TMS Outstanding StudentCONTENTS |
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The behavior of materials is controlled by their microstructure. 1 The characteristics of a material’s microstructure, such as size, distribution, and morphology, control the mechanical and thermal behavior and properties of the material . Thus, establishing a link between microstructure and properties is vital to fully understanding and predicting material behavior.
SiC particle reinforced aluminum composites are an excellent example of a material system where microstructure controls properties. These materials exhibit high strength and stiffness by combining strong, ceramic reinforcement particles in a soft aluminum matrix. In these composites, the SiC particle size, morphology, and orientation with respect to the loading axis play a significant role in determining the material’s stiffness, strength, and fatigue resistance.2, 3, 4
Traditional methods of examining the microstructure of composites as well as other materials involve simplifying the three-dimensional (3D) structure to a two-dimensional (2D) representation by a technique such as optical or scanning electron microscopy (SEM).5 While 2D representation of microstructures is common and gives some idea of the microstructure morphology, it is not fully representative of the 3D structure of the material. Therefore, to visualize and fully understand a material’s microstructure, a technique must be used that can capture the three dimensional nature of the microstructure. Serial sectioning is a technique that allows the quantification of 3D microstructures using classical metallography techniques coupled with computer-aided reconstruction.6 The technique has been used for over a century in, among other fields, paleontology7, biology8, 9, and materials science.10, 11, 15 Recently, computer-aided serial sectioning techniques have allowed visualization and study of several material systems, including Al-Si10, proeutectoid iron alloy11, and SiC/Al composites15. While visualization of the 3D microstructure of the material is important, prediction of the behavior and properties of the material is equally important. This requires microstructure-based modeling to evaluate the link between structure and performance.
In SiC particle reinforced aluminum composites, the SiC particles have a plate-like and angular morphology, and are often distributed inhomogeneously in the composite. The orientation of the SiC particles with respect to the loading axis can significantly affect the mechanical behavior and anisotropy in the composite2 3 4 12. Ganesh and Chawla2 reported on experimental evidence of the effect of SiC particle orientation, caused by hotextrusion, on tensile and fatigue properties.
Numerical modeling of the behavior of SiC/Al composites has typically been conducted by assuming a single, simple SiC particle in a unit cell model.13, 14, 15 Unit cell models approximate the highly variable and angular structure of SiC particles using simplified particle geometries such as spheres, ellipsoids, or cubes. This simplification aids in computation but fails to capture the complex morphology, size, and spatial distribution of SiC particles in the Al matrix. It follows that a true simulation of the material behavior can only be obtained by incorporating actual 3D morphologies as inputs to the models.This microstructure-based modeling approach can be accomplished by combining serialsectioning and computer-aided reconstruction with 3D finite-element modeling (FEM). By obtaining the 3D morphology of the composite’s microstructure through serial sectioning, microstructure-based models can be used to evaluate material performancewith a much higher degree of accuracy than unit cell models.
In this paper serial sectioning was used to reveal the characteristic 3D microstructure of SiC particle reinforced aluminum matrix composites. The reconstructed 3D microstructure obtained was then used as a basis for 3D FEM modeling of uniaxial tensile behavior. The process allowed 3D visualization of SiC particles as well as intrinsic and accurate microstructure-based modeling of the behavior of SiC/Alcomposites.
A serial sectioning method was employed to acquire 2D images of the microstructure as a basis for reconstructing 3D solids for modeling using FEM. The basic concept of the serial sectioning process is to cyclically polish material to generate a series of microstructure sections. These sections were then segmented and assembled into a 3D solid using computer software, followed by 3D FEM modeling. The challenge of the this work was in developing a methodology and procedure for reproducible serial sectioning, reconstruction, and FEM. This involved quantifying and controlling the parameters of the process, including material thickness loss per cycle, quality of the sample surface, and the use of software algorithms for constructing 3D solids. The refinement of these parameters allowed 3D rendering and modeling of SiC particle reinforced aluminum composites.
The serial sectioning process consisted of a series of steps that resulted in a 3D solid used in FEM analysis. The basic steps of the serial sectioning process and modeling were asfollows:
Figure 1 shows a flow chart of the serial sectioning process. The material was sectioned, mounted, and indented by a Vickers micro-hardness indenter to create fiducial marks. Systematic polishing and imaging of the sample surface generated a series of microstructure sections. Measurement of changes in the fiducial mark depth was used to determine the thickness between sections from material loss per polishing cycle. Using the 2D sections, a 3D solid was constructed using computer software. This solid wasthen used in modeling of deformation of the material using FEM analysis.
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Figure 1. Flow Chart of Serial Sectioning Process.
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Figure 2. Extrusion axis relative to the sample surface.
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In this work a SiC particle reinforced aluminum composite was examined. SiCreinforced 2080 aluminum with T6 heat treatment (peak-aged) was used (Alcoa Corp.). The SiC particles in the composite had an average particle size of about 25 µm (F280 designation). The SiC/Al composite samples were cut so that the extrusion axis was parallel to the cutting plane (longitudinal axis), as shown in Figure 2. The main focus of this work was to develop and implement a serial sectioning followed by finite element modeling. Thus, a majority of this work consisted of developing techniques and experimental methodology for accomplishing these tasks. We choose to report the detailsand results of different techniques and methodologies in the following section.
Fiducial marking by indentation
SiC/Al samples were cut and mounted for subsequent polishing. A representative region of the microstructure was selected, denoted here as the region of interest. Selection of the region of interest was important because it defined the volume of microstructure to be analyzed. It was desirable to obtain a stack of sections such that whole SiC particles were revealed, traversed, and bypassed in a given volume, for this would allow entire particles to be reconstructed and incorporate in modeling. It was determined that a 100 x 100 x 100 µm3 volume would be suitable for this composite, since the SiC particles were ~25 µm in diameter. This volume would yield a reasonable group of particles for reconstruction and modeling. A larger surface area (200 x 200 x 100 µm3 on average) was imaged so that a smaller, representative volume could be selected. It should be noted that a “representative” volume is a very subjective assessment that is based on the microstructure feature size, computational capability, and operator judgment.
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Figure 3. Geometry of Vickers Indenter.
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Figure 4. Micrograph of Vickers Indentation in Al matrix of SiC/Al composite.
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Fiducial marks, placed on the sample surface by Vickers indentation, were used to measure the material loss during serial sectioning as well for alignment of the sections during 3D construction. Figure 3 shows the geometry of the Vickers diamond indenter, while Figure 4 shows an indentation in the Al matrix of the composite. The impression made by the machine can be as deep as 100 µm (depending on the load applied). Previous serial sectioning methods have utilized micro-hardness indentations as fiducial markings16 because the geometry of the indentation enables measurement of the amount of material removed, which is equivalent to the thickness between sections. An optical/geometric method using the Vickers indentations was used to determine the amount of material lost. The indenter forms pyramidal impressions on the surface of depth (h) with a two-dimensional projection with diagonal distances D1 and D2. The height of the indentation, (h), is then given by:
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(1) |
Where (j) is the angle between the two diagonals (taken as 1350). Thus, if the diagonal distance of the indentation is known, the approximate depth can be determined. An average of the two diagonals was taken to determine D in equation 1. After the region of interest was selected, the Vickers indentations were made at four corners of the region ofinterest, as shown in Figure 5. Caution was taken to avoid indentation of SiC particles. During serial sectioning, the size of the two-dimensional projection of the Vickers indentation decreased with increasing depth, as shown in Figure 6. By calculating the depth of the indentation after each polishing cycle, the change in the depth was determined and equated to the section thickness.
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Figure 5. Region of interest (outlined in white) defined by four Vickers Indentations.
Notice that the region is actual larger than the target 100 x 100 µm2; this allows more
microstructure to be captured so that a specific region can be examined later.
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Figure 6. Progression of diminishing indentation with polishing.
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Polishing was a crucial step in the serial sectioning process since control of material loss rate and a sample of good quality are extremely important. As with indentation, polishing was repeated several times throughout a serial sectioning process. A micropolisher was used for each polishing cycle. The micro-polisher had four parameters that could be varied to control the polishing quality and the amount of material lost per cycle: Time, load, speed, and soft start (an option to begin and end polishing cycles with a slower speed to avoid surface scratching). Each polishing routine consisted of a set of control parameters. Six polishing routines were compared. Table 1 shows the polishing routines and their control parameters.
The purpose of polishing was two-fold: (a) control the amount of material removed and (b) obtain a surface quality acceptable for microstructure characterization. The latter objective was easy to obtain; long, slow durations of polishing at 1 µm grit generated a reasonable surface finish and the microstructure could be clearly resolved. Controlling the removal rate of material was more difficult. As demonstrated in the literature10, 11 the size of the microstructure features dictates the thickness between sections. Thus, with SiC particles 10-40 µm in diameter a section thickness of ~1 µm was chosen. This would give about 8 to 10 sections per particle in the analyzed volume.
In order to obtain the desired 1 µm / cycle target, it was decided to use a two-sequence routine, using first the coarser 15 µm polishing grit, followed by 15 min of 1 µm polishing to restore the microstructure quality. Figure 7 shows the average cumulative thickness of 1.1936 µm per cycle, which was adequate for achieving the desired 1 µm per cycle thickness loss rate.
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Figure 7. Cumulative thickness loss for polishing cycles for Run 2. Fitted line
approximates the slope for the first indentation.
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Figure 8. Imaging segmentation and alignment of sections of the microstructure.
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Image segmentation and alignment of images
After each polishing cycle, optical micrographs of microstructure were taken, and these were analyzed using conventional image analysis software. Image segmentation was performed to transform the optical micrograph of each section into black and white, simplified representations of the microstructure, as shown in Figures 8 and 9. Scratches and other polishing artifacts were eliminated so that they would not be rendered in the actual microstructure. The sections were then aligned to remove translation androtational errors. In order to simplify the microstructure for FEM, vectoral format software was used to transform the image analysis-induced jagged edges of the SiC particles into smoother lines, as demonstrated in Figure 10. It should be noted that these simplifications did not significantly detract from the overall morphology of the SiC particles. As seen in Figure 10, the general shape of the particles is retained in the vectoral segmentation.
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Figure 9. (a) Raw image of SiC particle reinforced aluminum composite. (b) Segmented
image with SiC (black) surrounded by Al matrix (white).
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Figure 10. Transformation from simplified image to vectoral image for FEM modeling.
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To reconstruct 3D solids from the serial sections a 3D image analysis and reconstructive software (SURF Driver) was used. In this step serial sections were stacked and a 3D solid generated, and exported for FEM analysis. Figures 11, 12, and 13 show a series of images of reconstructed SiC particles. Figure 11 shows a single SiC particle with characteristic irregular and angular morphology. Figure 12 shows a multi-particle reconstruction, where several of the particles are clearly aligned toward the extrusion axis. The somewhat irregular edges seen on the particles were an artifact of reconstruction caused by slight rotational misalignments in the serial sections. The relatively small errors induced by rotation do not reduce the overall accurate representation of the SiC morphology.
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Figure 11. (a) Visualization solid formed from 100 sections. (b) FEM solid formed from 3
sections. (c) Visualization solid wire frame. (d) FEM solid wire frame.
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Figure 12. (a) Visualization solid formed from 100 sections. (b) Visualization solid wire
frame. (c) Actual SiC particle for comparison. (d) Visualization solids formed from 100
sections. (e) Visualization solids wire frames. (c) Courtesy
of A. Drake,
St. Gobain
Corp.
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Finite Element Method Simulation
The 3D model of the microstructure was used as a basis for FEM analysis (ABAQUS version 6.3-1 CAE). Uniaxial loading was modeled by applying a 1% strain to the model. SiC was modeled as a linear-elastic materials, because it is a brittle ceramic that does not exhibit significant plasticity at room temperature. The aluminum matrix was modeled with both elastic and plastic behavior using experimental stress-strain data. Table 4shows the elastic properties used for SiC and aluminum metal matrix.
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Figure 13. (a) (b) (c) Reconstructed SiC particles for visualization. (d) (e) Simplified SiC
particles for FEM Modeling.
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Figure 14. (a) Wire frame of Model 1 matrix. (b) Wire frame of Model 1 par ticle. (c)
Final solid Model 1 particles. (d) (e) Model 1 final mesh. (f) Loading conditions for
Model 1; orange arrows indicate load direction.
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Material Type
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Young’s Modulus (GPa)
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Poisson’s Ratio
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Two FEM simulations were conducted: (a) a single SiC particle and (b) multiple SiC particles. We denote the single SiC particle as Model 1 and the multiple SiC particles as Model 2. Table 5 shows the modeling parameters for Models 1 and 2.
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Model
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Number
of Particles |
Number
of Sections |
Number
of Mesh Elements |
Volume
Fraction of Particles |
Approximate
Simulation Time (mins) |
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Figure 14 shows the single SiC particle and the mesh in both the particle and the matrix
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Figure 15. Model 1 output showing step-development of equivalent plastic strain. Gray
and red are the highest levels of strain (Gray = 5.047 x 10-2, Red = 3.365 x 10-2 ).
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Figure 16. Stress-strain curve for Model 1
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Figure 15 shows the development of equivalent plastic strain in the matrix surrounding the SiC particle. The plastic deformation became concentrated at the poles of the particles along the axis of loading, as originally predicted by Goodier17. The macroscopic stress-strain behavior from the model is shown in Figure 16 showing a Young’s modulus of 95.2 GPa.
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Figure 17. (a) Wire frame of Model 2 particles. (b) Meshed Model 2 particl es. (c) Final
solid Model 2 particles. (d) Aluminum matrix for Model 2. (e) Meshed volume for
Model 2. (f) Loading conditions for Model 2; orange arrows ind icate load direction.
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Figure 18. Model 2 output showing step -development of equivalent plastic strain. Gray
and red are the highest levels of strain (Gray = 2.350 x 10 -2, Red = 1.800 x 10 -2 ).
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Model 2 used sixteen SiC particles embedded in the aluminum matrix, Figure 17. In this model, one can clearly observed the particle distribution, particle clustering, and orientation of particles along the extrusion axis. Figure 18 shows the evolution of equivalent plastic strain showing the onset of plastic flow at sharp angular corners of the particles, followed by localization of strain between particles. Figure 19 shows the stress-strain behavior of this model; as observed, the Young’s modulus is around 84.5 GPa.
Comparison of 3D Microstructure Model with Unit Cell Models
To demonstrate the improvement of the 3D microstructure modeling over conventional unit cell models, simulations of 3D microstructure were compared with spherical unit cell models in 2D and 3D.2D unit cell models were simulate in plain strain and plain stress. A summary of these results is shown in Figure 20. Experimental data from Chawla and Shen12 shows that around 8% the modulus of the composite should be around 85 GPa. The highest and lowest simulated modulus and strength are given by 2D plane strain and plane stress, respectively. The plane strain condition causes a much higher degree of constraint since the in-plane strain ez = 0. The 2D behavior if also influenced by the nature of the model. In 2D, the SiC particle can be envisioned as a SiC disk, rather than aparticle. Thus, there is no surrounding matrix around the SiC particle in the 2D model, which will certainly influence the model response. As expected, the 3D Unit Cell model predicted a modulus of 79.5 GPa that is between the 2D plane strain and plane stress bounds. Under uniaxial loading, the 3D model is allowed to contract (as does the real specimen) in the transverse planes, so the predicted modulus is lower than that of the plane strain condition. Finally, the modulus obtained for the 3D microstructure model is 84.4 GPa, which is remarkably close to the experimental value. These observations prove two very important points: (a) the 3D microstructure model is the most accurate in predicting the experimental stress-strain behavior of the material and (b) the 3D microstructure model is a significant improvement over 3D or 2D unit cell models. Clearly, the accuracy of the 3D microstructure model can be attributed to the true morphology and distribution of the SiC particles and these type of models can be extremely powerful in predicting material behavior.
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Figure 19 Stress-strain curve for Model 2.
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Figure 20. Stress-strain curves of 2D and 3D models.
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The following conclusions can be made on this study to develop a serial sectioning methodology for visualization and FEM modeling of SiC particle reinforced Al composites:
The author would like to thank sincerely Dr. Nikhilesh Chawla for his advisement, encouragement, and the opportunity to conduct a thesis project; Dr. Jason Williams for his insight, assistance in the lab, and help with operating ABAQUS; Ganesh Vasudevanpillai for his assistance in ABAQUS and his help with resources; Dr. Xin Deng for his help with ABAQUS; and John Roman for his help with the digital camera coupling equipment.
1. W.D. Callister, Jr. Material Science and Engineering; an Introduction, 2nd edition, John
Wiley & Sons Inc., New York, NY, 1991.
2. V.V. Ganesh, N. Chawla, Metallurgical and Materials Transactions, (2003) in press.
3. N.J. Sorensen, S. Suresh, V. Tvergaard, A. Needleman, Materials Science and
Engineering (1995) A197 1-10.
4. H.K. Jung, Y.M. Cheong, H.J. Ryu, S.H. Hong, Scripta Materialia, (1999) 41 1261-
1267.
5. I.A. Ibrahim, F. A. Mohamed, E.J. Lavernia, Journal of Materials Science, (1991) 26
1137-1156.
6. L. Wojnar, Image Analysis; Applications in Materials Engineering, CRC Press, Boca
Raton, FL, 1999.
7. M. J. Herbert, C. B. Jones, Computers and Geosciences, (2001) 27 427-440.
8. M. Yanuka, F.A. Dullien, D.E. Elrick, Journal of Microscopy, (1984) 135 159-168.
9. V.A. Moss, D. McEwan Jenkinson, H.Y. Elder, Journal of Microscopy, (1990) 158 187-
196.
10. J. Alkemper, P.W. Voorhees, Journal of Microscopy, (2001) 201 388-394.
11. M.V. Kral, G. Spanos, Scripta Materialia, (1997) 36 875-882.
12. N. Chawla, Y.L. Shen, Advanced Engineering Materials, (2001) 3 357-370.
13. D. Saraev, S. Schmauder, International Journal of Plasticity, (2003) 19 733-747.
14. H. Shen, C.J. Lissenden, Materials Science and Engineering A, (2002) 338 271-281.
15. M. Li, S. Ghosh, O. Richmond, Acta Materialia, (1999) 47 3515-3532.
16. M. Li, S. Ghosh, T. N. Rouns, H. Weiland, O. Richmond, W. Hunt, Materials
Characterization (1998) 41 81-95.
17. J. Goodier, Journal of Applied Mechanics, (1933) 39 55-57.
Imaging Accuracy
The imaging process is a large source of information loss in the serial sectioning process. The reason for this is due to the resolution capabilities of the microscope and the digital camera. Since the camera has a limited number of optical elements with which to detect the incoming imagery, it is the camera that, in the end, limits the resolution and causes losses in microstructural data.
For the reconstruction process, the important information is actually only at the interfaces between the SiC particle and the aluminum matrix, for this is where the contour of the SiC particle is. The contour describes everything that is needed for the serial sectioning process, for it determines where the aluminum and SiC begin and end, and it gives all of the morphological data at the given depth. In going from the actual microstructure to the camera image causes losses in the contour resolution. Since only a certain number of pixels can exist to describe the contour at a given region in the image, not all of the contour information is recorded.
It is reasoned that these losses are not detrimental to the serial sectioning process or to use of the reconstructed solids as both visualization props and FEM models. Although the camera and microscope do reduce some of the information about the morphology, these reductions are small and do not affect the general shape of the microstructure. For this reason it is concluded that the imaging accuracy is adequate for the serial sectioning method and provides reasonable results in the depiction of the SiC/Al composite microstructure for the thesis.
Image Manipulation Accuracy
The major source of data loss in the serial sectioning process comes from the image manipulation process. This step deliberately reduces and simplifies the microstructure images in order to produce sections that can be used for visualization and modeling.
Figures 15, 16, 17 and 20 demonstrate the transformation of a serial section from its raw image into a final vectoral image. It is observed that with each step, the contours of the SiC particles are distorted and abstracted from their original form. It can be seen that while small features such as little ridges or rumpled edges are not retained, the general shape of each particle is. For visualization of solids, which are generated from the simplified/realigned section stacks, there are only minor losses in morphology. The vectoral format, however, reduces the particle shapes into complex polygons, which in some cases greatly diminishes the contour of the particle. This reduction is unacceptable from a visualization standpoint, since some of the finer features of the microstructure have been lost. From a modeling standpoint, however, this is perfectly acceptable for, as has been discussed, a simplified geometry is requisite for FEM. The simplifications performed in image manipulation do not reduce the SiC particles into simple geometric shapes such as ellipsoids, as would be found in unit cell models. The simplified FEM models still retain the major features of the SiC particles, including their high angular morphology and orientation. The simplified SiC particle solid approximates to a high degree SiC particle shapes, as seen in Figure 17; therefore it is taken to be a good approximate shape for the microstructure of SiC particle reinforced composites.
Reconstruction Accuracy
The reconstruction process itself removes morphological data. The main losses are caused by the contour drawing that is used to define boundary surfaces. Because the SURFDriver software defines solids using nodal contours, the actual rendered solid losses some data because the contour does not fit the surface exactly. Small morphological details are lost when the program takes the contour and generates a solid. Thus there is a lost of data when the SURFDriver program goes to generate the final solid, for this final solid is created from triangular planes, and does not contain any of the jagged edges found in the section images. It is reasoned that these small losses are acceptable, for while minute details have been discarded, the general shape of the particle remains and therefore gives a good approximation of the actual microstructure. In the case of FEM models, the situation is even more favorable, for the SURFDriver software is ideal for generating simplified shapes that can be used in the FEM analysis.
Serial Section Problem Solution Analysis
Problems arose in the serial sectioning process that required the development of solutions. The three major problems encountered were:
Alignment of sections is a major part of the serial sectioning process. Maintaining good alignment will produce three-dimensional solids with accurate morphology. Misalignment of serial sections causes distortions of the final solid, and reduces its usefulness as a depiction of actual microstructure. The major source of misalignment in the serial sectioning process was identified as the securing of the sample during imaging. It was observed that the major misalignment introduced by the securing of the mount was rotation, and that this misalignment is the most difficult to correct for during image manipulation. Therefore, it was necessary to develop a method of securing the mount that would correct misalignment as much as possible.
To reduce rotational and translation misalignments, the sample surface must be placed in the same orientation after every polishing cycle. This means that the same orientation and position of the mount must be reproducible after removing the mount from the microscope stage completely. In additional, a technical constraint is added which requires that the mount can be placed into the polishing machine. This requires that the mounting hole not be covered by any permanent mechanism.
Two methods were used for securing the sample: a clay/glass slide method, and a magnetic method. The first method used a ring of sculpting clay to secure the sample to a glass slide. A ring of clay was used to prevent clay getting into the mounting hole. A punch was used to reduce skew misalignment. To deal with rotational misalignment, permanent marks were put on the sides of the mount, and corresponding marks were drawn on the glass slide. By aligning these marks, a semi-consistent orientation could be maintained. The second method used strips of magnetic tape placed on the bottom of the sample. Corresponding, oppositely poled strips were placed on a glass slide. The magnetic attraction was used to give a reproducible orientation to the sample. To evaluate the effectiveness of each method, a sample mount was positioned and imaged, then removed and repositioned to see how well the orientation was preserved. Figure A1 shows the before and after images for both the clay/glass slide method and the magnetic method. It is observed that the clay/slide method introduces a larger misalignment than the magnetic method, since it can be seen in Figure A1(a) that the displacement of particles between the two sections is larger than in A1(b). This demonstrates the magnetic method gives, to some small degree, better alignment than the clay/slide method, but neither method produces total alignment. Suggested alternative methods for securing the sample for alignment were as presented in the future work section of the thesis.
The algorithm for measuring the indentations to acquire thickness loss was to measure both diagonals once, regardless of outcome, and take the average. The depth of the indentation was calculated from the average, and the difference in depths between two sections gave the amount of thickness loss and hence the section thickness. This algorithm has the obvious drawback that it generates “negative” depths, which occurs whenever the diagonals of one indentation section are measured larger than the diagonals of the preceding indentation section.
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Figure A1. Two sequential serial sections overlaid to show superposition. The sections were taken so that the sample surface was removed from the microscope and then replaced using (a) clay/slide mounting (b) magnetic mounting.
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Figure A2. Damaged Vickers Indentation from polishing routine P5(N).
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Several causes exist that can lead to negative depth. First, the serial sectioning method was targeting to remove a very small depth of material, ~ 1 µm per cycle ideally. This small amount of thickness loss means that even slight deviations in a measurement can cause large, observed thickness loss changes. Second, the depth is being measured indirectly by observing the change in dimensions of indentations. This method relies on the fact that the indentations represent the geometry from which the depth was calculated, and that the images of the indentations give an accurate view of the dimensions being measured. If an indentation was distorted, especially in its lower sections, by local plastic deformation, then the indentation’s shape would change from section to section due to this distortion and the diagonals would reflect this. Such distortions could lead to errors in the depth, which would include giving negative depths. When the P5(N) polishing cycle was used, severe damage to the indentation distorted the geometry, as seen in Figure A2. Damaged indentations were difficult to measure due to the ambiguity of exactly where an indentation diagonal began and ended. In these cases, a reasoned guess must be made based on the previous measurements and what parts of the indentation can be identified as the vertices. Such approximations will introduce error into the diagonal measurement and thus give the possibility for negative depths.
The validity of the method used for measuring the diagonals, and the resulting thickness loss data must be considered carefully. First, it is known that the sample surface is not gaining thickness after polishing (which is the equivalent of a negative depth); therefore the result of a negative depth is unrealistic. However it is seen that, after several serial sectioning cycles, that there is a near consistent accumulation of thickness loss. So though the cycle-by-cycle thickness loss appears variable, the overall total appears constant. One solution to this would be to continuously re-measure a diagonal until a value was obtained that was lower than the previous indentation; this would guarantee no negative depths would occur. However, attempting to re-measure the diagonals until a desired length is obtained can lead to operator-induced expectations on the data. In addition to this, it is observed from experience that attempting to reach this goal of getting a smaller diagonal for each section leads to having to make unreasonable adjustments to the measuring process, such as starting the measurement at different, arbitrary points. All of this is poor measurement technique and even if it were acceptable, it would vary from operator to operator, and thus is not suitable for process consistency.
Although the current method of measuring each diagonal once can produce negative depths for a given section, the method does provide a consistent algorithm that can be repeated by any operator on any stack of sections. This method tries to impose an ordered, repeatable system to the process, and thus lends itself to repeatability, if not total reliability. Since the long term, accumulated total thickness loss gives relatively linear results, it is concluded that the measurement system for the diagonals can be used to give an average thickness loss rate. This introduces an error in the exact thickness between any two individual sections, but gives a fair estimate of the overall serial section thickness, and produces 3D solids which are realistic in morphology, as seen in Figures 21, 22 and 23.
Development of Polishing Routines
Six polishing routines were used for the thesis and are reprinted in Table A1 for reference.
Of these routines, only P5(N) gave the target ~ 1 µm per cycle thickness loss. What must be evaluated about these polishing routines is how well the thesis was in developing such routines. It is reasoned that P5(N) will not work in removing 1 µm for every type of material used, since it was developed specifically for the F280 SiC 2080 Al T6 composite. Therefore, if a new material were to be used, what would be the best way of evaluating a new polishing routine?
The method used for this thesis can be summarized in the following:
Upon reflection this method is not considered reasonable. The fact that the routine development was initiated at the lowest size grit was done because, at the beginning of the thesis, there was no knowledge as to how much material was being removed by any of the grit sizes. The smallest grit size was thus chosen since, if it could remove the required material, it would be the most efficient. It would be more efficient because, if the desired depth could be removed in 5 or 10 minutes at 1 um, this would be more efficient than using coarser grit which would require (at least) an additional 15 min with 1 um to restore the surface quality. The problem with this method, however, was choosing to increase the time parameter instead of load or speed. Increasing the time per cycle increases the overall time for the process; an increase in 1 minute per cycle for a 100-section run is equal to an hour and forty minutes extra for the process. However changing the loading or the speed does not add time to the process, and thus, in the long run, makes the process more efficient. Since there was no experience with whether increasing the load or the speed would increase the thickness loss, experimentation must be done to determine the effects of these parameters on thickness loss. A future polishing routine development algorithm, based on these observations, is given as follows:
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