Vander 1992

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 percent 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 metallurgy because of the influence of grain size on properties and behavior. Manufactur- ers seek to control the grain size within certain limits, chosen based on the specific properties required. Measurement is required to verify control. Likewise, in structure-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 commonly, 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 methods. 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 requires 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)

294 G. F. Vander Voort and J. J. Friel

is necessary to control the grain size more tightly and, therefore, greater measurement 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 manually 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 diameter. 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 determined. To obtain an accurate count, the triple points must be marked, in the same manner as grains are marked in the planimetric method. This method, however, is rarely used.

The previous three measurement methods - the planimetric, intercept, and triple-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 directly 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 number 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-normal distribution [11]. Serial sectioning [12- 18], although extremely tedious, repre- sents another approach for performing spatial grain size analysis, and these studies also confirmed the log-normal distribution of grain volumes.

Planar grain size is far easier to determine 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 distribution 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 produce 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 instances where bimodal (duplex) distributions arise, e.g., in partially recrystallized specimens [1, 20, 21]. A number of types

Image Analysis of Duplex Grain Structures 295

of bimodal distributions have been observed. 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 boundaries are ignored.

However, progress in discrimination between twin boundaries and grain boundaries by image analysis is being made [23, 24] using an artificial intelligence (AI) approach. 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 intercept 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 average 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 number of grains. Frequency histograms would show whether the structure was unimodal or bimodal in each case, but the data cannot be used to determine the mean ASTM grain size number of the unimodal distribution, or of each portion of a bimodal distribution.

Grain intercept lengths could be measured 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 exponential 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 individual grain areas, can be converted to an equivalent ASTM grain size number G.

EXPERIMENTAL PROCEDURE

Seven 8 x 10in. micrographs of five different alloys depicting various types of du-


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 microstructure 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 example of a random duplex type with isolated coarse grains in a fine-grained matrix. Two micrographs of INCONEL (INCO- NEL is a registered trademark of INCO A1-


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 micrographs. 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 recrystallized 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 present in certain grains in the Mod. 625 and the SCF-19 specimens. Figure 2(a,b) shows two of these structure before and after digitization, image cleaning, and twin removal (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 curvature [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 removed (when present), the grain areas were measured. Additional measurements of each grain, such as their average diameter, maximum diameter, perimeter, etc., were made but are not reported.

The grain areas were grouped in histogram fashion based on the relationship between 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 distribution 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

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.

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 separated 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 determined using the average area of the actual 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 intersected 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


FIG. 3. Number-weighted (top) and area-weighted (bottom) histograms of the grain areas converted to their equivalent ASTM grain size number for the carbon steel specimen. Note that the area-weighted histogram clearly reveals two distinct grain size populations.


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 distributions very close to a log-normal distribution. When the areas are scaled in a logarithmic manner, rather than in linear fashion, 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 percent) over a numerical frequency size distribution (number percent). The area fraction 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, because 0.04% will not be visible on the Y axis. The value of an area-weighted distribution 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 percent curve. For this type of duplex condition with two distinct populations, the intersection 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 measurements. The total area of the large grains was 96,660.4~m 2. For the determination 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


I - . , . o ..... i

FIG. 5. Two separate Gaussian curves have been plotted for the two grain size populations for the carbon steel specimen.

Image Analysis Of Duplex Grain Structures 301

= 2.00) and 164.21xm 2 (G = 9.62) for the coarse- and fine-grained regions. The average 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 micrographs. Figure 6 shows the number percent 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 condition. The area percent histogram, however, clearly reveals a bimodal condition.

Figure 7 shows the two histograms super imposed on the same axis. Again, the number percent histogram is shifted toward the finer grain sizes. The two histogram 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


Ares % of Grains 25

0 2 3 4 5 e 7 8 9 10 11 12 13 14 15


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 overlapping 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


FIG. 7. The histograms in Fig. 6 have been super- imposed to demonstrate the differences between the two plots.

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 micrographs of Pyromet 31. This is an example of a random, wide-range type duplex 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 number. The number percent plot shows a slight left-hand tail at low grain size numbers. 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 plotted on the same axes. As before, the number 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 adequate 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 separate 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 fitted 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 between 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 average 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


experimental modified alloy 625 that exhibited 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 percent 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 pronounced 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 histogram 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


FIG. 13. Number-weighted (top) and area-weighted (bottom) histograms of the grain areas converted to their equivalent ASTM grain size number for the modified 625 specimen, which had a "necklace" type duplex 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


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


..... 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


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


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 selecting 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 classification 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


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 , showing 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 exhibited the most complex, overlapped grain area populations 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 arithmetic 25 class method broke the two populations 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 arithmetic 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 appear 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.


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 between 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 number 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 modified 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 discrimination 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 analysis. With image analysis, the grain boundaries cannot be made thinner than one pixel width; and, because of pixel shape and grain separation problems, boundaries probably should not be thinned to less than 2 pixel widths. Consequently, de- pending upon the grain size and magnification, the grain boundaries will occupy from about 6 to 12% of the field area. Thus, each grain will be undersized slightly, producing 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 isolated grain by one pixel before measurement 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 purposes of evaluating the nature of the grain size distribution (normal versus bimodal) is ideal. Only grain areas and grain intercept lengths can be directly related to the ASTM grain size number. Other measurements 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 measurements 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 histogram classes is ideal for revealing the nature 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


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 histogram 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 percent histograms. However, this approach is not always useful. For the carbon steel specimen, the area percent histogram showed that there were two distinct populations present, split at about ASTM 4. However, the intersection between the number percent and area percent histogram 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 histogram curve. Then, mathematical deconvolution 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 populations, based on the intersection of the area percent and number percent curves, produced only marginally better results than the same approach using the logarithmic scale based on the ASTM grain size numbers. The arithmetic approach worked better for the case of well-separated, nonoverlapping 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 fundamental 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 directly related to the ATM grain size number. 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 function 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 excellent for revealing the nature of the grain size distribution, while the numerical frequency histogram was insensitive. Also, because the area percent of each population 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 methods 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 purposes 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 distinct, nonoverlapping grain size distributions. 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 logarithmic approach, where the intersection point was wrong. The INCONEL alloy 718 specimen exhibited overlapping populations, 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 logarithmic area percent plot (using the ASTM grain size scale) appears to be the best approach for developing a good way to split the populations.

References

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25. ASTM E1382-91: Standard Test Methods for Deter- mining Average Grain Size Usin~ Semiautomatic and Automatic Image Analysis.


26. C. Peyroutou and Y. Honnorat, Characterization of alloy 718 microstructures, in Superalloys 718,625 and Various Derivatives, The Minerals, Metals & Materials Society, Warrendale, PA, (1991), pp. 309-324.

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Received February 1992; accepted May 1992.

Vander 1992

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