23 / 82
A D V A N C E D
M A T E R I A L S
&
P R O C E S S E S | F E B R U A R Y / M A R C H
2 0 1 7
2 3
TABLE 3—BINNING OF GRAIN AREAS BY G CLASS FOR 26-1 FERRITIC STAINLESS STEEL
G 1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
% 0
3.5 16.3 24.4 20.6 17.4 10.4 3.7 0.7 0.1 0.08 0.008 0.011 0.004 0.003
Area
No. grains ∑ grain areas, μm
2
Avg. grain area, μm
2
ASTM G, all grains
No. of G classes
339
804,976.1
2374.6
5.7
14
Fig. 6
—
Grain size distribution for 26-1 fer-
ritic stainless steel revealing non-Gaussian
grain size distribution, but without a clear bi-
modal, or duplex, grain size distribution. The
distribution covers 14 grain size classes with
a mean grain size of ASTM G = 5.7, which can
arbitrarily be divided into two classes with
47.1% of the grains having a mean grain size
of G = 3.7 and the balance with a mean grain
size of 6.5. A skew of 3.59 and kurtosis of
18.62 is non-Gaussian.
TABLE 4—BINNING OF GRAIN AREAS BY G CLASS FOR SC-19 AUSTENITIC STAINLESS STEEL
G 1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
% 0
28.2 17.3 12.3 6.97 5.08 2.77 2.6 4.19 6.4 6.5 4.29 2.1 0.99 0.38
Area
No. grains ∑ grain areas, μm
2
Avg. grain area, μm
2
ASTM G, all grains
No. of G classes
3901
578,437.1
148.28
9.77
14
Fig. 8
—
Bimodal grain size distribution in
partially recrystallized SCF 19 austenitic
stainless steel covering 14 grain size classes
where the mean grain size of all grains is
9.77, although such a measure is of no value
due to the duplex grain size distribution.
the maximum value of 5 for a normal
distribution. The grain size distribution
curve with a slight hump to the right of
the maximum value is shown in Fig. 6.
The mean overall grain size is G = 5.7.
The distribution curve is not bimodal,
and although not justified, it could be
broken into two parts and calculated
that 47.1% of the grains have a mean
grain size of G = 3.7, while 52.9% have a
mean grain size of G = 6.5.
Example 3.
Figure 7 shows a bi-
modal grain size distribution called a
necklace distribution in SCF-19* auste-
nitic stainless steel. The specimen was
cold reduced 10% in thickness and solu-
tion annealed at just 900°C, while the
recommended solution annealing tem-
perature is 1180°C. Grain boundaries
were selectively electrolytically etched
using aqueous 60% nitric acid at 1 V
dc for 60 s (annealing twin boundaries
are not revealed using this etch and
voltage). Table 4 contains the area per-
centage of grains per G class, covering
14 G classes, for 3901 grains measured.
The skew for the distribution shown in
Fig. 8 is 16.96 and the kurtosis is 320.04,
a very high value. The distribution is
clearly bimodal with 71.2% of the grain
area having a mean grain size of G = 4
and 28.8% having a mean grain size of
G = 11.5.
~AM&P
*Note: E-Brite 26-1 is a registered trade-
mark of ATI Allegheny Ludlum. SCF-19
is a registered trademark of Carpenter
Technology Corp.
For more information:
George F.
Vander Voort is a consultant for Stru-
ers Inc., 24766 Detroit Rd., Cleve-
land,
OH
44145,
847.623.7648,
georgevandervoort@hotmail.com,
www.georgevandervoort.com.
Fig. 7
—
SCF 19 austenitic stainless steel with a bimodal necklace-type grain structure
due to partial recrystallization after cold working: (a) partially recrystallized grain structure
etched using aqueous 60% nitric acid at 1 V dc for 60 s (100×); (b) detection of grain areas by
image analysis.