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This is to certify that the
thesis entitled

DESIGN AND PROCESSING OF PERSPIRABLE SKIN
THROUGH NUMERICAL ANALYSIS

presented by

BASAK OGUZ

has been accepted towards fulfillment
of the requirements for the

Master of degree in Mechanical Engineering
Science

 

 

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5/08 KthrqlAccstPres/CIRC/Dateoue indd

DESIGN AND PROCESSING oI= PERSPIRABLE SKIN THROUGH
NUMERICAL ANALYSIS
By
BASAK oeuz

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Mechanical Engineering

2009

 

ABSTRACT

DESIGN AND PROCESSING OF PERSPIRABLE SKIN THROUGH
NUMERICAL ANALYSIS
By
BASAK OGUZ
An autonomous and reusable self-cooling thermal protection system (TPS) was
designed for externally heated surfaces such as the surface of the space shuttle.
This material system, named ‘Perspirable Skin,’ contains cores shrink-fitted into

the holes on the Reinforced Carbon-Carbon (RCC) composite skin. The cores

are made of either pure ZrW208 (zirconium tungstate) or ZrW203-Zr02 (zirconia)

Functionally Graded Material (FGM). The choice of ZrW203 is due to its highly

negative coefficient of thermal expansion in a wide range of temperatures. When
the temperature increases, a gap is formed between the core and the RCC skin
due to the difference in thermal expansions. The compressed coolant gas
onboard is passed through this gap onto the surface. The coolant gaS is
expected to mix with the surface air to eliminate the frictional heating. The
geometry and gradient of the cores as well as the fiber arrangement for RCC skin
were designed by Finite Element Analysis (FEA). Optimal core design was
successfully fabricated using powder metallurgy methods. Influences of powder
metallurgy steps on the final properties of ceramic powders were also
investigated, both experimentally and numerically. The effects of powder mixing
on the compaction capabilities of ceramic powders, as well as dimension and

density variations in the green bodies after compaction are discussed.

To my Mother and in loving memory of my Father

iii

ACKNOWLEDGEMENTS

I would like to thank my advisor Dr. Patrick Kwon for giving me the opportunity to
work on the Perspirable Skin project and for his invaluable supervision
throughout my tenure as a Master’s student at Michigan State University. I would
also like to express my gratitude towards Dr. Dahsin Liu and Dr. Seungik Baek

for being on my thesis committee.

I am grateful that I had a chance to work with such knowledgeable colleagues.
Your willingness to help is incomparable and very much appreciated. I would like
to thank Li Sun for his constructive input and guidance throughout my entire
research project. I would also like to thankKyunghee Park for his assistance in
Finite Element Analysis of powder compaction, and Shantanu Joshi for helping

me with NX Modeling of the final designs.

Finally, I would like to thank my mother, Nurfer Oguz, for being such a great role
model; and my fiance, Steven Wagner, for his endless support. Without them, I
would not have been able to accomplish this mission. Thank you for always

being there for me.

iv

TABLE OF CONTENTS

LIST OF TABLES ................................................................................................ vii
LIST OF FIGURES ............................................................................................. viii
CHAPTER 1: INTRODUCTION ............................................................................ 1
1.1 . MOTIVATION ............................................................................................. 1
1.2. CURRENT THERMAL PROTECTION SYSTEM (TPS) .............................. 2
1.3. INTRODUCTION TO PERSPIRABLE SKIN DESIGN ................................. 6
1.4. POWDER METALLURGY .......................................................................... 9
1.5. FUNCTIONALLY GRADED MATERIAL (FGM) ........................................ 12
1.6. FINITE ELEMENT METHOD (FEM) ......................................................... 13
1.7. MODIFIED DRUCKER—PRAGER / CAP PLASTICITY MODEL ................. 15
CHAPTER 2: PERSPIRABLE SKIN DESIGN ..................................................... 18
2.1. DESIGN APPROACH ............................................................................... 18
2.2. MATERIAL SELECTION FOR THE CORE .............................................. 19
2.2.1. Materials with Negative Thermal Expansion Property ........................ 19
2.2.2. Negative Thermal Expansion Mechanism .......................................... 20
2.3. FABRICATION OF an203 ...................................................................... 21
2.4. FINITE ELEMENT ANALYSIS (FEA) ....................................................... 23
2.4.1. Material Properties and Boundary Conditions .................................... 23
2.4.2. Material Properties for RCC ............................................................... 24
2.4.3. Material properties for ZrW208 ........................................................... 26
2.4.4. Flow through Annular Space formed by Two Coaxial Tubes ............. 29
2.4.5. Determination of the best RCC structure ........................................... 31
2.4.6. Design of the ZrW203 core ................................................................ 35
2.4.7. Alternative Design for the NTE core ................................................... 42
2.5. FABRICATION OF THE FINAL FGM CORE ............................................ 49

CHAPTER 3: EFFECTS OF POWDER METALLURGY STEPS ON FINAL

PROPERTIES OF GREEN BODIES ................................................................... 51
3.1. INTRODUCTION ...................................................................................... 51
3.2. EFFECTS OF POWDER MIXING ON THE COMPACTION CAPABILITIES
OF CERAMIC POWDERS ............................................................................... 52

3.2.1. Materials and Experimental Procedure .............................................. 52
3.2.2. Results & Discussion ......................................................................... 56
3.3. DENSITY VARIATIONS IN GREEN COMPACTS ...................................... 62

V

3.3.1. Experimental Procedure ..................................................................... 63

3.3.2. Experimental Results & Discussion ................................................... 66
3.3.3. Finite Element Analysis ...................................................................... 67

3.4 DIMENSIONAL VARIATIONS IN GREEN COMPACTS .............................. 72
3.4.1. Experimental Procedure ..................................................................... 73
3.4.2. Experimental Results & Discussion .................................................... 74
3.4.3. Finite Element Analysis ...................................................................... 76
CHAPTER 4: DISCUSSION AND CONCLUSIONS ............................................ 78
4.1. DISCUSSION AND CONCLUSIONS ........................................................ 78
4.2. RECOMMANDATIONS FOR FUTURE WORK ......................................... 83
BIBLIOGRAPHY ................................................................................................. 85

vi

LIST OF TABLES

Table 1. Isotopic negative thermal expansion materials [19-25] ......................... 19
Table 2. Various parameters of RCC used in FEA [30] ....................... I ................ 25
Table 3. CTE of ZrW203 at various temperatures .............................................. 28

Table 4. The summary of gap distance at working temperature (750°C) and the
stress at room temperature (RT) between ZrW203 core and the various types of

RCC skin ............................................................................................................. 34
Table 5. Various parameters for the FGM core ................................................... 43
Table 6. CTE values for the FGM core at several temperatures ......................... 44

Table 7. Different FGM configurations for the Perspirable Skin core and their

corresponding gap distances and maximum stresses ......................................... 47
Table 8. Properties of the ceramic powders used in the experiments ................. 53
Table 9. Constant K for TMDAR+CR-1 mixture group for all mass ratios ........... 61

vii

LIST OF FIGURES

(Images in this thesis are presented in color.)

Figure 1. Maximum temperatures that different parts of the space shuttle
experiences during ascent and re-entry. All temperatures shown are in degrees

Celsius [3]. ............................................................................................................ 3
Figure 2. Schematic of the orbiter TPS [3] ............................................................ 5
Figure 3. Basic schematic of the Perspirable Skin design (a) at room temperature
(b) at maximum working temperature (750 °C) ...................................................... 8
Figure 4. Cold uniaxial powder compaction process ........................................... 10
Figure 5. Basic concept of functionally graded materials .................................... 12

Figure 6. Modified Drucker-Prager/ Cap Plasticity Model yield surface [15] ........ 16

Figure 7. Temperature dependence of the relative expansion of NTE materials.20

Figure 8. Schematic of thermal contraction caused by thermal motion ............... 21
Figure 9. The ramp/soak path used for producing ZrW208 ................................. 22
Figure 10. The microstructure of the ZrW203 substrate ...................................... 22
Figure 11. Boundary conditions for finite element modeling ................................ 24

Figure 12. Microstmcture of the RCC composite sample at a) fiber-cutting
direction and b) fiber-parallel direction ................................................................ 25

Figure 13. The temperature dependence of thermal conductivity of RCC [5] ...... 26

Figure 14. The temperature dependence of the CTE of ZrW203 ........................ 27

Figure 15. The temperature dependence of thermal conductivity of ZrW203 ..... 28

Figure 16. Several parameters used in equation (3) ........................................... 30

Figure 17. Maximum fluid velocity as a function of gap distance for different
compressed coolant gas pressures ..................................................................... 31

viii

Figure 18. Von Mises stress plot showing that full contact between the ZrW203
core and the RCC skin at room temperature is lost when inner radius of RCC is
higher than 14.98mm .......................................................................................... 32

Figure 19. The FEA results for the isotropic RCC case (a) assembly temperature
gap distance (b) von Mises stress at room temperature ..................................... 34

Figure 20. The modified geometry under the 100-750°C temperature gradient ..36

Figure 21. The tapered core geometry under the 100-750°C temperature gradient
(a) Gap distance (b) bottom view of the core showing the semi-circular channel
that provides larger flow area for the coolant gas ................................................ 37

Figure 22. The relationship between the gap distance and the bottom cylinder
radius or the core ................................................................................................ 39

Figure 23. Final geometry for the ZrW203 core ................................................... 40

Figure 24. The FEA results for the final ZrW203 core design a) temperature
distribution at working condition (in degrees Celcius) b) gap distance at working
condition and c) max principal stress at working condition (I) max principal stress
at room temperature ............................................................................................ 41

Figure 25. FEA results for the 5-Iayer uniform FGM core a) temperature
distribution at working condition b) gap distance at working condition c) max
principal stress at working condition d) max principal stress at room temperature
............................................................................................................................ 45

Figure 26. The relationship between the gap distance and number of layers of
the FGM core ...................................................................................................... 46

Figure 27. The FEA results for the final FGM core design a) temperature
distribution at working condition b) gap distance at working condition c) max
principal stress at working condition (I) max principal stress at room temperature

............................................................................................................................ 48
Figure 28. Final geometry for the FGM core with semi-circular channels for the
coolant gas to exrt49
Figure 29. Measured CTE of the best FGM core design ..................................... 50

Figure 30. Particle size distributions of the powders used in the experiments ....53
Figure 31. Relative density as a function of stress for two different alumina
powder mixture groups at various mass ratios (a) TMDAR+CR-15 group (b) CR-
6+GE-1 group ..................................................................................................... 58

ix

Figure 32. Initial relative density as a function of proportion of the course powder
for all six alumina powder mixture groups ........................................................... 59

Figure 33. Relative density as a function of axial true strain for (a) TMDAR+CR-

15 group and (b) CR-6+GE-1 group .................................................................... 60
Figure 34. Middle sections of the layered powder compacts (a) CR-15 sample (b)
TMDAR sample ................................................................................................... 65
Figure 35. Contour plots of the density distributions in green compacts (a) CR-15
sample (b) TMDAR sample ................................................................................. 67
Figure 36. Finite element model for powder compaction ..................................... 68

Figure 37. Density distribution of CR-15 powder for [3 =27° and d = 3.6OMPa (a)
After compaction (b) after the removal of top punch (c) after the removal of
bottom punch and die wall (relative density shown) ............................................ 70

Figure 38. Density distribution of CR-15 powder for B = 28° and d = 3.24MPa (a)
After compaction (b) after the removal of top punch (c) after the removal of
bottom punch and die wall (relative density shown) ............................................ 70

Figure 39. Density distribution of CR-15 powder for B = 29° and d = 2.88MPa (a)
After compaction (b) after the removal of top punch (c) after the removal of
bottom punch and die wall (relative density shown) ............................................ 71
Figure 40. Simple schematic of the setup for external shape measurements ..... 73

Figure 41. Experimental result for the diameter variation along the thickness of
the CR-15 green sample ..................................................................................... 74

Figure 42. Difference between the largest and smallest diameter aS a function of
proportion of the course powder .......................................................................... 75

Figure 43. The diameter variation along the thickness of the CR-15 green sample
obtained by FEA (B = 33°, d=1.34MPa) .............................................................. 76

Figure 44. The middle section of the FGM sample after different fabrication steps
(a) after compaction (b) after sintering ................................................................ 81

CHAPTER 1

INTRODUCTION

1.1. MOTIVATION

Thermal Protection System (TPS) is an essential component of reusable
aerospace vehicles like the space shuttle. It protects the vehicle from the
aerodynamic heating generated at the surface, which is caused by the
combination of compression and surface friction by the atmospheric gases.
During the reentry into the Earth’s atmosphere, the orbiter travels at speeds

exceeding 27,000 km/h, and the surface temperatures can reach as high as

1650°C [1]. The friction at the surface is caused by the attempt to slow the

vehicle down from such high speeds to the landing speed [2]. The maximum

temperature of 1650°C is reached 20 minutes before touchdown [1].

The space shuttle orbiter is composed of numerous advanced materials, but the

main structure is mostly made of 2024-T6 aluminum and graphite- epoxy [3].

Both of these materials can only endure temperatures up to 175°C; therefore, a

TPS is required to prevent heat from transferring into the vehicle so that the
structural frame does not go beyond this temperature limit [2, 3]. Without a TPS,
the whole structure would degrade at high temperatures. Thus, it is a crucial

element for the protection of the vehicle structure as well as the occupants.

The motivation of this thesis is to propose a multifunctional material system,
which provides cooling for several parts of the TPS that are exposed to the
highest temperatures during re-entry into the Earth’s atmosphere. The proposed
design, called “Perspirable Skin”, is an autonomous and reusable system, which
is expected to significantly reduce the surface temperature of the hottest areas

caused by frictional heating.

1.2. CURRENT THERMAL PROTECTION SYSTEM (TPS)

The main task of the TPS is to protect the orbiter from excessive heating during
re-entry; however, it must be designed such that it can accommodate several

other conditions during flight. These conditions include extremely cold

temperatures (as low as -156°C) and also local heating from several engines and

motors [2, 3]. Therefore, the TPS selected for a space shuttle is composed of
several different materials due to the wide variation of temperatures that the
vehicle experiences. Each material's thermal properties, durability, and weight
determine the extent of its application on the vehicle. The variety of temperatures
and the corresponding parts of the Space shuttle are Shown in Figure 1. This

figure is taken from a NASA contractor report from 1989 and shows the highest

temperature as 144000 [3]. However, it was later reported that the maximum

temperature reached is around 1650 OC [1, 2].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1260 1410
-" 1095
1095
Lower 1260
1 95 Surface
1260 / 144°
'60 V"
980 650 425 315 400
Upper 315 445
Surface 480
425
315
425
650 00 J ‘ c
.. o.
\ \
"40 980 1095 420 425 405 430 405

Figure 1. Maximum temperatures that different parts of the space shuttle
experiences during ascent and re-entry. All temperatures shown are in degrees

Celsius [3].

The original TPS is composed of four main materials. These materials include

Reinforced Carbon-Carbon (RCC), low-temperature reusable surface insulation

tiles (LRSI or white tiles), high-temperature reusable surface insulation tiles

(HRSI), and felt reusable surface insulation (FRSI or black tiles) blankets [2, 3].

The FRSI blankets are found on the upper section of the bayload doors and the

inboard sections of the wing upper surface and cover about 25 percent of the

3

vehicle. They protect these areas from temperatures between 175°C and 370°C.

The white tiles (LRSI) cover the upper surface of the vehicle. Due to their high
reflectivity, they reduce the solar heat gain from the sun. In contrast, the black
tiles (HRSI) have high emissivity, which becomes crucial for heat elimination
during the re-entry into the atmosphere. Black and white tiles are made of a

similar material, and together they guard the vehicle from temperatures between

648°C and 1345°C. Most of the white tiles have been replaced with fibrous

insulation blankets, also known as Advanced Flexible Reusable Surface
Insulation (AFRSI), in order to accommodate the flight requirements more

effectively [2].

The hottest areas of the orbiter during re-entry are the nose cone, the leading
edge of its wings, and the area directly behind the nose cap of the lower surface,
also known as the chin panel [1]. The surface temperature of the nose cone rises
almost instantly when the vehicle re-enters into the atmosphere [5]. RCC, a light
gray composite, along with lnconel foil insulators and quartz blankets, protect
these areas from the highest expected temperatures and aerodynamic forces [4,
5]. A schematic of the orbiter TPS and the areas covered with RCC panels is

shown in Figure 2.

 

RCC

Figure 2. Schematic of the orbiter TPS [3]

The leading edges of the wings contain 22 RCC panels, which are manufactured

at Lockheed-Martin’s Missile and Fire Control Facilities in Dallas, Texas. These

panels can withstand temperatures up to 1770°C. Even though they are able to

endure very high temperatures, the RCC panels have very high thermal
conductivity. For this reason, insulating blankets and tiles are needed behind the

panels [6]. RCC panels must also have an oxidation protection coating such as
SIC, Si3N4 or SiOz in order to resist the oxidizing environments [5]. However,
when surface temperatures reach as high as 1650°C, the thermal

ablation/erosion is expected to happen very rapidly. If the coating layer erodes,

the whole TPS will be damaged, which would jeopardize the safety of the whole

vehicle. Therefore, a new TPS design with self-cooling capability is introduced in

this study.
1.3. INTRODUCTION TO PERSPIRABLE SKIN DESIGN

The proposed design is a multifunctional material system, which is arranged in a
‘Peg and Hole’ fashion. The RCC skin of the space Shuttle is designed to have

multiple holes that contain cores (pegs). These cores would either be made of

zirconium tungstate (ZrW203) or Functionally Graded Material (FGM) containing

ZrW203 and zirconia (ZrOz). The choice of ZrW203 is based on its unusual

isotropic negative thermal expansion (NTE) over a wide range of temperatures

(0.3-1050K) [7, 8]. In this temperature range, its Coefficient of Thermal

Expansion (CTE) ranges from —6.5 to -13.2><10—°K'1 [7]. The M-O-M transverse

vibrations (where M is Zr or W in this case) in ZrW203 crystal cell causes the

contraction of the MM distance, resulting its negative thermal expansion [7].

In humans, perspiration is a part of the body’s therrnoregulation system. When
the temperature of the skin gets higher than normal temperature, the sweat
glands expand and produce a fluid consisting mainly of water and a small
amount of dissolved solids. When this fluid evaporates from the skin, it will result
in a cooling effect. Perspiration decreases when the temperature of the skin

decreases. Perspirable Skin design discussed in this thesis works in a similar

fashion as human perspiration to regulate the surface temperature of externally

heated surfaces such as the space shuttle orbiter.

When the surface temperature of Perspirable Skin increases during reentry, a
gap is formed between the core and the RCC skin, mainly caused by the
shrinkage of the core due to its negative thermal expansion property. Once the
temperature reaches the working temperature, this gap becomes large enough to
introduce coolant gas, which is onboard within the space vehicle, onto the
surface. The flow of coolant gas mixed with atmospheric air is expected to
significantly decrease the surface temperature at the orbiter‘s nose cone, chin
panel, and the leading edge of the wings caused by frictional heat during the

reentry.

The highest working temperature for Perspirable Skin is expected to be around

750°C, which is limited by the dissociation of ZrW208 at 777°C. However, it is
expected that the Perspirable Skin will function around 700°C, the surface will be

cooled, never reaching the highest surface temperature observed (1650°C) with

the current TPS design. As the surface temperature decreases, the gap starts to
close again. Therefore, the whole design of Perspirable Skin is an autonomous
cooling system for the reentry vehicle. A simplified schematic of this concept is

shown in Figure 3.

 

b
Figure 3. Basic schematic of the Perspirable Skin design (a) at room
temperature (b) at maximum working temperature (750 0C)

The space vehicle has a design life of 100 missions [3]. Perspirable Skin
provides a reusable and self-regulating system that meets this design criterion.
The current TPS of the orbiter only provides protection from the high
temperatures endured during re-entry to the atmosphere. The proposed design
combines protection as well as cooling, which provides for a safer design

alternative, protecting the vehicle structure and its occupants.

1.4. POWDER METALLURGY

Powder metallurgy is a method of manufacturing parts by compacting/forming
powders (metal, ceramic, pharmaceutical or glass) into shape and/or sintering
them. It is a commonly used method since it allows fabrication of parts of wide
range of sizes with good dimensional accuracy. The final products exhibit net or
near-net shape [9]. Precision, as well as economics make powder metallurgy the

best method for the fabrication of the Perspirable Skin core.

Powder metallurgy consists of three steps: powder mixing, forming operations,
and sintering. The initial step may involve combining different types of powders
or blending powders of the same type by breaking particles or agglomerates into
smaller particles through mechanical agitation. Particles may vary in Size and
Shape; thus, this is an important step to ensure that the properties will be uniform
throughout the finished part [9, 10]. During the mixing step, several additives
might be added to the powder mixture, such as lubricants or binders. Lubricants
improve the flow characteristics significantly, while binders help increase green

strength [9].

The shaping operations involve utilizing stress to form blended powders into
desired shapes. This step is performed with close dimensional control. There are
numerous shaping operations, such as injection molding, extrusion, slurry

techniques, freezing techniques, and compaction [11].

The most common method for pressing mixed powders into shape is the
conventional cold uniaxial compaction. It involves applying pressure along one
axis using hard tooling at room temperature. Generally, a die, along with an
upper and a lower punch, are used to perform the operation. The pressure may
be transmitted from both bottom and top punches, or in some cases the bottom
punch is stationary and the pressure is transmitted from a single punch. This
uniaxial compaction process is shown step-by-step in Figure 4. Samples
produced after compaction are called “greens”. The final density of a green
sample depends on the compaction pressure and the powder characteristics [9,

11].

 

Top Punch—-| I U -
Green
Die— Compact
Bottom Punch

Filling Flattenlng tEm'Y th Compaction Ejection
op punc

 

 

 

 

 

Figure 4. Cold uniaxial powder compaction process

After compaction, the green samples are not fully dense. Generally, in the case
of ceramics and metals, they require additional processing, such as sintering, to
obtain a denser part. Sintering is a thermal process that involves bonding of
particles together at high temperatures by solid-state atomic transport
phenomenon. The green compact is heated in a controlled-atmosphere furnace

to the temperatures below its melting point; however, in some cases the

10

formation of a liquid phase might be involved. The bonding occurs due to the
growth of the cohesive neck at particle contacts. After sintering, the properties
observed in the green state, such as strength and density, are significantly

improved [9, 11].

Subsequent to the three main steps of the powder metallurgy, occasionally some
additional finishing operations might be necessary in order to obtain specific
features or improve the dimensional accuracy of the final part. These operations
may include machining or surface finishing. Since such additional operations
would increase the manufacturing cost, it is often desired to obtain the final

geometry/dimensions through the previous step(s).

As mentioned previously, powder metallurgy is the most suitable method for
manufacturing the core of the Perspirable Skin. The fabrication process is
discussed in detail in sections 2.3 and 2.5 of this thesis. Additionally, the effects
of powder mixing in the compaction capabilities of ceramic powders, as well as
variations in final dimensions and densities of green compacts are investigated in

Chapter 3.

11

1.5. FUNCTIONALLY GRADED MATERIAL (FGM)

A functionally graded material is defined as a composite material that has
gradual change in the composition and structure over its volume. Due to this
gradual change, the material is non-homogeneous and the properties vary with
location. This basic concept is shown in Figure 5. FGM applications are used in
many fields, such as aerospace, biomedical, automotive and manufacturing [13].
The composition and properties of the FGM component depend on the specific

application for which it is made.

 

 

Homogeneous Material FGM With gradual
property change

Figure 5. Basic concept of functionally graded materials

In the current study, FGM containing ZrW203 and ZrOz is proposed as a

potential core material for the Perspirable Skin application. The important
property of this kind of FGM is the continuous variation from negative to positive
in the radial thermal expansion. During the reentry of the Space Shuttle, a

temperature gradient is expected along the thickness of the TPS. While the outer

surface temperatures are as high as 1650°C, the temperatures inside are

expected to be around 175°C [3]. Utilizing an FGM core that has a negative CTE

12

at the top surface and near-zero CTE at the bottom portion allows it to produce a
large gap opening with the skin at the top surface while the bottom portion
remains in contact. The FEA modeling and the fabrication of the FGM core are

discussed in detail in Chapter 2.

1.6. FINITE ELEMENT METHOD (FEM)

Recently, modeling physical phenomena with the aid of computers has made it
easier for engineers and scientists to be able to understand and predict complex
processes. Analytical descriptions of such physical phenomena are called
mathematical models, and they are described by complicated differential and
integral equations. Most of the time, the geometrical domains of these equations
are very challenging. Mathematical models and numerical methods, along with
the help of computers made it possible for scientists and engineers to compute

practical engineering problems with much less effort [14].

There are several numerical methods that are used in finding approximate
solutions to partial differential equations (PDE). Some of the most common ones
used for engineering applications include the Finite Element Method, Finite
Difference Method (F DM), and Finite Volume Method (FVM). The development of
FEM started in the mid-1950s for solving complex stmctural analysis problems

[15]. Currently, it is the most commonly used method in structural mechanics,

13

whereas FVM and FDM are more widely used in solving Computational Fluid

Dynamics (CFD) problems.

FEM is a powerful method because it allows for solving practical engineering
problems that have complicated geometries and boundary conditions. The
complex geometric domains are divided into numerous simpler subdomains
called finite elements, which are attached together at points called nodes. Once
the domain is divided into finite elements, algebraic equations are established for
each of these elements from the governing equations of the problem. Finally, the
relationships from all of the elements are collected back together in order to

obtain the solution for the entire domain [14].

Currently, numerous commercially available FEM software exist that are widely
used by engineers. Some of the most common ones include ANSYS (Ansys,
Inc., USA) and ABAQUS (Dassault Systemes Simulia Corp., USA), which were
implemented in this study. ANSYS (Version 11.0) was the choice of software for
the FEA of the Perspirable Skin design and the details are discussed in Chapter
2. For the numerical analysis of powder compaction, which is introduced in

Chapter 3, ABAQUS (Version 6.6) was preferred.

l4

1.7. MODIFIED DRUCKER-PRAGER I CAP PLASTICITY MODEL

The modified Drucker-Prager/ Cap plasticity model, which is offered in the library
of the ABAQUS software, is commonly used to model frictional materials, such
as granular-like soils and rocks. These types of materials exhibit pressure-
dependent yield, meaning that the material becomes stronger as the pressure
increases. This model can also be used for modeling the uniaxial compaction of

ceramic powders since they exhibit similar behavior [15].

The modified Drucker-Prager/ Cap plasticity model is based on the addition of a
cap yield surface to the original Drucker-Prager shear failure surface which was
introduced by Drucker and Prager [15, 17, 18]. Therefore, the yield surface has
two main segments: The pressure dependent Drucker-Prager shear failure
surface and a cap yield surface that intersects the equivalent pressure axis.
Between these segments, a transition section exits in order to provide a smooth
surface. The main purposes of the cap are [15]:

1. It bounds the yield surface in hydrostatic compression and therefore
provides an inelastic hardening mechanism to represent plastic
compaction.

2. It provides a softening function of the inelastic volume increase created as
the material yields on the Drucker-Prager shear failure and transition
surfaces in order to control volume dilatancy as the material yields in

shean

15

The yield surface is shown in Figure 6. The x-axis represents the equivalent

pressure, p, and the y-axis represents the square root of the second invariant of

the deviatoric stress, ,/J'2 [15, 16].

J'"2 transition surface

shear failure ,

 

 

'P

 

R(d+patanj3)
Figure 6. Modified Drucker-Prager/ Cap Plasticity Model yield surface [15]

There are several important parameters used in the formulation of the modified
Drucker-Prager/ Cap plasticity model and are required as input when modeling
ceramic powder compaction in ABAQUS. These parameters are also shown in

Figure 6. They include unique material properties, such as the internal angle of

friction (B) and the cohesion of the material (d). The transition surface parameter

(a) is usually a small number between 0.01 and 0.05 and is used to provide a

smooth transition between the cap and the shear failure surface. Cap eccentricity

(R) is a material parameter, which controls the shape of the cap. Also shown in

this Figure 6 are Pa and Pb, which represent the evolution parameter that

16

signifies the volumetric plastic strain driven hardening/softening and the

hydrostatic compression yield stress, respectively [15, 16].

For ceramic powder compaction, the modified Drucker-Prager! Cap plasticity
model allows the effects of stress states to be addressed during several steps of
the process, such as during compaction and the removal of the upper punch, and
after the ejection of the green sample from the die. Since the formulation of the
model satisfies the description of material responses to the environment and
applied stress states, it also allows calculation of the density distributions both

during the compaction and ejection processes as well as after ejection [16].

17

CHAPTER 2

PERSPIRABLE SKIN DESIGN

2.1. DESIGN APPROACH

The design process consisted of defining the concept, determining the best
materials for the application as well as establishing the final geometry using finite
element analysis (FEA), and testing the manufacturability of the final design. In
order to find the ideal design for the system, several components were

investigated. These components include:

1. Ideal material for the NTE core

2. Best carbon fiber arrangement for RCC skin

3. The optimal dimensions that will yield a large enough gap distance for
the coolant gas to exit

4. Core geometry that will provide an efficient route for the coolant gas to
be delivered to the surface

5. Alternative materials that will be most economical, while providing ease

in manufacturing of the core using powder processing methods

18

2.2. MATERIAL SELECTION FOR THE CORE

2.2.1. Materials with Negative Thermal Expansion Property

As mentioned previously, the core for the Perspirable Skin design should have
negative CTE in order to achieve a gap between the core and the RCC skin at
high temperatures. Isotropic negative thermal expansion is a very uncommon
property. Several NTE materials were investigated in the search for the best
material for the core. Five ceramic materials with isotropic negative thermal
expansion are Shown in Table 1 below.

Table 1. Isotopic negative thermal expansion materials [19-25]

 

 

 

 

 

 

Material CTE range (10-6 K4) Temperature range for NTE (K)
ThP207 -9.3 to 4.3 573.430
012207 -7.1 to 3.1 773-1773

ZI'V207 -II.1 to 15.4 380-875

ZrWzOg -I3.2 to -6.5 3-1050

HIM/208 -12.9 to -6.4 3-1050

 

 

 

 

 

Figure 7 shows the dependence of the relative expansion of these materials on

temperature. It can be seen that not all of the materials listed in Table 1 Show a

negative thermal expansion throughout their entire solid state. FThP207, UP207,
and ZrV207 exhibit positive thermal expansion when temperatures are lower

than their corresponding ranges listed in Table 1. Only ZrW203 and HfW203

feature negative CTE over the whole solid state. However, Hf (Hafnium) is a rarer

19

element than Zr (Zirconium). For this reason, ZrW203 was chosen as best core

material for the Perspirable application due to its isotropic negative thermal

expansion over a wide range of temperatures.

 

0.6
05 :I \ —ZrW203/HfW203
0.4 d \ - - 'ZI'V207

0.3 J

0.2 11

Relative expansion (%)
O
O

 

 

 

 

o - 260 '460 ' 600 V 860 .1000'12'00'14'007600
Temperature (K)

Figure 7. Temperature dependence of the relative expansion of NTE materials

2.2.2. Negative Thermal Expansion Mechanism

The basis for the isotropic negative thermal expansion of the ceramics discussed

in 2.2.1 is the M-O-M linear linkage. In the case of ZrW203, the M-O-M linkage is

either Zr-O—Zr or W-O-W. All of the five materials have an open, low-density
framework crystal structure. Their M-O bond is very strong and the coordination
of oxygen is only twofold. These characteristics have two closely related
outcomes. First, the thermal expansion of the M-0 bond is very low, and the
thermal vibration of oxygen will is very low in the directions of the M atoms.

Second, the thermal vibration of oxygen perpendicular to the M-O-M linkage

20

must be very high. With these unique thermal motions, as oxygen atoms vibrate,
M cations are pulled together and this causes the negative thermal expansion of

these materials [19, 20, 22].

A Simple schematic of thermal contraction caused by thermal motion is shown in
Figure 8. The solid circles represent cations and the hollow circles represent
oxygens. The low temperature bond positions are shown with solid lines, and the
high temperature bond positions are shown with dashed lines. The arrows

indicate the direction of vibration for the oxygens [19].

 

Figure 8. Schematic of thermal contraction caused by thermal motion

2.3. FABRICATION OF ZrWan

Our group has fabricated bulk ZrW203 through the in-situ reaction of W03 and

Zr02 [26, 27].The two powders were mixed with the 2:1 stoichiometric ratio of

WO3 and ZrOz (mass ratio is mwo3: erOZ =1:0.266). ZrOzNVO3 mixtures with

21

other mass ratios result in a wide variety of ZrW203/Zr02 composites [28, 29].

The ramp/soak profile shown in Figure 9 was used to produce ZrW203 and the

resulting microstructure is shown in Figure 10.The balanced reaction can be

expressed as follows:

ZrOz + 2WO3 —» ZrWzOg (1)

 

 

Sintering temperature (°C)
a)
o
‘5‘ .

 

 

O . . - .

 

4 5 1o
Sintering time (hours)

Figure 9. The ramp/soak path used for producing ZrW208

 

Figure 10. The microstructure of the ZrW203 substrate.

22

2.4. FINITE ELEMENT ANALYSIS (FEA)

2.4.1. Material Properties and Boundary Conditions

The finite element modeling was carried out using ANSYS (Version 11.0, Ansys,
Inc., USA). Both the assembly conditions and working conditions were simulated.
This required performing both thermal and structural analyses. The material
properties required for such analyses include elastic modulus, shear modulus,
Poisson’s ratio, temperature dependant CTE, and thermal conductivity of each
material. For modeling layered composites such as laminated RCC, ANSYS
offers a layered structural solid element (SOLID46). This element allows the user
to input the thickness, orientation and material properties of each layer. 3D
isotropic and 3D woven orthogonal RCC, as well as the core were modeled using

a different structural element (SOLID45).

The core and the RCC skin were modeled as quarter-cylinder and quarter-
hollow-cylinder respectively due to the symmetric structure. The axisymmetry
boundary conditions as well as several other displacement boundary conditions
were applied to both parts. The comer edge (axisymmetry) of the core was fixed
in the x and y directions but was free to move in the z-direction. This boundary
condition allows the core to expand and shrink in every direction. Additionally, the
RCC skin will apply constraining force on the core so it will not move in the z-

direction freely. The RCC skin was only constrained on the outer circular edge

23

such that it could not move in the z-direction. This allows the skin to expand,
shrink, and bend as the actual skin in flight may experience. Figure 11 shows

these boundary conditions graphically.

RCC Skin

NTE core

 

Figure 11. Boundary conditions for finite element modeling

2.4.2. Material Properties for RCC

Several different fiber arrangements were compared to find the optimized
structure for RCC. These arrangements included 3-D orthogonal, 2-D fabric
laminated, and isotropic. The microstructure of a 2D fabric laminate RCC
composite sample (Agency for Defense Development (ADD), South Korea) is

shown in Figure 12.

24

 

Table 2. Various parameters of RCC used in FEA [30]

 

 

 

 

 

 

 

 

 

 

 

 

 

Young's Modulus (GPa) Shear CTE (10.6K4)
Designation Modulus
Longitudinal Transverse (Gpa) Longitudinal Transverse

2” Fibric 118 4.1 6 1.3 6.1

Lammate

3D Woven

Orthogonal 55 96 17.5 1.3 1.3
3D Isotropic 14 - - 2E-7* 2E-7*
Testing results by the TMA

Most properties of the RCC used in FEA were taken from the report of Sheehan
et al. [30], such as the elastic modulus, shear modulus and CTE, which are listed
in the Table 2. The CTE of isotropic RCC was tested from the RCC samples
which were rectangular parallelepipeds with edge lengths 10.6mm, 7.0mm and
7.0mm. The value also is shown in Table 2. The temperature dependant thermal
conductivity data was obtained from the report of Savage [5]. The Poisson’s ratio

of 0.2 was used based on the report of Tanabe et al. [29].

 

a b
Figure 12. Microstructure of the RCC composite sample at a) fiber-cutting
direction and b) fiber-parallel direction

25

 

85
80 -
75:
70:
65 i
60:

I
55.

50-
45+

40

 

Thermal Conductivity (W/m/K)

 

 

 

0 1 200 '400 V 600 ' 800 '1000'12'00'14'00'16'00
Testing temperature (°C)
Figure 13. The temperature dependence of thermal conductivity of RCC [5]

2.4.3. Material properties for erzos

Most thermomechanical properties of ZrW203 were experimentally determined.

The CTE and Young’s modulus of the ZrW203 were measured using a

Thermomechanical Analyzer (TMA: Setaram 95, France) with the heating and

cooling rates of 1°C/min in the argon gas environment.

For the CTE testing, the ZrW203 samples used were cylindrical with 7.51mm

diameter and 5.68mm height. For Young’s modulus testing, the samples were
rectangular parallelepipeds with the edge lengths of 12.6mm, 4.2mm and 2.5mm.
Three samples were tested for CTE and Young’s modulus. The CTE variation is
less than 5% and the maximum discrepancy in the Young’s modulus data is 6%

in the three samples. Therefore, it was considered that the CTE and Young’s

26

modulus testing results are consistent; and each reported value in the paper is

the average of the corresponding results of three samples.

The Young’s Modulus of ZrWzOg was found to be 4.31i0.13GPa at room
temperature. The CTE-temperature relationship of the ZrW203 substrate is

shown in Figure 14. As expected, the CTE of erzOg is negative and uniform for

a wide range of temperatures before or after a sharp change around 160°C due

to the d- to B- ZrW203 phase transition [22]. The CTE of the ZrW203 at room

temperature is -8.09 i 0.65K-1.

 

-6.0x10‘6

 

J

-8.0x10'6 - ——‘

-1.0x105l

-1.2x10'5 -

CTE(K‘1)

-1.4x10’5 -

-1.6x10‘5- ii

 

 

 

 

 

'1 . 8X1 0.5 ' I V I ' r ' I ' I ' I f
0 1 00 200 300 400 500 600 700
Testing temperature (°C)

Figure 14. The temperature dependence of the CTE of ZrW203

The high temperature thermal conductivity of ZrW203 was measured using the

laser flash method (FIashLine 5000, USA) from room temperature to 710°C. The

results are shown in Figure 2.5 (Test was performed by Dr. Xun Shi at Prof. Uher

27

group at University of Michigan, USA). Around 160°C, a sharp peak,
corresponding to the a-to-B ZrW203 phase transition can be observed. The room
temperature phase is phase a, and its thermal conductivity is around 0.89 Wm'
1K", a result that is very close to the reported value of 0.82 Wm‘1K'1 [30]. The

high temperature phase [3 features a nearly constant thermal conductivity at

0.985 Wm'1K‘1 between 500 to 710°C. The results can be seen in Figure 15 and

 

Table 3.
1.00
J I
0 98- 1 . .llllllllllll
. l .
0.96 d

0.94d

0.92- '
T l
0901
0 '100'200'300'400'500600300 taco
Testing temperature (°C)

 

Thermal Conductivity (WIm/K)

 

 

Figure 15. The temperature dependence of thermal conductivity of ZrWan

Table 3. CTE of ZrW208 at various temperatures

Temperature 25°C 100°C 150°C >300°C

cm (104?? -8.09 :I: 0.65 -8.56 :l: 0.67 -l6.5 a 0.98 -7.3 :h 0.45

 

 

 

 

 

 

 

 

 

Our data indicate that the thermal conductivity of the phase B is higher than the

phase a. It is known that ZrW203 exhibits a crystalline structure, and usually a

crystalline material possesses a high thermal conductivity. However, our data

28

show the thermal conductivity of ZrW203 is very low. From the report of Mary et

al. [22], the dimension of the unit cell ZrW203 is extremely large when compared

with common ceramics. This structural characteristic provides more phonon

vibration modes to hinder the heat flow in solid. Consequently, the thermal

conductivity of ZrW203 is very low.

The Poisson’s ratio was taken as 0.3 from the report of Drymiotis et al [33]. Then
its shear modulus (G) was calculated using the Young’s Modulus and Poisson’s
ratio.

G: E
2(1+v)

 

(2)

2.4.4. Flow through Annular Space formed by Two Coaxial Tubes

In order for compressed coolant gas to be successfully discharged to the surface,
a large enough gap opening must be obtained between the core and the RCC
skin. The minimum gap distance that makes the flow possible will also assist in
determining the appropriate dimensions, such as the diameter for the cores and
the holes. Assuming laminar steady flow, the velocity of the fluid flow through the
annular space formed by two coaxial tubes can be expressed as function of
radius using the following equation [34]:

2 2
u(r)=id—P[r2—a2-° ”a 111(1)] (3)
4,11 dx In(b/a) a

 

29

In equation (3), r represents the radius and a and b are inner and outer radii
respectively. [J is the kinematic viscosity of the coolant fluid and dP/dx is the
pressure gradient. These dimensions are shown graphically in Figure 16 below.
Equation (3) used to calculate radial location of maximum velocity.

b2 —a2
21n(b/a)

(4)

 

     

 

 

dx

Figure 16. Several parameters used in equation (3)

 

Assigning a value for the outer radius and the gap distance, the inner radius can
simply be obtained by subtracting the gap distance from the outer radius value.
The inner and outer radii dimensions have very little effect on the velocity; rather
the gap distance and the length of the tube have the most influence. Assuming
the coolant fluid is nitrogen gas, the maximum fluid velocity was plotted as a
function of gap distance at different pressures. The length of the tube was taken
as 8mm, which is equal to the thickness of the RCC TPS [2, 35]. The relationship

is shown in Figure 17. It is obvious that the fluid velocity increases as the gap

30

distance and the pressure of the compressed coolant gas increases. For gap
distances below 60 pm, the velocity was very close to zero. Considering this, it
was determined that the minimum gap distance should be at least 80 pm in order

to accomplish successful discharge of the coolant gas to the surface. The

dimensions of the core and the RCC skin hole were selected accordingly.

 

12-1

10-

 

Velocity (m/s)

 

 

fT‘f

2‘0 ' 4'0 ' 60 ' 80 '100 120 12101601530200

Gap Distance (1.1m)

Figure 17. Maximum fluid velocity as a function of gap distance for different
compressed coolant gas pressures

2.4.5. Determination of the best RCC structure

The assembly of the system is a shrink-fitting process expected to occur at a

high temperature such as 750°C. When the RCC TPS and the core are

isotherrnally heated to 750°C, the core shrinks and the hole on the RCC TPS

expands creating a diametrical interference. This interference makes it possible

to slide the core into the hole of the RCC skin. The assembled structure is then

31

cooled to room temperature. In order to achieve a secure contact between the
two materials, the system should be designed such that the diameter of the hole
becomes smaller than the diameter of the core at room temperature. This causes
the stresses on the core a as well as skin at lower temperatures, guaranteeing a

tight fit.

As mentioned previously, the gap distance opening should be 80 pm or larger in
order to for the coolant gas to be released successfully to the surface. Through
FEA, it was determined that the radius of the pure ZrW203 core should be at

least 15mm to satisfy this requirement. Several smaller radii for the core were
tested and the results were not satisfactory. For the RCC skin, a 14.98mm for
the hole radius was used, which guarantees a secure fit. Any larger radius

causes loss of contact between the two materials at room temperature, meaning

that the ZrW203 core slides off the hole as shown in Figure 18 [36].

.196E-06
.846E-05
.167E—04
.250E-04
.333E-04
.415E-04
.498E-04
.580E-04
.663E-04
.746E-04

 

IDDDEDDDI

Figure 18. Von Mises stress plot showing that full contact between the ZrW203
core and the RCC skin at room temperature is lost when inner radius of RCC is
higher than 14.98mm

32

In order to determine the best fiber arrangement for the RCC skin, four RCC
structures were investigated. These structures included 3D isotropic, 3D woven
orthogonal, and two 20 laminates with [0/45l-45/90js (quasi-isotropic) and [0/90]s
(cross-ply symmetric) configurations. In the evaluation of the best design, the
maximum gap opening at working and assembly temperatures as well as
minimum stresses at contact surfaces at room temperature were considered. In

order to calculate the gap distance between the two materials caused by the

shrinkage of ZrW203 core and the expansion of RCC in the assembly conditions,
the temperature was increased to 750°C in the FEA model for both parts. The

gap distance was calculated by adding the shrinkage value of the ZrW203 core

diameter to the expansion value of the RCC hole diameter. Figure 19(a) Shows

gap distance for the isotropic RCC modeling.

From 750°C, both materials were cooled back down to room temperature. This

causes the core to expand and the skin to shrink. Since the radius of the hole
becomes smaller than the radius of the core, stresses are expeCted in the
structure for a secure fit. Figure 19(b) shows the von Mises stress result for the
isotropic RCC modeling. This two-step modeling process also represents the

whole assembly process.

The FEA results for the other three RCC structures are similar to Figure 19.

However, the gap distance and the stress values vary depending on the RCC

33

structures due to the variations in the thermal and mechanical properties. A
comparison of the results for each RCC structure is shown in Table 4 as well as

the corresponding tensile strengths [30].

Table 4. The summary of gap distance at working temperature (750°C) and the
stress at room temperature (RT) between ZrW203 core and the various types of

Stress RT tensile
(Mpa)

Designation Gap (pm)

77.19

 

resource:

Iannuuual

 

928454
.214E+07
.335E+07
.457E+07
.578E+07
.699E+07
.821E+07
.942E+07
. 106E+08
. 1 1 8E+08

    

'IEUUHUDUI

b

Figure 19. The FEA results for the isotropic RCC case (a) assembly temperature
gap distance (b) von Mises stress at room temperature

34

Table 4 shows that the quasi-isotropic RCC ([0/45/-45/90]s) and cross-ply
symmetric RCC ([0/90]s) resulted in the maximum gap distance of 79.4pm.
However, for both cases, the maximum stress at room temperature exceeded the
tensile strength in the transverse direction. This result also applies to 3D isotropic
RCC, leaving the 3D woven orthogonal RCC the only fiber arrangement
applicable to Perspirable Skin. Despite the slightly lower gap distance resulting
from the 3D woven orthogonal RCC, its highest tensile strength in both directions

provides the safest operation.

2.4.6. Design of the erzoa core

During the reentry of the space Shuttle, rather than a uniform temperature, a
temperature gradient is expected along the thickness of the TPS [3]. In the

proposed design, with the cooling provided by Perspirable Skin, the highest

surface temperature is assumed to be only 750°C. Thus, the temperature

gradient in the design was assumed to be 750°C for the outer surface and 100°C

for the interior part. This assumption is reasonable since the interior temperature

is 175°C for the 1700°C outer surface temperature for the RCC panels [3].

In order to accommodate the temperature gradient, the geometry of the ZrW203

core can not be a simple cylindrical Shape as shown in Figure 19. It has to be

changed so that it has a larger radius at the top surface and a smaller radius at

35

the bottom part. When this new geometry experiences this temperature gradient,
the top surface of the core will shrink significantly due to the endured high
temperature resulting In a large gap at the top surface, while the bottom part of
the core will still maintain contact with the RCC skin because of the much lower

bottom temperature. This will also avoid sliding conditions shown in Figure 18.

The first geometry considered consisted of two attached cylinders with the same
height. At room temperature, the top cylinder had a radius of 15mm and the
bottom one had a radius of 7.5mm. The hole radius was 14.995mm at the top
and 7.49mm at the bottom. In order to model a thermal gradient throughout the
material, a coupled thermal and structural analysis was performed in ANSYS.
Figure 20(a) shows the temperature distribution in the structure under the new

temperature gradient and Figure 20(b) shows the gap opening.

 

 

IUDDEDDDI
9

Figure 20. The modified geometry under the 100-750°C temperature gradient

(a) temperature distribution (b) gap distance between the ZrW203 core and RCC
skin

36

The problem with the geometry shown in Figure 20 is that the bottom horizontal
part of the upper cylinder always stays in contact with the RCC, making it difficult
for the coolant gas to be channeled through the core and out to the exterior
surface. Therefore, a slightly different geometry was considered. In this new
geometry, the top part was tapered down resulting in a frustum of a cone with a
top radius of 15mm and a bottom radius of 7.5mm. The bottom part remained

cylindrical with a radius of 7.5mm.

4105-04
-.689E-04
-.569E-04
41995-04
-.429E-04
-.359£-04
-.2ese-04
-.218E-04
-.148E-04
Sem i-circular 4315435
channel

(1mm radius)

 

IBEDEDEEI

   

b

Figure 21. The tapered core geometry under the 100-750°C temperature
gradient (a) Gap distance (D) bottom view of the core showing the semi-circular
channel that provides larger flow area for the coolant gas

Figure 21 shows the gap distance of modified structure under the 100-750°C
temperature gradient. It can be clearly seen that the tapered geometry provides a
better and shorter route for the coolant gas. However, small channels should be
incorporated into the cylindrical bottom half of the core in order to achieve a
higher surface area for continuous flow for the coolant gas._ Semi-circular shaped

37

channels starting from the bottom surface and extending half way up through the
core has been simulated. These semi-circular channels had a 1mm radius. There
were a total of 4 channels in the core geometry (one channel in the quarter-
geometry). The incorporation of the thin channels does not have a significant

effect on the gap distance.

It can be seen in Figure 21 that the design with tapered top portion does not
provide a gap distance (71 pm) as large as the one with the cylindrical top (85.3
pm). This is caused by the fact that the top portion has a larger dimension,

yielding a smaller shrinkage. In order to compensate for this issue, the radius of

the bottom cylinder of the ZrW203 core was increased. This increases the taper

angle, resulting in a larger dimension of the core; thus, provides more shrinkage

at the top portion at high temperatures.

Several larger radii were tested in order to investigate the relationship between
gap distance and the radius of the bottom cylinder, as shown in Figure 22. It can
be clearly seen that the gap distance increases with an increase in the bottom
radius until 12mm is reached. For the radii larger than 12mm, the gap converges
to 94.2pm. Therefore, it proves that changing the bottom radius is an appropriate

way to alter the gap distance.

38

95

 

90-
1
85d

80-
,

75-

Gap Distance (urn)

 

 

 

70 - r fl I ' I ' 1 ' V f U
7 8 9 10 1 1 12 1 3
Radius of the bottom cylinder of the core (mm)

Figure 22. The relationship between the gap distance and the bottom cylinder
radius or the core

In order to get the optimal gap distance, the final modified design for the ZrW203

core had a radius of 12mm for the bottom cylindrical portion. The top radius was
kept at 15mm. This final design is shown in Figure 23. Figure 24(a) shows the
temperature distribution in the structure for this final design at working condition.
Figures 24(b) and 24(c) show the gap distance and maximum principal stress
contours at working conditions, respectively. This final design results in a
maximum gap distance of 900m at the working condition. There is a slight
decrease from 94.2um is caused by rounding off the corners and edges which
could create stress concentration in the structure. Figure 24(d) shows the
maximum principal stress in the structure at room temperature. The maximum
calculated stress of 127MPa does not exceed the tensile strength of RCC skin in

any directions.

39

 

Figure 23. Final geometry for the ZrWZOa core

One problem with this final ZrW203 core design is that it has a very complex

geometry. It was determined that it will be very difficult to manufacture using only
powder processing methods. It would require additional finishing operations,
which would result in higher costs and may result in a damaged final part.
Alternative designs had to be considered in order to make the fabrication less

intricate.

40

 

 

IEDUEDDDI
i

 

lunnlunnl
._..§.._
é

.110E+09
C

17613

.142E+08
.283E+08
.425E+08
.566E+08
.708E+08
.849E+08
.991E+08
.113E+09
.127E+09

IEIIEDHUUBI

 

Figure 24. The FEA results for the final ZrW203 core design a) temperature
distribution at working condition (in degrees Celcius) b) gap distance at working

condition and c) max principal stress at working condition (I) max principal stress
at room temperature

41

2.4.7. Alternative Design for the NTE core

For the core design, a large gap opening at the top part while maintaining a tight
fit at the bottom portion is desired. The complex shape shown in Figure 23 is
difficult to achieve with powder processing methods. However, considering the

gradient temperature characteristic, a cylinder-shaped FGM core containing

ZrW203 and Zr02 provides a solution. In order to achieve the similar effect of the

tapered design mentioned in the previous section, the top section of the FGM

core should consist of pure ZrW203 because of its large negative CTE. The

bottom section Should have the appropriate volume ratio of ZrW203 and Zr02 to

achieve zero CTE.

Experimentally, a powder mixture of Zr02+W03 and Zr02 powder was stacked,

compacted, and sintered in the processing steps commonly used to fabricate
multi-layer materials. The observation of the cross-sectional microstructures as

well as the measurement of the radial thermal expansion provided the evidence

that the sintered samples are continuous FGM made of ZrW203 and Zr02. The

continuous FGM structure is due to the diffusion and sublimation of W03 as well

as the reaction between W03 and Zr02 during sintering. Varying the soaking

time, component of each layer, or the mass/thickness ratio among layers affects

the final microstructures and axial CTE distribution [37]. The important property of

42

this kind of FGM is the continuous variation in the radial thermal expansion from
negative to positive. This finding provided the experimental support for the FEA

modeling.

In FEA, it is difficult to model a part with continuous property change. Therefore,
the modeling of the FGM core was simplified by creating separate layers with
different properties and attaching them together in ANSYS. Initially, a 5-Iayer
cylindrical FGM core with a 15mm radius at room temperature was simulated.

Each layer had a uniform thickness and linear thermal expansion coefficient

throughout the core. The properties as well as the volume ratios of Zr02 and

ZrW203 of each layer are shown in Tables 5 and 6. The values are taken from

the report of Sun et al [38]. The first layer represents the bottom layer, and the

fifth layer represents the top layer.

Table 5. Various parameters for the FGM core

 

 

 

 

 

 

Thermal
Layer # 3.33:? 132,2 Conductivity* Young's Modulus (GPa)

(W /m/K)

1 52:48 1.4531 2.24 :t 0.08

2 64:36 1.2099 2.71 :t: 0.08

3 76:24 1.1346 3.18:t0.10

4 88:12 1.0696 3.65 :l: 0.13

5 100100 0.9672 4.12 i: 0.13

 

 

 

 

 

 

* Calculated by Mori-Tanaka Method [39]

43

Table 6. CTE values for the FGM core at several temperatures

 

 

 

 

 

 

 

-6 -1
Layer# CTE (10 K )
100°C 150°C 300°C 500°C 800°C
1 -225 -7.41 -0.76 -0.76 -0.76
2 -3.83 -9.68 -251 -291 -291
3 -54 -1195 4.1 -503 -503
4 -6.98 -1422 -5.7 -73 -73
5 -8.56 -16.49 -7.3 -73 -73

 

 

 

 

 

 

 

 

The rest of the finite element modeling was carried out in the same fashion
explained in the previous section. Same temperature gradient and boundary
conditions were applied to the structure with the new core made of FGM. The

results show that the use of FGM core provides a larger gap distance at the top
surface (97.71.1m) while the bottom part of the core remains in contact with the

RCC skin at low temperatures. The maximum stress at contact at room

temperature is 5.66MPa, which is significantly smaller compared to the maximum

stress created with the tapered ZrW203 core design. This proves that FGM core

is a suitable design alternative to the pure ZrW203 core. These results are Shown

in Figure 25.

44

88889
177.778
266667
355556
444444
533333
622222
711.111
800

IEDDEDUEI

 

a977E-04
2868E-04
a760E-04
-.651E-04
a543E-04
a434E4M
a326E-04
-.217E-04
a109E-04

IEDUIUDDI

-374818
-4047
366723
737493
.111E+07
.148E+07
.185E+07
.222E+07
.2595+07
.296E+07

IHDDIDUDI

-646463
54582
755628
.146E+07
.216E+07
.286E+07
.356E+07
.426E+07
.496E+07
.566E+07

IEBDHDUDI

Figure 25. FEA results for the 5—layer uniform FGM core a) temperature
distribution at working condition b) gap distance at working condition c) max
principal stress at working condition d) max principal stress at room temperature

45

The effect of increasing the number of layers of the FGM core was studied. When
the number of layers is increased, the core becomes more like continuous FGM.
Keeping the thermal expansion coefficient linear and the uniform layer-thickness,
the number of layers was changed to 8, 10, and 12, and the gap distances were
recorded. The results are shown in Figure 26. It can be seen that increasing the
number of layers does not have a significant effect on the gap distance. Thus, it

is concluded that the results with 5-layer FGM are similar to those with the FGM

with more layers.

 

98.5- /
I

Gap Distance (um)

 

 

96.0 ,fi
5

 

Y

i' 6 ' 5764172
Number of layers

Figure 26. The relationship between the gap distance and number of layers of

the FGM core

6

Additional FEA was performed in order to determine if the gap distance of
97.7pm can be increased. Several different FGM configurations were

considered, where the thickness of each layer varied within the geometry. These

configurations as well as the corresponding gap distances and stresses can be

seen in Table 7.

46

Table 7. Different FGM configurations for the Perspirable Skin core and their
corresponding gap distances and maximum stresses

 

 

 

 

 

 

 

 

 

 

 

 

 

FGM Layer Thickness (mm)*
Configuration Layer 1 Layer 2 Layer 3 Layer 4 Layer 5
l 3 2 1 l 1
2 4 I 1 1 l
3 3 l 1 l 2
FGM Gap distance (pm) Maximum Stress (MP3)
Configuration
1 104 3.68
2 105 1.80
3 1 02 2 .90

 

 

 

 

* Layer 1- top layer, Layer 5-bottom layer

The results Show that having a thicker portion of pure ZrW203 at the top surface

while having a linear increase in CTE in the following layers gives a larger gap

opening compared to the FGM core with uniform layer-thickness. Since the

former contains more ZrW203, the result is as expected. It must also be noted

that the bottom layer of configuration 3 is twice as thick as the bottom layers of
the other two designs. This causes a larger portion of the FGM core to stay in

contact with the RCC skin providing a more secure fit.

47

0

88.889

177.778
266.667
355.556

533.333
622.222
711.111
800

IHDDHDDEI

-. 1 02 E-03
-.907E-04
n794E-04
a681E-04
-.567E-04
a454E-04
-.340E-04
-.227E-04
a113E-04
0

HBDUIDDGI

-338384
21038
380459
739880
.110E+07
.146E+07
.182E+07
.218E+07
.254E+07
.290E+08

IEDUIUDUI

-152414
-44236
63942
172120
280297
388475
496653
604831
713008
821186

Figure 27. The FEA results for the final FGM core design a) temperature

distribution at working condition b) gap distance at working condition c) max
principal stress at working condition (I) max principal stress at room temperature

 

IBDDEDUBI

48

Even though configurations 1 and 2 provide a slightly larger gap opening, the
difference is very small; and, thus, FGM configuration 3 was chosen as the best
design. Figure 27 shows the FEA results for the gap opening and maximum
principal stress at different conditions for this design. This FGM design also
needs channels at the bottom portion for the coolant gas to be passed through
since this portion stays in contact with the RCC skin at all times. The final design

is also shown in Figure 28.

 

Figure 28. Final geometry for the FGM core with semi-circular channels for the
coolant gas to exit

2.5. FABRICATION OF THE FINAL FGM CORE

In order to fabricate similar FGM of the best design experimentally, two W03+

Zr02 powder mixtures were made. In one powder, the mass ratio of W03 and

49

Zr02 is mwo3: erOZ =1:0.266 (Powder A), and it is mwo32 mzm =1 :0.38 for the
other powder (Powder B). Powder A produces pure ZrW208 after sintering and

Powder B produces a composite of ZrW203 and Zr02 with 0 CTE [26]. 1.3g

Powder A and 1.79 Powder B were measured and stacked together. After

compaction and sintering by the same sintering process for pure ZrW203 [26], a

continuous ZrW203+ ZrOz FGM was made. The height of the sintered sample is

7.7mm. The axial CTE of the sample is shown Figure 29, which is very close to

the FEA requirement.

 

 

 

l\i

-2.
«3° 44
$3
1‘3 —6«
o

.I— I
’8 1 1 1

 

 

 

6'1'2'5'4'6'6'1'5
Measurement position (mm)

Figure 29. Measured CTE of the best FGM core design

50

CHAPTER 3

EFFECTS OF POWDER METALLURGY STEPS ON FINAL
PROPERTIES OF GREEN BODIES

3.1 . INTRODUCTION

As explained in the previous chapters, the best method for fabricating the core of
the Perspirable Skin is powder metallurgy. Since the gap distance at both
working and assembly conditions is quite small, it is essential to obtain final parts
with net-shape and high dimensional accuracy. Large variations in the final
dimensions will result in non-uniform gap openings. Additional finishing
operations after the fabrication increases costs and may produce defects in the
final part [40]. Therefore, it is important to minimize such variations in the powder
metallurgy steps. For this reason, the influence of fabrication steps on the shape

and density of the final parts must be investigated.

The three main steps of powder metallurgy (mixing, compaction and sintering)
explained in Section 1.4 are strongly related to each other. Each step highly
influences the subsequent step(s). The initial powder characteristics, such as
average particle size [41-44], particle shape [45], particle size distribution [42-44,
46, 47] and specific surface area [42] achieved during powder mixing, influence
the compaction and sintering capability. The compaction pressure [43, 48] and
the die wall friction [49] of the compaction step can affect the final shape of green

compacts as variations in the density distributions can exist in the compact [16,

51

49]. In this study, the effect of powder mixing on the compaction capabilities of

alumina (A1203) powders as well as the dimension and density variations in the

green bodies after the compaction step are investigated. The choice of alumina is
due to the fact that it is one of the most commonly studied ceramic powders. It is

also inexpensive to test, making it the most attractive material for this study.

3.2. EFFECTS OF POWDER MIXING ON THE COMPACTION CAPABILITIES
OF CERAMIC POWDERS

3.2.1. Materials and Experimental Procedure

In this study, several different powder mixtures were produced by mixing any two
of four alumina powders. The powders used were TMDAR (Taimei Chemical
CO., LTD., Japan), CR-1 5, CR-6, and GE-1 (Baikowski Ind. Corp., USA). All four
types of alumina powders were high-purity, undoped powders with
submicron/micron particle sizes. Several properties of these powders are shown
in Table 8. CR-15, CR-6, and GE-1 are all produced by the same manufacturer
and have nearly identical chemical components. However, they differ in particle
size distributions and mean particle sizes, resulting in different compaction
characteristics. The reason for choosing TMDAR powder is because it is
physically and chemically treated. Its particle size distribution has a very narrow
non-lognormal range which results in a sintered product with very low porosity.
These two features of TMDAR powder gives rise to its high compaction and

sintering capabilities.

52

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 8. Pro oerties of the ceramic powders used in the experiments
Smallest Lairtgeit Mean Mean
Material Powder particle pasizlec ° particle size pore size
size m m 111
(II ) (pm) In I (u )
TMDAR 0.1 0.33 0.17 0.09
, CR-IS 0.17 1.15 0.41 0.18
Alurmna
CR-6 0.23 1.72 0.6 0.27
GE-l 3.5 23.9 9.76 0.24
Material Powder Chemical analysIS (ppm) Bulk degsity
Na K Fe Ca Si Mg (g/m )
TMDAR 4 2 5 3 3 1 0.9
Alumina CR—15 12 15 3 2 21 <1 0.45
CR-6 13 22 2 3 14 <1 0.6
GE-l 12 15 5 2 42 <1 0.45

 

 

 

 

 

 

 

 

The particle size distribution for each powder was measured in a water solution
by the Malvern Mastersizer Micro (Malvern Instruments, England). The results
are very close to the manufacturer’s report and are Shown in Figure 30. It can be

seen that the size distributions of CR—15, CR-6 and GE-1 are nearly lognormal.

28"

 

 

 

 

 

v

23: 80-

g .

(U

E 504

E

c 1

it:

0 40-1

3% q 1 +TMDAR /'

E 1 —e—CR-15

E 2°° 1 +CR-6 I

5 1 -v-—GE-1
0‘ T'I'I'I'I'T’I'I'I'T'
0.0 0.3 0.6 0.9 1.2 1.5 5 10 15 20 25

Particle size (m)

Figure 30. Particle size distributions of the powders used in the experiments

53

The powders were mixed using the Speed Mixer DAC 150 (FlackTek, Inc, USA)
for 3 minutes (1 minute for each cycle and totally 3 cycles) at the angular velocity
of 1700 rad/s. A total of six powder mixture systems were produced by mixing all
possible two-powder combinations of the four alumina powders with different
mass ratios. These mixture systems were: TMDAR+CR-15, TMDAR+CR-6,
TMDAR+GE-1, CR-15+CR-6, CR-15+GE-1, and CR-6+GE-1. In addition to four
unmixed powders, each system contained nine powder mixtures, in which the
proportions of one powder in the mixtures range between 10% and 90% in 10%

increments. Therefore, a total of 54 powder mixtures were investigated.

Six grams of each powder mixture was measured by Adventurer AR 2140

(Ohaus Corp. USA) with a 0.0001g resolution; and then poured into a single-

action die made of 1144 Stress Proof steel. The inner diameter of the die (0;) was

22.19mm. Before pouring the powders into the die, the die wall was lubricated
with graphite powder (Panef Corp., USA). The top surface of the powder was
flattened and then the top punch was inserted into the die until it contacted the
powder (refer to Figure 4). The compaction load was applied on the top punch by
MTS Insight 300 (MTS Systems Corp., USA). First, a pre-Ioad of 0.5MPa was
applied at 5mm/min to set an initial state. This step is necessary in order to
measure the compact characteristics accurately before starting the main
compaction process. After applying the pre-Ioad, the initial height of each sample,
h, was measured using a Marathon electronic digital caliper with a 0.02mm

resolution and a 150mm measurement range. This was done by measuring the

54

total height of the two punches and the pre-loaded compact inside the die, then

subtracting the height of the two punches. Since the diameter of each compact is

equal to the inner diameter of the die (0:), the initial relative density, (R;) can be
calculated by the following equation:

P- m
12.: l = (5)
z
pf 3.975 211.
4 l l

 

 

where m, V, and p stand for mass, volume, and density, respectively. The
subscripts iand fstand for the initial and theoretical fully values. The theoretical

fully-density of alumina was taken as 3.975g/cm°.

After calculating the initial relative density, the die set with the pre-loaded
compact was placed back in the load frame. It was compacted to 80MPa at a
speed of 10mm/min. The stress resolution of the MTS was 0.013MPa. During the

compaction, only the top punch moved and the bottom one was stationary. The

compressive forces applied on the top (Ft) and bottom punches (Fb) as well as

the displacement of the top punch (Zt) were recorded continuously as a function

of time by the load sensors.

The heights of the final green samples ranged from 7.05mm to 9.1mm depending
on the powder mixture. Their diameters were 22.19mm. resulting in

height/diameter ratios between 0.3 and 0.4. Due to the low height/diameter ratio,

55

the force transmitted force to the bottom punch and the applied force on the top
punch were almost identical in the compaction. The discrepancy between the two
recorded forces was less than 0.2%. The masses of the green samples were
measured again after compaction. An expected mass change always existed due
to the attachment of powders to the die wall and the punches as well as the
powder loss during the transport. However, this change was less than 0.4% and
was neglected. Several green samples were coated with lacquer and then their
volumes were measured in water by Archimedes’ principle. Those values were

then compared to the corresponding volumes calculated by the final sample

heights (hf) and diameter (D1). The discrepancies between the two groups of

values were less than 1.1%. Therefore, only the calculated volumes are reported

in this study.

3.2.2. Results 81 Discussion

3.2.2.1. Relative Density vs. Stress Relationship

The sample height at any time t (ht) during the compaction can be calculated

using the recorded displacement of the top punch (21) and either the initial

compact height (hi) or initial compact height (hf) using equations (6) and (7).

Using each equation, ht was calculated to check for consistency and the results

obtained from both equations were identical.

56

h, = h- — z, (6)

h, =h +2, (7)

f

Using ht, the relative density at any given time (Rt) can now be calculated in by
the following equation (8). The corresponding stress (Gt) can be obtained by

dividing the recorded load, Ft, by the cross sectional area of the punch as shown

in equation (9).

 

 

t‘ :3975 2 (8)

 

(9)

Relative density was plotted as a function of stress for each powder mixture
system. Figures 31(a) and 31(b) Show the plots for TMDAR+CR-15 and CR-
6+GE-1 mixtures systems, respectively. Only six different mass ratios are shown

in these figures for clarity.

It is obvious from Figure 31 that the relative density increases when the
compaction load/stress increases. It can also be seen that two different powder
mixture groups Show different range of relative densities for the same compaction
stress. This difference can be directly related to the compaction capabilities of
these powder mixtures. A higher relative density shows better compaction

capability. It can also be concluded from Figure 31 that the relationship between

57

the powder proportions remains similar, even though the overall relative density
increases with increasing compaction loads. Thus, this shows that the
compaction capability highly depends on the starting powder combination.
Additionally, the initial relative densities obtained from the starting powders can

be used to quantify and compare the compaction capability of each powder

 

 

 

 

   

 

 

 

 

mixture.
50
554 j
501 45‘
a? ‘ 3:5 ‘
v45. V a
a . a”
C 40 . c: ‘
8 ,1 g 35-
o . O . ,‘
112 30 7;." —-TMDAR - - -80%TMDAR g ’ ,I' ' 602/0 08-6
.,- -- -- 60% TMDAR --—-40% TMDAR .r “"3040“
25 -----20% TMDAR ----- CR—15 25 ' “W654
6 ' 2'0 ' 4'0 ' 6'0 ' 80 6 ' 2'6 ' 4'0 7 ' T 80
Stress (MPa) Stress (MPa)
a b

Figure 31. Relative density as a function of stress for two different alumina
powder mixture groups at various mass ratios (a) TMDAR+CR—15 group (b) CR-
6+GE-1 group

Figure 32 shows the relationship between the initial relative density and the
powder proportion for all six of the powder mixture groups. In the each of the
powder mixture groups, one of the powders is referred to as the “fine” powder
and the other one is referred to as the “course” powder depending on their
average particle sizes Shown in Table 8. For each of the curves in Figure 32, the
mass ratios increase from left to right for the coarse powder, and from right to left

for the fine powder.

58

 

' +TMDAR+CR15 —O—TMDAR+CR6
40 +CR15+GE1 -v—CR15+CR6
+CR6+GE1 +TMDAR+GE1

.‘

en ity (%)

.7328

 

 

 

0'2'0'4'0'6'0'8'0'100
Proportion of coarse powder (%)

Figure 32. Initial relative density as a function of proportion of the course powder
for all six alumina powder mixture groups

Figure 32 shows that there are two different kinds of relationships between the
initial relative density and the proportion of the course powder. TMDAR+CR-15
and CR-15+CR-6 groups show a linear relationship, where the maximum relative
density corresponds to 100% of one of the powders. TMDAR+CR-6, CR-15+GE-
1, and CR-6+GE-1 mixture groups show a nearly parabolic relationship. The
proportions of coarse powder in the powder mixture that obtained the maximum
relative density are between 40% and 60%. Westman [41] and McGeary [50]
reported a similar parabolic relationship for sand and metal balls; however, they
found the proportion of the coarse powder that had the maximum relative density
to be 30%. Finally, for the TMDAR+GE-1 powder group, the maximum relative

density was found to be at 100% TMDAR.

59

3.2.2.2. Relative Density vs. Strain Relationship

The axial true strain at any given time during the compaction process (St) for

ceramic powders can be calculated using equation (10) [16, 51]. Using this
relationship, relative density was plotted as a function of strain for the

TMDAR+CR—15 and CR-6+GE-1 powder mixture groups. These plots can be

In it— (10)
hi

seen in Figures 33(a) and 33(b).

 

 

 

 

         

 

 

 

 

 

 

60 50
4—TMDAR ‘
55« - - -80% TMDAR 45 ,
60% TMDAR ‘ '
$50. " o ’0‘ 1 I
2.! 1 , ° . a: 40‘ I
.2455 ,e’ . a
2 1 ' ..’ o g 1 ,
.3 404 "n 8 354 . ‘ .";—CR-6
o 1 . . O "" o . .I 'l - - -
.3 35» , . .’.z , , x .g I . x . 80:4CR-6
.e - ,v’ , , - g 30. . eoxoce-e
g 30‘ J. ",5 ---— 40%TMDAR m ‘ .. ----40%CR—6
.’..,.o’ """" -----20% TMDAR 25 V x." .....20% CR-6
25" ----------- CR-15 , ....... GE—1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 071 012 073 0:1 015 0:6
Strain Strain
a b

Figure 33. Relative density as a function of axial true strain for (a) TMDAR+CR-
15 group and (b) CR-6+GE-1 group

The relationship between relative density and true axial strain can be obtained by
finding the equations of the trend lines from the plots using Microsoft Excel 2003.
This was carried out for all six powder mixture groups, and it was determined that

the relationship is exponential as shown in equation (11):

R, =Ke3’ (11)

60

where K is a constant that varies for each powder mixture group as well as

different mass ratios of each powder. It has the same units as density (g/cm°). It

can be seen that powders with a higher K value will have a higher relative density
meaning that they have better compaction capability. Table 9 shows the values
for K for the TMDAR+CR-15 mixture group at all mass ratios. It was also
determined that the values Shown on this table correspond to the initial relative
density values from Figure 32. This means that the physical meaning of the
constant K is actually the initial relative density of the powder mixture. This
conclusion can also be verified by combining equations (5), (8) and (10). The

final equation is given in equation (12).
Rt = Re“ (12)

Table 9. Constant K for TMDAR+CR-1 mixture group for all mass ratios

 

CR-15 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

 

 

K

3 1.423 1.384 1.34 1.3 1.24 1.189 1.13 1.069 1.013 0.962 0.91
(g/cm)

 

 

 

 

 

 

 

 

 

 

 

 

It can be concluded that when comparing compaction capabilities of different
powder mixtures either using the relative density vs. stress curves or relative
density vs. strain curves, the initial relative density is the key parameter that must
be considered. The difference in compaction capabilities can simply be compared
by using the relationship shown in Figure 32. It must also be noted that the initial
relative density is dependent on the pre-load. If the pre-Ioad is decreased, so will
the initial relative density. However, the relationship between the strain and initial

relative density as well as the order of the compaction capabilities of the different

61

 

powder mixtures will remain the same.

3.3. DENSITY VARIATIONS IN GREEN COMPACTS

Green samples may contain two kinds of inhomogeneities, caused by the several
operation steps in ceramic powder processing: density distributions as the
variation of the internal form and dimensional variability in the external shape of
the compact [40, 51-53]. Shape changes that take place during the sintering step
are controlled to a large extent by the density distributions within the green
compact. A non-uniform density distribution usually results in variations in the net
dimensional change from low density to high density areas in the compact. In
worst cases, this might cause cracking in the sample due to the stress fields

induced by the local variation of Shrinkage ratio [51].

Aydin et al. [16, 51] studied the measurement and prediction of the density
variations in die-pressed green compacts. In order to detect densification
experimentally, they used lead balls as tracers. However, in this method, the lead
balls are placed at several positions at a certain distance apart from each other,
rather than in a continuous way. In order to overcome this disadvantage, our
group used several layers of colored ceramic powder to understand the powder

flow, which can indicate the density variations in the green compacts.

62

3.3.1. Experimental Procedure

Two different types of alumina powders (CR-15 and TMDAR) were dyed using a
red-colored water-based stamp ink (2000 plus, COSCO, Germany). The colored

powders were then put into a furnace (Carbolite-HTF1700, UK) for four hours at

70°C to dry out. The remaining solid powders were then poured into 12mm

diameter alumina mixing media in order to break the solids into smaller particles.
The bottles were kept on a jar mill (U.S. Stoneware 64AVM, USA) for 48 hours,

and then were sifted to get colored powder with particle size less than 0.3mm.

As discussed in Section 3.1, powder mixing has a significant effect on the
compaction capability. If the colored powders have different compaction
capabilities than the pure powders, they would alter the density distribution of the
green compacts. In order to test the compaction capabilities of the colored
powders, they were compacted to 0.5MPa and their initial relative densities were
obtained using the methods mentioned in Section 3.1. These values were then
compared to the initial density values of pure CR-15 and TMDAR. The colored
powder that has the same compaction capability as the pure powder is used as

indicator for the experiments.

In order to study the density distribution inside a green body, the height to
diameter ratio Should at least be around 1. If the height is too Short, then the

density range will be small making it difficult to identify the high and low density

63

regions. In this study, the height/diameter ratio was kept between 1.1 and 1.2. A
uniaxial compaction method was used in a similar fashion explained in Section

3.1.1. The inner diameter of the die was 19.05mm.

In the experiments, the thickness of each colored powder layer was uniform and
equal to around 1/15 of the main powder layers, which had uniform layer
thickness as well. Based on the desired height/diameter ratio of the green
compact, the mass required for each layer was calculated. The mass for each
main powder layer varied between 1.29 and Zg and the mass for the each
colored powder layer varied between 0.19 and 0.29 depending on different
powders. The use of different mass for different powders is due to the variation in

compaction capabilities.

First, the die wall was lubricated with graphite powder (Panef Corp., USA). Then,
the first layer of powder, which was always the main powder, was poured into the
die. The powder was flattened, and then the top punch, which was also
lubricated with graphite powder, was inserted into the die until it touched the
powder. After this, a pre-loading stress of 0.5MPa was applied to the powder in
order to compact the first layer to a firm enough state. The die set was then
removed from the MTS (MTS Insight 300, MTS Systems Corp., USA) and the
thickness of the pre-loaded layer was measured. This was done by subtracting
the height of the two punches from the total height when the compact is inside

the die. The top punch was then carefully removed out of the die and the second

64

layer (colored powder) was poured in. Following the same steps as the first layer,
the colored layer was pre-Ioaded to a stress of 0.5MPa. This procedure was
repeated until all of the layers were pre-loaded. Finally, the layered sample was

compacted to 80MPa.

 

 

 

a b
Figure 34. Middle sections of the layered powder compacts (a) CR-15 sample
(b) TMDAR sample

The compacted green samples were ejected from the die. They were polished on
the lateral surface until the middle axis was reached in order to observe the
curves created by the colored powder layers, which are indicators of the
densification behavior of the main powder. Each sample was then placed on the
sample holder and images of their middle sections were captured using a
dissection microscope (Wild M5A, Wild Heerbrugg Ltd, SwitzerIand) with an
attached camera. Figures 34(a) and 34(b) show the images for the CR-15 and
TMDAR samples respectively. The bottom side shown in the figures is also the

side that contacts the bottom punch during compaction.

65

3.3.2. Experimental Results 81 Discussion

The images were analyzed using lmageJ (US. National Institutes of Health,
USA) software which allows the user to calculate actual distances on the images.
The heights of several points on each of the colored powder curves were

measured using the bottom surface of the green body as the reference line.

Then, using the measured heights (ht) and initial heights (hi) as well as the initial

relative density-true axial strain relationship from equation (12), the
corresponding final relative densities were determined. Density distribution
contours were created using MATLAB software (Version R2007b, The
MathWorks, Inc., USA). Figures 35(a) and 35(b) shows the contour plots of
TMDAR and CR-15 powders, respectively. Due to the symmetry in the density
distribution, only half section of the powder was plotted. Thus, the 0 position
corresponds to the center axis of the cylindrical shape. It is obvious from these
figures that the high-density regions are on the central axis, and the highest
density is observed in the bottom central region. The top central regions as well
as the bottom edges are the low-density regions. These results are similar to the
reports of Aydin et al. [16, 51], and Train [53]. Another point that should be noted
is that the density distribution range is different for TMDAR and CR-15. This is
due to the fact that TMDAR powder has a better compaction capability, which

results in larger overall densities in its density distribution graph.

66

 

 

 

 

 

 

 

 

 

1.8-
1.7
1.6 , / 1 8
" 1.65
1-4 1.
1.6
-1 I- Q 1.
g i 1.55 E
a 51.
' ' 1.5 -
1° 5
0-8 1.45 08
0.6 1.4 0 6
0.4
0 0.2 0.4 023 0.5 1'3 0'" 02"" 0.47 07.6”"0787' 1‘7
Radius (cm) Radius (cm)
a b

Figure 35. Contour plots of the density distributions in green compacts (a) CR-15
sample (b) TMDAR sample

3.3.3. Finite Element Analysis

Finite element analysis was carried out using ABAQUS (Version 6.6, Dassault
Systemes Simulia Corp., USA) in a similar fashion explained in Aydin et al.’s
report [16]. The modified Drucker-Prager / Cap Plasticity model was employed in
the modeling of the compaction and ejection process. This plasticity model is
available in the library of the software. A 2-dimensional axisymmetric model of
the powder bed was created. The die wall as well as the upper and lower
punches were modeled as rigid surfaces. A 4-node bilinear axisymmetric
quadrilateral element type was used from the axisymmetric stress family. A
tangential contact behavior with a friction coefficient of 0.2 was implemented for

the interaction property between the die wall and the powder. Figure 36 shows a

67

schematic of the model with the mesh. The upper punch could move in the z-

direction, where the die wall and bottom punch were fixed in all directions.

The compaction process was modeled in three steps similar to Aydin et al.’s
method [16]. First the compaction load was applied on the powder by the upper
punch. After the powder was compacted to 80MPa, the upper punch was
removed which allows the compact to relax in the z-direction while it is still in the
die. Finally, ejection was simulated by removing the bottom punch and the die

wall.

top punch

symmetry
axis

powder

bed
2

I...

Figure 36. Finite element model for powder compaction

 

bottom punch

68

There are several parameters required as user input for the modified Drucker-
Prager / Cap Plasticity model in ABAQUS. These parameters include bulk

modulus (K), shear modulus (G), Young’s modulus (E), Poisson’s ratio (v), angle

of internal friction (8), material cohesion (d), cap shape parameter (R), and

transition surface parameter (a) [15, 54]. In the current study, we used a similar
technique used by Chen et al [54] for determining the bulk, shear, and elastic
moduli as well as Possion’s ratio. The transition surface parameter and the cap
shape parameter were also taken from the report of Aydin et al. [16] as 0.03 and
0.558 respectively. The angle of internal friction (B) was varied from 27 to 33.6
degrees and the corresponding material cohesion (d) values were calculated.
These two parameters are paired together and the relationship is based on Aydin
et al.’s method [16]. The paired numbers are related to the Young's modulus and
other mechanical properties as well as the yield surface function. The choice of

the minimum angle of 27 degrees is from findings of Zeuch et al. [55].

Contour plots of relative density were created for all three steps of the
compaction process. The relative density was a user defined variable which was

computed using a subroutine. Figures 37, 38, and 39 show the relative density
variations of the CR-15 powder for angle of internal friction values (8) of 27, 28,
and 29 degrees, respectively. The results were quite similar for all 8 values when

the compact is in the die before the removal of the top punch. At this step, the

density distributions agree with Aydin et al.’S report. The density range however

69

is different, due to the fact that the Young’s Modulus value of our powder was

much lower because no binder was used in the experiments.

0.4169

   

 

 

0.4356 0.4169

0.4318 0.4152 0.4151
0.4200 0.4134 0.4134
0.4241 0.4116 0.4116
0.4203 0.4099 0.4098
0.4165 0.4061 0.4081
0.4126 0.4064 0.4063
0.4088 0.4046 0.4045
0.4049 0.4029 0.4028
0.4011 0.4011 0.4010
0.3973 0 3994 I 03992
0.3934 0 3976 0.3975
0.3896 0 3959 0.3957

a b c

Figure 37. Density distribution of CR-15 powder for B =27° and d = 3.60MPa (a)
After compaction (b) after the removal of top punch (c) after the removal of
bottom punch and die wall (relative density shown)

   

0.4355 0.4152 0,4152
0.4317 0.4133 0,4133
0.4279 0.4115 0,4115
0.4241 0.4096 0.4096
0,4202 0.4078 0.4078
0.4164 0.4060 0.4060
0.4126 0.4041 0.4041
0.4088 0.4023 0.4023
0.4050 0.4005 0.4005
0.4011 0.3986 0.3986
0.3973 0 3968 O 3968
0.3935 0 3950 0.3950
0.3897 0 3931 0.3931
b c

 

Figure 38. Density distribution of CR-15 powder for B = 28° and d = 3.24MPa (a)
After compaction (b) after the removal of top punch (c) after the removal of
bottom punch and die wall (relative density Shown)

70

0 . 41 36
0 41 14
04092
0.4070
0.4048
0.4025
0.4003
0. 3901
0.3959
03937
' 0.3914
0. 3892
0.3870

     

b c

Figure 39. Density distribution of CR-15 powder for B = 290 and d = 2.88MPa (a)
After compaction (b) after the removal of top punch (c) after the removal of
bottom punch and die wall (relative density shown)

The main change in the relative density distributions for different B values was
observed when the top punch was removed. The high- and low- density regions
varied significantly for B values between 27 to 29 degrees. After 29 degrees, little
change was detected. It should also be noted that after the removal of the top
punch, the density variation in the green compact is close to final. The ejection
step of removing the die wall and bottom punch has close to no effect in the

density distributions which is similar to Aydin et al.’s findings [16].

The high-density region at the top central section and the low-density region at
the bottom right comer are in good agreement with the findings from the
experiments. However, the high- and low-density regions in middle section did
not exactly agree. This is due to the fact that most of the parameters for the

modified Drucker-Prager / cap model are unique material properties. With so

71

many parameters, there are numerous possible combinations. An accurate way
of determining all parameters is discussed in Zeuch et al.’s [55] report. They
performed hydrostatic and triaxial compression experiments and developed a
two-stage process to determine the pressure-density relationship of a powder in
hydrostatic compression, as well as the properties of the same powder compact
under deviatoric loading. However, at this time the equipment required to run
similar tests is not available in our facilities. Further analysis is required when

necessary devices are obtained.

3.4. DIMENSIONAL VARIATIONS IN GREEN COMPACTS

One of the most important requirements in the production of ceramic products is
to attain overall dimensions that are within specified tolerances. However, as
mentioned earlier, due to the series of steps in powder metallurgy, green
compacts may exhibit dimensional variability in their external shapes [40, 51-53].
This means that the geometry of the external surface of the ceramic green body
will not be exactly the same as the terminal geometry of die cavity after the green
ejection. Important questions remain regarding the evolution of the external

shape of the green compacts during the compaction process [40].

72

3.4.1. Experimental Procedure

In this study, the external shapes of the various green bodies from Section 3.1
were measured using a Veelo-DEKTAK 6M Stylus Profiler with a resolution of
0.5nm (Fraunhofer, LLC, Coating Technology Division, USA). In order to support
the samples, a special base was designed and fabricated. A simple schematic of
the setup is shown in Figure 40. The green sample was placed on the base and
the probe of the profiler contacted the external surface of the green sample. A
3mg force was applied on the probe and then the probe moved from one edge to
the other edge to measure the external surface profile. After one measurement,
the sample was rotated by 90 degrees on the base and another measurement

was performed. Atotal of four measurements were taken for each sample.

Probe of the

profiler ‘
‘\P‘robe movement

/" direction

%_ "— _ 9* 7

Sample

     
     

l

Sample holder/ 3
base

l
l
l
l

I

Figure 40. Simple schematic of the setup for external shape measurements

 

73

3.4.2. Experimental Results & Discussion

The variation in the diameter along the thickness of the sample was calculated by
taking the average of the four measurements for each of the samples. The
diameter variation of the CR-15 sample is shown in Figure 41. It was determined

that all of the samples exhibited a lateral shape similar to a barrel.

l l
l

v I v I ' If ' I ' I '
-11.10 41.05 11.00 11.05 11.10
Diameter ending position (mm)
Figure 41. Experimental result for the diameter variation along the thickness of

the CR-15 green sample

 

00
l

O)
1

 

 

Thickness position (mm)
't’ . 4?

 

 

O
1 .

 

Aydin et al. [40] reported that a green compact takes its final form after the
ejection step. They determined by FEA that after compaction, the green samples
inside the die have large residual radial stress at about the middle of the
compact, and small redial residual stress on the top and bottom surface. After the
ejection of the green sample, the compact is freed in the radial direction.
Therefore, the high stress regions relax radically and form regions with larger
diameter regions in the final greens. This results in a final shape similar to a
barrel.

74

From Figure 32, it is obvious that CR-15 powder has the lowest compaction

capability. From the measurements, it was determined that the difference
between the largest and the smallest diameter for the CR-15 sample is 23.21 pm.
Pure TMDAR powder, which is has best compaction capability, exhibited a

difference of 6.3pm between the largest and smallest diameter. For all the other

samples, this diameter variation is between 6.30m and 23.21pm. Figure 42

shows the diameter difference for the TMDAR+CR-15 and CR-15+GE-1 mixture
groups. When this figure is compared to Figure 32, it can be determined that the
powder mixtures that have better compaction capability exhibit smaller diameter
difference. Since such powders are denser; hence shorter in height, the residual
stress variation while inside the die will also be smaller. This will result in less
barreling for the powders with better compaction capability. It must also be noted
that the curves in Figure 32 exhibit almost a mirror image of their corresponding
curves in Figure 42. This means that the dimensional variations of the green

samples can be estimated by their compaction capabilities.

 

   
 

 

 

24
‘15 A 21-
5 i .
g V
g g 18"
g 1
55 1s-
E 1;; 4
.8 % 12.
8 E l
5:; gj +Cr15+GE1
g g ‘ —o—TMDAR+CR15
“u
6

 

6'20'40'60'60'160

Proportion of coarse powder (%)
Figure 42. Difference between the largest and smallest diameter as a function of
proportion of the course powder

75

3.4.3. Finite Element Analysis

A preliminary finite element analysis was carried out in a similar fashion
explained in Section 3.3.3. The powder bed had a diameter of 22.19mm. Several
simulations were performed with different B-d pairs. in all cases, the green
compact showed a lateral shape similar to a barrel after ejection, agreeing with
the experimental results. The final dimensions were calculated by obtaining the
coordinates of all the external surface nodes of the deformed shape. These
values were then input into Mircocal Origin software to create a plot similar to

Figure 41. Figure 43 shows the FEA results for the CR—15 powder with an angle
of internal friction of (B) 33 degrees and a material cohesion (d) of 1.34MPa.

10 .7

 

(D

0')

  
 

Thickness position (mm)
'1’ . ‘3

 

 

O
l A

 

 

' I ' F ' I I] I ' V ' I fit
-11.0 -10.8 -10.6 10.6 10.8 11.0
Diameter ending position (mm)
Figure 43. The diameter variation along the thickness of the CR-15 green

sample obtained by FEA ([3 = 33°, d=1.34MPa)

It is obvious from Figure 3.14 that the location of maximum diameter was close to
the experimental results. However, the green sample from FEA exhibited a

thinner bottom portion than the experimental sample. This is due to the same

76

 

reason explained in Section 3.3.3. At this time, it is not possible to obtain an
exact match between the experimental and FEA results without determining all of
the parameters needed for the constitutive model used in the finite element
modeling. The next step is to determine the required parameters experimentally
by running hydrostatic and triaxial compression tests. FEA should then be

performed again in order to verify the experimental results.

77

CHAPTER 4

DISCUSSION AND CONCLUSIONS

4.1. DISCUSSION AND CONCLUSIONS

Perspirable skin, an autonomous and reusable self-cooling system, was

designed for externally heated surfaces of space vehicles, utilizing the negative

thermal expansion property of ZrW203, The best RCC fiber arrangement for the

Perspirable Skin was determined to be 3D woven orthogonal by finite element
modeling. Its high tensile strength in both longitudinal and transverse directions,
as well as its thermal expansion capabilities allow for a safe and efficient

application.

FEA was also used to determine the best design for the core geometry. Due to
the temperature gradient that the structure experiences, the design with a larger
radius at the top surface and a smaller radius at the bottom surface guarantees
the contact of the two materials while providing a large gap at working condition.

Tapering the top portion of the core into a frustum of a cone was necessary in

order to allow for an efficient flow path for the coolant gas between the ZrW203

core and the RCC skin; however this design did not provide a large enough gap

opening at the top surface. Increasing the bottom radius of the ZrW203 core

compensated for this problem. Additionally, thin semi-circular shaped channels

78

were incorporated into the cylindrical bottom half of the core to allow continuous

flow of coolant gas at high temperatures.

Initially, the tapered ZrW203 core design was chosen as the best design;

however it was determined that this design is difficult to manufacture by powder
metallurgy methods. Switching to a cylinder-shaped FGM for the core provided

ease in manufacturing, larger gap distance, and lower stresses in the overall

structure. The top surface of the FGM core consisted of pure ZrW203 due its

large negative CTE and the bottom portion had the appropriate volume ratio of

an203 and ZrOz that gave a linear increase in CTE all the way up to zero. The

final FGM design was successfully fabricated using powder metallurgy methods.

Since the gap opening both at working and assembly conditions is in the micro
scale, it is very important to fabricate the core with a net-shape and high
dimensional accuracy. Large variations in dimensions will result in non-uniform
gap openings. However, due to the series of operation steps in powder
metallurgy, the final parts may exhibit several structural inhomogeneities, such as

density variations and dimensional discrepancies [40, 51 -53].

The three main steps of powder metallurgy (mixing, compaction and sintering)
are strongly related to each other. Each step highly influences the following

step(s). Therefore, influences of fabrication steps on several properties of the

79

final parts were investigated. in the experiments, several different alumina
powders were used. The choice of alumina is due to the fact that it is one of the
most commonly studied ceramic powders. It is also inexpensive to test, which

made it the most appealing material for this study.

First, the effect of powder mixing on the compaction capabilities of ceramic
powders was studied. This was done by mixing several two-powder combinations
of four alumina powders at various mass ratios and examining their green
densities as a function of stress and true axial strain. It was concluded that
powder mixing has a strong influence on the compaction capabilities of ceramic
powders. It was also determined that the initial relative density of the powder

mixture is the key property that can be used to predict compaction capability.

The internal form of structural inhomogeneities in the green bodies is the density
variations [16]. Next, two different alumina powders were tested using layers of
colored powder in the main powder in order to detect density distributions. The
layered powder was compacted to 80MPa. After the ejection, the green body was
polished on the lateral surface until the middle axis was reached. It was observed
that the colored powder layers showed curved lines, rather than straight,

indicating that the density distribution is non-uniform. This trend can be observed

in the fabrication steps of ZrW203-Zr02 FGM samples as well. When a layer of
ZrOz and another layer of Zr02 + W03 powder mixtures are compacted to

produce FGM containing ZrW203 and Zr02, a boundary is formed between the

80

two layers due to the uneven powder distribution after compaction. It is easy to

see the curved boundary because of the color difference in the powders used
(Figure 44(a)). Fortunately, due to the diffusion and sublimation of W03 as well

as the chemical reaction between the two powders, this non-uniformity in the
density distribution will begin to decrease [56]. If the soak duration is long
enough, a sample with uniform density can be obtained, as shown in Figure

44(b), which was sintered at 1180°C for 16 hours.

‘7
1,1

,I‘ .

curved boundary

/

 

 

a b

Figure 44. The middle section of the FGM sample after different fabrication steps
(a) after compaction (b) after sintering

Shape changes that take place during the sintering step are controlled to a large
extent by the density distributions within the green compact. A non-uniform
density distribution usually results in variations in the net dimensional change
from low density to high density areas in the compact. In worst cases, this might
cause cracking in the sample due to the stress fields induced by the local

variation of shrinkage ratio [51].

81

It is essential to study density variations in green bodies, in order to predict and
minimize dimensional variations and cracks in the sintered samples. The density

distributions of the layered compacts mentioned in Section 3.3 were analyzed

both experimentally and numerically. Experimentally, the final heights (ht) of

several points on each of the colored layers were measured. Then, using the
initial relative density-true axial strain relationship from equation (10) the
corresponding relative densities were determined. Contour plots of density
distributions were created. It was concluded that the high-density regions are on
the central axis, and the highest density is observed in the bottom central region.
Top central regions as well as the bottom edges are the low-density regions. FEA
predicted the density range, as well as the high density regions at the top central

region and the low-density regions at the bottom edges quite well.

Finally, dimensional variations in the external shapes of alumina green compacts
from the compaction capability experiments were analyzed, both experimentally
and numerically. It was determined that geometry of the external surface of the
ceramic green body was not exactly the same as the geometry of die cavity after
the green ejection; rather it exhibited a barrel shape. This finding is similar to the
report of Aydin et al. [40] who explained the cause of such shape as a result of
the relaxation of the high stress regions in the radial direction after the ejection
step. It was also concluded that the powder mixtures that had the higher

compaction capability, had a lower difference in the maximum and minimum

82

diameter values. This shows that the compaction capability is a good indicator of

the final external shape of green bodies.

4.2. RECOMMANDATIONS FOR FUTURE WORK

One difficulty with the Perspirable Skin design is the incorporation of holes into
the RCC TPS. Drilling into the RCC structure will cut through the fibers, causing
a significant decrease of strength. In order to compensate for this, incorporation
of the holes must be completed during fabrication of the RCC TPS. Another

possible solution is the use of a 3D woven orthogonal RCC with a large enough

fiber bundle to accommodate the diameter of ZrW208 core within each bundle in

order to avoid damaging the carbon fibers in the structure. The assembly of the

core and the skin parts is the next step in the design process.

When comparing the experimental and numerical results of the density
distributions and final external shapes of green compacts, the findings were
overall in good agreement. However, some discrepancies were detected
between the FEA and experimental results. This is due to the fact that most of
the parameters used in the constitutive model in FEA are unique material
properties. With so many parameters, there are numerous possible
combinations. An accurate way of experimentally determining all the required
parameters is a combination of hydrostatic and triaxial compression tests [55].

However, at this time the equipment required to run similar tests is not available

83

in our facilities and further analysis is required when necessary devices are

obtained.

84

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