Abstract

Manual stereological methods and conventional image analyzer are sometimes difficult and time-consuming to obtain the informative data for some complicated microstructures in metals. To solve these problems, a computer assisted quantitative analysis was explored. Several examples, including the measurements of fine-scale ferrite grain size and pre-eutectoid ferrite volume fraction in low carbon steel, the determination of particle parameters in intermetallic matrix composite and the investigations of recrystallization dynamics and grain growth during annealing in ordered alloys, are presented. Also the error was evaluated.

Keywords:Quantitative metallography, Microstructure, Metals, Low carbon steel, Intermetallic matrix composites, Intermetallics

1. Introduction

Quantitative metallography plays very important role in materials science and engineering [1,2] . It can provide relations between processes, microstructures and mechanical properties and supply the first hand data that is necessary and important to establish a reasonable mathematical model. It enables the costly trial and error method to be replaced by a scientifically based experimental procedure resulting in the improvement of known materials and the development of new ones.

The manual quantitative metallography is sometimes difficult, tedious and time-consuming especially when the microstructure is complicated or of a fine scale. The automatic measurement of an image analyzer can give inaccurate data if the microstructure has a bad contrast or the analyzed features have a discontinuous outline. Recent fast development of computer techniques improve image processing remarkably [3,4]. Several famous softwares such as Corel Paint and Adobe PhotoShop have commercially been developed for image improvement. In the meantime the softwares such as ImageTool has also been developed for quantitative analysis of image. These achievements supply other approaches to quantitative metallography. In comparison with conventional methods the use of computer techniques offers much more flexibility: it can not only perform measurement automatically, but also self-automatically (described later).

For the use of computer techniques the essential problem is that the measurement of images generally requires that features of interest be well defined, either by edges or unique brightness or color. The present work will illustrate these by presenting several typical examples in metal materials science with the focus on the descriptions of methods to obtain the first hand data:

The measurement of ferrite grain size and pearlite volume fraction in the fine scale ferrite-pearlite microstructure and the quantitative analysis of pre-eutectoid ferrite in low carbon steel.
The determination of particle parameters in Fe₃Al-5%Cr based composites (unless otherwise stated, every composition is given as atom percent).
The characterization of recrystallization dynamics and grain growth dynamics in advanced intermetallic materials.

2. Ferrite grain size and pearlite volume fraction in the fine scale ferrite-pearlite microstructure

Grain size is a very important parameter to characterize the microstructure. It can set up the quantitative relation between the microstructure and mechanical properties. A famous example is the Hall-Patch equation:

(1)

Where s is flow stress,s₀ is lattice friction stress, k is constant and d is grain size.

Steel	C	Si	Mn	S	P	N	O
C-Mn	0.19	0.20	0.61	0.023	0.019	0.0045	0.019
Table 1: Chemical compositions of carbon steel used, wt%

Table 1 lists the composition of the low carbon steel (SS400) investigated. The rods with a diameter about 10 mm were produced by forging the continuous cast slab with a size of 80 mm´80 mm at 1250° C and followed by air cooling. The cylindrical specimens with a size of 8 mm (diameter)´ 15 mm (height) were cut from the rod. The fine scale ferrite-pearlite microstructure was produced by heavy deforming the specimen with a true strain about 1.6 who was cooled from the austenitising temperature 900°C to the deformation temperature 770°C at a cooling rate of 50°C/s. The microstructural observations were carried out using optical microscopy after polishing the sections and etching them in a 3% nital solution.

Fig 1a	Fig 1b
Fig 1: Fine scale ferrite-pearlite microstructure in the low carbon steel SS400 heavily deformed at 770°C, (a) original optical microstructure; (b) after image processing.

Fig. 1(a) gives the optical microstructure of fine scale ferrite-pearlite microstructure. Two frustrating problems arise for quantifying the microstructure. First, due to the small ferrite grains and pearlite (less than 5 mm), manual measurements may need to be performed at magnifications ranging from 500´ to 1000´ . At these magnifications, the problem of diffuse reflectivity results in a low contrast between grains and boundaries. Second, the fine pearlite with an appearance of island locates along ferrite grain boundaries or at triple junctions. When human counting of the intercepts is performed to measure the ferrite grain size considerable judgements must be employed to subtract that produced by pearlite.

After acquiring the image by scanner two methods can be taken to measure the ferrite grain size. One is to measure the grain size self-automatically by drawing a line on every grain using image analysis software. In many cases it is popular because people can judge the grain outline accurately. Another is to measure the grain size automatically by computer. In order to improve the precision an image processing is necessary, including thresholding, painting and delineating the grains if the boundaries are incomplete [5] . The data obtained shows that the results are very close for these two methods. The ferrite grain sizes are 3.3± 0.1 mm and 3.6± 0.1 mm for the self-automatic and automatic methods, respectively.

In practical applications the precipitation of second phases or second microstructure is often used to adjust the steel properties. The steels can be strengthened by the precipitation of carbide or pearlite. Therefore, a determination of their parameters is important. Here the measurement of pearlite volume fraction is taken as an example (Fig. 1(a)). It is not easy to accomplish it by manual stereological methods. However, we can extract the pearlite parts from the overall matrix by adjusting the image contrast, thresholding the image and painting the part of pearlite with the assistance of computer (Fig. 1(b)). The area fraction of pearlite with black can effortlessly be evaluated by the image analysis software. The volume fraction 20.2% is obtained. It is 23.0% calculated from Fe-C equilibrium diagram.

3. Volume fraction of pre-eutectoid ferrite (Widmannstatten microstructure)

During fast cooling from the austenite region the Widmannstatten microstructure, which is often harmful to the mechanical properties, is easily formed in low carbon steels. Its appearance with coarse and irregular acicular shape makes it very difficult to measure its volume fraction by manual stereological methods. Fig. 2(a) gives the original image in which two types of microstructure exist: ferrite (Widmannstatten microstructure) and martensite. The low carbon steel investigated is the same as that described in the section 2. The pre-eutectoid ferrite was formed by cooling the specimen from the austenitising temperature 900°C to 650°C at a rate of 50 °C/s, and then water quenched.

Fig 2a	Fig 2b
Fig 2: Morphology of pre-eutectoid ferrite in the low carbon steel SS400 cooled from 900°C, (a) original optical microstructure; (b) after image processing.

The ferrite is delineated with the use of magic wand mask and freehand mask tools and then painted by black color in the image processing software (Fig. 2(b)). After finishing the delineation the quantitative measurement could be done in a few seconds. The ferrite volume fraction measured is about 49.3%.

4. Reinforcement parameters in the Fe₃Al-based composites

The hard particles such as oxides, carbides and borides are often added to the metals and single phase alloys to obtain a strengthening effect, which greatly depends on their volume fraction, aspect ratio and distribution in the matrix. The quantitative analysis plays a very important role in modeling the mechanical properties as a function of particle parameters [6] . Iron aluminides with a composition near Fe₃Al are promising for applications used as oxidation and sulfidation resisting steel-like materials at ambient and intermediate temperatures [7]. However, they have a poor strength above the critical temperature of about 600° C. The addition of hard particle TiB₂ can increase the high temperature strength. The Fe₃Al-5%Cr alloy containing TiB₂ particles was melted by Exo-melting in vacuum. The microstructural observations were conducted using scanning electron microscopy (SEM) after polishing the specimens.

Fig 3: Cast microstructure of the Fe3Al-5%Cr alloy containing TiB2 particles, (a) no image processing; (b) after image processing.

Fig. 3(a) shows the cast microstructure. The large contrast difference between the particle and the matrix makes it easy to extract the particles by thresholding (Fig. 3(b)). The volume fraction of TiB₂ is determined to be 12.9%. Providing that the densities are 6.7 g.cm^-3 and 4.6 g.cm^-3 for Fe₃Al and TiB₂, respectively, a weight percent of 9.2% can be calculated for TiB₂. The lengths of major axis and minor axis are 11.9 mm and 6.2 mm, respectively. The corresponding aspect ratio is 1.8. It should be noted that particle touching affects the measurement precision. The computer may consider touching particles as one particle. Although this can not affect the determination of area fraction the aspect ratio may be misunderstood. Increasing the magnification to separate the particles can alleviate the error. Another effective method is to differentiate the touching particles using erosion function. Fig. 4 shows a comparison for the Fe₃Al-5%Cr alloy containing TiB₂ particles with and without erosion (see where pointed by the arrows).

Fig 4: TiB2 clustering in the Fe3Al-5%Cr alloy containing TiB2 particles, (a) without erosion; (b) with erosion.

5. Recrystallization dynamics in the Fe₃Al-based alloy

The determination of recrystallization volume fraction is absolutely necessary to check or establish recrystallization dynamic model. In general, there is no difference in contrast between the unrecrystallized and recrystallized regions. People must judge the recrystallized part when they measure its volume fraction with manual stereological methods. It is not possible to automatically distinguish them by conventional image analyzer. However, by using functions such as freehand mask and magic wand mask the outline of recrystallized or unrecrystallized parts can be sketched easily.

Fig 5a	Fig 5b
Fig 5: Recrystallized microstructure in the Fe3Al-5CrZrMoNbB alloy annealed at 750°C for 15 min. (a) original optical microstructure; (b) after image processing.

A typical example is given in Fig. 5. The Fe₃Al-5%Cr-0.1%Zr-0.5%Mo-0.5%Nb-0.05%B alloy used was prepared by vacuum induction melting. After homogenization at 1000° C for 24 h the ingot was forged to bars at 1000° C in air. Rolling processing sequences in the temperature range from 850° C to 600° C were then carried out and sheets of 2 mm thickness were obtained with a warm reduction of about 60%. The specimens cut from the sheets were annealed at 750°C with various times in order to investigate the recrystallization dynamics. All specimens were water quenched after annealing. The microstructural observations were conducted on the longitudinal sections using optical microscopy.

Fig 6: Plot of as a function of in the Fe3Al-5CrZrMoNbB alloy annealed at 750°C.

The results obtained by the image analysis software are presented in Fig. 6. It was reported that the recrystallization dynamics in intermetallics follows the Kolmogorov-Johnson-Mehl-Avrmi (KJMA) relationship as conventional metals or alloys [8,9]:

(2)

Here the F_v is the volume fraction of recrystallized grains during the time t and B and k are constants. Equation (2) may be written as:

(3)

If plotting a linear relation should be obtained. Fig. 6 confirms that the recrystallization dynamics in Fe₃Al-based alloys follows the KJMA equation in the same way. The least-square line that fits these data points yields a value of 0.63± 0.06 for k. It is comparative with other intermetallics such as Ni₃Al (0.8 to 1.0) , but much lower than conventional metals or alloys for which the k value is often 3 [11].

6. Grain growth in the Fe₃Al-based alloys

The microstructural refinement can improve the room temperature mechanical properties. It is interesting to investigate the dynamics of grain growth during annealing. Quantitative analysis of grain growth can not only setup the relationship between microstructure and mechanical properties, but can also be used for the thermomechanical process.

The recrystallized grains are formed at the original grain boundaries or at the deformation bands at the early stage. Their distribution appears disperse and discontinuous, leading to some difficulties for the manual intercept counting. For a conventional image analyzer it seems to be impossible to measure the grain size automatically because it can not distinguish which is the recrystallized grain. At that time the image processing with computer assistance is necessary in order to release people from this tedious and time-consuming work. With the assistance of freehand mask and magic wand tools and edging, filling and painting techniques, the recrystallized grains can be traced out and their size can be determined by the image analysis software automatically. In fact, the recrystallized grain size can be measured self automatically as described before (see section 2). The results obtained are close for these two methods. Fig. 7 gives the plot of (D is grain size) as a function of (t is annealing time). There is a linear relationship between them with a slope "n" of 0.18± 0.01, indicating that the measured data fits the basic equation:

(4)

Where C and n are constants. This is in agreement with the grain growth dynamics in conventional metals or alloys for which "n" value ranges from 0.20 to 0.40. Some other intermetallics such as Ni₃Al were reported to have the same result with "n" value 0.18 to 0.27 [10].

Fig 7: Plot of as a function of in the Fe3Al-5CrZrMoNbB alloy annealed at 750°C.

7. Error evaluation

It is not difficult to decrease the statistical error because the computer can do a large amount of measurements if you would. There is no any problem for the statistical confidence degree to arrive at a level of 95%. The error mainly comes from systematic error. It greatly depends on whether the analyzed objects are well defined. Other errors come from the microstructural duplication. It can be decreased by adjusting the machine to obtain a well state.

8. Conclusions

With the assistance of readily available computer image processing and analysis techniques the quantitative analysis of some typical microstructures in metal materials, which are difficult or time-consuming for manual stereological methods and conventional image analyzer, can be carried out with a high efficiency. The measurement error mainly depends on whether the analyzed objects are well defined.

Acknowledgements

The authors are grateful to University of Texas Health Science Center in San Antonia for the supply of free image analysis software Image Tool version 2.0. Thanks are also expressed to the authors of this software Don Wilcox, Brent Dove, Doss McDavid and David Greer. The research was supported by IUAP (Interuniversity Poles of Attraction) project P4/33, Belgium.

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