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Determining a material's macroscopic properties given its microscopic structure is of fundamental importance to materials science. The authors describe two public-domain programs that jointly predict macroscopic behavior: OOF (Object-Oriented Finite elements) and ppm2oof (Portable Pixel Map to OOF format translator). The programs start from an image of the microstructure and end with results from finite-element calculations
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MAY/JUNE 2001 15
cientists strive to develop and understand
materials (and the processes undertaken
to manufacture them) by associating
properties with a material’s microstruc-
ture. These properties can include chemical
composition, crystal structure, crystalline orien-
tation, magnetic susceptibility, and thermal con-
ductivity. Even single-phase materials have mi-
crostructures that affect properties significantly.
For instance, steel is composed of grains that
have the same chemical composition and crystal
structure, but metallurgists can vary their shape,
size, and degree of alignment by a judicious
choice of processing parameters. For example,
the materials in a transformer core are manufac-
tured so that their grains are primarily crystal-
lographically aligned to optimize mechanical and
magnetic properties. Materials often contain de-
fects and second phases in small fractions that
can ultimately affect integrity and reliability.
Because microstructures are such complex en-
sembles of materials and crystallography, few re-
searchers have attempted to correlate known mi-
crostructures with their properties.
Instead, they
have used mean-field and other spatial averaging
techniques to produce approximate models for ma-
terials behavior. In some cases, mean-field models
work well, but we can’t expect them to be predic-
tive for cases when material properties depend on
extremes of statistical or stereological distributions
or the spatial correlations of microstructural fea-
tures. In such cases—and even for cases where
mean-field calculations do pertain—direct com-
putations that use all pertinent microstructural in-
formation should provide a useful tool for mi-
crostructure property analysis. We have created
such a tool—OOF (named for its object-oriented
finite elements). Several groups are using it to in-
vestigate material behavior,
and it received a
Technology of the Year award from Industry Week
magazine in 1999. This article presents an
overview of OOF and some of its algorithms that
are in the public domain. OOF was developed at
the NIST Center for Theoretical and Computa-
tional Materials Science and is freely available on
the Web at
Program overview
OOF consists of two programs: oof and
ppm2oof. Conceptually, ppm2oof combines
Determining a material’s macroscopic properties given its microscopic structure is of
fundamental importance to materials science. The authors describe two public-domain
programs that jointly predict macroscopic behavior. The programs start from an image of
the microstructure and end with results from finite-element calculations.
National Institute of Standards and Technology
Massachusetts Institute of Technology
1521-9615/01/$10.00 © 2001 IEEE
microstructural data, in the form of experimental
or simulated micrographs, with fundamental ma-
terials data (such as elastic moduli and so on) and
materials physics models. The result is a repre-
sentation of a material in terms of C++ objects.
Practically, ppm2oof reads an image in the
portable pixel map format, assigns material prop-
erties to the microscopic features in the image,
and creates a finite-element mesh for subsequent
computation, all with an easy-to-use graphical
interface. (The ppm format is simple to read, and
many programs can convert from popular image
formats to it.) oof takes ppm2oofs object rep-
resentation and performs virtual experiments that
employ the same graphical user interface to com-
pute effective macroscopic physical properties or
illuminate the microstructural physics.
OOF’s user interface is designed to be flexible,
expandable, and user friendly. The interface has
command windows, which present menus of
variables, functions, and submenus; graphics win-
dows, which present images and graphical tools
for manipulating the images; and function win-
dows, which set function arguments and serve as
a quick way to perform common operations.
Every action the user takes has a text representa-
tion, which the program can save in a log file.
The user can edit this log file and read it back
into the program, allowing for scripted sessions.
Currently, there are two versions of OOF. The
original OOF solves linear thermoelasticity prob-
lems with a constant temperature field and in-
cludes simple models of fracture, damage, and
ferroelastic domain switching. The “thermal”
OOF extends the original version by allowing the
temperature to vary in space, and it solves for
thermal diffusion as well as elasticity. This arti-
cle concentrates on the original elastic program.
An example problem
Figure 1 illustrates a typical microstructure.
Suppose that the overall (macroscopic) thermo-
elastic response of the microstructure in Figure 1
is a property of interest. If the two phases in Fig-
ure 1 have different elastic stiffnesses, then the av-
erage elastic response to an externally applied dis-
tortion will depend on the distortion’s direction.
The stresses in the interior will not be distributed
homogeneously and will depend in detail on the
boundary conditions. Figure 2 exhibits the stress
patterns generated by distorting this microstruc-
ture in the vertical and horizontal directions. For
this example’s purposes, we used fictitious mater-
ial constants for the two phases and took them
both to be isotropic with Poisson’s ratios of 0.33.
The Young’s modulus of the light material was 10
times that of the dark, and its thermal expansion
coefficient was three times as large.
If the phases in Figure 1 have differing coeffi-
cients of thermal expansion, thermal strains will
be anisotropic and inhomogeneous, even if the
component materials are isotropic and homoge-
neous. The microstructure’s overall response will
have the symmetry of the composite architecture.
Combining images with constitutive
The purpose of ppm2oof is to assign proper-
ties to features in a material’s image and to gen-
erate a finite-element mesh representing the ma-
terial. This involves approximations from the
first step; the digital image is a discretized ap-
proximation to the real material. Boundaries be-
tween grains in the real material might be
smooth (have no sharp corners) and distinct (de-
lineate a sudden transition from one material to
another), but the boundaries between features
in the image might be jagged (due to pixeliza-
tion) and fuzzy (due to limited experimental res-
olution). Fuzzy images almost always require
some user input and judgment. With image pix-
elization, it’s almost never a good idea to make
the finite-element mesh resolve all the details in
an image, because that would also resolve pix-
elization artifacts.
Figure 1. A micrograph of a lamellar directionally solidified eutectic
of NiO (lighter phase) and yttria-stabilized ZrO
(darker phase).
The image’s width is approximately 12
m. (Figure data courtesy of
T.C. Isabell and V.P. Dravid.)
MAY/JUNE 2001 17
Identifying features in the image
The first order of business when using ppm2oof
is to identify the image’s features and assign mate-
rial properties to them. Identifying features means
selecting groups of pixels, to which the user may
give names and store for later retrieval.
The ppm2oof program includes a number of
tools for choosing pixels. Demography tools se-
lect pixels within a given range of gray or RGB
(red, green, and blue) values. Users can set the
minimum and maximum values explicitly or
choose a target pixel interactively with the
mouse, leading to the selection of all the pixels
within a specified range of the target’s color.
The demography tools ignore the selected
pixels’ locations. In contrast, the burn algorithms
select sets of contiguous pixels. A burn starts at a
given pixel and spreads outward like a (relatively
benign) forest fire, selecting pixels as it goes.
Specified “flammabilities” determine whether
the selection spreads from one pixel to the next.
(Our burn and demography tools are examples
of simple image segmentation algorithms. More
sophisticated methods appear elsewhere.
The micrograph in Figure 1, although typical, is
actually not a good candidate for the demography
or burn tools because the boundaries are not dis-
tinct. Figure 3 shows the results of a burn and a
roughly comparable demography application. If it
is possible to modify an image to make the bound-
aries more distinct, then the selection tools be-
come more precise. In Figure 4, we applied the
same selection tools as in Figure 3, but we applied
them after 10 iterations of a nonlinear smoothing
operation designed to reduce noise while preserv-
ing boundaries. (Interpreting the image’s gray val-
ues as a field
on a lattice, we take a set number of
time steps of Euler’s method on an anisotropic dif-
fusion equation suggested by Allen Tannenbaum:
is a parameter between 0 and 1.)
This nonlinear smoothing operation is one of
a handful of image modification routines built
into ppm2oof—it isn’t meant to be a general-
φφ φφφ φφ
αφ φ
xx y x y xy yy x
Figure 2. The results of OOF calculations on Figure 1. The mesh has
3,798 nodes and 7,440 elements. Stresses increase as color
progresses from black to red to yellow to white. This example uses
fictional material parameters, so the absolute values and units for
the stresses are not meaningful. (a) Stress
in response to strain
= 1 percent. (b) Stress
in response to strain ε
= 1 percent—
the microstructure’s influence is clear. (c) Hydrostatic stress in
response to thermal strain with free boundaries.
purpose image manipulation package, although
it does have a number of tools that we have
found to be useful in working on micrographs.
In addition, ppm2oof can import many differ-
ent versions of an image into an image gallery
and work on them all simultaneously. A user can
therefore enhance different features of an image
with external programs and then select any of
the visible features in one of a set of overlaid im-
ages in ppm2oof. All the images in an image
gallery share the set of selected pixels, the mate-
rial properties assigned to them, and the finite-
element mesh (which is created from the mate-
rials specified in the selection algorithms).
Once the user makes a selection, he or she can
modify it in ppm2oof with one of several com-
mands. For example, expand selects all the pixels
within a specified distance of the current set of
selected pixels. Despeckle recursively selects all
pixels with a specified minimum number of se-
lected neighbors. The inverses of these opera-
tions—shrink and elkcepsed (“despeckle” spelled
backwards)—reduce the selected set’s size. Fig-
ure 5 is Figure 4c after using both despeckle and
Assigning material properties to image
After selecting pixels in ppm2oof, the user
can assign material properties and a corre-
sponding grayscale value to them to form a ma-
terial image (see Figure 6). OOF understands lin-
ear elasticity, thermal expansion, and thermal
conductivity. Although it always performs calcu-
lations in two dimensions (either in plane stress
or plane strain), OOF materials can have any 3D
crystal symmetry and any 3D crystallographic
orientation. The material parameters always
have their full 3D form.
OOF’s object-oriented nature makes it rela-
tively easy to add new materials. For example, al-
though OOF can handle general crystal symme-
try with 21 elastic constants, the user interface
for such a material would be a mess. Therefore,
OOF started with only two types of elastic ma-
terials: isotropic and anisotropic. The anisotropic
material class provided no way to set the material
parameters, but had all the rest of the machinery
necessary for constructing finite-element stiff-
ness matrices, computing stress and strain, and
so forth. When the need arose for specific
anisotropic materials (hexagonal, trigonal, and so
on), we easily added them by deriving new ma-
terial classes from the anisotropic base class.
Generating and refining meshes
In most finite-element programs, you specify a
problem’s geometry, and the computer fits a mesh
to mathematical boundaries. However, when
working with micrographs, the geometry is not
so well defined. One approach would be to force
the boundaries to be well defined, but even in Fig-
ure 5, where the image is smoothed and the se-
lection despeckled, you would not want to claim
that the red region is a precise representation of
the ZrO
phase in Figure 1. Remember that the
image is an approximate representation of the
physical system, the material image is an approx-
Figure 3. The upper left corner of Figure 1, showing regions selected for (a) burning and (b) demography. The selected
pixels appear in red—the burn started from a pixel near the center of the red region in (a).
(a) (b)
MAY/JUNE 2001 19
imation of the image, and the generated mesh is
an approximation to the material image. Forcing
the boundary to be well defined and then approx-
imating the boundary by the boundaries of the fi-
nite elements just introduces another level of ap-
proximation into the existing hierarchy.
A second approach would be to take every
pixel in the material image and create one
quadrilateral or two triangular elements from it.
ppm2oof can do this (with triangular elements
Figure 5. The image from Figure 4c, after despeck-
ling the selection and applying elkcepsed.
Despeckle has filled in small holes, and elkcepsed
has eliminated small islands and peninsulas.
Figure 6. A material image. The two colors corre-
spond to the two material properties assigned to
the micrograph in Figure 1. The few remaining
small light regions inside dark areas are artifacts
of the selection tools used, and user intervention
can easily clean them up.
Figure 4. A portion of Figure 1 after applying (a)
a nonlinear smoothing operation and repeating
the (b) burn and (c) demography selections from
Figure 3.
through its “simple_mesh” menu), but this ap-
proach has two drawbacks. First, it almost always
creates far too many elements—the interiors of
large homogeneous regions should be dis-
cretized more coarsely than inhomogeneous re-
gions. Second, it resolves the jagged edges of the
pixels on the boundaries between materials, as
in Figure 7, even when the boundary in the real
material is smooth. This can result in pixeliza-
tion errors.
The approach ppm2oofs adaptive mesh rou-
tines use is to subdivide triangles and move nodes
to minimize a functional E of the mesh. E is min-
imized by equilateral triangles that overlie a ho-
mogeneous set of pixels in the material image.
Thus, at any given level of refinement, the edges
of the triangles approximate the interfaces in the
material image as well as they can on the length
scale of the triangles. The user determines the
length scale by deciding when to stop the refine-
ment process—the caveat is that he or she should
generally not refine below the pixel level. There
is no need to describe the material boundaries as
mathematical curves—the homogeneity part of
E automatically finds the boundaries. Further-
more, as long as the mesh is not too fine, it will
smooth out the sharp corners of the pixels.
The functional E is a sum of two terms for
each triangular element:
E =
+ (1 –
is a tunable parameter between 0 and 1,
and E
and E
are functionals that depend on
the element’s homogeneity and shape, respectively.
= 1, the mesh triangles tend to be highly acute,
because nodes move to put the triangle edges on
the material boundaries. If
= 0, the triangles tend
to be equilateral (providing good finite-element
convergence properties), but their positions are
uncorrelated with the material microstructure. A
value of
= 0.3 seems to work well in practice.
We compute the homogeneity term E
by sep-
arating the pixels in the material image into N cat-
egories, where all the pixels in each category have
the same material type and parameters and belong
to the same pixel groups. Then for each mesh tri-
angle T, we compute the fraction a
(T) of its area
that overlies pixels in category i. E
is defined by
If a triangle lies over only one category of pixel,
then it is homogeneous, a
(T) = 1 for some i, and
that triangle makes no contribution to E
. If a
triangle contains equal areas of each pixel cate-
gory, then a
= 1/N for all i, and that triangle’s
contribution is the maximum value, 1.
The shape term E
in Equation 2 is defined
where A
is the area of triangle T, and L
is its
perimeter. The parenthesized expression is 0 for
equilateral triangles and 1 for degenerate trian-
gles with collinear vertices.
Figure 8 shows how creating a mesh for the
sample problem might proceed. ppm2oof con-
tains a number of tools for mesh manipulations;
their most effective order of application might
vary from image to image. The process shown
here is typical but does not illustrate the full range
of tools. For simplicity, Figure 8 shows only the
upper left corner of the image. First, in Figure 8a,
the program creates a uniform mesh with a size
the user chooses to be roughly the size of the
largest features to be resolved. Figure 8b shows
the results of 10 iterations of an annealing proce-
dure. Note that many nodes have moved to the
internal material boundaries and that the edges
of the elements are beginning to follow the edges
of the materials. The annealing is a Monte Carlo
algorithm, where nodes are moved at random,
and moves are accepted if they reduce the total E.
In each iteration, the program attempts to move
each node once, choosing the node’s displacement
Figure 7. Jagged pixelized representation of smooth boundaries,
taken from Figure 6. The finite-element mesh should not resolve
the sharp corners on such boundaries.
MAY/JUNE 2001 21
Figure 8. Steps in the meshing process. (a) The initial uniform mesh overlaid on the material image. (b) The mesh after
10 annealing steps. (c) The triangles with the largest E are divided in two. (d) The mesh after 10 more annealing steps
and one interface refinement. (e) After further annealing and refinement, the mesh closely follows the material bound-
aries. (f) A final refinement resolves some of the smaller features. In (e) and (f) the triangles are colored according to the
material type that they inherit from the pixels.
from a Gaussian with a given width
(here, 1
pixel width). The method is called annealing be-
cause it can, in fact, operate at a nonzero effective
temperature in which moves that increase E are
accepted with a thermal probability. In practice,
this has not proved to be terribly useful.
In Figure 8c, triangles with E greater than 0.3
have been divided in two, with the direction of the
separatrix chosen to minimize the total E of the re-
sult. We chose the 0.3 threshold so that a reason-
able number (approximately 20 percent) of the tri-
angles were divided. Figure 8d shows the mesh
after a further 10 annealing steps, and the applica-
tion of the refine interface command. This subdi-
vides all triangles that have neighbors of a differ-
ent material type. ppm2oof determines a triangle’s
type from the types of the pixels underneath it, ei-
ther by choosing the pixel at the center of the tri-
angle or by voting, with each pixel getting a vote
proportional to the area of its intersection with the
triangle. In this image, almost all triangles are in-
terface triangles at this stage of the process.
Figure 8e shows the result of another 10 an-
nealing steps, another interface refinement, 10
more annealing steps, an edge swap (in which the
diagonals of quadrilaterals formed by two trian-
gles are swapped, if it lowers E), and one more an-
nealing with a smaller
. Here the triangles are
colored according to the material properties that
they inherit from the pixels. The mesh follows the
overall boundaries quite well on the triangle size’s
scale. Further refinement is needed to resolve
smaller features, at the risk of resolving individ-
ual pixels. The small light dot within a dark re-
gion near the upper left corner of Figure 8d is not
reproduced in Figure 8e, but it has affected the
boundary’s shape in that region. Similarly, the
narrow isthmus between the upper and lower
portions of the large light island in the upper por-
tion of Figure 8d is not resolved in Figure 8e.
Whether details such as these should be resolved
is a choice the user must make. If necessary, he or
she can define a restricted “active area” and refine
and anneal only those elements in those regions.
In fact, this example improves significantly with
one more iteration of interface refinement and
annealing, as Figure 8f shows.
Virtual experiments
oof is the part of OOF that performs virtual ex-
periments on the meshes ppm2oof produces. It is
designed with the expectation that users can per-
form useful computations by intuitively setting
boundary conditions and distortions. In its most
simple usage, oof is a basic finite-element solver.
It can calculate stresses, strains, and thermal dis-
tortions and display the results. This does not dif-
fer from other finite-element solvers, but because
elements in oof are instances of a programmable
object, each element can develop a behavior that
the current solution or the user can alter.
For example, one element in OOF is called the
Griffith element. The Griffith element is designed
to compare the stored elastic energy within the
element to the amount of energy released by
fracturing the element and creating surface area.
The Griffith element can “mutate” when the lo-
cal conditions suggest that it should fracture. The
mutated element has a new compliance that re-
flects the softening that would occur due to a
crack proceeding through the element.
Because the user can intervene and modify an
element’s properties within oof, users can con-
duct hypothetical or “what-if” experiments on a
particular microstructure and its possible modi-
fications. For example, a user might surmise the
effect of a crack by simply creating a crack in the
microstructure; he or she might determine the ef-
fect of an unknown residual stress by increment-
ing its value and determining what effect such an
increase has on, for instance, the elastic energy
density in abutting microstructural regions.
oof has a fairly advanced graphical display of
results that a user can save and incorporate into
presentations or papers (as in Figure 2). It has
built-in functions designed to perform simple
statistical analysis on all elements or specified
groups of elements. For example, using published
for the coefficients of thermal expansion
of NiO and yttria-stabilized ZrO
and measured
crystallographic orientations for lamellar mi-
crostructures such as that in Figure 1, calculated
residual stress distributions in each phase are in
excellent agreement with those measured by X-
ray diffraction.
oof also has methods for data
output in a form that can act as input to other
programs and perform post-calculation analysis
such as a particular microstructure’s reliability.
A separate program, oof2abaqus, can convert
OOF data files into a form that Abaqus, a com-
mercial finite-element program, can read.
ork is currently under way on
OOF2, which is a major rewrite
of OOF that will be extendible to
a wide variety of problems. In
particular, it will handle any problem in which the
divergence of some generalized flux is a general-
MAY/JUNE 2001 23
ized external force and that flux is a linear combi-
nation of fields and gradients of fields. This en-
compasses thermoelasticity, piezoelectricity, and
heat and mass diffusion, among other topics. Non-
linear solvers will let OOF2 users experiment with
various nonlinear models, such as plasticity and fer-
roelasticity. OOF2 will use higher-order adaptive
triangular and quadrilateral elements, and although
OOF1 is entirely written in C++, OOF2 will be a
mix of C++ and Python, giving it greater flexibility.
OOF1 is meant to be easily extendible to new ma-
terial types, but in our experience it has only been
easy for a subset of OOF’s authors, not to mention
users. In OOF2, users will be able to add new ma-
terial types, new fields, and couplings between
fields by writing some simple Python code.
We thank Edwin Garcia, Mark Locatelli, Andrew Reid,
Andrew Roosen, Nita Parekh, and Daniel Vlacich for
valuable contributions. The oof2abaqus program is
provided as a convenience to OOF users and should not be
construed as an endorsement of Abaqus. NIST does not
endorse any commercial products. OOF is supported in part
by the NIST Center for Theoretical and Computational
Materials Science and the US Department of Energy’s
Advanced Turbine Systems Program, under contract DE-
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Stephen A. Langer is a physicist in the Mathematical
and Computational Sciences Division of the Informa-
tion Technology Laboratory at the US National Insti-
tute of Standards and Technology. His research inter-
ests include theories and simulations of liquid crystals,
glasses, ferrofluids, biomembranes, and foams, as well
as computational methods for analyzing material
microstructure. He received his PhD in physics from
Cornell University. Contact him at the Information
Technology Lab., Nat’l Inst. of Standards and Technol-
ogy, Gaithersburg, MD 20899-8910; stephen.langer@
W. Craig Carter is the Lord Foundation Associate Pro-
fessor of Materials Science and Engineering at the Mass-
achusetts Institute of Technology. His research interests
are computational and mathematical developments in
materials science, especially microstructural evolution
and the fundamental properties of microstructures. He
received a PhD in materials science from the University
of California, Berkeley. Contact him at the Dept. of Ma-
terials Science and Eng., Massachusetts Inst. of Tech-
nology, Cambridge, MA 02139-4307;
Edwin R. Fuller, Jr. is a research physicist in the Ce-
ramics Division at the National Institute of Standards
and Technology. His research interests include meso-
scopic computer simulations of micromechanical be-
havior of heterogeneous, stochastic microstructures,
and theoretical modeling of fracture behavior and
toughening mechanisms in brittle and quasi-brittle ma-
terials. He received a BS and PhD in physics from the
University of North Carolina at Chapel Hill and the Uni-
versity of Illinois at Champaign-Urbana, respectively.
He is a fellow of the American Ceramic Society. Con-
tact him at the Materials Science and Eng. Lab., Nat’l
Inst. of Standards and Technology, Gaithersburg, MD
... The two general approaches to modeling material properties with complex microstructures are (i) compute average properties of a microstructure using mean-field approximations, and (ii) model a specific microstructure using geometrical data (direct computation approach) [62]. Meanfield models are not predictive for cases when material properties depend on extremes of statistical or stereological distributions, or the spatial correlations of microstructural features [63]. Object-Oriented Finite (OOF) element analysis, developed by the US National Institute of Standards and Technology (NIST), was used to model microstructures using the direct-computation approach. ...
... In this method, the user has the ability to assign material properties to the micrograph that generates a finite element mesh and performs virtual experiments to observe the macroscopic response of the microstructure to external conditions. This was followed by computing the effective macroscopic material properties from the material microstructures for optimal performance [62][63][64]. OOF2 can easily be extended to solve any problem that can be expressed in Equations 37 and 38 [62]. ...
When moving at hypersonic velocity, heat is generated by air and gas in the atmosphere with temperatures as high as 3000 °C; therefore, the need for stable, light materials with good mechanical properties at these temperatures is paramount. These materials can be challenging to fabricate for hypersonic and high-temperature power generation systems; because the parts are complex in nature, and machining of refractory and ceramic materials is challenging. There has been extensive research on optimizing the mechanical and thermophysical properties of different single-phase alloys and material pairs in various environments. High-temperature carbide/metal composites exhibit excellent ultra-high temperature and hypersonic properties such as desirable flexural strength at elevated temperatures, high hardness, low density, and resistance to wear, creep, and corrosion. These properties are useful in aerospace, automotive, energy production, defense, and others. W-ZrC composites are promising for use in ultra-high temperature and hypersonic environments because they combine the properties of the two materials. W and ZrC are mechanically, chemically, and thermally stable, i.e., they have similar thermal expansion coefficients, low solid solubility in each other at elevated temperatures, and high melting points, respectively. W-ZrC composites were successfully prepared by reactive melt infiltration (RMI) of stoichiometric and excess amounts of Zr2Cu into sintered and un-sintered WC preforms made through binder jet 3D printing. Fabrication of composites using powders and reactive melt infiltration (RMI) is a relatively inexpensive method used to fabricate not only simple but also complex-shaped composites at modest temperatures. The direct mixture of ZrC and refractory metal such as W requires high sintering temperature and pressure. RMI, also called displacive compensation of porosity (DCP), is employed to fabricate W-ZrC composites. Reactive melt infiltration is a process where a low melting metallic liquid wets and infiltrates into a porous, rigid-shaped ceramic preform at ambient or sometimes high pressure. The liquid infiltrate undergoes a displacement reaction with the preform to yield new ceramic and metal phases. As the reaction progresses, the pores of the reactant ceramic are filled with new solid, and the excess solid within the preform gradually squeezes out until a dense, refractory composite is produced. DCP involves three steps: porous preform fabrication by different methods such as binder-jet 3D printing and cold isostatic pressing; the porous preform is then infiltrated, with a reactant melt, which reacts with the solid preform, in the final step. Sintering is a powder consolidation method based on self-diffusion and can reduce the pore size of metals or ceramics through necking and consolidation that causes bulk volumetric shrinkage. It also can be used to form near-net shaping of particles. Sintering showed the effects of partial consolidation and pore size reduction on the reactant phases and near-net shaping of the W-ZrC composites by infiltrating sintered and un-sintered WC preforms. W-ZrC samples prepared from sintered samples showed better RMI than samples prepared from un-sintered samples. Zr2Cu alloy has been used as a lower-melting pressure-less infiltrant in the displacement reaction of WC and Zr to make W-ZrC composite. The effect of the amount of Zr2Cu, on the composition of W-ZrC ceramic-metal composite, was investigated using stoichiometric amounts of Zr2Cu and excess amounts of Zr2Cu. W-ZrC samples prepared from excess Zr2Cu showed better RMI compared to samples prepared from stoichiometric amounts of Zr2Cu. The effect of infiltration parameters, specifically, the effect reaction/infiltration time on the cermet composition, was also studied. The focus of this work is to (i) study the conversion of reactant powders and liquid infiltrant, with varying preform density and infiltrant amount by controlling the processing time to achieve high conversion yield while understanding the phase composition, microstructure, and hardness; (ii) simulate multifunctional properties, and elucidate influences of microstructural features, on physical properties and damage evolution processes and; (iii) to study the conversion of reactant powders and reactive melt by varying reactant powder compositions, to increase ZrC conversion yield while understanding the phase composition and microstructure. To investigate the effect of time, the reactive melt infiltration was conducted at 1400 °C for 2, 4, and 8 hours in a furnace with 96% Ar - 4% H2 gas atmosphere. The increase in reaction time from 2 to 8 hours increased the W and W2C phase contents and decreased the ZrC phase content when using sintered WC preforms. Samples prepared from un-sintered WC preforms showed improved reactive melt infiltration compared to the sintered samples; also, there was no detectable W2C phase and nearly complete consumption of WC. Similar to sintered WC samples, the content of W and ZrC phases increased with the increase in time from 2 to 8 hours. The interfaces and phases at reaction interfaces were investigated using electron diffraction analysis and S/TEM-EDS to study material stability; the phases that were identified were in correspondence with XRD analysis. Additionally, there was no Cu phase identified at the interfaces. Increasing the amount of Zr2Cu led to improved reactive melt infiltration. Generally, the hardness increased with reaction time, and therefore, the highest Vickers hardness was found in the W-ZrC sample formed from sintered WC reacted with excess Zr2Cu. This research addresses the critical comparison of sintering and RMI time and shows that by using un-sintered samples for 8 hours, W-ZrC composites, with fewer undesired phases, can be achieved. To simulate the influence of microstructural features, the effect of W-ZrC microstructure evolution, due to different processing parameters (RMI time and sintering), on stress and thermal displacement was studied. Microstructural thermal stress was successfully modeled using OOF2 for all W-ZrC samples prepared by reactive melt infiltration of molten Zr2Cu into binder jet 3D printed preforms. The phase distribution in the composites affects the stress distribution in the composite. Stress decreases, within the microstructure, with an increase in reaction time due to the formation of a more stable ZrCx phase. When adding carbon for stabilization of the final W-ZrC phases, the objective was to increase the ZrC phase in the W-ZrC composite, relative to W, without the formation of other unwanted phases in the composite. The W-ZrC sample prepared using WC/C powders gave the W-ZrC composite with the highest ZrC phase compared to W and showed promise for final phase stabilization studies. Binder jet 3D printed WC/C preforms should be used for the phase stabilization RMI studies.
... If ind = 1, the mesh triangles tend to be highly acute, because nodes move to put the triangle edges on the material boundaries. If ind = 0, the triangles tend to be equilateral (providing good FE convergence properties), but their positions are uncorrelated with the material microstructure [44]. By assigning fields and equations to the model, a simulation is performed based on the boundary conditions defined by the user. ...
Additive manufacturing appears to facilitate the accurate manufacturing of alumina-zirconia technical ceramics. Nevertheless, the fine tuning of the manufacturing of these components by 3D printing requires an analysis of the parameters that influence their final thermoelastic properties. In this context, this work presents the application of (finite element-based) numerical procedures that aim at the prediction of the effective thermoelastic properties of 3D-printed alumina-zirconia ceramics. The numerical modelling considers three different scales: micro-, meso- and macroscale. The microscale corresponds to the microstructural level of, sintered at 1500 ° , slip-casted samples with different compositions of alumina-zirconia. On the other hand, the macroscale corresponds to the macrostructural level of porous lattice of 3D-printed ceramics, being defined at the mesoscale level by a periodic unit cell. Thus, an initial microstructural analysis (at microscale level) provides the influence of the alumina/zirconia ratio on the (macroscopically homogeneous and isotropic) material thermoelastic properties, which together with the definition of the geometry of a periodic unit cell (at mesoscale level), provides, by a second analysis (at both the meso- and macroscale levels), the coupled influence of material and geometry of the macrostructural lattice on the structural (macroscopically heterogeneous and anisotropic) thermoelastic properties. Moreover, experimental thermoelastic properties of the sintered slip-casted specimens were obtained for several alumina/zirconia ratios and analyzed together with microstructure patterns. Prediction of the microstructural effective thermoelastic properties was also made using micromechanics and composite theory (analytical) models. All the numerical, experimental and analytical results for the microstructural level are presented and compared. Numerical results for the meso- and macrostructural levels are also presented.
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The fate of Mercury’s exospheric volatiles and, in a lesser way, of the refractory particles absorbed in the first few centimeters of the surface both depend highly on the temperature profile with depth and its diurnal variation. In this paper, we review several mechanisms by which the surface temperature might control the surface/exosphere interface. The day/night cycle of the surface temperature and its orbital variation, the temperature in the permanent shadow regions, and the subsurface temperature profiles are key thermal properties that control the fate of the exospheric volatiles through the volatile ejection mechanisms, the thermal accommodation, and the subsurface diffusion. Such properties depend on the solar illumination from large to small scales but also on the regolith structure. The regolith is also space-weathered by the thermal forcing and by the thermal-mechanical processing. Its composition is changed by the thermal conditions. We conclude by discussing key characteristics that need to be investigated theoretically and/or in the laboratory: the dependency of the surface spectra with respect to temperature, the typical diffusion timescale of the volatile species, and the thermal dependency of their ejection mechanisms.
The main focus of this study is on simulation of coating formation on substrates with arbitrary shapes. For this purpose, several substrate geometries shaped as inclined step, cylinder and sphere are considered. The stress analysis for these complex coating geometries is also performed. The formation of Nickel coatings on various shapes of stainless-steel substrates and Yttria-Stabilized Zirconia (YSZ) on NiCrAlY in the atmospheric plasma spray (APS) process is investigated. The topography of the coatings, as well as their microstructure, e.g., porosity, average thickness and average roughness, are evaluated. An algorithm, which is based on the Monte-Carlo stochastic model, is employed in this work. The parameters of the droplets impacting the surface, including their velocity, temperature and size, are predicted through the use of this stochastic model. Simulation results show that on the inclined part of the step or peripheral parts of the cylinder/sphere, the coating porosity is considerably lower than the flat parts, while the roughness is remarkably higher. A significant difference between the coating temperature and that of the substrate leads to the formation of residual thermal stresses. These stresses are analyzed using the object oriented finite-element (OOF) software, which utilizes an adaptive meshing technique and finite-element method to calculate residual thermal stresses. The maximum stress in the coatings occurs at the interface between the coating and the substrate. The coatings' topography and microstructure are compared with those of the experiments.
Crystallographic orientations can be measured using scanning electron microscope-based techniques, such as electron backscatter diffraction (EBSD). The orientation data thus obtained may contain noise and misindexed data. There are several methods to restore the orientation data. The restorations from these methods may have varying levels of quality. Moreover, many such methods are parameter-dependent. Therefore, finding suitable parameter settings for optimal restorations can take time and effort for users of such methods. In this paper, we propose an algorithm to obtain high-quality restorations of noisy orientation data and to circumvent the parameter selection problem by automating it. We estimate the noise variance in the data to determine the amount of denoising to apply. We then use this information to determine the stopping criteria for a vector-valued weighted total variation flow, a nonlinear diffusion applied to the noisy orientation map. We compare the results obtained by our approach with the results from other commonly used denoising filters. As benchmarks, we used simulated EBSD maps with varying noise levels. Our proposed method outperformed denoising methods, such as mean, median, spline, half-quadratic, and Kuwahara filters. The denoising results were statistically significantly better for higher levels of noise.
This chapter focuses on obtaining optimal mechanical properties of polypropylene‐organically modified montmorillonite (PP‐OMMT) nanocomposite for different objectives. The primary objective was to minimize the cost of the PP‐OMMT nanocomposite. The other objective was to obtain specific desired properties of the nanocomposite (irrespective of the nanocomposite cost). The later simulation results are useful in designing products where quality of the nanocomposite cannot be compromised (while the cost of the PP‐OMMT is secondary). The properties that were optimized include tensile Young's modulus and permeation. Regression models were obtained and used to predict these properties as functions of corresponding compositions of the composites. Further, optimization procedures were simulated using these models along with other constraints and objective functions. All simulations are programmed using MATLAB version 7.10.0 (R2010a). The study was published in “Journal of Polymer Engineering” and included with license number 1150452‐2.
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With the advent of increasingly more complex heterogeneous materials, new methodologies are being developed to accurately predict their mechanical behaviour. At the microscale, a material is usually composed of multiple heterogeneities that, by interacting with the surroundings, may influence the macroscopic performance of the component. During this thesis, a Digital Image Based (DIB) microstructure recognition technique was employed to model the microstructure of heterogeneous materials. This method enables the use of any given real 2D or 3D micrograph to identify different constituents, create a Representative Volume Element (RVE) and generate a finite element mesh that correctly fits these singularities. Following this, Multi-Scale models take advantage of RVEs generated with this approach to study the homogenized elastic properties of heterogeneous materials, such as the acquisition of the full stiffness tensor for orthotropic cases. In addition, a study on the RVE and mesh size is performed for two- and three-phase materials. The influence of different stiffness ratios between fiber and matrix materials on the RVE size and on the homogenized properties is analysed and compared with analytical models, such as the Hashin-Hill bounds and the Mori-Tanaka method. Moreover, the insertion of an interface material in-between, changes the overall behaviour of a composite material, hence, a study of this factor is presented. Analytical expressions with extremely high accuracy against the numerical results were deduced to estimate the homogenized plane Young's modulus under these circumstances. Finally, this method does not consider simplifications at the microscale, being able to model any constituent with arbitrary shapes or constitutive behaviours. Therefore the micrograph recognition technique is an inspiring and breakthrough method that aims to develop and characterize new and more elaborated heterogeneous materials.
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Both analytical modeling and numerical simulations were performed to analyze residual thermal stresses and coefficients of thermal expansion (CTEs) of intergranular two-phase composites in a two-dimensional sense. A composite-circle model was adopted for analytical modeling. Model microstructures consisting of square-array, hexagon-array, and brick wall-array of grains with an intergranular phase as well as an actual microstructure of random-array grains with an intergranular phase were adopted for numerical simulations. The results showed that in predicting CTEs, the simple analytical model represents the two-dimensional composite well except that with brick wall-array grains, which induced significant anisotropic CTEs in the composite. The residual thermal stresses in composites were also discussed.
Phase-to-phase residual stresses due to thermal expansion mismatch were measured in lamellar NiO-ZrO{sub 2} (cubic) directionally solidified eutectics (DSEs). The triaxial strain tensors for both phases were measured using single-crystal X-ray diffractometry techniques on isolated grains of the DSE. From the strain tensors, the stress tensors were calculated, taking into account the full elastic anisotropy of the phases. The resulting stress tensors indicated that very large compressive stresses accumulated in ZrO{sub 2} whereas large tensile stresses were amassed in NiO parallel to the lamellae during the solidification process. The large magnitudes of the stresses indicated that the interfaces between the lamellae were very well bonded and did not facilitate slip or other stress-relieving processes.
Residual stress distributions in ceramics can be calculated for a coordinate system fixed by the specimen geometry as well as for the crystal system. Computations were performed using alumina as a model system with the residual stresses caused by thermal expansion anisotropy. Mean values and standard deviations of the stress distributions are calculated for a plane stress as well as a plane strain scenario in a laboratory coordinate system and compared to distributions of stresses occuring along the a-axis and c-axis of alumina. In addition, stress fluctuations in the whole assembly of grains are compared with stress fluctuations within and between individual grains.
Both analytical modeling and numerical simulations were performed to analyze the stress transfer in platelet-reinforced composites in a two-dimensional sense. In the two-dimensional model, an embedded elongated plate bonded to a matrix along its long edges was considered. The system was subjected to both tensile loading parallel to the plate's long edges and residual thermal stresses. The ends of the plate can be debonded from or bonded to the matrix during loading, and both cases were considered in the analysis. Good agreement was obtained between the present analytical and numerical solutions. However, better agreement between analytical and numerical models was obtained for the case of bonded ends than for debonded ends. (C) 1999 Elsevier Science S.A. All rights reserved.
The orthorhombic pseudobrookites have served as model material systems for investigating the role of thermal expansion anisotropy on the microcracking behavior in single phase ceramics. Among those typically studied are MgTi_2O_5, Fe_2TiO_5 and Al_2TiO_5. Fe_2TiO_5 is anisotropic in both thermal expansion and paramagnetic susceptibility. Fe_2TiO_5 has an orthorhombic crystal structure and belongs to the Bbmm space group. It belongs to the class of titanates under investigation as second-phase toughness enhancers and as coatings for engine manifolds. The coefficient of thermal expansion of Fe_2TiO_5 is 10.1 × 10^(−6) K^(−1), 16.3 × 10^(−6) K^(−1) and 0.6 × 10^(−6) K^(−1) in the a, b and c directions, respectively. The goal of the present work is to examine residual stresses and study the effect of interface properties on fracture and propensity toward microcracking of Fe_2TiO_5 using finite element analysis.
Microstructure-level residual stresses occur in polycrystalline ceramics during processing, as a result of thermal expansion anisotropy and crystallographic misorientation across the grain boundaries. Depending on the grain size, the magnitude of these stresses can be sufficiently high to cause spontaneous microcracking when cooled from the processing temperature. They are also likely to affect where cracks initiate and propagate under macroscopic loading. The magnitudes of residual stresses in untextured and textured alumina samples have been predicted using experimentally determined grain orientations and object-oriented finite-element analysis. The crystallographic orientations have been obtained using electron-backscattered diffraction. The residual stresses are lower and the stress distributions are narrower in the textured samples, in comparison with those in the untextured samples. Crack initiation and propagation also have been simulated, using a Griffith-like fracture criterion. The grain-boundary-energy:surface-energy ratios required for computations are estimated using atomic-force-microscopy thermal-groove measurements.
The finite-element method (FEM) is used to study the influence of porosity and pore shape on the elastic properties of model porous ceramics. Young's modulus of each model is practically independent of the solid Poisson's ratio. At a sufficiently high porosity, Poisson's ratio of the porous models converges to a fixed value independent of the solid Poisson's ratio. Young's modulus of the models is in good agreement with experimental data. We provide simple formulas that can be used to predict the elastic properties of ceramics and allow the accurate interpretation of empirical property–porosity relations in terms of pore shape and structure.
Microstructures of engineering alloys often contain features at widely different length scales. In this contribution, a digital image processing technique is presented to incorporate the effect of features at higher length scales on the damage evolution and local fracture processes occurring at lower length scales. The method is called M-SLIP: Microstructural Scale Linking by Image Processing. The technique also enables incorporation of the real microstructure at different length scales in the finite element (FE)-based simulations. The practical application of the method is demonstrated via FE analysis on the microstructure of an aluminum cast alloy (A356), where the length scales of micropores and silicon particles differ by two orders of magnitude. The simulation captures the effect of nonuniformly distributed micropores at length scales of 200 to 500 µm on the local stresses and strains around silicon particles that are at the length scales of 3 to 5 µm. The procedure does not involve any simplifying assumptions regarding the microstructural geometry, and therefore, it is useful to model the mechanical response of the real multi-length scale microstructures of metals and alloys.
Microcracking due to thermal expansion and elastic anisotropy is examined via computer simulations with a microstructural-based finite element model. Random polycrystalline microstructures are generated via Monte Carlo Potts-model simulations. Microcrack formation and propagation due to thermal expansion anisotropy is investigated in these microstructures using a Griffith-type failure criterion in a microstructural-based finite element model called OOF. Effects of the grain size distribution on the accumulation of microcrack damage, as well as on the threshold for microcrack initiation, are analysed. Damage evolution is rationalised by statistical considerations, i.e. damage accumulation is correlated with the statistical distributions of microstructural parameters.
The effects of curvature and height of the interface asperity on residual thermal stresses in a plasma-sprayed thermal barrier coating were numerically simulated. In the tip region of a convex asperity, the residual stress normal to the interface, σy is tensile in the ceramic top coat and increases with both curvature and height of the asperity. However, this residual tensile stress is lower for a periodic array of asperities than for an isolated asperity. The effects of thickness of the thermally grown oxide at the top coat–bond coat interface on residual thermal stresses were also numerically simulated. In the tip region of a convex asperity, σy in the ceramic top coat is tensile for a thin oxide but becomes compressive for a thick oxide. In the tip region of a concave asperity, σy in the ceramic top coat is compressive for a thin oxide and becomes less compressive for a thick oxide. The physical meaning of the above trend was qualitatively interpreted using an analytical model of three concentric circles.