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Figure 1. A macrograph of a “freckle chain” on the surface of a single-crystal superalloy casting. The solidification direction is <100>, which is horizontal in the figure.

INTRODUCTION

Recent advances in computing power have enabled the development of 3-D microstructural models on all length scales from atomistic simulations to dislocation-dislocation interactions, 3-D crystal plasticity models for deformation, and 3-D fracture mechanics for failure analysis.

Serial sectioning is a well-established technique for obtaining 3-D microstructural data. In its simplest form, the technique involves the careful removal of a layer of material, followed by imaging of the freshly created surface. This is repeated many times in order to build up a series of two-dimensional (2-D) images (slices) which is then reconstructed (i.e., stacked) to form a data volume.

In the past, layer removal has been done by hand, using standard metallographic polishing techniques. This is a very delicate and time-consuming operation. In addition, the minimum slice thickness that can be repeatedly obtained in practice is 5–10 µm. Since a fundamental limitation of the serial sectioning technique is that features smaller than the minimum slice thickness will be missed, this places serious limitations on resolution. Furthermore, the repeated removal of a fixed depth of material by hand is challenging in a practical sense, and the accuracy of the final 3-D data volume depends entirely on the well-controlled removal of material in each slice. Add to this the time needed to carefully align and assemble the individual 2-D images and the prospect of obtaining a data volume comprising a few hundred slices becomes a daunting one.

CASE STUDIES

Freckle Defects in Single-Crystal Ni-Superalloys

Recently, the Air Force Research Laboratory’s Materials and Manufacturing Directorate and UES, Incorporated demonstrated the capabilities of the machine by using automated serial-sectioning to extract the 3-D microstructural features of freckle defects in an experimental nickel-based superalloy casting. Freckles are casting defects that result in separate grains or sub-grains on the surface of a single crystal or directionally solidified casting. The surface features often occur in “freckle chains” extending along the solidification direction, as shown in Figure 1.

Misoriented regions on the surface of the casting indicated the presence of complex sub-surface features that can extend deep into the interior of the crystal. After automated serial sectioning (130 slices, with a slice thickness of 2.7 ± 0.1 µm), the main body of the freckle is shown to be much larger than apparent on the surface (Figure 2, which is also available for viewing on-line as a QuickTime movie). The freckle region appears to be separated into smaller sub-domains, each with a slightly different crystallographic orientation. Nickel-based superalloys have been well documented¹ as both elastically and plastically anisotropic. It is therefore likely that the effect of the spatial arrangement of these sub-domains coupled with their individual crystallographic orientations will strongly influence the stress state within the freckle. The 3-D information gathered in this study will therefore form part of a modeling effort to identify the combined effects of morphology and orientation on the criticality of freckle defects under specific loading conditions.

Figure 2. A 3-D rendering showing an 80 µm thick central region of a freckle defect in an experimental superalloy casting. The figure shows the spatial arrangement of different crystallographic sub-domains within the main freckle region as different gray levels. The largest sub-domain shows remnants of a dendrite structure, suggesting its origin as a dendrite tip from earlier in the casting process. The broken line shows the surface of the cylindrical casting.	Figure 3. A surface rendering of extruded DRA 2009/SiC/15p microstructure. The extrusion direction is parallel to the z axis.	Figure 4. A surface rendering of 3-D models of an individual SiC particle, comprising 35 serial section slices. Spacing between slices = 0.16 ± 0.01 µm.
Click Here to view this three-dimensional figure as a movie (.mov) using QuickTime (~800 kb).	Click Here to view this figure as a 3-D movie as a .mov file using QuickTime (~15 Mb).	Click Here to view this figure as a 3-D movie as a .mov file using QuickTime (~15 Mb).

Table I. Classification Scheme for SiC Particle Morphologies in DRA Material*
Morphological Descriptor		Attributes
Rod		dmax > 1.5dmin, dmax> 1.5dmid
Plate		dmax> 1.5dmin, dmax< 1.5dmid, and dmid> 1.5dmin
Ellipsoid		dmax> 1.5dmin, dmax< 1.5dmid, and dmid< 1.5dmin
Sphere		dmax< 1.5dmin
* Based on ratios of measured caliper diameters.
Figure 5. A histogram showing statistics of particle alignment, obtained from 3-D morphological data from a sample population of 100 SiC particles.

3-D Metallography of Discontinuously Reinforced Aluminum

Discontinuously reinforced aluminum (DRA) is a material system with a broad range of applications in ground transportation, thermal management, and both military and commercial aerospace, due in part to improvements in process control leading to well-characterized materials with improved mechanical and physical properties. In this context, the spatial arrangement (spacing and orientation) of reinforcement phases is of particular interest. It has been established through experimentation that the spatial distribution and/or morphology of the reinforcement has a strong influence on the mechanical properties of the final material.^2,3 However, the influence of particle orientation on the anisotropy of mechanical properties is less tractable beccause it is experimentally difficult to measure.

Robo-Met.3D was used to automatically serial-section the 2009/SiC/15p DRA material using a slice thickness of 0.16 ± 0.01 µm. The total volume of material sectioned was 280 µm × 210 µm × 20.5 µm (1.2 µm × 10⁶ µm³), with the sectioning done along the extrusion direction. It is possible to obtain large fields of view such as this by using an image montage technique to form a single, large image that has both high resolution and high spatial coverage. Figure 3 (which is also available for viewing on-line as a 3-D movie) shows a typical sub-volume (~3 µm × 10⁴ µm³) of the DRA data set obtained via automated serial sectioning. In this rendering, the aluminum-alloy matrix phase is made transparent so that the SiC particles are clearly visible, with the extrusion direction parallel to the z axis.

The ability to capture a large field of view at a high resolution is key to providing a reasonably sized population of microstructural features for statistical analysis. A sample population of 100 particles was identified. The individual particle sections were then carefully cropped out of the 2-D slices and reconstructed as individual 3-D models (Figure 4, which is also available for viewing on-line as a 3-D movie).

In the analysis that follows, a and b are the caliper diameters parallel to the x and y axes and c is the measured caliper diameter parallel to the z axis. Typically the three measured caliper diameters can be ranked according to size, as d_max, d_mid, and d_min. However, in some instances, d_mid and d_min are measured to be the same within the resolution of the technique. In order to ascertain the influence of particle morphology on particle rotation during processing, a scheme was adopted for classifying the particle morphologies according to the ratios between their measured caliper diameters. For example, particles were classified as “rods” if the ratios between dmax and each of the other two dimensions (d_mid and d_min) were calculated to be greater than a critical ratio of 1.5 (Table I). The particles were further classified as being either “well aligned” or “badly aligned” depending on whether d_max was parallel to the extrusion axis or not. Figure 5 is a histogram showing the percentages of well-aligned and badly aligned particles as a function of their morphology.

The presence of well-aligned particles in the extruded product (especially the rods and plates) suggests substantial particle rotation occurs during extrusion processing and the extent of rotation is a function of the morphology of the particles themselves. This information is valuable for conducting process modeling of these materials and is unobtainable by using standard statistically based 2-D stereological methods.

ROBO-MET.3D

The Case for Automation From the previous discussion, it is clear that the drive for automating the layer-removal step is already quite strong; however, Robo-Met.3D was also designed to fully automate the three-dimensional (3-D) data-volume generation process, from specimen preparation and polishing to digital image capture and 3-D reconstruction. At the heart of the machine is a high-end personal computer (PC) station running custom-written code that controls a robotic arm used to translate a specimen between the metallographic polishing unit and a fully automated optical metallograph. The PC also runs the image capture and 3-D reconstruction software. Chemical etching is carried out automatically, increasing the number of material systems that can be investigated (e.g., nickel-superalloy specimens are routinely etched in this manner). The application of advanced automation techniques represents a significant advance in serial sectioning, reducing the time to acquire data volumes by around two orders of magnitude compared with manual techniques. The higher data acquisition rates of Robo-Met.3D enable the systematic study of microstructural evolution and trends so that the influence of such factors as heat treatment, deformation processing, and damage evolution can be investigated. Rather than being limited to academic research, 3-D microstructural analysis is now also a feasible technique for manufacturing quality control, real-time failure analysis, and a host of other functions. Serial sectioning is fundamentally a destructive technique. Robo-Met.3D allows the 3-D reconstructed data volume to be made available to the operator in real time, providing immediate feedback in case the optimum polishing or imaging conditions should change during the run. Care is also taken to ensure data integrity for the large datasets produced, typically around 1–2 Gb. A “0 + 1” redundant array of inexpensive disks is used for data striping and data mirroring on each of the PC’s four hard drives. Capabilities The current and projected capabilities of the Robo-Met.3D system are shown in Table A. Among the material systems that have been investigated, two systems with very different length scales stand out; one is an experimental single-crystal cast nickel superalloy, and the other is a commercially available 2009/SiC/15p discontinuously reinforced aluminum (DRA) composite material comprised of 15 vol.% SiC particles in a 2009 aluminum-alloy matrix. Each of these systems presents different and specific challenges to serial sectioning. The Robo-Met.3D system, which uses metallographic polishing to obtain the serial sections, offers greater flexibility than other techniques such as micro-milling, which tend to be limited in terms of the material systems that can be sectioned. Robo-Met.3D can rapidly produce the series of 2-D images needed for 3-D reconstruction of the data volume for any single polished surface that can be produced using standard metallographic polishing techniques. Table A. Current and Projected Capabilities of Robo-Met.3D Capability Currently Projected Slice thickness 0.16–2.7 µm ± 0.01 µm 0.1–20 µm ± 0.01 µm Number of slices 100 100–500 Slice rate 5–20/h 5–20/h Max. sample volume (mm) 1.0 × 0.7 × 1.2 (0.8 mm3) 2.0 × 1.0 × 15 (30 mm3) Material systems Ni-based superalloys, DRA, carbon foams Ti alloys, Fe alloys, metallic composites, intermetallics Chemical etching Automated Automated Illumination Bright field, polarized light Dark field, Nomarski Microstructure data Real time Real time Orientation data Semiautomated Real time

ACKNOWLEDGEMENTS

This work was supported in part by the Air Force Office of Scientific Research under Task 01ML05-COR (Craig S. Hartley, program manager). In addition, the authors thank the following individuals for technical discussions and support during this research: Daniel B. Miracle, Michael D. Uchic, Clayton A. Smith, and Tresa M. Pollock, who supplied the Ni-6.8Al-6.2Ta-0.14Hf- 2.4W-4.6Re-1.5Mo-7.0Cr-7.5Co alloy used in this study.