Robert K. Goldberg and Peter J. Bonacuse

Glenn Research Center, Cleveland, Ohio

Subodh K. Mital

The University of Toledo, Toledo, Ohio

Investigation of Effects of Material Architecture 

on the Elastic Response of a Woven 

Ceramic Matrix Composite

NASA/TM—2012-217269

January 2012
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Robert K. Goldberg and Peter J. Bonacuse

Glenn Research Center, Cleveland, Ohio

Subodh K. Mital

The University of Toledo, Toledo, Ohio

Investigation of Effects of Material Architecture 

on the Elastic Response of a Woven 

Ceramic Matrix Composite

NASA/TM—2012-217269

January 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
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Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2012-217269 1

Investigation of Effects of Material Architecture on the 

Elastic Response of a Woven Ceramic Matrix Composite

Robert K. Goldberg and Peter J. Bonacuse

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Subodh K. Mital

The University of Toledo

Toledo, Ohio 43606

Abstract

To develop methods for quantifying the effects of the microstructural variations of woven ceramic 

matrix composites on the effective properties and response of the material, a research program has been 

undertaken which is described in this paper. In order to characterize and quantify the variations in the 

microstructure of a five harness satin weave, CVI SiC/SiC, composite material, specimens were serially 

sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source 

quantitative image analysis tools were then used to isolate the constituents and collect relevant statistics 

such as within ply tow spacing. This information was then used to build two dimensional finite element 

models that approximated the observed section geometry. With the aid of geometrical models generated 

by the microstructural characterization process, finite element models were generated and analyses were

performed to quantify the effects of the microstructure and its variation on the effective stiffness and areas 

of stress concentration of the material. The results indicated that the geometry and distribution of the 

porosity appear to have significant effects on the through-thickness modulus. Similarly, stress 

concentrations on the outer surface of the composite appear to correlate to regions where the transverse 

tows are separated by a critical amount.

Introduction

Ceramic matrix composites (CMCs) are being investigated for use in high temperature applications.

Potential application areas include hot-section engine components such as blades, vanes, combustor liners 

and nozzles, as well as airframe structural components, particularly for hypersonic applications such as 

wing leading edges. Ceramic matrix composites offer several advantages over monolithic ceramics 

including higher stiffness and strength, improved toughness and a more graceful failure mode. However, 

design and analysis methods for these materials are still under development.

Researchers such as Murthy, et al. (Ref. 1) have found that there is a significant amount of variability 

in the physical properties of ceramic matrix composites such as elastic modulus and the proportional 

limit. Morscher, et al. (Ref. 2) (as one example) has determined that the microstructure of a ceramic 

matrix composite can have a significant effect on the effective properties and response of the material.

Furthermore, researchers such as Lamon and co-workers (Refs. 3, 4, and 5) have quantified ways that the 

damage that takes place on the microscale can be reflected in the effective response of the composite. As 

shown in Figure 1, a micrograph of a five harness satin weave CVI SiC/SiC composite, the microstructure 

of a woven ceramic matrix composite displays significant amounts of variability and irregularity in areas 

such tow spacing, ply alignment, nesting of adjacent plies and matrix thickness. Furthermore, particularly 

for a CVI SiC/SiC composite, there is a significant amount of porosity that is arranged in irregular 

patterns. Therefore, a need exists to investigate the effects of the complex material microstructure on the 

effective properties and life of these materials. In addition, a need also exists to determine how the 
NASA/TM—2012-217269 2

characterized variability in the microstructure correlates with the known variability in the material 

properties of ceramic matrix composites.

As discussed in Nemeth, et al. (Ref. 6) and Mital, et al. (Ref. 7), in many analytical approaches that 

have been derived to model the response of woven ceramic matrix composites, the representative unit cell 

(the smallest repeating unit that is assumed to be representative of the composite as a whole) of the 

composite has been modeled using an idealized, ordered architecture with average dimensions for the tow 

geometry and spacing. A sample of a finite element model of a five harness satin weave ceramic matrix 

composite developed using this approach is shown in Figure 2. The regular geometry of the modeled 

composite can be seen in this figure. The areas between the fiber tows are assumed to be composed of 

matrix material. The effects of porosity are accounted for by uniformly degrading the properties of the 

pure matrix regions based on the overall percentage of porosity in the composite.

By comparing the actual microstructure of the composite shown in Figure 1 with the idealized 

microstructure shown in Figure 2, several key differences can be identified. In the actual composite, the 

undulation of the woven tows is much more gradual than is seen in the idealized model. In the actual 

composite, the outer boundary is very uneven due to the methods that are used to infiltrate the matrix 

material, while in the idealized model the outer boundary is smooth. In the idealized composite, the 

porosity is assumed to be evenly distributed throughout the composite, while in the actual composite the 

matrix is located in concentrated areas around the fiber tows, and the porosity is spread throughout the 

composite in irregular patterns. All of these differences indicate that by idealizing the composite using the 

methods applied classically, effects of the material response resulting from the irregular material 

microstructure and its variability on the material response may not be properly captured. The fact that the 

microstructure of the composite may affect the overall response and damage of the material is hinted at in

the analyses discussed in Mital, et al. (Ref. 7), where in the simulation of a tensile test regions of higher 

stress were found in the areas where the fiber tows crossed over each other.

Figure 1.—Micrograph of a five harness satin weave CVI SiC/SiC Composite

Figure 2.—Finite element models of a woven SiC/SiC composite generated using a classical analysis approach.
NASA/TM—2012-217269 3

To develop a method for quantifying the effects of the microstructure of a woven ceramic matrix 

composite and its variability on the effective properties and response of the material, a research program 

has been undertaken which is described in this paper. For this research study, the model material 

examined is a CVI SiC/SiC eight ply five-harness satin weave material. The composite has continuous 

Sylmaric-iBN fiber tows (20 ends per inch) woven into a five-harness woven fabric preform in a mutually 

orthogonal [0°/90°] pattern. A silicon-doped boron nitride (BN) coating was deposited on the surface of 

the individual filaments within the fiber tows. The fiber preform was infiltrated with a CVI-SiC matrix, 

which filled the area within the fiber tows and formed a thin coating around the fiber tows. The overall 

fiber volume fraction was approximately 0.36. Specifically, in this report, methods which have been 

developed to systematically characterize the microstructure of the material will be described. With the aid 

of the geometrical models generated by the microstructural characterization process, finite element 

models were generated and analyses were performed to quantify the effects of the microstructure and its 

variation on the effective stiffness and areas of stress concentration of the material.

Microstructural Characterization

In order to quantify the ways in which the variation of the microstructure in woven ceramic matrix 

composites affects the mechanical response of these materials, the variability needs to be accurately 

quantified. To address this issue, an effort has been undertaken to capture the distributions of various 

composite architectural parameters such as: distance between tows, size and shape of pores, relative 

alignment of plies, etc. The first step in this process involved the controlled removal of material from a 

sample of the composite material, in stages, while collecting high resolution imagery of the subsequently 

polished surfaces. Quantitative image processing techniques were then used to: correct for uneven 

illumination, “segment” the pixel intensity groups that correspond to the composite constituent materials, 

and isolate the “connected” segmented groups (individual pores, tows, etc) in order to systematically 

identify the constituents of the composite. The details of carrying out this process will be described here.

The procedures and algorithms for determining the microstructural parameter distributions in an 

automated fashion will be the subject of a subsequent report.

Serial Sectioning

For this study, a destructive technique for obtaining high resolution images of the details of the 

composite microstructure was selected. Samples of the composite were serially polished and high 

resolution images were acquired at each polishing step. Three specimens of the woven SiC/SiC composite 

were simultaneously polished, in stages, until the entire specimen was consumed. Figure 3 shows the 

orientation of the specimen during the polishing procedure, a photograph of the samples in the polishing 

fixture, and an example of a polished specimen cross section. The target removal rate was 0.2 mm per 

polished section. Accurate measurements (in three locations around the perimeter) of the height of the 

sample mounts were taken initially and after each polishing step to determine the amount of material 

removed. The specimens were initially 12.7 mm square with a thickness of approximately 2 mm. Images 

of the polished sections were acquired with an optical microscope that had an integrated, motorized, 2 

degree-of-freedom translation stage, with associated software, that allowed for the automated acquisition 

of high resolution images of the whole specimen cross section. Because the camera on this system had a 

resolution of 640 by 480 pixels (fairly low by current standards) and the features of interest in the 

composite are relatively small compared to the size of the specimen, a trade-off between the size of the 

image (amount of memory required to hold the image; the computation time for image analysis tends to 

increase exponentially with image size) and the needed resolution of the microstructural features had to 

be determined. After some iteration, an adequate compromise was achieved using a 50 times optical 

magnification which required 12×3=36 slightly overlapping images to acquire the entire specimen cross 

section. After stitching the 36 images together, the resulting mosaic came in at about 10 MB (a large 

image, but still computationally tractable).
NASA/TM—2012-217269 4

Figure 3.—Specimen mounted in epoxy for polishing (a), three specimens in the polishing apparatus (b), and an 

example of a polished CVI SiC/SiC composite cross section (c).

Image Segmentation

With the cross section images in hand, the next task was to develop an automated, objective, and 

repeatable process to identify the composite constituents. This is a necessary step toward the collection of 

statistics needed for the generation of analysis models for characterizing the effect of microstructural 

variability. The process of identifying the component parts of an image is often referred to as 

“segmentation”. When there is sufficient separation between the intensities of the various constituents in the 

image (contrast), it is possible to use statistical techniques to isolate these constituents (Ref. 8). To perform 

this function, with the goal of having a capability that could be readily shared and expanded by other 

researchers, it was decided that the implementation should be open source. The Python programming 

language [http://www.python.org/] was chosen with the addition of the image processing and matrix 

manipulation tools in the SciPy and NumPy libraries [http://www.scipy.org/]. In the process of 

implementing the algorithms for the segmentation process, it was found that there was a marked and 

irregular gradient in the illumination of the specimen. This gradient was first observed when the images 

making up the specimen cross section were tiled together and there was a noticeable step in the intensity 

across individual images. To compensate for this, several images of the fairly featureless epoxy surrounding 

the specimen were acquired to be used for gradient removal. Using a Gaussian blur to smear out the detail in 

the epoxy images and averaging over the three images gave an approximation of the illumination gradient 

(Ref. 8). Subtracting the mean of this gradient image from itself gave a matrix of the deviation of the 

illumination from the mean. This was then subtracted from each of the collected images to correct for the 

illumination gradient. An image stitching algorithm was also implemented in Python to seamlessly overlay 

the illumination corrected images into a single image of the specimen cross-section. Figure 4 displays the 

histogram of the pixel intensities after illumination gradient subtraction. The figure illustrates the 

identifiable modes in the pixel intensities that are associated with the composite constituents. Using just the 

intensity information, a simple one dimensional cluster analysis technique was sufficient to separate the 

modes. The k-means algorithm (Ref. 9) (coded into the SciPy library) does an adequate job of separating the 

image constituents (pores, boron nitride (BN) fiber coating, and the SiC matrix and fibers (Fig. 5)). Note 

that specifically identifying and separating out the boron nitride fiber coating is required in order to isolate 
NASA/TM—2012-217269 5

the fiber tows. Since the silicon carbide fibers and silicon carbide matrix are essentially the same material, 

they have similar pixel intensities, making it difficult to identify the fibers separately from the matrix.

However, since the boron nitride fiber coating surrounding the fibers has a different pixel intensity, isolating 

the fiber coating is possible and leads to identifying the fiber tows in the segmented image.

Figure 4.—Histogram of pixel gray scale intensities showing identifiable

modes that correspond to the identified composite constituents

Figure 5.—Three segments of a typical composite cross section isolated using the k-means algorithm: top—porosity; 

middle—fiber coating; and bottom—SiC matrix and fibers. All three are binary images with the isolated constituent 

in white.
NASA/TM—2012-217269 6

Quantitative Image Analysis

The next step was to use the information in the segmented images to isolate the microstructural 

features of interest: transverse sectioned tows, longitudinally sectioned tows, pores, and the SiC matrix 

surrounding the tows. Using binary morphological operations on selected segments of the images, it was 

possible to isolate these constituents with reasonable accuracy. The purpose of these morphological 

operations was to fill in the microstructural features of interest and eliminate the features (at least 

temporarily) that were not of interest. The transverse tows were isolated first by taking the binary image 

of just the BN coating segment (all pixels that fell into the fiber coating cluster are “ON” and all other 

pixels are “OFF”), performing a binary closing (dilation followed by erosion) operation weighted in the 

horizontal direction to fill in the transverse sectioned tows, followed by a binary opening (erosion 

followed by dilation) operation weighted to the vertical direction to eliminate the longitudinal sectioned 

tows. Morphological dilation can be thought of as adding pixels to the periphery of a connected group of 

pixels. For example, a square group of pixels dilated with a square structuring element would become a 

larger square grouping. Erosion is simply the inverse of dilation. These operations took advantage of the 

difference in the shape of these microstructural features. For instance, the fiber coating cluster was chosen 

for the tow identification because this isolated cluster represented the shapes of the tows best. With a few 

more filtering operations to eliminate spurious remnants and to fill in and refine the shape resulted in a 

reasonable approximation of the transverse sectioned tows.

With the transverse tows isolated, an image of the transverse tows was used as a mask for the 

isolation of the longitudinal tows. Starting again with a binary image of the tow coating segment, the 

pixels associated with the transverse tows were eliminated with an exclusive OR operation (any pixels 

ON in both images were turned OFF). Table I contains a brief review of Boolean operations as applied to 

binary images. Another sequence of binary operations aimed at enhancing and filling in the longitudinally 

sectioned tows was then performed. To find the matrix, the best solution was to OR the SiC segment with 

the fiber coating segment (collecting everything that is not a pore) and then to XOR this with the 

combined isolated transverse and longitudinal tows. This eliminated any overlap that could occur if 

matrix were to be isolated without any information about the tows. To capture the inter-tow pores in the 

composite, including those that were surface connected, an operation was performed that set boundaries 

for the specimen. This was accomplished by again combining the SiC and fiber coating image segments 

and performing a short sequence of binary morphological operations to fill all the interior voids and close 

off the surface connected pores. The result of a binary AND operation involving the binary image of the 

specimen and the inverse of the combined matrix, transverse and longitudinal tows gave an image of the 

pores. Figure 6 shows the results of the automated constituent isolation for a section.

TABLE I.—BOOLEAN OPERATIONS FOR BINARY IMAGES (PIXELS CAN BE ONLY ON OR OFF)

Operator Both ON One ON, One OFF Both OFF

AND ON OFF OFF

OR ON ON OFF

XOR (exclusive OR) OFF ON OFF

Figure 6.—Composite constituents isolated with an automated procedure utilizing binary morphological operations. 

Isolated constituents are overlaid on the image of the cross section. Transverse sectioned tows—green; 

longitudinally sectioned tows—blue; matrix—red; inter-tow porosity—white; and outside specimen—black.
NASA/TM—2012-217269 7

Segmented to Simplified

The images of the isolated composite microstructures were not amenable to the generation of finite 

element models for structural analysis due to the irregular sizes and shapes of the constituents and, 

because of ply misalignment, the discontinuous appearance of the longitudinally sectioned tows. To 

compensate for these irregularities, techniques were developed to generate simplified geometries based on 

the segmented images while still maintaining relevant microstructural details. This process (illustrated in 

Fig. 7) started with the transverse sectioned tows. The area and dimensions of the full transverse sectioned 

tows were determined, taking care to exclude incomplete tows near the cut specimen edges, and used to 

generate a lenticular shaped object with an area, height, and width equal to mean values of these 

parameters for the transverse sectioned tows. The centroids of the transverse tows in the segmented image 

were then determined and copies of the lenticular transverse tow approximation were placed at these 

centroids as the starting point of the simplified model. The longitudinally sectioned tows were addressed 

next. Several continuously sectioned tows were found in the sectioned images and a sinusoid was fit to 

the path of these continuous longitudinal tows. The thickness of the longitudinal sectioned tows was 

determined by calculating the average thickness of the longitudinal sectioned tows in the segmented 

images. This thickness value was calculated by summing the number of pixels in each column of the 

specimen cross section that were identified as belonging to a longitudinally sectioned tow. The mean 

number of pixels from this calculation was then divided by the number of plies to arrive at an 

approximate mean longitudinally sectioned tow thickness. Next the specimen micrograph was used to 

approximate (by eye using open source image editing software, GIMP [http://www.gimp.org/]) the 

locations of the eight longitudinally sectioned tows. This was complicated by the fact that misalignment 

of the plies relative to one another caused some longitudinal tows to have only short segments of their 

paths through the composite exposed in the polished section (see the fourth ply from the bottom in 

Fig. 7). The transverse sectioned and longitudinally sectioned tow approximations were then overlaid 

using GIMP and the locations of some of the transverse tows were adjusted to minimize interference with 

the longitudinal tows and other transverse tows. With this image of the transverse and longitudinal tows 

as a starting point, the matrix was “grown” uniformly using a function written to dilate the matrix 

symmetrically on the tows until the matrix volume fraction matched that determined from the segmented 

image.

Figure 7.—Transverse and longitudinal tow approximation placement. Note incomplete paths of some longitudinal 

sectioned tows and displacement of some transverse tows to accommodate continuous longitudinal tows.
NASA/TM—2012-217269 8

Description of Sections and Simplified Idealizations (Volume Fractions, Distribution of Porosity)

Four section images of a single approximately 12.8- by 12.8- by 2.2-mm sample of CVI SiC/SiC 

composite specimen were selected to generate simplified specimen geometries. Shown in Figures 8 

through 11 are the segmented section and the simplified approximation for each of the four sections 

(designated 03, 10, 22, and 37 based on the sequence of sections taken from the specimen). Four sections 

were chosen in order to make available for analysis samples with differing microstructures, to facilitate 

the process of determining how the variation in the material microstructure affects the elastic properties 

and response of the material. As can be seen in the figures, each of these sections displays a significant 

amount of porosity arranged in irregular patterns. Furthermore, the fiber tows within a ply display 

irregular spacing, and the stacked plies are nested within each other. The amount and distribution of the 

porosity and the relative spacing of the fiber tows can be observed to vary significantly between the 

various sections. Table II compares the constituent volume fractions calculated from the four actual 

sample cross sections and the constituent volume fractions in the simplified models (along with analysis 

results to be discussed later). Note that, unlike classical methods which typically use average values and 

identical repeating unit cells, the simplified idealizations capture the variations in the composite 

microstructure observed in the actual specimens. In addition to the four sections generated based on the 

actual material, an artificially generated “aligned” model was generated using the fit sinusoidal 

longitudinal tow shape and regularly spaced transverse tows from the simplified specimens, appropriately 

arranged for a five harness satin weave configuration (Fig. 12). A single unit cell was constructed with 

these assumptions and used to generate a perfectly aligned and stacked cross section. Note that, as is the 

case with the composite specimens, alternating plies of the composite are ‘flipped’, i.e., the satin faces 

(four tows over in the warp direction) are always mated with adjacent satin faces. This “aligned” model, 

which still captures key features of the actual microstructure such as the uneven top and bottom surfaces 

and the large areas of porosity, was created to be used as a baseline to contrast with the more random 

nature of the idealized, as-manufactured, composite models.

TABLE II.—COMPARISON OF AREA/VOLUME FRACTIONS FOR THE SEGMENTED CROSS SECTIONS AND THE 

SIMPLIFIED MODELS FROM WHICH THEY WERE DERIVED, ALONG WITH EFFECTIVE MODULUS VALUES

Pore Tow Matrix Ex, 

GPa

Ez, 

GPa

Section 03 Segmented 0.087 0.575 0.338 ---- ----

Simplified 0.032 0.630 0.338 237 103

Section 10 Segmented 0.069 0.608 0.323 ---- ----

Simplified 0.048 0.628 0.324 227 77

Section 22 Segmented 0.085 0.591 0.324 ---- ----

Simplified 0.035 0.639 0.326 234 51

Section 37 Segmented 0.109 0.577 0.318 ---- ----

Simplified 0.055 0.623 0.322 229 39

Ideal-01 0.047 0.616 0.338 230 110
NASA/TM—2012-217269 9

Figure 8.—A comparison between a specimen section and the idealized version constructed 

for FEM generation (Section 03).

Figure 9.—A comparison between a specimen section and the idealized version constructed for FEM 

generation (Section 10).
NASA/TM—2012-217269 10

Figure 10.—A comparison between a specimen section and the idealized version constructed for FEM generation 

(Section 22).

Figure 11.—A comparison between a specimen section and the idealized version constructed for FEM 

generation (Section 37).
NASA/TM—2012-217269 11

Figure 12.—An aligned CMC approximation constructed from a repeated unit cell that was in turn 

constructed by placing evenly spaced transverse sectioned tow approximations about the approximation 

of the sinusoidal fit to the longitudinal tows.

Differences Between Segmented Sections and Simplified Idealizations

In the simplified models, there were several shortcomings of growing the matrix uniformly on the 

fiber tows. First, the physics of the chemical vapor infiltration process leads to non-uniform deposition of 

the matrix material on the fiber tows; the matrix is typically thicker on the outer surface of the composite 

and gets progressively thinner the closer to the centerline. Because of this, the simplified models had a 

lower porosity than the specimen sections at the same matrix volume fraction. Second, because there was 

less matrix material on the outer surface of the simplified models, the overall size of the specimen 

compared to the specimen sections was smaller which, in combination with the lower porosity, led to a 

high side bias in the tow volume fraction. Also, because the surface tows in the composite tend to be 

flattened during fabrication, the simplified approximation tended to exaggerate the surface irregularity 

(especially the deeper intrusions between the tows). When these simplified sections are used as the basis 

of conducting finite element analyses (which will be described in more detail later in this paper), one 

consequence of the exaggerated irregularity on the outer surfaces may be that stress concentrations in the 

matrix near the boundaries of the transverse tows may be somewhat overemphasized.

Another difference between the simplified and actual sections was that that the longitudinally 

sectioned tows in the simplified approximations did not show the variation in thickness displayed in the 

sections, both along the length of the tow and from ply to ply. The apparent non-uniform thickness of the 

longitudinal sectioned tows was mostly due to both the non-uniform cross sectional area of the tows and 

the slight misalignment of the plies with the sectioning plane causing the apparent thickness of the tow to 

change. This also contributed to the difference in the porosity between the section images and the 

simplified models in that the spaces between the longitudinal tows could not be represented in a two 

dimensional approximation that had continuous longitudinal tows. If the maximum tow thickness were 

used for the thickness of the longitudinally sectioned tows: 1) it would have presented a packing problem

for the simplified model and 2) it would have led to an overestimation of the stiffness in the direction of 

the longitudinal tows. In constructing the two-dimensional models, few perpendicular sections, through 

even a perfectly aligned composite, would section the tows through their maximum thickness, therefore 

an average thickness was necessary to approximate the stiffness appropriately. Future efforts will focus 

on developing the ability to generate three-dimensional representations of the actual microstructure in 

order to reduce the effects of these assumptions. Note, however, that even with all of the approximations 

and simplifications required in the generation of the “simplified” sections, the key features of the material 

microstructure and their variability were still captured.
NASA/TM—2012-217269 12

Finite Element Analysis

To explore the effects of the complex microstructure of the woven ceramic matrix composite on the 

effective properties and response of the material, the two-dimensional simplified sections, discussed in 

the previous section, were analyzed. Two-dimensional finite element models of both the actual and 

artificially generated “aligned” sections were developed using the software tool OOF2 (Object Oriented 

Finite Element Analysis of Material Microstructures (Refs. 10 and 11). The finite element models were 

analyzed using the ABAQUS general purpose finite element program (Ref. 12) in order to examine the 

effects of the material microstructure and its variability on the effective in-plane and through-thickness 

moduli, and the location of stress hotspots given a purely elastic load. The stress hotspots would most 

likely be the locations where damage would initiate in the material under load. For the analyses described 

in this study, the material response was assumed to be purely elastic. Incorporation of the ability to 

analyze the progressive damage and nonlinearity in the material response will be described in a future 

report.

Finite Element Mesh Generation and Model Details

The OOF2 software was used to create the two-dimensional finite element meshes for the twodimensional sections (slices) examined in this study. OOF2 is a public domain software product created at 

the National Institute of Standards and Technology (NIST). OOF2 can generate an appropriate finite 

element model (among other simulation capabilities) starting from a two-dimensional representation, or 

image, of arbitrary geometrical complexity. For OOF2, the microstructure is a data structure composed of 

image and property data. The inputs necessary to generate an appropriate mesh include: 1) a 

microstructure (based on a real micrograph or computer generated image), 2) material properties and 3) 

boundary conditions. The OOF2 software, which runs on any computer running a variant of the UNIX 

operating system, is completely scriptable in Python. It can export the finite element meshes generated 

from the image analysis directly into the ABAQUS finite element program, which can then analyze the 

meshes generated using OOF2.

The procedure for creating good meshes using OOF2 is quite involved with several steps, and also 

involves significant user intervention. The process starts by identifying pixels of different colors and 

assigning them to different groups of materials that will be meshed such as the matrix, longitudinal tows 

and transverse tows. The process then continues by the generation of an initially very crude mesh, 

followed by iteratively refining and rationalizing the mesh to remove ill shaped elements with features 

such as sharp corners or high aspect ratios. The mesh is then homogenized to reduce the elements that are 

not homogeneous, i.e., contain more than one group of materials. This process then goes on iteratively 

along with a mesh refinement process to ensure good elements and a high quality mesh. One feature of 

the software is that the whole process, including user inputs, can be carried out using a user-friendly 

graphical user interface. All of the user inputs can be recorded in a Python script file akin to a history of 

commands. If needed this Python script file can then be run in a batch mode to recreate the finite element 

mesh with no user intervention required. A screenshot of the OOF2 graphical user interface is shown in 

Figure 13.

Finite element models were generated for the four actual (simplified) sections discussed earlier (and 

shown in Figure 14(a) to 14(d)) which were designated as Sections 03, 10, 22 and 37. In addition, a finite 

element model was also generated for the artificially generated “aligned” section identified earlier in this 

report (and shown in Fig. 14(e)), designated Ideal-01. Analyzing the “aligned” section and comparing the 

results to those obtained from analyzing the sections based on the actual microstructures facilitated the
NASA/TM—2012-217269 13

Figure 13.—Screenshot of OOF2 graphical user interface.

process of examining how the variability in the microstructure affected the response of the material. From 

the simplified images of these sections, image analysis was performed using the OOF2 software and 

detailed two-dimensional finite element meshes of these sections were created. A typical mesh, a twodimensional finite element model of Section 03, is shown in Figure 15. The section consisted of 

longitudinal and transverse tows, CVI-matrix and porosity. To simplify the analysis and keep the size of 

the finite element mesh reasonable, the longitudinal and transverse tow material was treated as a 

homogenized material in this model even though the tow consisted of fibers, interfacial coating, matrix 

and inter-tow porosity. Due to the fact that the areas of inter-tow porosity were found to be relatively 

small and evenly spaced throughout the fiber tow, the inter-tow porosity was not explicitly modeled, and 

the effects of the porosity were just accounted for in determining the effective properties of the fiber tows.

The finite element model consisted of 17,442 nodes and 19,502 plane stress elements of which 14,545 

were linear quadrilateral elements and 4,957 were linear triangular elements. While detailed mesh 

sensitivity studies were not conducted, the level of mesh refinement used for the analyses were deemed to 

be adequate. Due to the nature of the simplified models, there were a number of sharp corners near tow 

boundaries, which could potentially be the source of stress singularities, leading to an inaccurate 

determination of areas of stress concentrations. However, the level of mesh refinement along and near 

these corners was assumed to be fine enough to minimize these difficulties. Since the top and bottom 

surfaces of the sections were not uniform, to allow for applied loads in the through-thickness direction 

some extra artificial material was added to the sections to make the top and bottom surfaces flat and 

uniform as shown in Figure 16. When applying in-plane loads in the x-direction (in-plane), this extra 

material was assigned a very low modulus in the x-direction so as not to change the actual in-plane 

modulus of the section. On the other hand, when applying a through-thickness load to compute the 

effective through-thickness modulus, the extra material was assigned a very high z-direction (throughthickness) modulus so that it acted as a rigid material. The modulus of the extra material was kept low in 

the x-direction. Symmetric boundary conditions were generally used when applying either the in-plane or 

through-thickness load. For example, when applying in-plane tensile loads in the x-direction, the left edge 
NASA/TM—2012-217269 14

was held fixed in the x-direction and the right edge was prescribed a fixed displacement, thus applying a 

fixed strain on the right edge. Following the finite element analysis, the effective force and thus the stress 

level corresponding to the applied strain was computed. A similar set of boundary conditions and 

displacements were applied for computing the through-thickness composite modulus, with the bottom 

edge being held fixed and fixed displacements being applied on the top edge. As mentioned above, the 

finite element meshes generated by the OOF2 software were exported to the ABAQUS finite element 

program to conduct the analyses shown in this work.

(a) Simplified image of Section 03

(b) Simplified image of Section 10

(c) Simplified image of Section 22

(d) Simplified image of Section 37

(e) Simplified image of Section Ideal-01

Figure 14.—Images of various sections analyzed (red is CVI-matrix, blue and green are 

longitudinal and transverse fiber tows respectively, porosity is shown in white space).

Z

X
NASA/TM—2012-217269 15

Figure 15.—Finite element model of Section 03 (17,742 nodes, 19,502 elements of which 14,545 are 

linear quadrilateral and 4,957 elements are linear triangular).

Figure 16.—Simplified image of Section 03 with extra material added (shown in yellow) mainly for throughthickness analysis.

Analysis Results and Discussion

Following the analysis technique outlined above, the in-plane and through-thickness modulus of each 

of the four actual sections and the “aligned” section discussed above were computed. The constituent 

material behavior was assumed to be linear elastic. All of the results were computed at room temperature 

based on room temperature material properties. The effective, smeared properties for the fiber tows were 

computed based on the fiber, matrix and coating constitutive properties by using classical

micromechanics techniques (Ref. 7). The constituent properties of the Sylmaric fiber and boron nitride 

(BN) coating were assumed to be those given in Mital, et al. (Ref. 7). The fiber tows had a relatively high 

amount of porosity, on the order of 15 percent, but micrographical examinations revealed that this 

porosity was relatively uniformly distributed and each pore was relatively small in size compared to the 

dimensions of the fiber tow. Therefore, in computing the effective tow properties, the elastic properties of 

the matrix used in the calculations were merely degraded by an appropriate amount to reflect the presence 

of the porosity. In modeling the matrix material that is present outside of the fiber tows, since the intertow porosity is large, unevenly distributed, and explicitly accounted for in the finite element models, the 

bulk matrix properties were used for this material. The inter-tow porosity was explicitly modeled as holes 

within the finite element mesh. The effects of the inter-tow porosity were not smeared into the matrix 

properties as is usually done in classical analysis methods. The computed effective elastic properties of 

the fiber tows and the bulk matrix properties are given in Table III.

Z

X
NASA/TM—2012-217269 16

TABLE III.—MATERIAL PROPERTIES USED AT ROOM-TEMPERATURE

Tow Properties

800 filament Sylramic-iBN, Filament diameter = 9.5 μm, BN 

coating thickness = 0.6 μm, 15 percent porosity (assumed 

uniformly distributed) 

EL = 260 GPa

ET = 105.5 GPa

νLT = 0.18

GLT = 42.5 GPa 

CVI-SiC Matrix Modulus = 420 GPa

Poisson’s ratio = 0.2 

The effective homogenized in-plane (Ex) and through-thickness (Ez) moduli computed by the finite 

element analyses for each of the sections are given in Table II. The results indicate that the computed inplane modulus values displayed a relatively small amount of variability, with the variability that was 

present being roughly inversely proportional to the amount of porosity in the analyzed sections (i.e.,

higher levels of porosity yielding lower modulus values). The computed values of the in-plane modulus 

also correlated with the experimental values (and values obtained by a variety of analytical methods) 

shown by Mital, et al. (Ref. 7), albeit for a slightly different material. Future efforts will involve obtaining 

experimental data for the specific material that was examined in this study. The computed throughthickness modulus values, on the other hand, displayed a large amount of variability. Furthermore, the 

variation in the through-thickness modulus did not directly correlate to the volume fractions of the various 

constituents. For example, Sections 03 and 22 had very similar amounts of overall porosity but their 

through-thickness modulus differed by a factor of two. The ratio of the predicted through-thickness 

modulus to the predicted in-plane modulus obtained in this study was much smaller than the modulus 

ratio obtained by classical methods for a similar material as shown in Mital, et al. (Ref. 7). Furthermore, 

the ratio between the mean value of the predicted through-thickness modulus to the in-plane modulus 

obtained by the current analyses was closer to what was observed experimentally for a similar material 

described in Mital, et al. (Ref. 7). The maximum through thickness modulus value predicted by the 

current set of analyses also was much lower than the value predicted using classical methods and much 

closer to experimentally obtained values.

One possible contributing factor explaining the relatively low predicted values and large variability in 

the through-thickness modulus computations can be observed by examining contour plots of the 

transverse displacements for Sections 03 and 22 (which had similar overall amounts of porosity), shown 

in Figure 17. In Section 22, there were several long, thin areas of porosity, leaving very small continuous 

areas of fiber tow and matrix from top to bottom in the section, which inhibited load transfer. The lack of 

load transfer from the top of the section to the bottom resulted in low values of transverse displacement 

(and by extension low stresses) in the bottom half of the section, with high levels of transverse 

displacement only in the upper portion of the section, which led to a low through-thickness modulus. In 

Section 03, on the other hand, the porosity was more uniformly distributed in smaller thicker clumps, 

leaving more area available for load transfer through the thickness which led to a higher throughthickness modulus, almost double the value obtained for Section 22. However, even in Section 03, the 

areas of porosity that were present did still serve to inhibit the load transfer to some extent, as reflected in

the moderately extended areas of low transverse displacement observed in the contour plot. As mentioned 

previously, by using traditional analysis methods, much higher relative values of the through-thickness 

modulus were predicted. The higher relative through-thickness modulus values obtained using classical 

methods are most likely due to the fact that the porosity is not explicitly modeled in the classical 

approaches and also that in the classical approaches the fiber tows in each layer are assumed to be 

perfectly aligned and stacked. Both of these assumptions allow for increased load transfer (and thus

overall higher stress levels leading to a higher modulus) to result in the analysis. The effect of fiber tow 

alignment on the through-thickness modulus can be inferred from the results in the present study where 

the artificially generated “aligned” Section Ideal-01 had the highest predicted value for the throughthickness modulus. For this section (Ideal-01), since the transverse tows were perfectly aligned 
NASA/TM—2012-217269 17

Figure 17.—Through-thickness displacement contours for Sections 03 and 22 (displacement 

values range from zero (shown in blue) to maximum displacement (shown in red).

and stacked on top of each other, the applied loads could be transferred through the entire thickness, 

leading to overall higher levels of stress in the entire section and thus higher through-thickness modulus 

values.

Von Mises and maximum principal stress values resulting from an elastic stress analysis with an 

applied in-plane strain of 0.07 percent were also plotted for all of the sections analyzed in this study. Due 

to the fact that only an elastic stress analysis was performed, the level of strain that was applied was 

somewhat arbitrary. However, this strain value is most likely near the strain level where the stress-strain 

behavior for the actual composite shows a significant deviation from linear elastic behavior. The purpose 

of these analyses was to identify the locations of stress risers, to determine if the location of the stress 

risers were related to any specific architectural feature(s) and to examine the general pattern of stress 

distribution. The goal of future efforts will be to determine if the predicted locations of the stress risers 

are the same or related to the locations where cracks are observed to initiate in experimental testing of the 

actual composite, as cracks would be likely to initiate in high stress locations. Figures 18 through 22 show 

the von Mises and maximum principal stresses in Sections 03, 10, 22, 37 and Ideal-01 resulting from an 

applied strain of 0.07 percent in the x-direction. Von Mises stresses were analyzed as a way to quantify an 

effective stress state resulting from multiaxial loading. While perhaps not completely applicable for the 

analysis of ceramics and ceramic matrix composites, von Mises stresses could also at least serve as a 

starting point for the development of damage and failure models. The regions shown in circles are areas 

of relatively high stresses in these sections. While the specific locations of high stresses vary for each of 

the sections, for each of the actual sections the areas of high stresses in the matrix on the surface appear to 

correlate to locations where the transverse tows are separated by some critical distance. There appears to 

be lower stress concentrations if the transverse tows are farther apart. High stresses in the matrix also 

were noted in the interior of the sections near some of the areas of large porosity. These points are 

emphasized in Figure 23, where the maximum principal stresses in the matrix constituent for Section 10 

are plotted in a simplified manner, with the high stress regions highlighted in red. As mentioned earlier, 

these stress concentrations may be somewhat exaggerated due to the exaggerated irregularity in the outer 

surfaces resulting from the methods used to generate the simplified models. However, the general trends 

are most likely still valid and correlate with observations that have been made experimentally (Ref. 2).

Furthermore, the exact locations of the stress concentrations were located away from the sharp corners 

Z

X
NASA/TM—2012-217269 18

and tow boundaries. Therefore, the stress concentrations were assumed to be real and not the result of 

stress singularities resulting from the finite element mesh. These preliminary analyses provide indications 

of how the architecture of the microstructure might affect the initiation of damage in the composite.

Further studies are required to rigorously quantify the linkage between architectural features and stress 

concentrations.

Figure 18.—Von Mises (top) and max. principal (bottom) stresses in Section 03 for applied in-plane strain of 0.07

percent (circles indicate typical locations of damage initiation sites in matrix)

Figure 19.—Von Mises (top) and max. principal (bottom) stresses in Section 10 for applied in-plane strain of 

0.07 percent
NASA/TM—2012-217269 19

Figure 20.—Von Mises (top) and max. principal (bottom) stresses in Section 22 for applied in-plane strain of 

0.07 percent.

Figure 21.—Von Mises (top) and max. principal (bottom) stresses in Section 37 for applied in-plane strain of 

0.07 percent.
NASA/TM—2012-217269 20

Figure 22.—Von Mises (top) and max. principal (bottom) stresses in Section Ideal-01 for applied in-plane strain of 

0.07 percent.

Figure 23.—Plots of high stress regions (shown in red) for the matrix constituent in Section 10.

Cracks in the matrix would most likely initiate from these stress concentration locations, which is 

why developing a relationship between architectural features and stress concentrations is important. 

However, an important point to note is that the stress concentration sites in the matrix identified in this 

study are not necessarily the only potential sites for crack initiation. For example, the stresses in the 

transverse direction in the fiber tows (related to the x-direction stresses in the transverse tows in the twodimensional sections discussed here) are also significant. The maximum allowable strain in the transverse 

direction for the fiber tows is likely to be around 0.05 percent, which when converted to stress is 

approximately 7.5 ksi. Therefore, even though the actual x-direction stresses in the transverse tows are 

relatively low in these analyses, the stress levels are actually relatively close to the transverse strength 

values of the fiber tows indicating that cracks could also initiate in the transverse tows due to matrix 

cracking or debonding.

Figure 24 shows the distributions of matrix stress in the x-direction due to an applied in-plane strain 

of 0.08 percent. Matrix stresses were chosen for this plot since these stresses potentially display the 

greatest variability both within and between sections. Furthermore, since in classical methods the 

“effective” matrix included both the matrix material and the porosity (in an implicit manner), examining 

the matrix stresses potentially would illustrate most dramatically the difference between results obtained 

by modeling the matrix and porosity separately, as is done in this study, and the results obtained using 
NASA/TM—2012-217269 21

Figure 24.—Probabilistic variation of matrix stress in x-direction (applied strain 

0.08 percent) for analyses using actual and classical (idealized) 

microstructures.

classical methods. The stresses in Figure 24 are plotted both for Section 10 and for an ideal section 

analyzed using classical three-dimensional finite element analysis. The “classical” analysis model 

assumed an ordered or nominal architecture and only one ply was modeled. Also in the classical analysis, 

the porosity was not explicitly modeled but instead was smeared with the inter-tow matrix and degraded 

matrix properties were used. Even though the results for only one actual section are shown in Figure 24, 

the results obtained for the other actual sections followed these results very closely. As shown in the 

figure, the average non-zero stress is higher for the analysis based on the realistic microstructure as 

compared to the results obtained using classical analysis methods. However, when the second stress peak 

at zero obtained for the realistic section (resulting from the explicitly modeled porosity) is factored in, the 

average stress obtained for the realistic section is approximately equivalent to that obtained using classical 

analysis methods. In the results shown for the classical analysis, since the porosity is incorporated into the 

effective matrix response, the response of the porosity cannot be explicitly determined. Of more 

significance, however, is the fact that the results obtained using the realistic microstructure has a 

distribution with expanded tails and a higher probability of higher stresses as compared to the distribution 

obtained using classical methods. Since damage would most likely initiate at the areas of high stress, the 

ability of the analyses conducted utilizing the realistic microstructures to capture the high stress tails of 

the probability distribution indicates that these analyses would be more likely to accurately identify sites 

for damage initiation.

Conclusions

A procedure has been developed to systematically characterize the microstructure of a five harness 

satin weave ceramic matrix composite. In these efforts, representative “slices” of a CMC coupon were 

examined, both to generate realistic microstructural geometries that could be used for analysis, and to 

begin to quantify the variability in the microstructure. Using the geometrical models generated by the 

microstructural characterization process, finite element models were then generated and analyses 

performed to quantify the effects of the microstructure and its variation on the effective stiffness and areas 

of stress concentration. By combining the results of the finite element analyses and the microstructural 

characterization, initial attempts have been made to link the variation in elastic moduli and stress 
NASA/TM—2012-217269 22

concentrations obtained by the analyses to specific areas of variability identified by examining the 

microstructure.

Future efforts will involve more detailed quantification of the microstructural variability both within 

and between slices. Efforts will also be conducted to modify the procedures used to generate the 

simplified models to better represent the non-uniform distribution of the matrix throughout the crosssection. Methods to obtain representative three-dimensional images and simplifications of the actual 

microstructure will also be explored. In the analysis efforts, progressive damage procedures and 

algorithms will be incorporated into the analysis in order to quantify the effects of the microstructure on 

initiation and propagation of local damage as well as the first matrix cracking stress and the overall stressstrain response of the composite. Methods to systematically link the variability of the microstructure to 

the variability observed in the effective properties and response of the composite will also be developed.

References

1. Murthy, P.L.N.; Nemeth, N.N.; Brewer, D.N.; and Mital, S.: “Probabilistic Analysis of a SiC/SiC 

Ceramic Matrix Composite Turbine Vane,” NASA/TM—2004-213331, 2004.

2. Morscher, G.N.; DiCarlo, J.A.; Kiser, J.D.; and Yun, H.M.: “Effects of Fiber Architecture on Matrix 

Cracking for Melt-Infiltrated SiC/SiC Composites,” International Journal of Applied Ceramic 

Technology, Vol. 7, pp. 276–290, 2010.

3. Guillaumat, L.; and Lamon, J.: “Probabilistic-Statistical Simulation of the Nonlinear Mechanical 

Behavior of a Woven SiC/SiC Composite,” Composites Science and Technology, Vol. 56, 

pp. 803–808, 1996.

4. Lamon, J.; Thommeret, B; and Percevault, C.: “Probabilistic-statistical Approach to Matrix Damage 

and Stress-Strain Behavior of 2-D Woven Sic/Sic Ceramic Matrix Composites,” Journal of the 

European Ceramic Society, Vol. 18, pp. 1797–1808, 1998.

5. Lamon, J.: “A micromechanics-based approach to the mechanical behavior of brittle-matrix 

composites,” Composites Science and Technology, Vol. 61, pp. 2259–2272, 2001.

6. Nemeth, N.N.; Mital, S.; and Lang, J.: “Evaluation of Solid Modeling Software for Finite Element 

Analysis of Woven Ceramic Matrix Composites,” NASA/TM—2010-216250, 2010.

7. Mital, S.K.; Bednarcyk, B.A.; Arnold, S.M.; and Lang, J.: “Modeling of Melt-Infiltrated SiC/SiC 

Composite Properties,” NASA/TM—2009-215806, 2009.

8. Russ, J.C.: “The Image Processing Handbook,” fifth edition, CRC Press, 2007.

9. Johnson, R.A.; and Wichern, D.W., “Applied Multivariate Statistical Analysis,” 5th edition, Prentice 

Hall, 2002.

10. Langer, S.A. et al.: “OOF: An Image-based Finite-element Analysis of Material Microstructures,”

Journal of Computing in Science and Engineering, Vol. 3, Issue 3, pp. 15–23, 2001.

11. Reid, A. et al.: “Modeling Microstructures with OOF2,” Int. J. Materials and Product Technology, 

Vol. 35, pp. 361–373, 2009.

12. ABAQUS General Purpose Finite Element Program. Version 6.8, SIMULIA, Providence, RI, 2009.

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Investigation of Effects of Material Architecture on the Elastic Response of a Woven Ceramic 

Matrix Composite 

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Goldberg, Robert, K.; Bonacuse, Peter, J.; Mital, Subodh, K. 

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WBS 599489.02.07.03.02.11.01 

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14. ABSTRACT

To develop methods for quantifying the effects of the microstructural variations of woven ceramic matrix composites on the effective 

properties and response of the material, a research program has been undertaken which is described in this paper. In order to characterize 

and quantify the variations in the microstructure of a five harness satin weave, CVI SiC/SiC, composite material, specimens were serially 

sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools 

were then used to isolate the constituents and collect relevant statistics such as within ply tow spacing. This information was then used to 

build two dimensional finite element models that approximated the observed section geometry. With the aid of geometrical models

generated by the microstructural characterization process, finite element models were generated and analyses were performed to quantify the 

effects of the microstructure and its variation on the effective stiffness and areas of stress concentration of the material. The results indicated 

that the geometry and distribution of the porosity appear to have significant effects on the through-thickness modulus. Similarly, stress 

concentrations on the outer surface of the composite appear to correlate to regions where the transverse tows are separated by a critical 

amount. 

15. SUBJECT TERMS

Ceramic matrix composites; Woven composites; Finite element analysis 

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