Dm 2 (G = 8.13) covering 43.02% of the
surface. There are 9 grains in the "coarse" population with an
average area
of 19,096.4p, m 2 (G = 2.76) covering 56.98% of the surface
area. Again, these results demonstrate the critical importance of
se- lecting the proper breakpoint between the two (or possibly
three) populations. Table 6 summarizes all of the grain size
analysis results.
An alternate approach for splitting the populations, suggested
by Peyroutou (per- sonal communication from C. Peyroutou, February
13, 1992), is to use an arithmetic grain class scale, dividing the
grain area range into 25 classes (equal weighting) while again
plotting the number percent and area percent of the grains per
class. The intersection of these two curves would be used to
separate the two populations. Tables 7-10 list the results of such
a clas- sification scheme for the carbon steel, IN-
Table 6 Summary of Grain Size Data
"F ine" pfwulatioll "C~Jarse" population
Avg. Avg. ~rain Break grain Avg.
Number area ASTM point Number area ASTM Area Number ,~rain area
ASTM Area Specimen grains (la, m 2) G '~ (~m 2) ~rains (~,m 2) G
perce~t y, rains (~m 2) (; percent
Carbon Steel 7180 177.6 9.51 5700 7177 164.2 9.62 92.42 3
96,660.4 2.00 7.58 Inconel 718 915 154.4 9.71 356 861 90.6 10.48
55.24 54 1171.1 6.78 44.76
Pyromet 31 323 7172.3 4.17 11,400 270 4246.4 4.93 49.49 53
22,078.1 2.55 50.51 Pyromet 31 18,000 304 5377.2 4.58 70.56 19
35,894.4 1.85 29.44 Modified 625 291 1036.6 6.96 1430 256 224.8
9.17 19.08 35 6974.6 4.21 80.92 Modified 625 2850 272 332.0 8.60
29.94 19 11,123.1 3.54 70.06 Modified 625 5700 282 460.2 8.13 43.02
9 19,096.4 2.76 56.98
a [hese values art' invalid because the grain structures are
dup]ex. They are ]isted for comparison to the G values for the two
populations
-
306 G. F. Vander Voort and J. J. Friel
Table 7 Arithmetic Classes for Carbon Steel Micrograph
Top of Number Area class Number percent Area per class percent
(p,m 2) grains per class (i.um 2) per class
15 0 0 0 0 1957 7166 99.81 1,151,392 90.28 3899 11 0.15
27,306.66 2.14 5841 0 0 0 0 7783 0 0 0 0 9725 0 0 0 0
11,667 0 0 0 0 13,609 0 0 0 0 15,551 0 0 0 0 17,493 0 0 0 0
19,435 0 0 0 0 21,377 0 0 0 0 23,319 0 0 0 0 25,261 2 0.03
48,111.44 3.77 27,203 0 0 0 0 29,145 0 0 0 0 31,087 0 0 0 0 33,029
0 0 0 0 34,971 0 0 0 0 36,913 0 0 0 0 38,855 0 0 0 0 40,797 0 0 0 0
42,739 0 0 0 0 44,681 0 0 0 0 46,623 0 0 0 0 48,565 1 0.01
48,548.96 3.81
7180 1,275,359.06
CONEL al loy 718, Pyromet 31, and mod- i f ied al loy 625 spec
imens , respect ive ly . The area class l imits g iven are the top
of the classes w i th the first class beg inn ing wi th the smal
lest observed gra in areas (15.79, 10.88, 378.07, and 16.051.um 2
for the carbon steel, INCONEL 718, Pyromet 31 and mod- i f ied al
loy 625 spec imens) .
The ar i thmet ic area d is t r ibut ions , show- ing number
percent and area percent data, for the four al loys, are shown in
Figs. 18- 21 (the same spec imen order) . Note that this manner of
p lo t t ing does not reveal the d is t r ibut ion of gra in areas
in the excel lent fash ion of the logar i thmic plots, but it
does
Percent , oo l . Number j 7O
6O 5O 4O 3O
20 - Area % ,O l . . . . . . . . . . . . . . . . . =
1967 7783 13609 19435 25281 31087 36913 42739 48666
Area, sq. ~,Lm
~1 Number % ~11 Area %
Fie. 18. Arithmetic classification of the grain areas into 25
classes showing the number percent and area percent frequency
distributions for the carbon steel specimen. Note that the two
curves intersect at the second size class. This specimen exhibits
two distinct, nonoverlapping grain populations.
Table 8 Arithmetic Classes for Inconel 718 Micrographs
Top of Number Area per Area class Number percent class percent
(l~m 2 ) grains per class (p,m 2) per class
10 0 0 0 0 259 833 91.04 69,616.44 49.28 508 47 5.14 16,580.73
11.14 757 9 0.98 5843.06 4.14
1006 5 0.55 4681.53 3.31 1255 4 0.44 4459.38 3.16 1504 6 0.66
8051.9 5.70 1753 2 0.22 3322.31 2.35 2002 2 0.22 3665.97 2.59 2251
1 0.11 2188.88 1.55 2500 1 0.11 2259.61 1.60 2749 1 0.11 2701.19
1.91 2998 0 0 0 0 3247 1 0.11 3023.09 2.14 3496 0 0 0 0 3745 0 0 0
0 3994 0 0 0 0 4243 1 0.11 4123.88 2.92 4492 0 0 0 0 4741 1 0.11
4528.29 3.21 4990 0 0 0 0 5239 0 0 0 0 5488 0 0 0 0 5737 0 0 0 0
5986 0 0 0 0 6235 1 0.11 6227.53 4.41
915 141,273.79
-
hnage Analysis of Duplex Grain Structures 307
Percent 100
80 i
60
40 Number %
239 1006 1753 2500 3247 3994 4741 5488 3236
Area, sq./.L m
FK;. 19. Arithmetic classification of the grain areas into 25
classes showing the number percent and area percent frequency
distributions for the INCONEL alloy 718 specimen. Note that the two
curves intersect at the second size class. This specimen exhibited
the widest separation of those that had overlapping
populations.
Table 9 Arithmetic Classes for Pyromet 31 Micrographs
Top of Number Area class Number percent Area per class percent
(~m 2) grai~ s per class (~,m 2) per class
378 0 0 0 0 6112 204 63.16 601,787.39 25.98
11,846 69 21.36 578,893.26 24.99 17,580 29 8.98 418,228.02 18.06
23,314 11 3.41 214,252.95 9.25 29,048 4 1.24 109,807.97 4.74 34,782
2 0.62 63,85L6 2.76 40,516 0 0 0 0 46,250 0 0 0 0 51,984 0 0 0 0
57,718 1 0.31 53,909.8 2.33 63,452 1 0.31 59,622.84 2.57 69,186 0 0
0 0 74,920 1 0.31 72,211.13 3.12 80,654 0 0 0 0 86,388 0 0 0 0
92,122 0 0 0 0 97,856 0 0 0 0
103,590 0 0 0 0 109,324 0 0 0 0 115,058 0 0 0 0 120,792 0 0 0 0
126,526 0 0 0 0 132,260 0 0 0 0 137,994 0 0 0 0 143,728 1 0.31
143,722.13 6.20
323 2,316,287.09
Table 10 Arithmetic Classes for Modified 625 Micrograph
Top of Number Area per Area class Number percent class percent
(#,m 2) ~{rains per class (p.m 2) per class
16 0 0 0 0 1952 262 90.03 67,690.2 22.44 3888 13 4.47 33,048.24
10.96 5824 7 2.41 29,045.71 9.63 7760 1 0.34 7249.41 2.40 9696 0 0
0 0
11,632 1 0.34 10,471.11 3.47 13,568 1 0.34 12,969.25 4.30 15,504
2 0.69 29,041.13 9.63 17,440 1 0.34 17,237.37 5.71 19,376 1 0.34
19,096.67 6.33 21,312 0 0 0 0 23,248 0 0 0 0 25,184 0 0 0 0 27,120
0 0 0 0 29,056 1 0.34 27,397.08 9.08 30,992 0 0 0 0 32,928 0 0 0 0
34,864 0 0 0 0 36,800 0 0 0 {} 38,736 0 0 0 0 40,672 0 0 0 0 42,608
0 0 0 0 44,544 0 0 0 0 46,480 0 0 0 0 48,416 1 0.34 48,405.7 16.05
50,352 0 0 0 0
291 301,651.87
separate the populat ions. Note that in each case, the area
percent and number percent curves cross in the second grain area
size class. Hence, the upper l imit of the second class (see Tables
7-10) was used as the di- v id ing point between the "f ine" and
"coarse" populat ions . The area % of fine and coarse and the
average grain size of the fine and coarse grains were determined as
before, but based on these limits.
For the carbon steel spec imen with two very distinct, well
separated populat ions , the ar ithmetic 25 class method gave the
same break between the two popu la t ions as by the logarithmic
method. This result
-
308
Percent 70
5O
4O Number %
30
2o ~ e a %
100 II1 , i J . , , , , ,, I I I I I I I
6112 23314 40618 67718 74920 92122 109324 126528 143721
Area. sq././,m
FIG. 20. Arithmetic classification of the grain areas into 25
classes showing the number percent and area percent frequency
distributions for the Pyromet 31 specimen. Note that the two curves
intersect at the second size class. This specimen exhibited more
tightly overlapped grain area populations than the alloy 718
specimen.
Percent 100
60
Number % 40
ao ~ Area % ,s
o1 , . . . . . . . / I 1982 77804 13568 19378 25184 30992 368004
426086 464168
Area. sq.lZ, rn
FIG. 21. Arithmetic classification of the grain areas into 25
classes showing the number percent and area percent frequency
distributions for the experimental modified alloy 625 specimen.
Note that the two curves intersect at the second size class. This
specimen ex- hibited the most complex, overlapped grain area pop-
ulations of the four specimens.
G. F. Vander Voort and J. J. Friel
should be expected. Table 11 summarizes the final grain size
results for the carbon steel specimen, which are identical to that
shown in Table 6 based on the logarithmic plots.
For the alloy 718 specimen, the arith- metic 25 class method
broke the two pop- ulations at 508p~m 2 yielding 61% of the grain
area (880 grains) at G = 10.36 and 39% of the grain area (35
grains) at G = 6.36. These results are quite close to those
obtained before, shown in Fig. 8, where the break was at 356~m 2
producing 55.24% of the grain area (861 grains) at G = 10.48 and
44.76% of the grain area (54 grains) at G = 6.78. This degree of
disagreement is rather small and might be satisfactory for most
work.
For the Pyromet 31 specimen, the arith- metic class approach
split the populations at 11,846~m 2 which yielded 51% of the grain
area (273 grains) at G = 4.9 and 49% of the grain area (50 grains)
at G = 2.5. These results are fairly close to that of the first
logarithmic split at 11,400~m 2 (Fig. 11), which yielded 49.49% of
the grain area (270 grains) at G = 4.93 and 50.51% of the grain
area (53 grains) at G = 2.55. The al- ternative logarithmic split
at 18,000~m 2 (Fig. 12) produced substantially different results.
It may be difficult to determine, unambiguously, which split is
most cor- rect. Note that the grain size numbers ap- pear to be
less affected by the different breakpoints than the area percents
of each population.
Table 11 Summary of Grain Size Data Using Arithmetic Classes
Avg. grain Break
Number area ASTM point Number Specimen grains ( p.m 2) G" ( ~m 2
) grains
"Fine" population "'Coarse" population
Avg. grain Avg, area ASTM Area Number grain area ASTM Area
(~m 2) G percent grains (~m 2) G percent
Carbon Steel 7180 177.6 9.51 3899 7177 164.2 9.62 92.42 3
32,220.1 2.00 7.58 Inconel 718 915 154.4 9.71 508 880 97.95 10.36
61.0 35 1573.6 6.36 39.0 Pyromet 31 323 7172.3 4.17 11,846 273
4324.8 4.9 51.0 50 22,712.1 2.50 49.0 Mod. 625 291 1036.6 6.96 3888
275 366.3 8.46 33.4 16 12,557.1 3.36 66.6
a These values are invalid because the grain structures are
duplex. They are listed for comparison to the G values for the two
populations.
-
Image Analysis of Duplex Grain Structures 309
For the modified alloy 625 specimen, the arithmetic area class
approach suggested splitting the populations at 3888p, m 2 which
yielded 33.4% of the grain area (275 grains) at G = 8.46 and 66.6%
of the grain area (16 grains) at G = 3.36. These results are be-
tween the logarithmic split at 2850~,m 2 and 5700p, m 2, shown in
Figs. 16 and 17, respectively.
Separation of the populations by the arithmetic grain area
distribution based on 25 classes and the intersection of the num-
ber percent and area percent curves worked well for the carbon
steel and alloy 718 microstructures but did not appear to be
satisfactory for the Pyromet 31 and mod- ified alloy 625
microstructures. Results with the arithmetic approach were only
slightly better than with the logarithmic approach. It seems
coincidental, however, that in all four cases using the arithmetic
25 class approach, the intersection point of the number percent and
area percent curves occurred in the second area class. Because this
is an empirical approach, there is nothing fundamental in nature
about the choice of 25 classes. The greater the number of classes,
the smaller are the area increments and the greater the dis-
crimination potential. Additional work will be performed to
determine how variations in the number of area classes influence
the separation of grain populations. Also, these methods should be
performed on data from specimens with unimodal grain size
distributions.
DISCUSSION
The work showed that the IMAGIST could recognize annealing twins
as long as they are "classic" in appearance. Curved twins could not
be recognized. Fortunately, the vast majority of twinned austenite
grains have straight twin boundaries.
In this work, the area occupied by the grain boundaries was
ignored, i.e., the grain interiors were measured. In manual
methods, the area occupied by the grain boundaries does not
influence the analy- sis. With image analysis, the grain bound-
aries cannot be made thinner than one pixel width; and, because of
pixel shape and grain separation problems, bounda- ries probably
should not be thinned to less than 2 pixel widths. Consequently,
de- pending upon the grain size and magni- fication, the grain
boundaries will occupy from about 6 to 12% of the field area. Thus,
each grain will be undersized slightly, pro- ducing a small bias in
the data. This bias is estimated as about a 0.2 increase in the
ASTM grain size number. For the majority of measurements, this
degree of error is insignificant.
One approach to eliminate this minor degree of bias would be to
dilate each iso- lated grain by one pixel before measure- ment of
its area. For such work, if the grain boundaries are thinned to a
two pixel width, dilation of each grain by one pixel should,
statistically, reduce the grain boundary area to zero. This
technique needs to be developed and evaluated.
Measurement of grain areas for pur- poses of evaluating the
nature of the grain size distribution (normal versus bimodal) is
ideal. Only grain areas and grain inter- cept lengths can be
directly related to the ASTM grain size number. Other measure-
ments could be made that would reveal the nature of the
distribution, but none of these can be used to compute G for each
population. Grain intercept length mea- surements would generate
much more data for the same number of grains, and analysis would be
less efficient.
Use of the grain areas relative to the ASTM grain size scale for
establishing his- togram classes is ideal for revealing the na-
ture of the distribution. This produces a logarithmic scale on a
linear plot. Because grain areas exhibit an approximately log-
normal distribution, use of ASTM grain size numbers on a linear
scale produces a Gaussian distribution curve if the grain size
distribution is unimodal. Non-Gaus- sian distributions are readily
observed
-
310 G. F. Vander Voort and J. J. Friel
using this approach, but only if an area- weighted distribution
is plotted.
The work clearly demonstrates the su- periority of an
area-weighted histogram over a numerical frequency histogram of the
grain areas. The duplex condition must be extreme before the number
percent his- togram suggests that the distribution is not unimodal.
In comparison, the area percent histogram is quite sensitive.
In general, the area-weighted histogram could be used, by
itself, for deciding how to separate the two populations when a
duplex condition is present. In this work, we started by using the
intersection point between the number percent and area per- cent
histograms. However, this approach is not always useful. For the
carbon steel specimen, the area percent histogram showed that there
were two distinct pop- ulations present, split at about ASTM 4.
However, the intersection between the number percent and area
percent histo- gram curves occurred at about ASTM 9.
Better analytical methods are required to separate duplex grain
area populations using a logarithmic grain size scale, unless there
is a very clear, nonoverlapping type distribution. The test results
suggest that measurement of about 1000 or more grains would be
adequate for most work. This should produce a reasonably good
histo- gram curve. Then, mathematical decon- volution methods (not
presently available with image analysis software packages) could be
applied. This should be a more objective, reproducible approach.
Future work should concentrate on this problem.
The use of an arithmetic grain area scale with 25 classes for
splitting the popula- tions, based on the intersection of the area
percent and number percent curves, pro- duced only marginally
better results than the same approach using the logarithmic scale
based on the ASTM grain size num- bers. The arithmetic approach
worked bet- ter for the case of well-separated, non- overlapping
populations, as exhibited by the carbon steel microstructure. For
the arithmetic method, the number of classes chosen will influence
the breakpoint and
the results, except for a structure with two distinct
populations. There is nothing fun- damental to the choice of 25
classes, but it does represent a good practical choice. Sensitivity
is improved by increasing the number of classes, but many more
grain measurements would be required as the number of classes is
raised beyond 25. Fur- ther work is recommended using this
approach.
CONCLUSIONS
Annealing twins with straight interfaces can be recognized and
deleted from the image using appropriate software. Grain size
distributions are best evaluated using grain area measurements that
can be di- rectly related to the ATM grain size num- ber. Intercept
lengths could be used, but the amount of data would be much greater
for the same number of grains, making analysis less efficient.
Because G is a func- tion of the grain area, histogram classes can
be based on the ASTM grain size scale. Such a classification yields
an ideal number of classes for histograms. The area- weighted
histogram was shown to be ex- cellent for revealing the nature of
the grain size distribution, while the numerical fre- quency
histogram was insensitive. Also, because the area percent of each
popula- tion is required, the area percent histogram is ideal.
The work has demonstrated the need for future work. First, grain
boundaries in etched specimens cover about 6-12% of the surface
area on most specimens. In reality, grain boundaries are only a few
atom diameters in width, although etching widens them
substantially. Manual meth- ods for measuring grain size are
essentially insensitive to the area per field occupied by the grain
boundaries. Although the bias introduced is small, and for many
pur- poses could be ignored, image analysis methods could be
developed to reduce the grain boundary area. Even though the error
is small, we should try to reduce it further.
-
Image Analysis qf Duplex Grain Structures 311
The micrographs chosen for this work exhibited a range of duplex
conditions. The carbon steel specimen had two dis- tinct,
nonoverlapping grain size distribu- tions. The arithmetic approach
separated these nicely based on the intersection of the number
percent and area percent curves. This was not the case for the log-
arithmic approach, where the intersection point was wrong. The
INCONEL alloy 718 specimen exhibited overlapping popula- tions, but
they were better separated than that of the Pyromet 31 specimen or
the very complex distribution of the modified alloy 625 specimen.
Both approaches worked well for separating the populations for the
alloy 718 specimen, but neither worked well for the Pyromet 31 or
the modified alloy 625 structures. Use of mathematical
deconvolution techniques on only the log- arithmic area percent
plot (using the ASTM grain size scale) appears to be the best ap-
proach for developing a good way to split the populations.
References
1. G. F. Vander Voort, Grain size measurement, Practical
Applications of Quantitative Metallography, ASTM STP 839, ASTM,
Philadelphia, (1984), pp. 85-131.
2. Z. Jeffries, A. H. Kline and E. B. Zimmer, The determination
of grain size in metals, Trans. A IME 54:594-607 (1916).
3. Z. Jeffries, Grain-size measurements in metals, and
importance of such information, Trans. Far- aday Soc. 12:40-56
(1916).
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Received February 1992; accepted May 1992.