Use An Inverse Algorithm For 2D-3D Particle Size Conversion. And Its Application To Non-Metallic Inclusion Analysis In Steel

Use An Inverse Algorithm For 2D-3D Particle Size Conversion And Its Application To Non-Metallic Inclusion Analysis In Steel Simon N. Lekakh, Vivek Tha...
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Use An Inverse Algorithm For 2D-3D Particle Size Conversion And Its Application To Non-Metallic Inclusion Analysis In Steel Simon N. Lekakh, Vivek Thapliyal and Kent Peaslee Missouri University of Science & Technology 1400 N. Bishop, Rolla, MO, 6409 Phone: 573-341 6469 Email: [email protected]

Keywords: Particle size, non-metallic inclusions, inverse converter ABSTRACT Modern automated SEM/EDX analysis provides morphological and chemistry statistics for precise determination of phases, porosity and non-metallic inclusions using two-dimensional observations (polished random sections). However, the knowledge of the real three-dimensional distribution of these features in the microstructure is necessary for metallurgical process analysis and product property predictions. A special algorithm for the conversion of two-dimensional round particle distribution obtained from an automated SEM/EDX or optical imaging to the real three-dimensional spherical particle distribution was developed based on inverse modeling. A program generates a virtual two-dimensional distribution from 9-12 sets of normal distributions of spherical particles covering all size ranges using arbitrary slicing. These sets are optimized by comparison with particle sections observed in experiments. The applied inverse algorithm uses the built-in optimizer and error function in EXCEL. The method was applied for three-dimensional analysis of near spherical phases and inclusions in different iron alloys. In ductile iron with spherical graphite, the method revealed that spheroids could be mono or poly-dimensional depending on solidification kinetics. In high-alloyed Al-Mn steel, different dimensional classes of nitrides, sulfides and oxides were observed and related to the free energy of formation. INTRODUCTION The knowledge about the real three-dimensional geometrical topology and chemical composition of phases and non-metallic inclusions in steel are important for advanced analysis of metallurgical process and product property predictions. There are two possible ways to obtain the real three-dimensional distribution of phases: (i) to employ three-dimensional instrumental methods and procedures or (ii) to convert two-dimensional experimental statistics, obtained from a random section, into the real three-dimensional data. These methods are schematically shown in Figure 1. The known three-dimensional structure analysis methods can be divided into several main groups including: -extraction methods1, based on full or partial dissolution of the metal matrix followed by direct observation of the not dissolved features (non-metallic inclusions or carbide/nitride precipitates); -in-situ nondestructive methods for direct observation of features 2 (for example, third generation synchrotron radiation has a resolution of the order of 1 μm); -indirect methods, link the specific bulk properties to the size and distribution of the dispersed structure features. The extraction methods are used in metallurgical research as well as in industry. However, in-situ observation methods are solely used for research purposes because they are time consuming and costly. The former group of indirect methods is not sensitive enough for micron-sized inclusions at the low total volume percentage (less than 1%) typical in steel. Three-dimensional analysis also can be done by reconstruction of sequential two-dimensional slices. The different methods can be used for serial sectioning, e.g. mechanical or laser cutting, chemical polishing, electrical discharge ablation or applying FIB (focused ion-beam) with sub-micron spatial resolution3. However, slicing techniques are very time consuming. Thus, three-dimensional control of micron and sub-micron size range structural features is not used in day-to-day steel manufacturing. In comparison to three-dimensional techniques, two-dimensional methods, such as an automated SEM/EDX analysis, are widely used in modern metallurgical practice for analysis of non-metallic inclusions and steel cleanliness4,5. These methods provide precise morphological and chemistry statistics of phases, porosity, and non-metallic inclusions using two-dimensional observations of polished random sections. Many attempts had been done to convert two-dimensional statistics from observation in a random section to the real three-dimensional volume distribution6-9. These methods were designed for mono-size or narrow classes of spherical particles, randomly distributed in the volume.

Non-metallic inclusions in steels have many different origins. They can be formed as solid compounds directly growing from the melt (Al2O3, TiN) or during solidification (MnS) or originate as liquid solutions (Ca-Al-O). They can be formed in multiple steps, when fine primary particles with large ΔG0 values serve as heterogeneous nuclei for precipitate of layers with lower ΔG0 (Al2O3 core surrounded by MnS). Multiple mechanisms of nucleation, growth and particle interactions in the melt result in the formation of wide ranges of dimensional distributions of non-metallic inclusions in steels. Thus, it is difficult to predict and model these types of multivariable distributions.

Figure 1. Classification of methods used for three-dimensional microstructure characterization. In this article, a special algorithm for the conversion of two-dimensional data to the real three dimensional distribution of spherical particles was developed. 2D-3D SPHERICAL PARTICLE SIZE DISTRIBUTION CONVERTER The traditional automated SEM/EDX quantitative analysis of structural features in a random section represents two-dimensional experimental data which differs from the real three-dimensional structure parameters. This limitation can be illustrated for the simplest case when the structure has mono-size spherical particles with a radius R or diameter D. In this case, the frequency (φ) and probability (P) of observing particles with a radius r of circular sections in a random two-dimensional slice (Figure 2a) are given as6-9:

𝜑𝑟 =

𝑟 𝑅 2 −𝑟 2

1

P(r1 1) in the total particle population (∑mi=1), the sum of probabilities of “visible” diameters d in the slice was numerically simulated for a given number of groups (g) of diameters for each normal distribution (g=12) and slices (s) of each diameter Di (s=5). The calculations were done using a spreadsheet that automatically generated a set of “visible” diameters di in the section based on its probabilities (Eq. 1) and fraction mi of normal distributions. The generated set, consisted of k*g*s=12*12*5=720 of di, was distributed into size classes and presented as a probability P(d) and frequency φ(d) graph for an arbitrary set of mi. In the final step, the generated distribution of diameters di for the arbitrary set of mi was compared and fitted to an experimentally measured distribution of particle diameters dexp by applying an inverse optimization method. To do this, the special error function was introduced in the EXCEL SOLVER and minimized by varying mi values. The simulations deliver the set of normal distributions of spheres Di, the random slice of which generates a set of diameter di similar to experimentally observed diameters dexp. To verify the algorithm, two virtual experiments were conducted. In the first experiment, the one normal distribution of spheres with diameters DAi was divided into 12 size classes. Each size class was cut 5 times using Eq. 1. These calculations generated a “visible” set of diameters di in a random slice. After that, a new 3D distribution of spheres DBi was generated from this 2D distribution using an inverse solver. The comparison of the original data (DAi) with the twice reprocessed 3D distribution (DBi) is shown in Fig. 3a. In the second test, a virtual experiment was done for 3D data consisting of two normal distributions (Figure 3b). These simulations gave reasonable quantitative similarity between the original and 3D-2D-3D reprocessed data with some smoothing of curves. The precision of the method can be improved by increasing the number of normal distributions (k), groups (g) and slices (s); however, these tests showed that the combination used: k=12, g=12, and s =5, provided satisfactory accuracy for most applications.

a) b) Figure 3. Method verification using (a) one class and (b) two classes of normally distributed spheres. EXAMPLES OF 2D-3D STRUCTURE FEATURES CONVERSION Ductile iron with spherical graphite Shape, size, quantity and distribution of the graphite phase are some of the most important microstructural parameters in high carbon iron alloys (cast irons). Magnesium treatment transforms flake graphite to spheroids and dramatically improves mechanical properties. An accurate quantitative analysis of the real three-dimensional spherical graphite structure parameters is important for process control and predicting properties. The simplest practical way of graphite structure evaluation is based on a comparison of the microstructure viewed at a particular magnification (typically 100x) with standardized, tabulated microstructures. More advanced quantitative optical metallography generates data including total quantity (% area), nodule number per unit area, size distribution, and graphite particle shape factor, which are calculated based on several geometrical rules. However, the different approaches that calculate these characteristics obtained from the optical image of random two-dimensional slices have significant limitations: (i) the calculated twodimensional data does not represent the real three-dimensional structure parameters and (ii) the optical imaging technique does not distinguish the small graphite particles from the others structure features, such as micro-porosity or non-metallic inclusions. Figure 4 illustrates the differences in counted particles obtained from optical and automated SEM/EDX analysis of the same ductile iron. Optical data was overloaded by small particles counted as graphite; however automated SEM/EDX analysis separates the carbon containing phase from non-metallic inclusions. 160 ASPEX

nodule number, 1/mm2

140

Image J

120 100 80

60 40 20 0 0

10

20

30 2D diameter, µm

40

50

60

Figure 4. Comparison of optical (Image J) and automated SEM/EDX (ASPEX) data collected from polished section of ductile iron. The additional tests showed that the “noise” from non-metallic inclusions increased with decreasing the total graphite nodule number per unit area. Figure 5 shows data obtained from a heavy cast section. 30 Graphite Inclusions

25

Particles #/mm2

Total 20

15

10

5

0 0

20

40 2D diameter, µm

60

80

Figure 5. Classification of features in ductile iron using automated SEM/EDX (ASPEX) method.

A combination of automated SEM/EDX ASPEX analysis and the 2D-3D conversion methods were used to analyze the actual threedimensional graphite nodule distribution in ductile iron castings produced by different processes. In continuous casting processes, mainly radial heat transfer creates a significant temperature gradient and provides a different cooling rate near the surface than in the middle of the 5” diameter bar. The resulting microstructures differ by a factor of three in nodule count. These specimens also showed two principally different modes of 3D nodule size distribution. The graphite nodules near the surface had close to a normal distribution of nodule diameters, while the nodule size distribution near the center of the bar comprised a bi-modal distribution with predominant large sizes (25-50 µm) and fine sizes (5-10 µm) (Figure 6a). Inoculation and lowering the pouring temperature both generally promote heterogeneous nucleation increasing nodule counts in thinwalled sand castings (Figure 6b). At the same time, melt treatment generally changed the normal distribution of graphite nodules to a bi-modal distribution. An even more complicated graphite nodule size distribution was observed (Figure 6c) in low Si ductile iron solidified in a heavy section (4” wall thickness casting poured into no-bake sand mold). Three major classes of 3D nodule size distribution were observed: large (40-90 µm), medium (10-20 µm) and very fine (1-5 µm). It is important to note, that 2D-3D conversion revealed changes in the distribution mode from a normal mode with mainly mono-size to an abnormal mode having a bi-modal distribution of graphite nodule size. These distributions could be linked to solidification kinetics. Information about the real 3D graphite structure is also important to predict a structure of ductile iron matrix. For example, a large amount of small graphite nodules promotes ferritization of the matrix during austenitic decomposition and decreases alloying element segregation in the as-cast condition, which is important for low temperature toughness12.

a)

b)

c) Figure 6. Effect of processing on distributions of spherical graphite (3D diameter) in ductile irons: a) continuous cast 5” diameter bar: near the wall and at the center, b) 1” wall castings (1-not treated, 2-inoculated, and 3-inoculated and poured at low temperature), and c) 4” wall no-bake mold casting. Non-metallic inclusions in steel castings Cleanliness of steel castings is a serious challenge because of the intensive re-oxidation during pouring. It is difficult to protect the metal from re-oxidation because the pour stream has high levels of turbulence as well as a high surface area to melt volume ratio. Additional factors such as high alloying with aluminum, manganese, chromium and other elements highly reactive with oxygen and nitrogen, small heat sizes, and high superheat intensify the liquid metal-environment (gas, lining, mold) reactions. Cleanliness of cast steel was studied using automated SEM/EDX analysis4,5. In this article, previous data were 2D-3D reprocessed to illustrate the method capability. Converted data of the real 3D diameter distribution were recalculated to volume population density applying the rule of equality of area and volume fractions. Figure 7 illustrates the effect of metal casting processing on steel

cleanliness (number of inclusions per volume unit). At two foundries, similar medium carbon (0.2-0.3%C) low alloyed steel was deoxidized by Al followed by Ca-additions in the ladle. In the first case, steel was statically poured into a no-bake mold and, in the second case, castings were produced by centrifugal casting. Centrifugal forces removed both types of inclusions (oxides and sulfides) from the metal. However centrifugal forces were not capable of removing fine inclusions of less than 2 µm diameter. 5000 Ocides (static casting) 4500

Oxides (centrifugal)

MnS (static casting) 4000

MnS (centrifugal)

Number, 1/mm3

3500 3000

2500 2000 1500 1000

500 0 0

2

4 6 3D diameter, µm

8

10

Figure 7. Effect of casting processing on medium carbon steel cleanliness. Cleanliness of steel highly alloyed with Mn (above 5%) and Al (above 2%) to produce high strength dual-phase steel in castings is a great concern because of the intensive surface re-oxidation of the liquid steel. The reaction products can be formed by multiple reactions having different Gibbs free energy of formation and have diverse nucleation and growth kinetics. The real 3D size distribution of classified inclusions, using automated SEM/EDX ASPEX system, showed (Figure 8) that inclusion sizes inversely correlated to the free energy of formation: strong oxides with higher ΔG0 absolute values had smaller sizes when compared to sulfides and aluminum nitrides. 0.2 0.18 Mn-Si-Al-O

Frequency

0.16

Mn-Al-O

0.14

Mn-S

0.12

Al-N

0.1 0.08 0.06 0.04

0.02 0 0

2

4 6 3D diameter, µm

8

10

Figure 8. Non-metallic inclusion distributions in dual-phase high strength steel alloyed by Al and Mn. Non-metallic phase populations can be engineered to achieve desired effects: for example, austenitic grain refinement in cast stainless steel. A special melt treatment technique was applied for in-situ formation of TiN. In this case, fine TiN inclusions were formed just before casting solidification and resulted in smaller sizes when compared to MnS (Figure 9). The resulting cast macrostructure had refined austenitic grains.

Base

Refined

Figure 9. Non-metallic inclusions engineering for in-situ grain refined stainless steel. CONCLUSIONS A special algorithm for the conversion of two-dimensional spherical particle distribution obtained from an automated SEM/EDX or optical imaging to the real three-dimensional spherical distribution was developed based on inverse modeling. A program generates a virtual two-dimensional distribution from sets of normal distributions of spherical particles covering all size ranges using arbitrary slicing. These sets are optimized by comparison with particles observed in experiments. The method was applied for threedimensional analysis of near spherical phases and inclusions in different iron alloys. In ductile iron with spherical graphite, the method revealed that spheroids could be mono or poly-dimensional depending on solidification kinetics. In high alloyed Al-Mn steel, different dimensional classes of nitrides, sulfides and oxides were observed and related to the free energy of formation. REFERENCES J. Lu, D. Ivey, and H. Henein, “A Review of Methods to Quantify Nanoscale Precipitates in Microalloyed Steels”, AIST transactions, Vol. 10, No. 1, 2013, p.232. 2. L. Babout, E. Maire, J. Buffiere, and R. Fougeres, “Characterization by X-ray computed tomography of decohesion, porosity growth and coalescence in model metal matrix composites”, Acta Materialia, Vol. 49, Issue 11, 2001, p. 2055. 3. J. Konrad, S. Zaefferer, D. Raabe, “Investigation of orientation gradients around a hard Laves particle in a warm-rolled Fe3Albased alloy using a 3D EBSD-FIB technique”, Acta Mat. 54 (2006), p.1369. 4. E. Martinez, K. Peaslee, and S. Lekakh, “Calcium Wire Ladle Treatment to Improve Cleanliness of Centrifugally Cast Steel”, AFS Transactions, vol. 119 (2011), Paper 11-037. 5. K. Peaslee, V. Singh, and S. Lekakh, “Inclusion Engineering for Improved Properties in Steel Castings,” Proceedings of the Richard J. Fruehan Symposium (2011). 6. Sahagian, D. L., Proussevitck, A., A., “3-D particle size distributions from 2-D observation: stereology for natural applications”, J. of Volcanology and Geothermal Research, 84, pp. 173-196 (1998). 7. Underwood, E., Quantitative Stereology, Adddison-Wesley Publishing Company (1970). 8. Saltykov, S., Sterometric Metalurgy, Moscow, USSA (1958). 9. Basak, C., Sengupta, A.,” Development of a FDM based code to determine the 3-D size distribution of homogeneously dispersed spheroidal second phase from microstructure: a case study on nodular cast iron”, Scripta Materialia, 51, pp. 255–260 (2004). 10. ASTM E1245 “Standard Practice for Determination the Inclusions or Second-Phase Constituent Content of Metals by Automatic Image Analysis. 11. K. Pedersen and N. Tidje, “Graphite Nodule Count and Size Distribution in Thin-walled Ductile Cast Iron”, Materials Characterization, 59 (2008), p. 1111. 12. Lekakh, S., Richards, V., and Medvedeva, N., “Effect of Si Segregation on Low Temperature Toughness of Ductile Iron”, Trans. of the 116th Metalcasting Congress (2012). 1.

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