by rhye garrett hamey - university of...
TRANSCRIPT
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PARTICLE DEFORMATION DURING STIRRED MEDIA MILLING
By
RHYE GARRETT HAMEY
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2008
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© 2008 Rhye Garrett Hamey
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My family and fiancé Yun Mi Kim, for their encouragement
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ACKNOWLEDGMENTS
I would like to acknowledge the friendship and the wisdom of the late Professor Brian
Scarlett, whose instruction and support were the reasons for the pursuit of a Ph. D. Dr. Brian
Scarlett, taught me how to be a better engineer and a better person.
I am grateful for the help of Dr. Hassan El-Shall for his countless hours of guidance
through out this study. Dr. El-Shall was a constant inspiration. I would also like to thank Dr.
Mecholsky, Dr. Fuchs, Dr. Whitney, and Dr Svoronos for serving as committee members and for
their guidance and discussions during this Ph..D. study.
A special thanks goes out to all the friends I have made during this study, Maria
Palazeulos, Scott Brown, Milorad Djomlija, Vijay, Krishna, Stephen Tedeschi, Nate Stevens,
Kerri-Ann Hue, and Dauntel Specht. I would like to acknowledge Marco Verwijs for being a
great friend and roommate for so many years. I would also like to thank Yun Mi Kim for her
love and support.
I would like to acknowledge the financial support of the Particle Engineering Research
Center (PERC) at the University of Florida, The National Science Foundation (NSF) and the
Industrial Partners of the PERC for support of this research. Thanks are extended to the US
Army for their support of the project.
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TABLE OF CONTENTS page
ACKNOWLEDGMENTS ...............................................................................................................4
LIST OF TABLES...........................................................................................................................8
LIST OF FIGURES .......................................................................................................................10
ABSTRACT...................................................................................................................................14
CHAPTER
1 INTRODUCTION ..................................................................................................................16
Impact of Milling Metallic Powders.......................................................................................16 Research of Particle Deformation during Milling ..................................................................18 Method for Understanding Particle Deformation during Milling...........................................18
2 BACKGROUND ....................................................................................................................21
Comminution Equipment........................................................................................................22 Crushers...........................................................................................................................23 Grinders ...........................................................................................................................23 Ultrafine Grinders............................................................................................................24 Cutting Machines.............................................................................................................24
Particle Deformation and Particle Breakage...........................................................................24 Particle Deformation .......................................................................................................24 Particle Breakage.............................................................................................................27 Cracks and Defects ..........................................................................................................28 Particle Deformation during Milling ...............................................................................29 Effect of Milling Parameters on Particle Deformation....................................................31 Particle Breakage during Milling ....................................................................................32 Effect of Milling Parameters on Particle Breakage .........................................................33 Summary..........................................................................................................................35
3 MATERIALS, CHARACTERIZATION AND EXPERIMENTAL PROCEDURE.............41
Materials .................................................................................................................................41 Metal Powders .................................................................................................................41 Milling Media..................................................................................................................41
Experimental Procedures ........................................................................................................42 Media Mill .......................................................................................................................42 Milling Procedure............................................................................................................42 Drying of Aluminum Slurry and Milling Samples..........................................................43 Sample Preparation by Dispersion of Dry Powder..........................................................44
Statistical Design of Experiment ............................................................................................45
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Characterization......................................................................................................................45 Light Scattering ...............................................................................................................46 Microscopy and Image Analysis .....................................................................................47
Electron microscopy.................................................................................................47 Optical microscopy ..................................................................................................48 Occhio optical particle sizer .....................................................................................48
Surface Area Analysis (BET)..........................................................................................48 Inductively Couple Plasma Spectroscopy (ICP) .............................................................49 Fourier Transform Infrared Spectroscopy (FTIR)...........................................................49
Light Scattering Results..........................................................................................................50 Results of Aluminum Powder .........................................................................................50 Results for Aluminum Flake ...........................................................................................51 Summary of Characterization and Light Scattering ........................................................52
Milling Condition Selection ...................................................................................................52 Preliminary Milling Study...............................................................................................52 Preliminary Milling Results ............................................................................................53 Establishing Milling Conditions......................................................................................54
Milling medium........................................................................................................54 Mill loading and grinding aids .................................................................................55 Milling time and temperature...................................................................................56 Media properties and rotational rate.........................................................................57
4 RESULTS AND DISCUSSION.............................................................................................72
Experimental Results of Stirred Media Milling......................................................................72 Effect of Mill Parameters ................................................................................................72 Kinetic Energy Model .....................................................................................................73 Stress Model ....................................................................................................................75 Deformation Rate ............................................................................................................79
Strain Energy and Milling Efficiency.....................................................................................81 Strain Energy ...................................................................................................................81 Mill Efficiency.................................................................................................................83
Empirical Modeling of Particle Deformation through Statistical Design of Experiment ......88 Microstructure Analysis..........................................................................................................92 Summary.................................................................................................................................93
5 CASE STUDY: MATERIAL SELECTION AND DEVELOPMENT FOR INFRARED OBSCURANTS....................................................................................................................127
Introduction...........................................................................................................................127 Development of New Obscurant Materials ..........................................................................128 Material Characterization and Obscurant Performance Measurement Method ...................131 Production of Infrared Obscurant .........................................................................................132 Summary...............................................................................................................................135
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6 SUMMARY, CONCLUSIONS, AND FUTURE WORK ...................................................143
Summary and Conclusions ...................................................................................................143 Future Work..........................................................................................................................146
LIST OF REFERENCES.............................................................................................................149
BIOGRAPHICAL SKETCH .......................................................................................................154
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LIST OF TABLES
Table page 3-1 Statistical data comparison for light scattering and image analysis performed using
the Occhio particle counter. ...............................................................................................66
3-2 Stirred media milling equipment variables. .......................................................................67
3-3 Stirred media milling operating variables..........................................................................67
3-4 Experimental parameters used in the hexagonal statistical design of experiment.............67
3-5 Milling conditions for preliminary study...........................................................................68
4-1 Calculated stress intensity for experiments performed in this study. The table indicates that it is possible to achieve equivalent energies and different milling conditions.........................................................................................................................101
4-2 Maximum mean particle size of milling experiments. Even though the kinetic energy of some of the milling experiments are equivalent the maximum particles sizes differ.................................................................................................................................101
4-3 Force, radius of contact area, and stress acting on the milling media as a function of media size and rotation rate (calculated using Hertz theory)...........................................103
4-4 Number of particles stressed in a single collision between grinding media and the stress exerted on an individual particles. .........................................................................103
4-5 Stress frequency as calculated from Kwade’s model. The frequency is the number of times milling media collide with each other. ...................................................................103
4-6 The time required to reach the maximum particle diameter. As milling speed increases the time it takes to obtain the maximum particle diameter decreases. .............104
4-7 Total number of particle compressions in 60 minutes, as calculated using stress frequency and number of particles, Equation 4-2 and 4-6. ..............................................104
4-8 Strain energy per particle for deformation study. ............................................................107
4-9 Total strain energy for deformation study. The 1.5 mm media milling experiments resulted in the largest amount of stain energy. ................................................................108
4-10 List of constants for equations used to calculate milling power......................................108
4-11.Milling efficiency as a function of percent amount of strain the material has experienced at 1000 rpm and varying media size. The 1.5 mm media reaches over 60 % of the maximum strain while milling at 37% efficiency. The last few percent of the maximum strain result in the most inefficient milling...............................................113
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4-12 Experimental design for central composite design 1. ......................................................114
4-13. Analysis of variance for the central composite design 1 described in table 4-12. .............114
4-14 Experimental design for central composite design 2. ......................................................118
4-15 Analysis of variance for the central composite design 2 described in table 4-10............118
5-1 Experimental parameters used in the statistical design of experiment used to determine milling parameters. .........................................................................................137
5-2 Experimental parameters used in the full 2 factorial (22) statistical design of experiment........................................................................................................................139
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LIST OF FIGURES
Figure page 1-1 Methodology for understanding particle deformation during stirred media milling. ........20
2-1 1) Particle stressed by compression or shear, 2) particle stressed by impaction on rigid surface, and 3) particle stressed in shear flow...........................................................36
2-2 Milling efficiency variations by machine type. .................................................................36
2-3 Types of grinding mills......................................................................................................37
2-4 Diagram of a stirred media mill, energy is supplied to the grinding media by the rotation of the agitator........................................................................................................37
2-5 Face centered unit cell for aluminum.................................................................................38
2-6 Slip planes and directions for FCC aluminum...................................................................38
2-7 True stress- true strain curve for a material undergoing plastic deformation and strain hardening............................................................................................................................39
2-9 Effect of impact..................................................................................................................40
3-1 Particle size distribution of as received H-2 aluminum, along with particle size data, obtained from Coulter LS 11320. ......................................................................................59
3-2 Image of Yttria-stabilized zirconia grinding media obtained form an optical microscope, 1mm in diameter............................................................................................60
3-3 Union Process stirred media mill use in study...................................................................61
3-4 Phase diagram for carbon dioxide, indicating the region of supercritical fluid formation............................................................................................................................62
3-5 SPI pressure vessel used for supercritical drying of powder samples taken from milling ................................................................................................................................63
3-6 Galia partial vacuum chamber used to disseminate powder..............................................63
3-7 Scanning electron microscope image of as received H-2 aluminum powder. ...................64
3-8 Differential volume and number distributions for as received H-2 spherical aluminum powder measured by light scattering. ...............................................................65
3-9 Volume particle size distribution of milled aluminum flake as measure by light scattering. ...........................................................................................................................65
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3-10 Volume particle size distribution of milled aluminum flake as measured by the Occhio image analysis. ......................................................................................................66
3-11 SEM image of US Bronze “as received” brass flake used in preliminary milling experiments. .......................................................................................................................68
3-12 Surface response of figure of merit with respect to media loading and RPM. .................69
3-13 Stearic acid a saturated fatty acid found in many animal fats and vegetable oils..............69
3-14 Cumulative undersized versus particle size as at varying milling time for H-2 aluminum. ..........................................................................................................................70
3-15 Scanning electron microscope images of a) as received aluminum, b) milled for 240 minutes aluminum and c) milled for 600 minutes aluminum. ...........................................71
4-1 Volume percent particle size distributions for experiments using 1.0 mm grinding media at 2000 rpm. Bimodality in the particle size distribution is indicative of particle deformation and particle breakage occurring simultaneously. .............................95
4-2 Volume percent particle size distributions for the experiments with 1.5 mm grinding media at 1000 rpm, a visible shift in the particle size distribution to larger sizes is seen due to particle deformation. .......................................................................................96
4-3 Maximum mean particle size achieved for each milling experiment versus media size, the 1.5 mm milling media produced the largest amount of deformation...................97
4-4 Particle deformation versus milling time at a milling speed of 1000 rpm for varying grinding media sizes. .........................................................................................................98
4-5 Particle deformation versus milling time at a milling speed of 1500 rpm for varying grinding media sizes.. ........................................................................................................99
4-6 Particle deformation versus milling time at a milling speed of 2000 rpm for varying grinding media sizes.. ......................................................................................................100
4-7 Mean particle size versus milling time as a function of rotation rate ..............................101
4-8 Contact between colliding elastic spheres. Aluminum particles are caught in the contact area between the media. ......................................................................................102
4-9 Diagram of the change in dimensions of particle and the measurements used to calculate stress and strain.................................................................................................104
4-10 Stress-strain behavior for experiments performed at 1000 rpm.......................................105
4-11 Stress-strain behavior for experiments performed at 1500 rpm.......................................106
4-12 Stress-strain behavior for experiments performed at 2000 rpm.......................................107
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4-13 A plot of milling efficiency as a function of milling time at 1000 rpm, for all media sizes..................................................................................................................................109
4-14 A plot of milling efficiency as a function of milling time at 1500 rpm, for all media sizes..................................................................................................................................110
4-15 A plot of milling efficiency as a function of milling time at 2000 rpm, for all media sizes..................................................................................................................................111
4-16 A plot of milling efficiency as a function of milling time for the 1.5 mm at varying rotational rates..................................................................................................................112
4-17 A plot of milling efficiency at failure, right side of figure 4-13 used for comparison of efficiencies as a function of rotational rate..................................................................113
4-18 Contour plot for central composite design 1, a minimum strain of 2.17 can be seen at approximately 0.9 mm milling media..............................................................................115
4-19 Surface response for central composite design 1, a trough exists at the 1.0 mm media size. ..................................................................................................................................116
4-20 Standard error associated with central composite design 1, error increases at the limits of the study.............................................................................................................117
4-21 Contour plot for central composite design 2, shows a maximum at approximately the 1.6 mm media...................................................................................................................119
4-22 Surface response for central composite design 2, a peak can be seen at intermediate media size.........................................................................................................................120
4-23 A plot of the interaction between the media size and rotation rate, it can be seen that there is only a slight interaction at low. ...........................................................................121
4-24 Standard error associated with central composite design 2. ............................................122
4-25 Transmission electron microscope image of “as received” aluminum particle. ..............123
4-26 Diffraction pattern obtained from particle in Figure 4-20. ..............................................124
4-27 Transmission electron microscope image of sectioned flake after 4 hours of milling. ...125
4-28 Single crystalline diffraction pattern of sectioned flake after 4 hour sof milling. ...........126
5-1 A chart of relevant material properties of materials for use as an infrared obscurant. High values in each property are preferred for candidate materials. ...............................136
5-2 The performance of various milled metals, the copper has the highest performance to due to the properties being the highest in all the desired area. ........................................137
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5-3 The results of the initial design of experiment, indicating that higher media loading increase the performance of the material. ........................................................................138
5-4 Plot of FOM for as received and ground brass at specific milling condition of 480ml media volume and 700 rpm rotational speed ...................................................................139
5-5 The results of the affect of varying media size and rotation rate on the performance of a milled brass flake. .....................................................................................................140
5-6 Differential volume particle size distribution at increasing milling times.......................141
5-7 Figure of merit versus IR wavelength for increasing milling times. ...............................141
5-8 Mean particle size as a function of milling time for different density milling media, zirconia (6 g/cc), stainless steel (9.8 g/cc), and tungsten carbide (16 g/cc)....................142
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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
PARTICLE DEFORMATION DURING STIRRED MEDIA MILLING By
Rhye Garrett Hamey
August 2008
Chair: Hassan El-Shall Major: Materials Science and Engineering
Production of high aspect ratio metal flakes is an important part of the paint and coating
industry. The United States Army also uses high aspect ratio metal flakes of a specific dimension
in obscurant clouds to attenuate infrared radiation. The most common method for their
production is by milling a metal powder. Ductile metal particles are initially flattened in the
process increasing the aspect ratio. As the process continues, coldwelding of metal flakes can
take place increasing the particle size and decreasing the aspect ratio. Extended milling times
may also result in fracture leading to a further decrease in the particle size and aspect ratio. Both
the coldwelding of the particles and the breakage of the particles are ultimately detrimental to the
materials performance. This study utilized characterization techniques, such as, light scattering
and image analysis to determine the change in particle size as a function of milling time and
parameters.
This study proved that a fundamental relationship between the milling parameters and
particle deformation could be established by using Hertz’s theory to calculate the stress acting on
the aluminum particles. The study also demonstrated a method by which milling efficiency could
be calculated, based on the amount of energy required to cause particle deformation. The study
found that the particle deformation process could be an energy efficient process at short milling
times with milling efficiency as high as 80%. Finally, statistical design of experiment was used
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to obtain a model that related particle deformation to milling parameters, such as, rotation rate
and milling media size.
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CHAPTER 1 INTRODUCTION
In today’s market there is a need to develop new and improved products at an increasing
rate. Particle deformation by milling is important to many areas of product development, such as,
powder metallurgy (P/M), paints and coatings, and military applications. Understanding and
predicting particle deformation during milling, will lead to more rapid development of products
in which these materials are used.
Impact of Milling Metallic Powders
Generally, milling is used to reduce the size of a material or for the processing of brittle
materials. However, large quantities of ductile metals used in the powder metallurgy industry
(P/M) are processed through milling [1]. Powder metallurgy is estimated to be a $1.8 billion
industry annually with an estimated 70 % spent in the automotive industry [2]. Below is a list of
reasons for the milling of materials in the P/M industry [1]:
• Particle size reduction (comminution or grinding) for sintering
• Particle size growth
• Shape change (flaking)
• Agglomeration
• Solid-state alloying (mechanical alloying)
• Solid-state blending (incomplete alloying)
• Modifying, changing, or altering properties of a material (density, flowability, or work hardening)
• Mixing or blending of two or more materials or mixed phases
• Nonequilibrium processing of metastable phases such as amorphous alloys, extended solid solutions, and nanocrystalline structures
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During the processing and subsequent stressing of metallic powders, several phenomena
may occur; the metal can fracture, deform, coldwork, coldweld, or transform into other
polymorphs [3]. Coldwelding is used to mechanically alloy (MA) and refine the microstructure
of immiscible metals [4]. Coldworking is used to strengthen metallic particles. This study will
focus on deformation of metallic particles during milling. This technique is used to make
metallic flakes for paints, coating, and obscurants [5-9]. The metallic flakes in paints give what is
termed a “metallic look” which means the randomly oriented flakes in the paint will give a
“shiny” appearance. Radiation shielding in devices such as cell phones will use metallic particles
to form a conductive coating. The US Army uses metallic flakes in smoke bombs to obscure
infrared light (IR). The conductive metallic particles are capable of attenuating the IR signal
which provides a shield against missiles and IR imaging devices.
The most common metallic pigment is aluminum, which when milled deforms into flakes
with highly reflective surfaces. In order for the metallic flakes to be effective at scattering and
reflecting light, the particle size, size distribution, particle shape, and particle morphology must
be controlled. The particle size and size distribution affect the optical reflectance and light
scattering properties of the flake. If the particle size distribution of these paints is broad the
reflectiveness will be diminished and the paint will appear dull. The particle morphology and
surface roughness also affect the optical reflectance i.e. the smoother the surface the more
reflective the pigment. An additional difficulty to this processing method is that most of the
aluminum pigments are produced in batch milling processes and there exists large batch to batch
variations due to lack of process knowledge [10]. In the end, these variations lead to additional
processing costs from classification.
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Research of Particle Deformation during Milling
Most milling studies focus on particle breakage with limited research on particle
deformation. The particle deformation studies have focused on the mechanical alloying process
and do not investigate optimizing the flake dimensions, which are necessary for paints and
coatings. Zoz showed how the dimensions of flakes are affected by the material hardness[11].
Several researchers have investigated the change in the microstructure and material properties of
metals during milling [12-14]. None of these studies has shown the effect of milling parameters
on particle deformation. The research to date does not provide any methodology for predicting
the magnitude or extent of particle deformation during milling. In order to improve the
production and quality of the products it is important to understand the effects of milling
parameters on the materials being processed. Even though particle breakage during milling has
been studied extensively, there is very little knowledge of the particle deformation process
during milling. This study will attempt to apply some of the knowledge gained from particle
breakage during milling to the deformation process and to fill the gaps in the theories between
the two processes.
Breakage during milling has been studied at nearly every length scale [15-19]. Numerous
researchers have modeled milling kinetics and energetics for particle breakage [20-22]. Others
have used population balance modeling to predict particle size during milling [19, 23]. The
response of the product material to nearly every milling parameter has been investigated for
particle breakage. Wear on equipment and process optimization studies have also been
researched [24, 25].
Method for Understanding Particle Deformation during Milling
The goal of this study is to understand and predict particle deformation during stirred
media milling. Figure 1-1 shows the methodology that was used to accomplish this goal. The
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study investigated the affects of mill speed and media size on the particle size and morphology of
an aluminum powder. The study shows how milling breakage models fail to describe particle
deformation during milling. New models were derived from the stress-strain behavior of
aluminum during milling to describe particle deformation. Hertz theory was used to calculate the
stress acting on a particle during. The stress acting on a particle and the affect it had on particle
deformation was then determined. Statistical analysis was used to determine the magnitude of the
interaction between milling parameters. Design of experiment was used to construct a model
that relates milling parameters to particle deformation. From these studies a more comprehensive
understanding of particle deformation during milling was achieved. This may ultimately lead to a
method to better predict and optimize milling processes where the deformation of metallic flakes
is desired.
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Figure 1-1. Methodology for understanding particle deformation during stirred media milling.
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CHAPTER 2 BACKGROUND
Comminution is arguably the oldest material processing technique. Earlier civilizations
employed simple mortars and pestles to reduce the size of agricultural and medicinal products.
Even though there have been significant changes in technology, these simple devices that were
employed thousands of years ago can still be found in nearly every lab today. A simple definition
of comminution is the reduction in particle size through the application of an applied load. In
order to study and improve a milling process it is important to understand how the load is applied
and to analyze the response of the material to that load. Rumpf suggested four modes by which
stress can cause particle breakage [26]:
1. Compression-shear stressing 2. Impact stressing 3. Stressing in shear flow 4. Stressing by other methods of energy transmission (electrical, chemical, or heat)
Figure 2.1 is a representation of the modes of stressing a material as indicated by Rumpf.
The first two modes are caused by contact forces and are important for milling. Mode 3 is
important for the dispersion of materials under shear, and only exerts enough force to break apart
weak agglomerates [26]. The fourth mode is not applicable to milling where mechanical
stressing is important. There are several types of machines designed to apply stress to a material
by modes 1 and 2.
The beginning of this chapter will describe the types of milling equipment used today. A
review of literature on single and multi particle breakage will be presented. Followed by a
discussion of the response of a material to the load applied during milling. This information will
be used as a basis for this study and it will shed light on the deformation process during milling,
which has not been studied as thoroughly. This chapter will conclude by discussing material
deformation and reviewing deformation during milling processes. Ultimately, this study will
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compile what has already been done to study particle deformation during milling and use that
knowledge, combined with particle breakage and further experimentation, to more accurately
develop the understanding of particle deformation during milling.
Comminution Equipment
Comminution is a diverse process, found in nearly every industry. Therefore there are
numerous types of milling equipment. The equipment must be able to operate in rigorous, high
throughput environments of the mineral processing industry and in the ultra pure, contamination
free pharmaceutical industry. McCabe, Smith and Harriott identified four classes of milling
equipment each with subclasses [27]:
A. Crushers (coarse and fine)
a. Jaw crushers
b. Gyratory crushers
c. Crushing roll
B. Grinders (intermediate and fine)
a. Hammer mills, impactors
b. Rolling-compression mills
i. Bowl mills
ii. Roller mills
c. Attrition mills
d. Tumbling mills
i. Rod mills
ii. Ball mills; pebble mills
iii. Tube mills; compartment mills
C. Ultrafine grinders
a. Hammer mills with internal classification
b. Fluid-energy mills
c. Agitated mills
D. Cutting machines
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a. Knife cutters; dicers; slitters
The differences in equipment are due to the mode in which stress is applied to the material
and the final achievable particle size. Some of the equipment may work in clean environments
and process small quantities of products while other may process large amounts of material in
wet and dry environments. Schonert has shown that some of these machines can operate at high
energy efficiencies >90% while others operations are a fraction of a percent efficient. Most of
this inefficiency is associated with the increase in energy required to achieve smaller particle
size. Examples of the efficiency of select mills can be seen in Figure 2-2, obtained from
tabulated data given by Prasher for the energy consumption associated with milling to a specific
size [28].
Crushers
Jaw crushers, gyratory crushers and crushing roll mills are used to process large quantities
of materials. They are often used in the mineral processing and cement industries to reduce the
size of rock and ore for further processing.
Grinders
Grinders are one of the most diverse sets of milling equipment. They are most often used
to reduce large aggregates to a powder. Grinding mills can supply a load to a material by
impaction, attrition, or compression. Hammer mills apply a load via impaction by dropping a
weight repeatedly on a bed of material. Attrition mills wear away a material by the breakage of
small fragments from the surface. Roll mills and ball mills apply a load through compression by
trapping material between colliding media or in between two heavy rollers. Figure 2-3 is a
diagram of a ball mill and a roller mill. Ball mills have been the subject of a considerable amount
of research because they can be used in wet and dry environments and their large capacities. Ball
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mills operate by rotating a drum containing hard dense balls and product material. The balls fall
from a height equal to the diameter of the drum and compress the material.
Ultrafine Grinders
Ultrafine grinders have recently become very popular due to there ability to produce
nanoparticles. The most popular ultrafine grinders are fluid energy mills such as jet mills and
agitated mills such as stirred media mills. Jet mills stress a material by entraining particles in a
gas stream and impacting the particles on a hard surface or against each other. Jet mills are used
extensively in the pharmaceutical industry due to their ability to produce fine particles without
the wear of mechanical parts. Another class of mills used to produce fine particles, are the stirred
media mills, which are similar to ball mills except they contain an agitator, which supplies the
necessary energy instead of rotation of the vessel. The agitator allows the media to collide with a
much higher force than is possible in the ball mill. Due to their importance in this study, stirred
media mills and particle breakage during stirred media mills will be discussed in more detail
later. Figure 2-4, is a diagram of a stirred media mill. Products in a stirred media mill are often
ground in a wet environment to allow for easier stabilization of the product.
Cutting Machines
Cutting machines are used to reduce the size of resilient materials that are not easily
fractured [27]. Some examples of materials that are processed using cutting machines are tire
rubber for recycling, paper products, and plant materials. Cutting machines apply a shear stress
to materials, which causes them to fail or break.
Particle Deformation and Particle Breakage
Particle Deformation
Plastic deformation in a metal occurs when the material is stressed beyond its yield stress;
the atomic bonds inside a material are broken and then reformed as planes of atoms are moved
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past each other. Plastic deformation results in a perment change in the shape of the object being
stressed. Plastic deformation is affected by the stress (σ), strain rate (dε/dt), temperature (T), and
the microstructure of the material [29, 30]. This study focuses on the deformation of aluminum
particles when subjected to a compressive stress.
Aluminum is a crystalline material with a face center cubic (FCC) structure with atoms at
each corner and in the center of each face of a cube. Figure 2-5 is a sketch of a FCC unit cell. For
such a structure, deformation often occurs by slip, the process of plastic deformation by
dislocation motion, along the preferred crystal planes. The {111} plane for aluminum is the most
atomically dense plane and it is in this plane, along the <110> direction, that slip occurs [31].
There are 4 slip planes for aluminum and 3 slip directions this means that there are 12 total slip
systems for dislocation motion to occur in. Figure 2-6 show the highlighted {111} plane and the
<110> direction is denoted by the arrows beneath the highlighted areas.
When dislocations encounter each other and a strengthening of the material will occur
resulting in a loss of ductility. This strengthening is called work hardening, cold working, or
stain hardening; and is due to the increase in dislocation density and decrease in the allowable
dislocation motion. Equation 2-1 is the work hardening equation, σy is the true yield stress, ε is
the true strain of the material, Kw is the strengthening or work hardening coefficient, and n is the
work hardening exponent. In the equation the stress and strain are true stress and true strain. The
exponent and coefficient for the work hardening equation are generally obtained experimentally.
Many researchers have calculated the exponent for numerous materials under numerous
conditions [32-34].
nwy K εσ = 2-1
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According to this relationship, higher stresses are required to obtain greater amounts of
deformation. The material will eventually work harden to the extent that no additional
deformation may be achieved and the material will ultimately fail.
In a milling process, a material will undergo multiple loading and unloading cycles. This
behavior can be characterized by a stress strain curve. Figure 2-7 is a generic representation of a
stress-strain curve for plastic deformation followed by failure. When the material is unloaded
after experiencing plastic deformation, it will remain in the deformed state. The area under the
elastic region of the curve is called resilience. It is the strain energy due to elastic deformation of
the material. The total area under the curve until fracture is called toughness. This is the same
toughness discussed earlier for particle breakage. The area under the curve represents the amount
of energy the material can absorb before it will fracture, or the strain energy due to plastic
deformation. It should be noted that the area under the linear part of the curve is the energy due
to elastic deformation.
Strain rate, dε/dt, is the rate at which a material is deformed. Schönert referred to strain
rate as stress velocity and theorized that it could affect material breakage. The strain rate also
affects deformation. Several researchers have investigated the effects of strain rate on the
deformation of materials [35-37]. Tome and Canova investigated the stress strain response of
aluminum and copper at different strain rates[37]. They showed that over the strain rate range
tested, copper did not appear to have strain rate dependence. However, aluminum did have strain
rate dependence; lower strain rates resulted in less deformation before failure. Nieh observed
superplastic-like behavior, also known as extended ductility, of aluminum composites at very
high strain rates. Meyers has also shown that at very high strain rates it is possible for a material
to even recrystallize and form new grains [38]. Hines also observed this result in copper [39]. In
27
order to achieve a greater understanding of particle deformation during milling it is important to
review particle breakage and to correlate these results to deformation.
Particle Breakage
Numerous authors have studied single particle and multi particle breakage [40-43]. They
have found that particles can break in different ways depending on the method in which the load
is applied. In a stirred media mill, load is applied to particles trapped between colliding grinding
media, media and the wall of the vessel, and between the stirrer and media. Therefore, particle
breakage is a complex phenomenon with numerous stages to study. Schönert extensively studied
breakage, crack propagation, and crack velocity for many particulate materials and found that the
strain rate or stressing velocity can influence material failure [44]. Polymer materials, for
example, are strongly affected by strain rate. Metals also have been shown to have some strain
rate dependence, however, the effect is much less than that of polymers [44].
There are three modes by which a material can fracture, which are a function of the
material as well as the stress applied to the material.
(1) Opening mode that corresponds to an applied tensile load (2) Sliding mode where the force is applied in the plane of the defect or crack (3) Tearing mode where a force is applied in a direction out of the plane of the crack or defect
For most particles, breakage is considered to take place in the first mode of failure. This
may be due to artifacts in the techniques developed to measure particle breakage. For this reason,
most techniques for measuring particle failure involve stressing the particle in tension. If a
normal load is applied to a particle a load equal in magnitude is acting internally in the direction
perpendicular to the load and can then be considered to be a tensile load. Tensile failure is more
likely than compressive failure for many materials.
Particle breakage can take place through many different mechanisms of loading. These
mechanisms of loading as well as the material being stressed can affect how the particle will
28
break. The mechanisms of breakage were alluded to earlier when discussing the types of milling
machines and now will be discussed in more detail. Rumpf suggested there are three ways by
which a particle can break, which are fracture, cleavage or attrition [26]. During fracture a
mother particle will break into daughter particles or fragments that have a wider size distribution.
During cleavage a mother particle will break into smaller daughter particles of roughly the same
sizes.
Attrition takes place when a mother particle has surface asperities removed from the
particle. This leads to much smaller daughter particles. Figure 2-8 represent the three different
mechanisms of particle breakage. If a brittle material experiences a normal load such as
impaction in a milling process it would undergo a fracture or attrition mechanism of breakage. If
a ductile material experiences a shear force, it is most likely to fail by a cleavage mechanism
[45].
Cracks and Defects
Understanding crack formation and propagation is of fundamental importance to the study
of particle breakage. Particle breakage is preceded by crack growth, which is preceded by crack
formation. Crack formation is enhanced by local defects in a material. Defects are separated into
four classes, which correspond to their dimensions.
(1) Point defects (vacancies, interstitials, or substitution) (2) Line dislocations (screw or edge) (3) Interfacial (4) Volume
The strength of a material is related to the number, size and types of defects present. Most
materials are only a fraction as strong as the theoretical strength would predict due to the
presence of defects. A method by which cracks are initiated is when the applied stress exceeds
the strength of the material. Following crack initiation is crack growth, which leads to particle
29
breakage. Schönert extensively studied crack growth and found that crack velocity can vary
widely depending on the material, environment, and mode of stressing [46]. Schönert also
studied particle breakage during milling, however few researchers have studied deformation
during milling [47].
Particle Deformation during Milling
A significant amount of work has gone into investigating particle deformation during
milling, however, that work has focused on the mechanical alloying process[1]. This process is
important because it is used to make alloys that can be made in no other way. Beside the
formation of novel alloys, mechanical alloying can be used to refine the microstructure of the
materials to increase their strength. Mechanical alloying and microstructure refinement involves
adding a metallic powder(s), fatty acid/dispersant, and grinding media to a ball mill. The mixture
is then milled until an equilibrium particle size is reached [4]. The particles generally produced
in this process are semi-spherical agglomerates.
Benjamin is the pioneering researcher of mechanical alloying. The author was the first to
form an indium alloy [48]. Since then numerous authors have studied mechanical alloying (MA)
[49-53]. Most of the studies on MA have focused either on alloying or on refinement of
microstructure. Weeber studied the effect of different ball milling operations on the final product
and found that the milling equipment can affect the final product [52]. The author found
microstructure can vary using different types of ball mills. Gilman investigated the effect of
additives on the alloying process and found that if too little quantity of dispersant was added that
the metal would coldweld together and not effectively alloy[4].
Even though mechanical alloying and the production of metallic flakes involve similar
equipment and similar physics, the final product for flake production is very different. The
desired product of the flake making process is a powder with a large major dimension and a
30
narrow particle size distribution. It is not possible to run a flaking process to an equilibrium
particle size, as is the case with MA. Further milling will cause the flakes to break, no longer
scatter light effectively, and perform poorly as metallic effect pigments. The major differences
between the MA and flaking process are the use of dispersant and the grinding time. Many
flaking processes mill in a solvent to prevent the metal particle from coldwelding together and
the processes are run for shorter lengths of time to limit breakage.
The production of metallic flakes for use as pigments has been ongoing for over 50 years.
Some of the first available works are patents for devises made to produce metallic flakes [54].
More recently metallic flakes have found increasing use in other applications such as conductive
and electromagnetic resistant coatings and infrared obscurants [7, 8]. It is important for flakes to
have a large major dimension in order to function in the specific part of the electromagnetic
spectrum desired for these applications. Breakage during milling of these metallic particles
ultimately leads to poorly performing obscurants and paints. It is necessary to understand the
relationship between particle deformation and milling.
Moshksar has shown that when milling aluminum powder that the aspect ratio of the
material [major dimension divided by minimum dimension (d/t)] increases to some maximum,
then begins to decrease at longer milling times [55]. The decrease is due to particle breakage and
a subsequent reduction in aspect ratio. The results suggest that an ideal product may be produced
by monitoring the aspect ratio as a function of milling time. The author also found that the cold
welding and agglomeration of the powder particles was hindered by the fracture of the flakes at
longer milling times. Zoz showed that the maximum value of the d/t ratio varies with the
hardness of the metal being milled [56]. The lesser the hardness of the metal and the greater the
d/t ratio, the more likely the material will form flakes. Material selection and strain rate can
31
significantly affect whether the material breaks or deforms. It may also be possible to relate
material properties such as hardness and strain rate to the aspect ratio. This relationship would
enable the development of a model that relates material properties, and milling parameters to
particle deformation.
Effect of Milling Parameters on Particle Deformation
The deformation process has yet to be studied as extensively as the breakage process; the
studies that have been performed are mainly focused on a specific application. Much of the
research that has been performed is directed at understanding the microstructure development
during mechanical alloying (MA) [4]. For the paint industry, changes in particle morphology are
important and not the change in the microstructure of the material [57]. Few researchers have
investigated the milling of metals for use in the paint industry [5, 56, 58]. Zoz’s work was
discussed above [11]. Sung studied the affect of particle morphology on the reflectance and
quality of the paint.
Hashimoto studied the effect of milling media diameter on the total energy consumption as
well as the energy per impact on a metal powder in a simple vibratory mill [14]. From this, the
average energy per collision was calculated. The author found that the total energy consumption
was higher for larger media. The author also found that as media loading increased, the average
energy per collision is reduced due to ball-ball interactions. Kwade’s models of stress frequency
and stress intensity neglect ball-ball interactions. Hashimoto measured the change in the
hardness of the metal with milling time, the work hardening of the metal, and found that the
increase in the hardness of the powder was greater with larger media. This increase was
attributed to cold working of the material during the milling process. Riffel determined that an
optimum media size existed when mechanically alloying (MA) Mg2Si compounds. The author
determined that if the media was too small it did not provide enough kinetic energy to alloy or
32
reduce the size of the material [59]. Riffel’s results for MA also agree with the Kwade’s
predictions of an optimum stress value (milling conditions) for particle breakage. Kwade and
Riffel’s result suggest that it may be possible to use particle breakage equations to describe the
particle deformation process.
Rodriguez milled aluminum in a stirred ball mill, and measured the hardness as a function
of milling time [60]. The researcher found an initial increase in Vickers hardness which reached
a maximum at a value of 130 kg/mm2. The increase in hardness measured by Rodriguez agrees
with the increase also observed by Hashimoto. Huang also measures an increase in hardness with
milling time in copper [12]. Huang used the change in the diffraction pattern measured from the
high-resolution transmission electron microscope (HRTEM) to determine the lattice strain and
measured a 0.2% increase in lattice strain. Hwang also used powder x-ray diffraction data
(XRD) to investigate the effect of milling time on lattice strain and determined that it
increased[13]. Huang and Hwang’s results agree and provide other methods of characterizing the
work hardening of a material during milling.
Particle Breakage during Milling
Prasher gives a chronology of proposed laws relating energy for breakage to simple
parameters such as changes in surface area or change in particle size [28]. Two of the most
notable relationships are Rittinger’s and Kick’s Law. Rittinger states that, energy E, to break
particles is equal to the new surface area times a constant as described by Equation 2.1.
sKxx
E Δ=⎟⎟⎠
⎞⎜⎜⎝
⎛−∝ 1
12
11 2-1
The terms x1 and x2 describe the particle diameter of the feed and product material
respectively, K1 is a constant and Δs is the change in surface area. Kick’s Law, Equation 2.2,
33
finds the energy to break a particle is equal to a constant, K2, times the log of the starting particle
size divided by the ending particle size.
⎟⎟⎠
⎞⎜⎜⎝
⎛=
2
12 log
xx
KE 2-2
These relationships apply to a limited number of cases with precise particle sizes and specific
materials and have not been shown to apply to processes where particle deformation is desired
[28].
Figure 2-9 shows a comparison of brittle materials and ductile materials trapped between
impinging grinding media. Brittle particles are compressed and fractured by the media, whereas
ductile particles are plastically deformed and flattened. Both processes represent an increase in
overall surface area, however, during particle deformation the volume of the particle is
conserved.
Effect of Milling Parameters on Particle Breakage
Choosing the proper milling parameters can have a significant effect on the breakage rate,
energy consumption, and efficiency of the milling process. Grinding media density and size, for
example, directly affects the magnitude of the load on the particles, and thus can be expected to
alter milling. Many authors have studied the effects of milling parameters on particle breakage in
a stirred media mill [21, 25, 61, 62]. Kwade formulated a simple equation (eq. 2-3) to
mathematically relate media size, media density, and rotational rate to the stress intensity.
Kwade’s stress intensity term is merely a representation of the kinetic energy of the media and is
not a representation of the actual stress acting on the particles. Stress intensity (SI) is directly
proportional to circumferential velocity v, media size Dp, and media density ρp less the fluid
density ρf through Equation 2-3 [63]:
34
( ) 23 υρρ fppDSI −= 2-3
Kwade then showed that at a specific energy input an optimum in stress intensity existed
that provided minimum particles size for a minimum energy input. The optimum energy input
for producing a maximum fineness exists between a stress intensity of 0.01 Nm and 0.1 Nm.
Kwade also derived an expression that relates the stress frequency (SF) to media size [63]. The
stress frequency is a representation of the number of media-particles interactions, i.e. the number
of times a particle is contacted by the media, and described by Equation 2-4.
TDDSF
p
ss
2
⎟⎟⎠
⎞⎜⎜⎝
⎛= ω 2-4
Here, T is milling time, Dp is the diameter of grinding media, Ds is diameter of the stirrer, and ωs
is angular velocity. Kwade showed that the greatest stress frequency results from the smallest
media size. Large stress frequency also results in the smallest particle size. The author was able
to provide a method for optimizing and even scaling a milling process. However, these results
have only been shown to apply to a system where particle size reduction is desired. The effect of
stressing velocity on the deformation of materials in a milling system has not been studied.
Stressing velocity and strain rate in a mill can be assumed to be equivalent terms as previously
discussed by Schönert [44]. Using Kwade’s model of SI it is now possible to relate specific
milling parameters (media size, media density, and rotational rate) to the strain rate. This would
be the first step in obtaining a realistic model to describe the deformation process in a stirred
media mill.
Eskin et al. developed a more sophisticated approach to modeling the energetics of a
milling process. The authors calculated granular temperature, and used it to represent the
velocity of the grinding media in their process [20]. The authors then calculated the force, and
35
stress of the grinding media based on Hertz’s theory and rigid body impact. Equation 2-5
demonstrates how force, F, is related to media size, R, granular temperature(velocity), Θ, and
materials properties, such as, Poisson’s ratio, η, density, ρ, and modulus of elasticity, Y [20].
( ) ( ) ( ) ( )532
535
2
2196.1 Θ⎥
⎦
⎤⎢⎣
⎡−
= RYF ρη
2-5
Eskin derived a relationship determining the number of compressions a particle would
experience as a function of media size. This relationship is similar to Kwade’s stress frequency
term. Eskin concluded by calculating a milling efficiency term based on the energy input into the
mill. The work by Eskin was found to be important to this study and the equation and derivations
of his work will be revisited in more detail in Chapter 4.
Summary
In summary, Kwade has provided models that describe the stress intensity and stress frequency
in a stirred media milling process for particle breakage. These models may also be valid for
describing the stress intensity in a milling process where deformation is desired. It is known that
some metals have a strain rate dependent behavior and that greater deformation may be achieved
from a lower strain rate. Zoz showed that the amount of deformation a material can undergo in a
milling experiment is also related to the hardness of the material. Researchers have also shown
that the extent of work hardening varies with media size, concentration and milling time. The
researchers have provided three methods by which work hardening can be characterized,
including indentation, XRD, and HRTEM. From these studies, it is now possible to begin to
construct models that can predict material deformation based on the hardness of the material,
deformation, milling time, media size, media density and rotational rate of the stirred media mill.
36
Figure 2-1. 1) Particle stressed by compression or shear, 2) particle stressed by impaction on rigid surface, and 3) particle stressed in shear flow.
0 10 20 30 40 50 60 70 80 90 100
Fluid Energy 2%
Pin Mill 5%
Ball Mill 8%
Ball Roce Mill 13%Swing Hammer Mill 22%
Roll Crusher 80%
Free Crusher 100%
0 10 20 30 40 50 60 70 80 90 100
Fluid Energy 2%
Pin Mill 5%
Ball Mill 8%
Ball Roce Mill 13%Swing Hammer Mill 22%
Roll Crusher 80%
Free Crusher 100%
Figure 2-2. Milling efficiency variations by machine type.
1) 2) 3)
37
Ball Mill Roll mill
A) B)
Ball Mill Roll millBall Mill Roll mill
A) B)
Figure 2-3. Types of grinding mills, A) ball mill and B) roll mill.
Figure 2-4. Diagram of a stirred media mill, energy is supplied to the grinding media by the rotation of the agitator.
Stirred media
38
Figure 2-5. Face centered unit cell for aluminum.
Figure 2-6. Slip planes and directions for FCC aluminum.
39
σy
σUTS
Elastic region
Plastic region
Unloading
Stress
Strain
σy
σUTS
Elastic region
Plastic region
Unloading
Stress
Strain
Figure 2-7. True stress- true strain curve for a material undergoing plastic deformation and strain hardening.
40
Increasing relative particle sizeIncreasing relative particle size
Figure 2-8. Relative particle size distributions for attrition, cleavage, and fracture, respectively.
Figure 2-9. Effect of impact (a) brittle single particle, and (b) ductile single spherical particle.
a) b)
41
CHAPTER 3 MATERIALS, CHARACTERIZATION AND EXPERIMENTAL PROCEDURE
The goal of the study was to understand and predict particle deformation during milling. In
order to achieve this goal it was necessary to develop experimental procedures and
characterization techniques for performing and assessing particle deformation. This chapter
describes the milling equipment and procedures used in this study. Characterization techniques
and validation of the results are discussed in this chapter. In addition, the chapter describes the
statistical analysis techniques used for predicting particle deformation during stirred media
milling. The chapter concludes with identification of the milling parameters used in this study.
Materials
Metal Powders
The aluminum powder (product name H-2) used in this study was purchased from Valimet
Inc, which is generally used in the production of metal effect paints and aluminum based
explosives. Valimet manufactures the aluminum by atomization. Molten aluminum is sprayed
through a high pressure nozzle and solidifies when it is exposed to argon atmosphere forming
semi-spherical aluminum particles. The aluminum is then classified to obtain the desired size
distribution. The powder has a purity of 99.7 weight percent aluminum and a median particle
size of 3.2 μm as measured by the manufacture. In house measurements of the particle size using
light scattering determined the median size to be 3.8 μm, and a mean of 4.2 μm. Figure 3-1
shows the size distribution of the “as received” H-2 aluminum as measured by the Coulter
LS13320 light scattering particle sizer.
Milling Media
The milling media used in this study was yttria-stabilized zirconia, purchased from Advanced
Materials Inc. in sizes of 0.5, 1.0, 1.5, and 2.0 mm. The density of the media is 6.0 g/cm3. Figure
42
3-2 is an image of the 1.0 mm grinding media used in this study. In order to maintain a consistent
size distribution the media was sieved after each experiment to remove fines and fragments
caused by fracture and wear [1].
Experimental Procedures
Media Mill
The mill used in this study was a bench top Union Process attrition mill as seen in Figure 3-3.
The mills operational speed is between 500-5500 rpm. Numerous types of milling vessels and
stirrers can be equipped on this model. This study used a 750 ml stainless steel milling vessel and
a 4 bar stainless steel agitator, the bars of the agitator are approximately 60 mm in length. It is
important to note that the length of the agitator arm and the rotational rate was used to calculate
the tip speed of the mill and ultimately the kinetic energy of the grinding media. The vessel is 90
mm in diameter and 90 mm in height. Figure 3-3 is a picture of the milling vessel and the
agitator used in the study. The mill is attached to a recirculation reservoir that maintains the
temperature of the mill contents at 25oC. The mill is attached to a digital controller, which
provides speed and power control over the mill.
Milling Procedure
The mill was assembled according the specification provided in the mill manual. To assure
experimental continuity, the volume of material used and the distance between the bottom of the
agitator and the bottom of the milling vessel (1/4 in.) was maintained in all experiments. The
contents and milling sequence were performed in the following order:
1. 25 grams of H-2 aluminum powder 2. 5 grams of stearic acid 3. 300 ml of isopropyl alcohol 4. Initial dispersion 5. 400 ml of grinding media 6. Start milling experiment (sample at appropriate times)
43
The milling medium used in this study was isopropanol with 5g of stearic acid dispersant. A
more detailed description of these materials will come later in the chapter. Prior to the loading of
milling media, the mill was run for 5 min at 500 rpm to disperse the metal powder in the medium
(liquid suspension). Following the 5 minutes of dispersion the mill was ramped up to the desired
milling rotational rate. It was then shut off. The milling experiment was then restarted when the
milling media was added. Samples were taken from the mill at times of 1, 3, 5, 8, 12, 15, 30 45,
and 60 minutes then at 1.5, 2, 4, 6, 8, and 10 hours. In order to reduce the effect of the change in
volume on milling kinetics the samples removed from the mill were less than 1.0 ml. Samples
were diluted with 20 ml of isopropyl alcohol, sealed and then stored for either drying or
characterization.
At the end of each experiment, the mill was stopped and dissembled. The contents of the
mill were pored through two sieves, one of sufficient size (i.e. 1.0 mm mesh for 1.5 mm media)
to catch grinding media and another of 90 μm to catch fragments of grinding media. After the
slurry was separated form grinding media it was placed in a Nalgen® bottle for storage and later
drying. Every part of the mill that was exposed to the aluminum slurry was rigorously cleaned
with soap and water and allowed to dry in an oven before performing another experiment. The
grinding media caught in the sieve was placed in a 1000 ml Erlenmeyer flask and washed with a
3 M hydrochloric acid (HCl) solution. The contents of the flask was then emptied into a sieve
and placed in a sonic water bath. The sonicator was flushed repeatedly with water to remove
HCl. The media was then placed in an oven and allowed to dry.
Drying of Aluminum Slurry and Milling Samples
There has been a considerable amount of effort put into establishing the best way to dry a
liquid suspension. A review of the work can be found in a dissertation on dry dispersion by
44
Stephen Tedeschi [64]. This study will use a supercritical drying technique to dry samples
obtained from the milling process. When liquid CO2 is heated to above 31.2 oC in a confined
volume, CO2 becomes a meta stable fluid termed a supercritical fluid Figure 3-4. The
supercritical drying method involves solvent exchanging the suspensions fluid with that of liquid
CO2, then heating the pressure vessel above 31.2oC and releasing the meta stable fluid. The
importance of drying across each phase boundary was discussed in Tedeschi work; it was found
that supercritical drying reduced capillary forces that are present in conventional drying
techniques [64]. Figure 3-5 is the pressure vessel used in this study, it was purchased from SPI
Inc. The vessel is capable of sustaining a pressure of 2000 psi and a temperature of 50oC.
The method we used is as follows. The particle suspension samples removed during
milling was placed in a 25,000 Dalton dialysis bag and diluted with isopropyl alcohol. The
dialysis bag was used to allow diffusion of solvents, while capturing the particles. The bags were
then placed in the pressure vessel, which was then filled with liquid CO2 and allowed to sit for 2
hours. After two hours, approximately 70% of the fluid inside the vessel was released and the
vessel was again filled with CO2. The step of emptying and refilling the vessel was continued
until all the isopropyl alcohol was removed, which took approximately 10 washes. After the final
solvent exchange, the vessel was heated to above 31.2 oC and the meta stable fluid was slowly
released as a gas. The samples were then removed from the vessel and placed in Nalgen bottles
for storage and later analysis and testing.
Sample Preparation by Dispersion of Dry Powder
For many of the characterization and analytical techniques used in this study the milled
product must be dispersed in the dry form. A particle vacuum chamber was used to disperse the
powder. Samples prepared in this way were used in image analysis, obscuration tests, and mass
measurements. They were also used for calculating IR obscurant performance. Obscurant results
45
will be discussed later in the case study. The device used for this study was a Galai partial
vacuum chamber. Approximately 2 mg of supercritically dried sample was dispersed in the
chamber using 5 bars of vacuum. The amount of sample used was found by trail and error, and
was determined to be enough to give a near monolayer of particles. Figure 3-6, shows a) the
Galia chamber, as well as, b) a glass slide used for mass and image analysis measurements, c) a
silicone wafer chip used for scanning electron microscope measurements, and d) a double pass
transmission (DPT) slide used for Fourier transform infrared spectroscopy measurements
(FTIR). The exact use and importance of the samples prepared by this method will be discussed
in the appropriate characterization section.
Statistical Design of Experiment
Statistical design of experiment (DoE) is a powerful tool used to optimize and analyze
many industrial and commercial processes. This study first used statistical design to understand
and choose the parameters that are important to particle deformation during stirred media
milling. The variables studied were rotation rate, media loading, and media size. Additional
designs and analysis were used to determine the interaction between milling parameters and
define their significance. A central composite design was used to analyze the measured material
response to milling (strain) as a function of milling parameters. The DoE software used in this
study was purchased from Stat-Ease, and is called Design-Expert 7. The software is capable of
performing statistical analysis of the data, based on analysis of variance (ANOVA). It is also
capable of developing and experimental design that can then be modeled by the software.
Characterization
Characterization is a vital part of any study, it is important to understand and relate process
variable to product qualities. By characterizing and interpreting the product materials, it is
possible to determine and predict the behavior of a material or process. This study used
46
characterization techniques to measure the response of aluminum to process parameters before,
during, and after mill. The characterization techniques used in this study and the sample there
importance are discussed in the following sections.
Light Scattering
Light scattering has been used to rapidly and accurately measure particle size and size
distributions. The main principle of light scattering for particle size analysis is that light scatters
at different angles based on the size of the particle. A detector measures the angle and intensity
of the scattered light and is able to reconstruct a particle size distribution from that data. One
limitation of light scattering is that it assumes all particles are spherical for size calculations. This
limitation will be addressed in more detail in chapter 4. This study uses the Coulter LS11320
which is capable of measuring particle sizes from 40 nm to 2,000 µm. The Coulter measures the
particles size distribution of the samples taken from the mill. In order to achieve accurate
measurements, the samples from the mill are further diluted with isopropyl alcohol to a
concentration fit for size measurement. To achieve an accurate measurement from the LS11320,
light must be able to pass through the sample, the approximate concentration must be <1 %. The
data from the Coulter is used for calculations of stress, strain energy, strain, milling efficiency
and strain rate, these results will be shown in chapter 4.
The LS11320 is capable of providing data output in number, surface area, and volume
distributions. The differences in these measurements are due to how they are calculated. If the
particle size distribution were narrow, these three methods would provide equivalent. However,
if the distribution is bi-model or broad a number would appear to have smaller particles size and
a volume distribution would appear larger.
47
Microscopy and Image Analysis
This study produced high aspect ratio metallic flakes with major dimensions as large as 10
μm and minimum dimension sizes as small as 10 nm. This led to challenges in obtaining clear
images from one specific device. Some of these challenges were getting both quantitative and
qualitative flake thickness measurements due to difficulty in getting the flakes to stand
perpendicular to the surface. There were also challenges in getting quantitative particles size
measurements of the flake diameter to verify light scattering data. This challenge will be
addressed later in this chapter.
Electron microscopy
Most of the images used in this study were taken using a scanning electron microscope
(SEM). The SEM functions by focusing a beam of electrons onto a surface. The beam of
electrons then excites and emits electrons from the surface that are then detected and used to
reconstruct the surface topography. The microscope used in this study was a JEOL 6330 cold
field emission microscope. Samples for the SEM image were prepared by disseminating the
powder onto a silicone wafer and attaching the wafer to an aluminum stub with carbon tape. This
procedure allows for a conductive contact between the flakes and the instrument. SEM images
were used to verify light scattering data using image analysis software called ImagePro®. The
software was capable of thresholding the images and counting and measuring the particles. SEM
was used to study particle morphology and determine when particle breakage occurred.
Transmission electron microscope (TEM) was used in this study to measure particles size,
and crystallinity. TEM image materials by passing an electron beam through a thin slice of
sample. TEM can also determine crystallinity and microstructure of materials. Two TEMs were
used in this study, the JEOL TEM 200CX was capable of imaging at high magnification, and the
JEOL TEM 2010F was capable of measure crystallinity over a broad size range. Samples were
48
prepared for the TEM analysis by mixing the dry powder with an epoxy. The epoxy was then
allowed to cure. After curing, the epoxy was sectioned using a microtome to cut slices
approximately 100 nm thick.
Optical microscopy
Imaging was also done on an Olympus BX60 optical microscope equipped with a SPOT
Insight Digital CCD camera. The microscope was capable of magnifying and image between 2 to
100 times. This microscope requires very little sample preparation to obtain images. Optical
microscopy provided a quick way to estimate particle size and morphology. However, it was
challenging to measure particles of less than 5 μm due to the low magnification and low
resolution at that length scale.
Occhio optical particle sizer
The Occhio optical particle sizer was also used in this study. The instrument passes a
sample below a fixed high magnification CCD camera capable of imaging thousands of particles
in seconds. It then analyzes the images with Calisto software. The Occhio instrument specifies
that it is capable of measuring particles as small as 0.5 microns and as large as 3 mm. A
comparison of data between the Occhio and light scattering will be shown later.
Surface Area Analysis (BET)
Surface area analysis by gas adsorption was first achieved by Stephen Brunauer, Paul
Hugh Emmett and Edward Teller in 1938 and was later termed the BET technique [65]. BET
involves measuring the amount of gas condensed on the surface of a sample at low temperatures
and pressures. This study used the Quantachrome Autosorb 1C-MS to measure the specific
surface area of samples taken before, during, and after milling. Samples for BET analysis were
allowed to outgas under vacuum at 60oC for 12 hours before being placed in the BET for
analysis. The particle size of the before milling samples were verified by image analysis and
49
light scattering techniques. The after and during milling samples were used to study the change
in particle size as a function of milling time and were used to determine IR obscurant
performance.
Inductively Couple Plasma Spectroscopy (ICP)
Inductively coupled plasma spectroscopy is used to measure the elemental composition of
an organic or aqueous liquid. The ICP ionizes atoms is an argon plasma, the ionized atoms emit
light when electrons return to the ground state. The light is detected and correlated to specific
atoms. The instrument used in this study was the Perkin-Elmer 3200 Inductively Coupled Plasma
Spectroscope. It has the capability to measure contents to less than 1 part per million. ICP was
used to verify the purity of the starting material and to determine the mass used in the case study.
As mentioned previously approximately 2 mg of sample was disseminated into the particle
vacuum chamber. However, only a fraction of the would end up on the DPT slide, this lead to
difficulty in accurately determining the mass-transmission relation necessary for measuring
material performance as an IR obscurant. This was resolved by also disseminating on to a glass
slide of known dimensions then measuring the concentration of metal dissolved off the slide.
From the mass an accurate measurement of mass per area was obtained, which was then equated
to the mass per area of the DPT slide. The measurement of mass and obscuration values were
then used to determine the performance of the material.
Fourier Transform Infrared Spectroscopy (FTIR)
Fourier transform infrared spectroscopy (FTIR) is most often associated with
measurements used to identify compounds in liquids and on solid surfaces. The equipment used
was the Thermo Electron Magna 760. The FTIR is capable of measuring the transmission, and
reflectance of light at wavelengths from 400-4000 cm-1. This study used the FTIR to determine
the percent obscuration of light in the infrared (IR) spectrum for the development of IR
50
obscurants. The development of IR will be discussed in detail in chapters 7 & 8. As discussed
previously, sample was disseminated onto DPT slides, which were then place in the FTIR. Light
was then passed through the sample and a percent transmission was measured. This value was
then used to calculate the performance of the material, the calculation will be shown later.
Light Scattering Results
In this study, it was important to utilize techniques to characterize the response (particle
size) to varying milling conditions. This study used light scattering to measure particle size and
used image analysis to validate the techniques.
Results of Aluminum Powder
Experimental studies were performed on an aluminum powder (H-2) that deforms as a
function of milling time. It was also important to confirm light scattering particle size results for
the powders used in this study. Figure 3-7 shows an SEM image of the as received spherical
aluminum powder. The powder is roughly spherical with few non-spherical agglomerates. The
image also indicates that the particle size distribution for this particular powder may be broad as
can be seen by the large number of particles that are less than a micron and the large number that
are greater than a micron. The particle size of this powder was measured by light scattering.
Figure 3-8 gives the differential volume and number distribution data from this measurement.
Figure 3-8 also shows the error bars that represent the standard deviation obtained from three
separate measurements of the as received aluminum powder. The error bars are barely visible
due to the very low sample-to-sample variations in the measurement technique. A difference in
the volume and number distributions is apparent in Figure 3-8. If the particle size distribution
was narrow and mono dispersed the number and volume distributions would overlay each other.
However, the distribution is broad, as indicated by the SEM image. In addition, when there are
many fine particles present the number distribution tends to shift to the smaller particle size
51
range. The mean particle size diameter as measured from the number and volume distributions
are 1.0 μm and 4.2 μm, respectively.
Surface area measurements were performed on the “as received” H-2 aluminum powder
using a BET. This measurement was compared with the calculations of the specific surface area
based on the mean particle size obtained from the light scattering data. The mass of an individual
aluminum particle was calculated from the density (2700 kg/m3) for particles of mean diameters
of 1.0 μm and 4.2 μm. The calculated specific surface areas for the mean number and volume
particle sizes of 1.0 μm and 4.2 μm are 2.22 m2/g and 0.53 m2/g respectively. The measured
surface area from the BET was determined to be 1.55 m2/g. The measured and calculated values
are close only for the 4.2 micron particle indicating that the BET and light scattering techniques
are in close agreement.
Results for Aluminum Flake
However, this study focused on disk-shaped particles obtained from the deformation of the
spherical particles. It was therefore necessary to verify the light scattering techniques used in this
study with image analysis. To obtain a more accurate measurement of the aluminum flake we
employed the use of the Occhio® particle sizing system (specifications and functionality
discussed in chapter 3). Figures 3-9 and 3-10 are the particle size distribution data obtained from
light scattering and image analysis using the Occhio®. The data is for aluminum flakes that
were milled for 10 hrs. The figures show an agreement between the distributions obtained from
both measurement techniques. The mean particle size data obtained from the Occhio and light
scattering measurements were 4.6 and 6.9 μm, respectively. The Occhio counted over 16000
particles; this makes the measure more statistically significant [66]. Table 3-1 gives a
52
comparison between the light scattering and image analysis data. It can be seen that the d10, d50
and d90 have a close values.
Summary of Characterization and Light Scattering
In any application where particle size is a critical parameter, it is important to determine
what the desired form of the particle size distribution is for a process. If the number of particles
in the process is a key variable for quality control then a number distribution might be
considered. However, if the mass of the material being processed is an important process
condition the volume distribution may be important. This study will show later how the volume
of the particle is important for modeling the milling process. In this study the volume distribution
obtained from light scattering data was determined to be the most applicable.
Even though there are challenges with using light scattering to measure the particle size
and size distribution of disk shaped particles, the above work validating the technique shows that
can be used in this work. Particle size distribution of aluminum flakes obtained from light
scattering and image analysis techniques were comparable. This indicates that light scattering is
a valid technique for characterizing the major dimension of disc shaped materials.
Milling Condition Selection
Preliminary Milling Study
Stirred media milling is a complex process with numerous operating and equipment
variables affecting the performance of the mill and the final product. Some of the equipment
variables that can be manipulated are listed in Table 3-2. The vessel size, geometry, stirrer size,
and geometry were fixed. Table 3-3 gives a list of operating variables. Those variables were
media size and density, solvent, material, and surfactants. However, many other operating
variables need to be manipulated or determined in order to conduct a milling experiment.
53
Preliminary Milling Results
The best way to understand the effect of milling parameters is to vary conditions during a
series of experiments. A preliminary study of the effect of media loading on mill performance
was carried out using brass flakes obtained from US Bronze. The flake is the current material
used in infrared obscurant. Scanning electron microscope images of the starting material can be
seen in Figure 3-11. Statistical design of experiments was used to determine the effect of media
loading on deformation. A two factor design was used in this experiment. This design involves
varying the factor A (media loading) between five different concentrations (levels) and a second
factor B (rotational rate) between 3 different speeds (levels), then measuring a response (particle
size). Table 3-4 gives the experimental details used in this study. Experiments 4a-4c were used to
confirm the repeatability of the experiments. The other parameters such as milling medium and
medium volume, milling media size, material concentration and surfactant usage were held
constant; Table 3-5 gives the specific milling conditions used in this study.
The response variable used to measure mill performance was the figure of merit (FOM).
Figure of merit is a measure of how efficiently a material obscures infrared light (IR) and is an
indication of the specific surface area of the material. Equation 3-1 describes FOM where
transmission, T, is obtain from FTIR measurements, mass, m, is measured using the ICP and SA,
is the surface area of a microscope slide. The material constant, Cm, is considered proprietary.
m
slide
C
SAm
TLNFOM *
*2
100⎟⎠⎞
⎜⎝⎛
−= 3-1
A surface response plot of figure of merit versus the factors listed above can be seen in
Figure 3-12. The figure shows that as media loading is increased the figure of merit is also
increased. Higher media loading results in a larger number of grinding media that can impart
54
energy on the particles. The highest figure of merit was obtained at 21% media loading. These
results suggest that even higher media loading may further improve mill performance. However,
it was found that if media loading was increased to greater that 70% that the vessel contents
would overflow at velocities higher than 1000 rpm due to the turbulent environment inside the
mill. It was then possible to maximize mill performance by maximizing media loading, this also
allowed for the study of addition milling parameters by fixing media loading at a constant value.
Establishing Milling Conditions
This study also focused on using a specific mill and milling accessories described in Table
3-2. All milling experiments were conducted using the same mill geometry, vessel size and
stirrer geometries. Therefore, all the equipment variables used in this study were held constant.
We have established the importance of some of the operating variables on mill performance from
the preliminary study. However, numerous other operating variables can be manipulated and
may have a significant effect on mill performance.
Milling medium
The milling medium is also an important parameter for a wet stirred media milling process.
The medium affects the viscosity of the system, which in turn affects the energetic of the milling
process. The medium can also affect the ability to disperse particles during milling and the
selection of grinding aids used in particle dispersion. In this study, we milled an aluminum
material exposing a very reactive native aluminum surface in the process. It was important to
choose a milling medium that would have a favorable reaction with the exposed native aluminum
surface. Experiments performed using water as a medium led to the rapid oxidation of the native
aluminum surface. This caused the material to become brittle and fracture. It also led to the
production of hydrogen gas and the generation of large amounts of heat. It was decided that this
was not a favorable condition to make high aspect ratio metallic flakes due to the production of a
55
large amount of alumina particles. Instead, nonpolar solvents such as isopropyl alcohol or
heptane were considered. After consulting with Dr. Kremer at Silberline Inc. and reviewing
literature on metallic flake production, the explosive hazards of high surface area aluminum
powders were brought to light [10]. Milling in heptane would produce particles of high specific
surface area with a minimum amount of passivation. This could potentially be extremely
explosive. Therefore, isopropyl alcohol, which would provide a limited amount of passivation
during the milling process, was used to reduce the threat of explosions.
Mill loading and grinding aids
One of most important parameters in a wet milling study is the viscosity of the slurry. The
slurry viscosity is likely to change as a function of milling time due to increased surface area of
the product from deformation and/or particle breakage. Many researchers have investigated the
effect of viscosity on mill performance [67-69]. Viscosity directly effects the energetic of
milling. The higher the viscosity the more energy lost to viscous friction. One method for
improving performance is by using grinding aids [70]. In order to minimize the effect of
viscosity on experiments milling was done at very low solids loading to reduce any changes in
viscosity as a function of milling time. The solids loading is the amount of material that is to be
milled, in this case, it is the amount of aluminum powder added to the mill. In this experiment 25
g of aluminum was used which amounts to a solids loading of 8.3%.
At high solids loading it becomes important to select the proper grinding aid that reduce
the viscosity of the system. As stated above, this study maintained a low solids loading in the
mill thus eliminating the need for a viscosity reducing grinding aid. Generally, grinding aids are
used to disperse particles broken during stirred media milling and to prevent particle
agglomeration.
56
Dry ball mills use grinding aids to prevent coldwelding of metallic particles. The most
common grinding aid used to prevent coldwelding is stearic acid. Figure 3-13 shows the
chemical structure of stearic acid. Stearic acid is a saturated fatty acid used in firework
production to coat metallic particles and prevent oxidation. In this study, the wet milling
environment prevented the coldwelding of the metallic particles. However, stearic acid was used
to prevent oxidation of the metal during milling and after drying the product. An added benefit of
the stearic acid was that it aided in the dry dispersion of the metallic particles when used for IR
obscurants.
Milling time and temperature
Milling time is one of the most significant factors when running a milling experiment.
Time affects the overall amount of energy consumption of the mill, which will ultimately define
milling efficiently. The final product and final product quality is highly dependent on the amount
of time it has been milled. On the laboratory scale, it is possible to sample the milling process at
varying milling times in order to evaluate the temporal effects on the product. In this study,
samples were taken though out the milling experiment to identify when particle deformation
and/or particle breakage occurs. Figure 3-14 represents a typical particle size distribution data
obtained from a milling experiment where particle deformation and breakage occur. The graph
shows that samples taken from the mill up to 240 minutes show an increase in particle size, this
is due to particle deformation and an increase in the major dimensions. After 240 minutes, the
particle size begins to decrease due to particle breakage. From these results it is possible to
identify at what time particle deformation is the dominate mechanism and at what time particle
breakage was dominate. It is possible to see this effect in SEM images of samples taken at
different milling times. Figure 3-15 a-c are SEM images taken at a) 0 minutes, b) 240 minutes,
and c) 600 minutes of milling. At 0 minutes, the aluminum particles appear to be roughly
57
spherical. As milling time increases to 240 minutes the spherical particles were deformed and are
now disk shaped “silver dollar” particles. It is important to note that at roughly 240 minutes the
edges of the particles are smooth and rounded indicating that particle breakage has not occurred,
it is also important to note that since particle breakage has not occurred that the volume of the
particles in image a) and b) are equal. This observation of constant volume is important for
calculations and models developed later in this study. After 600 minutes of milling the particles
are much thinner and nearly transparent to the electron beam. They have irregular edges
indicating that breakage has occurred and the particles can no longer be taken to have the same
volume as the “as received” aluminum powder. This study focuses on the particle deformation
process; therefore, it is important to understand when deformation stops or slows and when
breakage begins. Experiments performed in this study were milled for 10 hrs with sample taken
at times of 1, 3, 5, 8, 12, 15, 30, 45 minutes and 1, 1.5, 2, 4, 6, 8, 10 hours. The time of 10 hrs
was selected because it was the longest time required to cause particle breakage.
Temperature can affect mill performance by changing the properties of the environments
such as viscosity of the medium. This study found that temperature has an added effect from the
humid Florida environment where the experiments were preformed. Initial experiments were
performed at a constant temperature of 150C; however, condensation occurred and caused large
amounts of water to be added to the vessel. This problem was solved by increasing the milling
temperature to 250C.
Media properties and rotational rate
The preliminary study showed the effect of media loading on mill performance. It was
found that greater media loading improved mill performance. This was an intuitive result
because the greater media loading, the larger the frequency of contacts that result in deformation.
For this study, the media loading was fixed at 40% for all milling experiments. There are
58
additional properties of the grinding media that affect the milling process. Those properties are
hardness, density and media size. If the media hardness is not greater than the product material
then deformation and breakage will be difficult. This study uses yttria-stabilized zirconia
grinding media (mohs hardness 9.0) to mill aluminum powder (mohs hardness 2-3). Another
property of the media that can affect its performance is the media size. In previous studies,
Hamey showed that if the media is not of sufficient size it fails to impart enough energy on the
material to cause particle breakage. The author also showed that if the media is too large it does
not perform as optimally as smaller media [71]. This study will focus on grinding media of sizes,
0.5, 1.0, 1.5, and 2.0 mm, these sizes are several orders of magnitude larger than that of the
product material (mean particle size of as received aluminum powder 4.2 μm) . Media density
can significantly affect mill performance; higher density media possess more momentum. Kwade
showed the effect of media density on particle size, higher density media yielded better mill
performance for particle breakage [72]. This study focuses on one media density for the
aluminum experiments (zirconia 6 g/cm3).
Rotation rate of the stirrer directly affects the energy of the grinding media and in turn the
amount of energy the product material experiences. For this study, rotation rate was varied from
a high of 2000 rpm to 1000 rpm. Rotational rates higher than 2000 rpm also resulted in leakage
from the vessel, similar to the effect of very high media loadings. Many authors have
investigated the affect of rotational rate on breakage [61, 72]. They found that the greater the
rotational rate the more breakage that occurred. However, it is still unknown what effect rotation
rate will have on deformation. It is even difficult to postulate this effect due to the complex
nature of media-particle-media contacts. Chapter 4 will provide results of the effect of rotational
rate on deformation.
59
Figure 3-1. Particle size distribution of as received H-2 aluminum, along with particle size data, obtained from Coulter LS 11320.
60
Figure 3-2. Image of Yttria-stabilized zirconia grinding media obtained form an optical microscope, 1mm in diameter.
61
a)
b)
Union Process Attrition Mill
Vessel Stirrer
a)
b)
a)
b)
Union Process Attrition Mill
Vessel Stirrer
Figure 3-3. Union Process stirred media mill use in study, a) stirred media mill, and b) milling vessel and agitator.
62
Figure 3-4. Phase diagram for carbon dioxide, indicating the region of supercritical fluid
formation.
63
Figure 3-5. SPI pressure vessel used for supercritical drying of powder samples taken from milling
Figure 3-6. Galia partial vacuum chamber used to disseminate powder a) chamber, b) glass slide, c) silicone wafer chip, and d) DPT slide.
64
Figure 3-7. Scanning electron microscope image of as received H-2 aluminum powder.
65
0123456789
0.1 1 10 100Particle diameter (μm)
Diff
eren
tial
%
Volume distributionNumber distribution
Figure 3-8. Differential volume and number distributions for as received H-2 spherical aluminum powder measured by light scattering.
0
1
2
3
4
5
6
7
8
9
10
1 10 100
Particle diameter (μm)
Volu
me
perc
ent (
%)
Volume percent light scattering
Cummulative volume percentdivided by 10 light scattering
Figure 3-9. Volume particle size distribution of milled aluminum flake as measure by light scattering.
66
0
1
2
3
4
5
6
7
8
9
10
1 10 100
Particle diameter (μm)
Volu
me
perc
ent (
%)
Volume percent image analysis
Cummulative volume percentdivided by 10 image analysis
Figure 3-10. Volume particle size distribution of milled aluminum flake as measured by the Occhio image analysis.
Table 3-1. Statistical data comparison for light scattering and image analysis performed using the Occhio particle counter.
Image analysis Light scatteringmean 6.6 11.2d10 5.4 3.6d50 10.1 9.6d90 22.9 20.5
67
Table 3-2. Stirred media milling equipment variables.
Mill geometry (horizontal or vertical)Mill sizeVessel size
Equipment variable
Vessel material Stirrer geometryStirrer sizeStirrer material
Table 3-3. Stirred media milling operating variables. Operating variables
Mill speed (rotational rate)Media sizeMedia material (density, hardness)
TemperatureTime
Media loading (volume fraction)Liquid medium (viscosity, density, polarity)Material loading (volume fraction)Surfactant, grinding aids, lubricants, and dispersants
Table 3-4. Experimental parameters used in the hexagonal statistical design of experiment. Experiment number Media loading (%) Rotational rate (rpm)
1 0.0 20002 5.3 7003 5.3 3300
4a 8.0 20004b 8.0 20004c 8.0 20005 16.0 7006 16.0 33007 21.3 2000
68
Table 3-5. Milling conditions for preliminary study.
Milling parameter LevelMedia size 0.5 mmMeda type ZirconaMaterial Brass flake/90gMill temperature 20 CSurfactant Steric Acid/5gMedium 2-propanol/300ml
Figure 3-11. SEM image of US Bronze “as received” brass flake used in preliminary milling experiments.
69
Rotational rate (RPM)
Figu
re o
f mer
it
Media loading (%)
Rotational rate (RPM)
Figu
re o
f mer
it
Media loading (%)
Figure 3-12. Surface response of figure of merit with respect to media loading and RPM.
O
O
HH
H
H H
HH
H H
HH
H H
HH
HH
HH
HH
HH
H H
HH
H H
HH
H H
HH
H
Figure 3-13. Stearic acid a saturated fatty acid found in many animal fats and vegetable oils.
5.38.0
16.021.3
70
0
20
40
60
80
100
0.1 1 10 100Particle size (μm)
Vol
ume
per
cent
(%)
As recieved15 min.45 min240min 600 min
Figure 3-14. Cumulative undersized versus particle size as at varying milling time for H-2 aluminum.
71
a) b) c)a) b) c)
Figure 3-15. Scanning electron microscope images of a) as received aluminum, b) milled for 240 minutes aluminum and c) milled for 600 minutes aluminum.
72
CHAPTER 4 RESULTS AND DISCUSSION
In order to understand and predict particle deformation during milling it is important to
study and thoroughly characterize the milling experiments. Prediction of deformation can be
obtained by modeling the milling process and the change in particle size. By combining these
two methods of studies, it is possible to establish a more comprehensive understanding of the
flaking process during milling. This chapter will discuss the empirical, semi-empirical and
theoretical results obtained from milling. These results will then be used to construct models that
explain and predict the effect of milling parameters on particle deformation during milling.
Experimental Results of Stirred Media Milling
Effect of Mill Parameters
The goal of this study was to develop a better understanding of particle deformation during
stirred media milling. An observation was made from preliminary milling studies that indicated
certain milling parameters resulted in larger diameter flakes and less particle breakage than other
parameters. This was an important observation because most processes that use metal flakes
prefer flakes with high aspect ratios that have not been broken. The particle size distributions
shown in Figure 4-1 are for 1.0 mm milling media at 1000 rpm. In this figure samples were taken
at different milling times. The bimodality seen in the figure is due to particle breakage. It can be
seen that bimodality was present at short milling times. This indicates that the experiment
resulted in breakage at short milling times. Figure 4-2 shows the particle size distributions for an
experiment, which used 1.5 mm milling media and 1000 rpm. In this figure, the distribution was
monomodal and shifted to larger particle sizes indicating that the particle deformation occurred
and there was only limited breakage. The differences in the effects of milling media on the
aluminum flakes were also seen visually. The samples milled with 1.0 mm media appeared dull
73
and non-reflective and showed limited pearlescence. Whereas, the 1.5 mm media produced
flakes that were highly reflective showed a high amount of pearlescence[57, 73]. Figure 4-3
shows a comparison of the maximum particle diameter achieved in each milling experiment. It
can be seen that for all rotational rates the 1.5 mm result in the largest particle size. This result
correlates well with the visual observations. In order to understand the deformation process
during milling it was necessary to study the temporal effects of media size on mean particle
diameter.
The grinding curves (mean particle size versus milling time) for this study are shown in
Figures 4-4 to 4-6. In all the experiments the mean particle size increases to some maximum
value due to the flattening of the particles. This maximum particle size was than followed by a
decrease in particle size at long milling times, which can be attributed to breakage of the
particles. It can be seen that the 1.0 mm grinding media results in breakage at the shortest
milling times and that the 1.5 mm results in the largest particle diameter. Figure 4-7 shows that
rotational rate does not have a strong influence on maximum particle size. However, rotation rate
does affect how rapidly the maximum particle size was reached. The influence of rotation rate
on deformation will be discussed in more detail later in the chapter. At first, it was not
completely understood why certain media sizes resulted in larger diameter particles and
ultimately a greater amount of deformation before breakage. However, this study developed a
theory and methodology to explain the relationship between particle deformation and milling
parameters such as media size and rotational rate. The next section compares and contrasts data
using existing models for particle breakage to the deformation data.
Kinetic Energy Model
For particle breakage, researchers have related kinetic energy to the fineness of the
product. Several researchers have shown that the size of grinding media can significantly affect
74
the particle breakage and particle deformation process during milling [14, 21, 63, 71]. Media size
is an important parameter in Kwade’s equations of stress intensity (SI) (Equations 4-1). Stress
intensity is simply the kinetic energy (KE) of the grinding media in liquid slurry. In Equation 4-
1, Dp is the diameter of the milling media, υ is the linear velocity of the media, and ρf and ρp are
the density of the fluid medium and milling media respectively. A more detailed discussion of
Kwade’s equations can be found in chapter 2.
( ) 23 υρρ fppDSI −= 4-1
This equation has been the basis for the scaling up of many particle breakage processes.
However, there is no data or models relating grinding media size to particle deformation during
stirred media milling. As a first step, this study applied Kwade’s models to particle deformation.
The hypothesis, equivalent to that for particle breakage, is that if higher stress intensity (KE)
resulted in a greater amount of particle breakage, than higher stress intensity (KE) may also
result in a greater amount of deformation. Selection of the milling parameters chosen for this
study was discussed in chapter 3. The effect of four grinding media sizes (0.5, 1.0, 1.5, and 2.0
mm), and three rotation rates (1000, 1500, and 2000 rpm) on the resulting deformation. Table 4-
1 gives the calculated stress intensities for all the experiments performed in this study. As media
size and rotation rate increase, the stress intensity (KE) also increases. This is due to the higher
kinetic energy resulting from the larger mass and greater velocity objects. Kwade verified the
results with experimental data for breakage, however, no one has shown whether the models are
verifiable with deformation data. Table 4-2 shows the maximum mean particle size for each
milling experiment. By comparing the data in Tables 4-1 and 4-2 it is possible to determine if
there is a relationship between kinetic energy (stress intensity) and deformation (mean particle
size). It is logical that kinetic energy is dependent on both media size and rotation rate. Thus,
75
equivalent kinetic energies could be obtained at different combinations of these milling
conditions. However, it can be seen in Figure 4-3 and Table 4-2 that deformation does not vary
with rotation rate. The energies for the [1.5 mm, 1500 rpm] and [2.0 mm, 1000 rpm] are
equivalent. Thus, according to this theory the particles sizes for these experiments should also be
equivalent. However, the maximum particle sizes differ indicating that kinetic energy can not be
used to predict deformation. This result led to develop of a new model that was not based on
kinetic energy of the grinding media, such as a contact mechanic model based on Hertz’s theory
discussed in the next section.
Stress Model
Eskin et al. derived a model that relates milling parameters to particle breakage [20]. The
basis for Eskin’s model was the use of Hertz theory to calculate a contact area, which was then
used to calculate milling efficiency. Eskin used a term called granular temperature as a
representation of velocity was used to calculate the force. In this investigation the linear velocity
is used so a more direct comparison between this model and stress intensity (KE) could be
established[74].
In order to apply Hertz theory, the contact of the colliding bodies must be elastic. In this
research, the colliding objects are spherical zirconia grinding media with an elastic modulus of
approximately 200GPa and a Poisson’s ratio of 0.31. Thus, the assumption of elastic contact is
valid. The following equations were derived from Johnson’s book “Contact mechanics”, and can
also be found in Eskin [20, 74]. In Equation 4-2 the average normal force, Fb, of identical
elastic beads is related to the Young’s modulus of the bead, Yb, the Poisson’s ratio of the bead,
ηb, multiplied by the density, ρb, times the velocity, υ, and radius of the bead, Rb.
76
( ) ( ) bbb
bb R
YF 5
65
35
2
2 215
76.0 νπρη ⎥
⎦
⎤⎢⎣
⎡−
= 4-2
The radius of the contact area, αb, was calculated from the force acting on the bead and the area
of a circle. Dividing the force by the contact area is the stress, σb, exerted at the center of the
contact area by the beads, as described by Equation 4-3 and 4-4.
( ) 31
2143
⎥⎦
⎤⎢⎣
⎡ −= bb
b
bb FR
Yη
α 4-3
2)(23
b
bb
Fαπ
σ = 4-4
Figure 4-8 is a schematic of the collision of elastic spheres. Table 4-3 gives the force,
contact radius and stress calculated from Equations 4-2, 4-3, and 4-4. It was determined that the
force increases with increasing media size and rotational rate. The media size and rotational rate
also increase the contact area. The stress for a specific rotational rate is equivalent for all media
size. This indicates that stress exerted by the grinding media is not sufficient to describe the
variations in deformation from varying media size. However, the important quantity to know is
the magnitude of the stress exerted on the particle and not the stress acting on the media.
The stress acting on the particle ultimately results in the deformation of the material. A
schematic of the particles trapped in the region between two colliding grinding media can be
seen in Figure 4-8. From the size of the contact area of colliding media and the concentration of
particles inside the mill, it was possible to calculate the number of particles in the contact area
and subsequently, the stress acting on each particle. The stress exerted on the particle, σp, was
calculated by dividing the contact stress by the number of particles in the contact area for a
specific media size, as given by Equation 4-5 and Equation 4-6. The number of particle, Np, was
77
calculated by dividing the contact area by the projected area of the particle and then multiplying
by the solids volumetric concentration of aluminum particles in the mill, c.
cR
Np
bp 2
2α= 4-5
p
bp N
σσ = 4-6
Table 4-4 gives the values for number particles in the contact area and stress acting on the
particles as a function of media size and rotational rate. It can be seen that the stress acting on the
particle decreases with increasing media size due to the larger number of particles in the contact
area. Also, the number of particles in the contact area increases with increasing rotation rate due
to the increase in contact radius, which is attributed to the milling media colliding with greater
force. The yield stress and tensile strength of aluminum are 35 MPa and 90 MPa, respectively.
However, the aluminum in this study was heavily strained, therefore, it may be more appropriate
to consider the strain hardened values of aluminum for comparison purposes. The strained
harden values of yield strength and tensile strength of aluminum are 117 MPa and 124 MPa,
respectively [31].
Using the strained hardened values and Equations 4-2 to 4-6, data was calculated and the
following results were obtained. The 0.5 mm grinding media exerts the most stress on the
material, nearly two orders of magnitude greater than the strength of the material. Such high
stress could be responsible for low amount of deformation before breakage, this result can be
seen in Figure 4-7. In the figure the maximum particle size achieved for the 0.5 mm for any
rotation rate was approximately 13 μm. It should also be noted that out of all the media size the
0.5 mm milling media result in the longest amount of time to reach the maximum amount of
deformation as can be seen by the figure, where, the 100 rpm experiment took almost 10 hrs to
78
reach the maximum particle size. This result will be explained in the next section, which will
discuss deformation rate.
Similarly, the stress of the 1.0 mm grinding media is higher than the tensile strength of
the material thus resulting in particle breakage and a minimum amount of deformation. The high
normal stress of the 1.0 mm media resulted in rapid particle breakage, which can also be seen in
Figure 4-7 and in more detail in Figure 4-1. Conversely, the 1.5 mm media exerts a stress that is
closest to the yield stress of a strain hardened aluminum material. Each compression event for
the 1.5 mm media could be considered a loading to the yield strength of the particle resulting in
finite amount of deformation. Media of this size can therefore apply the maximum amount of
deformation to the material without failure. The largest media, 2.0 mm, apply a stress to the
particle that is below the yield stress of the material and thus resulting in less deformation then
the 1.5 mm media. These results can also be seen in Figure 4-7 where the 1.5 mm results in the
most rapid deformation and the largest magnitude of deformation.
However, it can be seen in Table 4-4 that the stress acting on the particles for a specific
media size does not change significantly with rotation rate. This stability in stress values may
explain the data in Figure 4-7, which shows that the maximum deformation was not significantly
affected by rotation rate. These results are in contrast to the breakage models that state rotation
rate has a large effect on breakage. The models described above give a fundamental
interpretation of particle deformation as a function of mill parameters. However, this study has
so far neglected the influence of number frequency of media collisions on particle deformation.
The next section will discuss the effect of media size on the frequency of media collisions and
the resulting affect on deformation and deformation rate.
79
Deformation Rate
This study demonstrated that rotation rate affected the rate at which deformation was
achieved. Eskin and Kwade developed models that expressed the rate at which collisions
between grinding media take place. Kwade’s Equation 4-7, was used to determine the rate at
which media collide. In Equation 4-7, stress frequency, SF, is equal to angular velocity, ωs, times
diameter of the stirrer, Ds, divided by the diameter of the bead, Db, multiplied by milling time, T.
TDD
SFb
ss
2
⎟⎟⎠
⎞⎜⎜⎝
⎛= ω 4-7
Kwade determined the necessary stress frequency for reaching a specific material fineness. The
author found a specific fineness could be obtained by using a high stress frequency and low
kinetic energy of grinding media, or vise versa. In addition, Kwade found this relationship held
up to a point of a minimum amount of kinetic energy. Kwade considered a constant volumetric
media loading, for comparisons of stress frequency. Eskin derived a similar model, but chose to
measure the number of times a particle encounters the media. Both authors found that the
frequency was dependent on the media size and rotational rate. Table 4-5 gives the values of
stress frequency for this study as calculated using Kwade’s model. The model shows that stress
frequency increases with media size. The model also gives a linear relationship between
frequency of collisions and rotation rate. However, values in the table refer to the collision of the
media and fail to give the number of compressions the particles experiences.
The time at which the particle size begins to decrease for each experiment, was estimated
from the data in Figure 4-7, and was recorded in Table 4-6. Kwade’s model indicates that smaller
media size had the largest collision frequency, as shown in Table 4-5. When this result is coupled
with the high stress acting on the particle associated with the 0.5 mm one would expect this
experiment to approach the maximum amount of particle deformation more rapidly than the
80
larger media sizes. However, it was shown in the previous section that the 0.5 mm reached the
maximum deformation slowly. It is challenging to compare the effect of media size on the onset
of particle breakage for all the media sizes due to the complex nature of breakage. However, it is
certain that rotational rate affects particle breakage. Higher rotation rates result in a more rapid
onset of particle breakage. In addition, Kwade’s model would predict a more direct correlation
between media size and breakage, which is not the case for particle deformation as observed in
this study. In order to explain the discrepancies in these models with the experimental data it
was necessary to formulate a new model.
Therefore, in this investigation the stress frequency (Table 4-5 and Equation 4-7) was
multiplied by the number of particles in the contact area (Table 4-4 and Equation 4-5) to obtain
the total number of particles stressed as a function of milling time, Table 4-7 gives the total
number of particles stressed in 60 minutes. From Table 4-6, it can be seen that the total number
of stressing events does not change as a function of media size. However, the total number of
stressing events does change as a function of rotation rate. These results explain the increase in
the breakage as the rotation rate increases, as shown by the experimental data in Table 4-6. The
frequency model suggests that the number of collisions is only a function of rotation rate and not
of media size. This is way rotation rate only effects the time it take to achieve the maximum
amount of deformation and does not effect the actual maximum deformation achieved.
In summary, it has been found that milling media size determines the maximum amount
of particle deformation until failure. This was explained by calculating the stress acting on the
particles using Hertz’s theory. Rotational rate was found to have only a minor effect on the
maximum achievable particle size, Table 4-2. The calculation of stress acting on the particle
showed that there was a minimal amount of change in stress as a function of rotational rate. Thus
81
confirming the result that rotation rate did not have a significant effect on maximum particle
deformation. The time it took a particle to break was modeled using stress frequency. Rotation
rate was shown to affect the rate of deformation. Existing models failed to explain how rotation
rate affects particle breakage. Therefore, a new model was derived that showed rotation rate
directly influenced the number of stressing events. The models give the fundamental relationship
between media size, and rotational rate on particle deformation.
However, the models above do not predict the energy efficiency of the milling process or
give any indication on how the milling parameters affect efficiency.
Strain Energy and Milling Efficiency
Strain Energy
One of the greatest challenges in any milling operation is the measurement and calculation
of milling efficiency. It is relatively easy to measure the amount of energy input to a milling
process, however, it is very difficult to determine how the energy is utilized. Many authors have
studied the amount of energy required to break either a single particle or an ensemble, a review
of this work was given in Chapter 2 [43, 47, 75]. However, the milling process consists of
numerous breakage events and a particle will likely fracture several times before it reaches the
desired particle size. It is then difficult to determine the energy required for a particle to break to
a specific size then break again to another size. This makes calculating the energy of breakage
difficult. Generally, milling efficiency is estimated by measuring the energy input and
subtracting the energy that is expended as heat. Most mills are cooled to maintain a constant
temperature, and the heat is usually measured from the coolant. This method does not directly
establish how much of the energy went into the material itself, only the energy dissipated as heat.
Efficiency calculated from this method does not represent the milling efficiency to cause particle
breakage, thus making it difficult to optimize the milling process.
82
However, the particle deformation process is unique in that the number of particles does
not change and the energy that goes into deformation is stored in the material as strain energy.
From measurements of the amount of deformation the material experienced, it was possible to
calculate the strain of the material. From the strain, it was then possible to determine the strain
energy. The strain energy was then used to calculate milling efficiency as a function of milling
parameters.
Usually strain is directly measured by studying the change in dimensions of the object. In
this study, it is difficult to measure all the dimensions of the particles being strained. It was
shown in Chapter 3 that light scattering could be used to characterize that major dimension of the
particles. However, there is no direct method for characterizing the minimum dimension, i.e.,
thickness of the flakes. Thickness was calculated by considering there was no change in the
volume of the material up to the point where the material fails. Failure is taken to be the point at
which the mean particle size begins to decrease. Equations 4-8, 4-9, and 4-10 were used to
calculate the thickness of the flake by calculating the volume of the “as received” particles. In
Equation 4-8, Vs is the volume of the “as received” spherical aluminum particles and Dp,o is the
diameter of the “as received” aluminum particles. The volume of the “as received” sphere is
equal to the volume of the flake in Equation 4-9. The volume of the flake was calculated using
the equation for the volume of a cylinder, Vcyl (a flake is essentially a cylinder with a small
height, ie., thickness), and the diameter of the flake, Dp,f, at some sampling time; tp,f is the
thickness of the flake at the corresponding sampling time. The thickness of the flake was
calculated by equating the volume of the sphere to the volume of the flake using Equation 4-10.
3,
234
⎟⎟⎠
⎞⎜⎜⎝
⎛= op
s
DV π 4-8
83
fpfp
cyl tD
V ,
2,
2 ⎟⎟⎠
⎞⎜⎜⎝
⎛= π 4-9
2,
3,
,
2
234
⎟⎟⎠
⎞⎜⎜⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛
=fp
op
fpD
D
t
π
π 4-10
The strain, ε, was then calculated form thickness of the flake by using the true stain,
Equation 4-11. A diagram for the change of the spherical particle to a flake can be seen in Figure
4-9. The true strain was calculated for every sampling time up to the point where the particle size
decreases.
op
fp
Dt
,
,ln=ε 4-11
The work hardening equation, Equation 4-12, was used to calculate the stress. The coefficient
and exponent (K and n, 180 MPa and 0.2 respectively) for the work hardening equation were
obtained form literature for aluminum [31].
nKεσ = 4-12
Figure 4-10 is the stress-strain curves at 1000 rpm for each media sizes. The 1.5 mm media
yields the highest strain for all the experiments at 1000 rpm rotational rate. Similar behavior can
be seen in the 1500 rpm and 2000 rpm stress-strain curves, as seen in Figure 4-11 and 4-12,
respectively. The number of data points on each set of data decreases as rotational rate increases
due to the more rapid particles breaking at the high rotational rates and thus shorter milling time.
Mill Efficiency
As discussed in Chapter 2, stirred media milling processes have been estimated to operate
at energy efficiencies of less than 2%. These estimates are for particle breakage processes and
84
are generally obtained from monitoring heat generated in a mill. There is no research, which
measures the amount of energy supplied to the material. The following section will demonstrate
that milling processes do not innately operate at low energy efficiencies, and will describe
methods of improving the milling efficiency for particle deformation. This study used
measurements of particle deformation to calculate the amount of energy stored in the material.
Strain energy was obtained by integrating the stress-strain curves and dividing by the
volume (volume of the particle remains constant at this point on the stress-strain curve) of the
particles. Table 4-8 is the strain energy as a function of media size and rotation rate. It is clear
that the particles milled with the 1.5 mm grinding media have the highest strain energy. It is
important to note that nearly the same strain energies were obtained at the higher rotational rates
in a much shorter amount of time.
The total strain energy divided by the energy input to the mill is milling efficiency. The
total strain energy was obtained by multiplying the strain energy by the total number of particles
in the mill. Table 4-9 gives the total strain energy from each milling experiment. The 1.5 mm
milling media resulted in the highest strain energy values, which was due to the large amount of
deformation produced by the media. The energy input into the mill was calculated using the
equations developed in Eskin [20]. In order to determine the energy input Eskin calculated the
energy for a stirred mixing tank modeled by Nagata [76]. Equation 4-13 describes the power
input, Pw, to the mill calculated from tank geometry, mill speed, and slurry density. The terms N,
H, D, and Δ, are the rotation rate, tank height, stirrer diameter and tank diameter, respectively.
HDNMP mw 2
33
Δ= ρ 4-13
Slurry density, ρm, was calculated from the density of media, ρb, liquid density, ρL, and media
solids loading, c as shown in Equation 4-14.
85
( )cc Lbm −+= 1ρρρ 4-14
M is a coefficient calculated using Equations 4-15 through 4-20. In Equation 4-15, Re is the
Reynolds number for the tank, which is calculated by Equation 4-16. The coefficients A, B, and
exponent h, are empirically determined constants [76].
h
BAM ⎟⎟⎠
⎞⎜⎜⎝
⎛++
+= 66.03
66.03
Re2.310Re2.110
Re 4-15
m
mNDμ
ρ2
Re = 4-16
In Equation 4-17, b is total stirrer diameter, and for this study b is equal to the diameter of the
stirrer multiplied by the number of stirrer, four (four stirrer arms on the agitator).
⎥⎥⎦
⎤
⎢⎢⎣
⎡+⎟
⎠⎞
⎜⎝⎛ −
ΔΔ+= 1856.067014
2DbA 4-17
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
Δ−⎟
⎠⎞
⎜⎝⎛ −
Δ−
=Db
B14.15.043.1
2
10 4-18
42
75.05.241.1 ⎟⎠⎞
⎜⎝⎛
Δ−⎟
⎠⎞
⎜⎝⎛ −
Δ−
Δ+=
bDbh 4-29
The dynamic slurry viscosity, μm, used in Equation 4-16 was calculated by Equation 4-20.
( )[ ]cccLm 20exp0019.0105.21 2 +++= μμ 4-20
Table 4-10 gives the values of the mill geometry and mill operating constants used in Equations
4-13 through 4-20. Mill power was then multiplied by the mill volume and milling time to obtain
the energy of the mill as a function of time. Equation 4-21 gives milling efficiency, η, which is
equal to total strain energy, SET, divided by mill energy, Em.
100*m
T
ESE
=η 4-21
86
The mill energy was estimated for a stirred tank, which may underestimate the true mill
energy. This is because a mill requires more power to move the high mass of milling media in
the chamber. This is not a major concern, because most milling processes can measure milling
energy directly from measurements of torque or power draw and therefore obtain a better
measurement of milling power and efficiency.
Figure 4-13 shows a plot milling efficiency versus milling time to breakage for the 0.5, 1.0,
1.5, and 2.0 mm media at 1000 rpm. At short milling times, the milling efficiency is very high
due to the rapid deformation of the material. It also can be seen that for the 1.5 mm media the
efficiency approaches 100 percent. This result is due to the method for estimating mill energy. It
was observed that the 1.5 mm milling process is much more efficient than the rest of the media
sizes, due to the more rapid and greater amount of deformation than the other media sizes. Figure
4-13 gives the efficiency for 1 hour of milling, however, the milling experiments were conducted
for 10 hours. It can be seen at 1 hour of milling that the efficiencies begin to approach the values
reported in literature of <2%. Further milling leads to an even more inefficient process. This
result would suggest that milling time is the leading cause of inefficiency. Therefore, it is
important to select parameters that will result in the most rapid deformation, such as, a high
rotation speeds.
Similar results are observed at rapid rotational rates as shown in Figures 4-14 and 4-15,
for 1500 and 2000 rpm respectively. The 1.5 mm media results in the most efficient milling
process, however it is difficult to determine from these plots whether efficiency was affected by
rotational rate. In order to understand the effect of rotational rate on mill efficiency, the results
for the 1.5 mm media was plotted in Figure 4-16 at varying rotational rates. By plotting the
milling efficiency at maximum strain, it is possible to obtain a relationship between rotational
87
rate and efficiency. Figure 4-17 is milling efficiency as a function of rotational rate. The plot
focuses on the data as it approaches particles breakage. It can be seen from the graph that the
2000 rpm speed resulted in a greater efficiency. This is due to the more rapid rate of particle
deformation. Ultimately, milling at rapid rotation rate would result in energy saving due to
increased efficiency. Rapid rotation rates would also increase time saving due to reduced
processing time. This study has shown that the benefits can be realized with no detrimental effect
to the product quality, i.e. strain. By investigating milling efficiency it was also possible to
determine the mechanisms by which energy is wasted, as discussed below.
As mentioned earlier milling processes are generally considered inefficient processes,
with efficiencies of approximately a fraction of a percent. Usually, most of the energy was
considered lost to viscous friction. This study found that milling could be a very efficient process
at short milling times, indicating that energy lost to viscous friction was grossly overestimated. It
can be assumed that the energy lost to friction is constant throughout the milling process due to
the low solids loading in the mill, and minimal change in viscosity during the milling process.
This indicates the low efficiency observed at longer milling times in this study must be due to
another mechanism. Table 4-11 shows the milling efficiency as a function of percent strain, and
table indicates that the efficiency decreases as percent strain increases. This could be explained
by the fact that it becomes increasingly difficult to cause plastic deformation in the material, due
to the increase in strain hardening with increased strain. The media contacts with the powder
results in increased elastic contacts that do not cause strain and result in a waste of energy or in
efficient milling.
In summary, this study has determined the most effective milling parameters for
maximizing particle deformation. The study demonstrated how stress acting on the particle
88
ultimately determines deformation. The strain energy stored in the material during processing
was also calculated , and the effect of milling parameters on efficiency was identified. However,
one of the goals of this study was to develop a model that predicts particle deformation based on
milling parameters. In order to achieve this goal, statistical design of experiments was used to
develop a milling model for predicting particle deformation.
Empirical Modeling of Particle Deformation through Statistical Design of Experiment
Statistical design of experiment (DOE) is a powerful tool used for, identification of
significant process parameters, development of semi-empirical models, and process optimization.
Many industries regularly employ the use of DOE in the development and implementation of
new process [77]. In Chapter 3, screening designs were used to identify the significant variables
affecting particle deformation. These designs successfully determined the effect of grinding
media loading on deformation. The results of these designs were used to plan future experiments
to study other milling parameters. The data presented in this chapter was the result of using DOE
to develop a model capable of predicting particle deformation. A central composite design
(CCD) was used for this purpose. The CCD was used to obtain the coefficients to a quadratic
model and to obtain a response surface. The surface response was used to obtain a relationship
between design variables (milling parameters) and the response variable (strain). A detailed
description of the CCD methodology can be found in Montgomery and in the design of
experiment software package Stat-Ease® [78].
Two CCD designs were used to model the milling experiments. Both designs were two-
factor designs. The first design’s data can be seen in Table 4-12. The media size for this design
was varied from 0.5 to 1.5 mm and the rotation rate was varied from 1000 to 2000 rpm.
Repetitions were used for the [0.5 mm, 1500 rpm], [1.0 mm, 1000], and [1.0 mm, 2000rpm] to
insure repeatability. The total design involved 12 experiments and the parameters modeled in this
89
study were rotation rate, media size, and the interaction between media size and rotation rate.
The analysis of variance (ANOVA) results are shown in Table 4-13. This study used a
significance level of 5 % or a confidence interval of 95 %, because this is a standard method of
determining statistical significance. It can be seen that the p-value for the model is 0.0165, which
means the model is statistically significant .When the p-value is less than 0.05 then it means the
terms in the model (media size and rotation rate) have a significant effect on the response
variable (strain). Equation 4-22 is developed based on the DOE and is in terms of coded factors.
The coded factors allow for a direct comparison of the coefficients in the equation. If the terms
were uncoded or the actual terms it would be necessary to normalize the equations by the
magnitude of the factors in order to evaluated there affects. For example, rotational rate has a
numerical value three orders greater than that of the media size 1000 rpm compared to 1.0 mm.
Which means the coefficient of the rotational rate in actual terms would need to be three orders
of magnitude less for the media and rotation rate to have a similar effect on strain.
The coefficients of the coded equation represent the significance of that factor effect on the
response, higher magnitudes of the coefficients indicate greater significance. In Equation 4-22, A
is the coefficient for rotation rate, B is the media size, and ε is the strain at failure.
22 54.0062.0067.02.012.018.2 BAABBA +−−+−=ε 4-22
From the equation, it can be seen that the media size (B) has the greatest effect on strain
and that the interaction between media size and rotation rate (A) has the smallest effect on strain.
To accurately model the mill performance it is important to model the process with respect to the
actual milling parameters.
90
Equation 4-23, models the design in terms of the mill parameters. The model was used to
predict the strain with respect to rotation rate and media size, within the framework of this design
(i.e. between 1000-2000 rpm and 0.5-1.5 mm media).
22744 18.210*48.210*70.256.310*65.738.3 BAABBA ++−−+= −−−ε 4-23
The contour plots and surface response can be seen in Figures 4-18 and 4-19, respectively.
Figure 4-20 is a plot of standard error associated with the experiments. It can be seen that the
error was low at the center points in the study but increased towards the limits. From the surface
response, Figure 4-19, a minimum strain at failure was obtained from the 1.0 mm media. The
existence of the minimum correlates with the analysis performed previously, that also showed
that 1.0 mm media resulted in the least amount of deformation. The surface response further
confirms the result that rotational rate does not significantly influence strain. This result can be
seen by the effect on strain at different rotational rates and constant media sizes. One of the
problems with this design is that extrapolation beyond the limits of the design may provide
misleading information. For example, the surface response and model indicate larger media size
will result in higher strains. However, this study has shown from empirical and theoretical data
that this does not occur. In order to develop a stronger model a second central composite design
was constructed that would investigate the effect of milling parameters on strain, beyond the
limits of the first design.
The second composite design investigated the effect of a larger media size on strain. Table
4-14 gives a list the experiments and response used in the second design. There were 11
experiments modeled in this design with repetitions of [1.0 mm, 1000 rpm], and [1.0 mm, 2000
rpm]. Table 4-15 gives the analysis of variance results for the second design. The p-value for this
design was 0.008, which means the model is statistically significant. Coded variable were used to
91
determine the significance of the milling parameters on strain. Equation 4-24 is the second
design’s model in terms of coded variables.
22 58.005.0045.018.012.085.2 BAABBA −−−+−=ε 4-24
The coefficients of the coded equation indicate the magnitude of the effect on the strain.
The rotation rate has a negative affect on strain meaning increasing rotational rate will decrease
strain. However, the media size has a greater effect than rotational rate, with a strong negative
second order effect. The second order effect of media size ultimately leads to a maximum in
strain at intermediate media sizes. The interaction term AB has a small coefficient, which means
that there is only a minor effect on strain from the combination of media size and rotational rate.
Equation 4-25 is the model for the second central composite design in actual terms. This model
can be used to predict maximum deformation within limits of the design.
22743 32.210*01.210*80.104.710*11.168.1 BAABBA −+−+−−= −−−ε 4-25
Figures 4-21 and 4-22 are the contour and surface response plots for the second model. Both
graphs indicate that an optimum amount of stress may be obtainable with grinding media of
approximately 1.6 mm. The plots also show that there is little effect on the deformation with
respect to rotational rate, which further confirms the qualitative result observed earlier in Figure
4-7. Figure 4-23 give a plot of the interaction between media size and rotational rate. If there was
a significant interaction the curves would intersect, but as they are, there is only a slight
interaction at the 1000 rpm rotation rate.
The small interaction terms seen in the first and second designs shown here strengthens the
hypothesis that stress determines the magnitude of particle deformation. This is because stress is
a function of media size and only moderately effected by rotational rate. It also strengthens the
theory that stress frequency is constant as a function of media size. The stress frequency only
92
varies as a function of rotational rate and constant as a function of media size. Both the proposed
models for stress and frequency indicate only a small interaction between the rotational rate and
media size. The standard error for the second central composite design can be seen in Figure 4-
24. In this model, the error increase at the limits of the rotation rate and at the highest media size.
In summary, design of experiments is a powerful tool for process optimization. In this
study, this experimental methodology enabled the development of models capable of predicting
particle deformation. This was proven by Equation 4-25 that relates media size and rotation rate
to strain. Design of experiments also allowed for the validation of the proposed milling theory
discussed previously by quantifying the effect and interaction of milling parameters. One more
method of validating the above results was to look at the changes in the microstructure of the
aluminum flake. If the number of dislocation is quantified as a function of milling time, it may
be possible to recalculate strain energy, which would offer another source of validation of the
milling models. However, this study only was able to perform a qualitative analysis with respect
to dislocation density as shown below.
Microstructure Analysis
The study of the microstructure and change to microstructure is an extensive part of
material science research. If the change in the number of dislocations could be characterized, it
may be possible to determine the energy per dislocation and ultimately the strain energy. An
attempt was made in this study to characterize the dislocations in the material by using
transmission electron microscopy (TEM). However, only information of crystallinity and flake
thickness were obtained, and the quantification of dislocation density was unsuccessful. It was
determined that the study of dislocation density was beyond the scope of this research.
Many of the processes that deform metallic flakes plan on the material to coldwelding to
refine the microstructure[48]. This study did not observe coldwelding taking place, and that the
93
wet milling process used in this study prevented the coldwelding of the metal powder. In order to
confirm these results transmission microscope images and diffraction patterns of the powder
before and after milling were taken. Figure 4-25 is a TEM image of an “as received” aluminum
particle and Figure 4-26 is the diffraction pattern for the particle. It can be seen from the
diffraction pattern that the aluminum particle in this study is single or nearly a single crystal.
Many more pictures would be needed to obtain a statistical representation of crystallinity,
however, the particles sampled here all gave similar results for crystallinity. Upon initial
inspection of the images, the dark regions in the image were thought to be grains; however,
Figure 4-26 shows a single crystal diffraction pattern which means they cannot be grains. The
discrete points indicate a single crystal pattern; a polycrystalline material would have filled or
nearly filled rings. Samples from the 1.5 mm, 1000 rpm milling experiments after 4 hr of milling
were sectioned and then imaged using a transmission electron microscope. The flakes in Figure
4-27 are approximately 100-200 nm thick after 4 hours of milling and this compares closely with
the estimated thickness from calculation of 200 nm. This indicates that the assumption that only
a small amount of failure has occurred and that the flakes maintain a constant volume was
correct. Figure 4-28 gives the diffraction pattern of a milled flake, which appears to be that of a
single crystal material as described above. This result confirms that coldwelding has not taken
place. If coldwelding was present the diffraction pattern of the milled flake would be
polycrystalline due to the welding of multiple particles together. It is possible to obtain
information about lattice strain and dislocation density from the TEM. However, this work was
beyond the scope of this dissertation.
Summary
This study has developed a fundamental relationship between milling parameters and
particle deformation. Through investigations of milling mechanics, it was possible to determine
94
the stress exerted on a particle as a function of rotational rate and grinding media size. The study
determined, for the first time, the frequency at which a particle was stressed during milling. It
also established a relationship between milling parameters and frequency. A novel approach was
used to calculate milling efficiency based on strain measurements and strain energy calculations.
Conformation of the frequency and stress models were obtained from statistical design of
experiment. A predictive model for particle deformation as function of milling parameters was
also developed using statistical design. Finally, TEM studies were performed that confirmed the
thickness calculations used in the strain measurements and the crystallinity of the material. The
above work is a significant step in the understanding of the deformation process during milling.
95
0
1
2
3
4
5
6
7
8
0.1 1 10 100Particle diameter (μm)
Volu
me
perc
ent (
%)
"as received" 15 minutes2 hours4 hours10 hours
Particle breakage
Particle deformation
0
1
2
3
4
5
6
7
8
0.1 1 10 100Particle diameter (μm)
Volu
me
perc
ent (
%)
"as received" 15 minutes2 hours4 hours10 hours
Particle breakage
Particle deformation
Figure 4-1. Volume percent particle size distributions for experiments using 1.0 mm grinding media at 2000 rpm. Bimodality in the particle size distribution is indicative of particle deformation and particle breakage occurring simultaneously.
96
0
1
2
3
4
5
6
7
8
9
0.1 1 10 100
Particle diameter (μm)
Volu
me
perc
ent (
%)
"as received" 15 minutes2 hours4 hours10 hours
Particle deformation
0
1
2
3
4
5
6
7
8
9
0.1 1 10 100
Particle diameter (μm)
Volu
me
perc
ent (
%)
"as received" 15 minutes2 hours4 hours10 hours
Particle deformation
Figure 4-2. Volume percent particle size distributions for the experiments with 1.5 mm grinding media at 1000 rpm, a visible shift in the particle size distribution to larger sizes is seen due to particle deformation.
97
6
8
10
12
14
16
18
0 0.5 1 1.5 2 2.5
Media SIze (mm)
Mea
n pa
rticl
e si
ze (
m)
1000 rpm1500 rpm2000 rpm
Mill Speed
6
8
10
12
14
16
18
0 0.5 1 1.5 2 2.5
Media SIze (mm)
Mea
n pa
rticl
e si
ze (
m)
1000 rpm1500 rpm2000 rpm
Mill SpeedMill Speed
Figure 4-3.Maximum mean particle size achieved for each milling experiment versus media size, the 1.5 mm milling media produced the largest amount of deformation.
98
4
6
8
10
12
14
16
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Mea
n pa
rtic
le d
iam
eter
( μm
)
0.5 mm zirconia media1.0 mm zirconia media1.5 mm zirconia media2.0 mm zirconia media
Figure 4-4. Particle deformation versus milling time at a milling speed of 1000 rpm for varying grinding media sizes.
99
0
2
4
6
8
10
12
14
16
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Mea
n pa
rtic
le d
iam
eter
( μm
)
0.5 mm zirconia media1.0 mm zirconia media1.5 mm zirconia media2.0 mm zirconia media
Figure 4-5. Particle deformation versus milling time at a milling speed of 1500 rpm for varying grinding media sizes.
100
0
2
4
6
8
10
12
14
16
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Mea
n pa
rtic
le d
iam
eter
( μm
)0.5 mm zirconia media1.0 mm zirconia media1.5 mm zirconia media2.0 mm zirconia media
Figure 4-6. Particle deformation versus milling time at a milling speed of 2000 rpm for varying grinding media sizes.
101
0
2
4
6
8
10
12
14
16
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Mea
n pa
rtic
le d
iam
eter
(μm
)
1000 rpm
1500 rpm
2000 rpm
0
2
4
6
8
10
12
14
16
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Mea
n pa
rtic
le d
iam
eter
(μm
)
1000 rpm
1500 rpm
2000 rpm
0
2
4
6
8
10
12
14
16
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Mea
n pa
rtic
le d
iam
eter
(μ
m)
1000 rpm
1500 rpm
2000 rpm0
2
4
6
8
10
12
14
16
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Mea
n pa
rtic
le d
iam
eter
(μ
m)
1000 rpm
1500 rpm
2000 rpm
a) 0.5 mm mediab) 1.0 mm media
d) 2.0 mm mediac) 1.5 mm media
0
2
4
6
8
10
12
14
16
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Mea
n pa
rtic
le d
iam
eter
(μm
)
1000 rpm
1500 rpm
2000 rpm
0
2
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6
8
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16
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Mea
n pa
rtic
le d
iam
eter
(μm
)
1000 rpm
1500 rpm
2000 rpm
0
2
4
6
8
10
12
14
16
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Mea
n pa
rtic
le d
iam
eter
(μ
m)
1000 rpm
1500 rpm
2000 rpm0
2
4
6
8
10
12
14
16
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Mea
n pa
rtic
le d
iam
eter
(μ
m)
1000 rpm
1500 rpm
2000 rpm
a) 0.5 mm mediab) 1.0 mm media
d) 2.0 mm mediac) 1.5 mm media
Figure 4-7. Mean particle size versus milling time as a function of rotation rate, a) 0.5 mm grinding media, b) 1.0 mm grinding media, c) 1.5 mm grinding media, and d) 2.0 grinding media.
Table 4-1. Calculated stress intensity for experiments performed in this study. The table indicates that it is possible to achieve equivalent energies and different milling conditions.
Table 4-2. Maximum mean particle size of milling experiments. Even though the kinetic energy of some of the milling experiments are equivalent the maximum particles sizes differ.
Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 3 21 69 1601500 6 46 160 3702000 10 82 280 660
Stress intensity *10^-5 (joule)
Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 11 11.0 +/- 0.6 16 121500 13.0 +/- 0.3 9 15 122000 11 9.4 +/- 0.8 14 11
Maximum mean particle diameter at failure (μm)
102
Fb
Fb
bα
Rb
Aluminum particles
Media
Media
Fb
Fb
bα
Rb
Aluminum particles
Media
Media
Figure 4-8. Contact between colliding elastic spheres. Aluminum particles are caught in the contact area between the media.
103
Table 4-3. Force, radius of contact area, and stress acting on the milling media as a function of media size and rotation rate (calculated using Hertz theory).
Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 3.5 14 32 561500 5.7 23 52 922000 8.1 32 73 130
Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 1.4 2.9 4.3 5.71500 1.7 3.4 5.0 6.72000 1.9 3.8 5.7 7.5
Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 8300 8300 8300 83001500 9700 9700 9700 97002000 11000 11000 11000 11000
Force of milling media (N)
Radius of contact area of milling media *10^-5 (m)
Stress acting on milling media (MPa)
Table 4-4. Number of particles stressed in a single collision between grinding media and the
stress exerted on an individual particles.
Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 7 30 67 1191500 10 41 92 1642000 13 52 116 206
Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 1115 279 124 701500 948 237 105 592000 845 211 94 53
Stress acting on an individual particle (MPa)
Number of 4.2 μm diameter "as received" aluminum particles in contact area
Table 4-5. Stress frequency as calculated from Kwade’s model. The frequency is the number of
times milling media collide with each other.
Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 54 14 6 31500 81 20 9 52000 110 27 12 7
Stress frequency (Hz) *10^8 in 60 minutes of milling
104
Table 4-6. The time required to reach the maximum particle diameter. As milling speed increases the time it takes to obtain the maximum particle diameter decreases.
Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 36000 14400 36000 280001500 14400 1800 14400 54002000 14400 3600 3600 2700
Milling time at breakage (second)
Table 4-7. Total number of particle compressions in 60 minutes, as calculated using stress frequency and number of particles, Equation 4-2 and 4-6.
Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 4 4 4 41500 8 8 8 82000 14 14 14 14
Number of particle compressions in 60 minutes *10^10 (Hz)
Dp,0
Dp,f
tp,f
Dp,0
Dp,f
tp,f
Figure 4-9. Diagram of the change in dimensions of particle and the measurements used to calculate stress and strain.
105
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
0.5 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
1.5 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
1.0 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
2.0 mm media
a)
c) d)
b)
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
0.5 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
1.5 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
1.0 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
2.0 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
0.5 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
1.5 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
1.0 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
2.0 mm media
a)
c) d)
b)
Figure 4-10. Stress-strain behavior for experiments performed at 1000 rpm a) 0.5 mm media, b) 1.0 mm media, c) 1.5 mm media, and d) 2.0 mm media.
106
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
1.5 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
2.0 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
0.5 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
1.0 mm media
a)
c) d)
b)
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
1.5 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
2.0 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
0.5 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
1.0 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
1.5 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
2.0 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
0.5 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
1.0 mm media
a)
c) d)
b)
Figure 4-11. Stress-strain behavior for experiments performed at 1500 rpm a) 0.5 mm media, b) 1.0 mm media, c) 1.5 mm media, and d) 2.0 mm media.
107
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
2.0 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
1.0 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
1.5 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
0.5 mm media
a)
c) d)
b)
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
2.0 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
1.0 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
1.5 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
0.5 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
2.0 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
1.0 mm media
0
50
100
150
200
250
0 1 2 3
Strain
Stre
ss (M
Pa)
1.5 mm media
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5
Strain
Stre
ss (M
Pa)
0.5 mm media
a)
c) d)
b)
Figure 4-12. Stress-strain behavior for experiments performed at 2000 rpm a) 0.5 mm media, b) 1.0 mm media, c) 1.5 mm media, and d) 2.0 mm media.
Table 4-8. Strain energy per particle for deformation study.
Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 1.6 1.5 2.2 1.71500 1.9 1.3 2.1 1.82000 1.6 1.2 2 1.7
Strain energy per particle *10^-8 (joule)
108
Table 4-9. Total strain energy for deformation study. The 1.5 mm media milling experiments resulted in the largest amount of stain energy.
Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 3900 3700 5300 42001500 4400 3100 5000 43002000 3800 2970 4700 4000
Total strain energy for each milling experiment (joule)
Table 4-10. List of constants for equations used to calculate milling power
0.533
0.00286 kg/(m*s)
0.028 m
785 kg/m^3
6000 kg/m^3
0.09 m
0.06 m
0.05 m
1000, 1500, 2000 rpm
ValuesConstants
0.533
0.00286 kg/(m*s)
0.028 m
785 kg/m^3
6000 kg/m^3
0.09 m
0.06 m
1000, 1500, 2000 rpm
ValuesConstants
c
b
DHN
L
L
b
μ
ρ
ρ
Δ
109
0
20
40
60
80
100
120
0 500 1000 1500 2000
Milling time (sec)
Milli
ng e
ffici
ency
, η (%
)
0.5 mm media, 1000 rpm1.0 mm media, 1000 rpm1.5 mm media, 1000 rpm2.0 mm media, 1000 rpm
Figure 4-13. A plot of milling efficiency as a function of milling time at 1000 rpm, for all media sizes.
110
0
5
10
15
20
25
30
35
40
0 500 1000 1500 2000
Milling time (sec)
Milli
ng e
ffici
ency
, η (%
)
0.5 mm media, 1500 rpm1.0 mm media, 1500 rpm1.5 mm media, 1500 rpm2.0 mm media, 1500 rpm
Figure 4-14. A plot of milling efficiency as a function of milling time at 1500 rpm, for all media sizes.
111
0
5
10
15
20
25
0 500 1000 1500 2000
Milling time (sec)
Milli
ng e
ffici
ency
, η (%
)
0.5 mm media, 2000 rpm1.0 mm media, 2000 rpm1.5 mm media, 2000 rpm2.0 mm media, 2000 rpm
Figure 4-15. A plot of milling efficiency as a function of milling time at 2000 rpm, for all media sizes.
112
0
10
20
30
40
50
60
70
80
90
100
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Milli
ng e
ffici
ency
, η (
%) 1.5 mm media, 2000 rpm
1.5 mm media, 1500 rpm
1.5 mm media, 1000 rpm
Efficiency at failure
0
10
20
30
40
50
60
70
80
90
100
0 5000 10000 15000 20000 25000 30000 35000 40000
Milling time (sec)
Milli
ng e
ffici
ency
, η (
%) 1.5 mm media, 2000 rpm
1.5 mm media, 1500 rpm
1.5 mm media, 1000 rpm
Efficiency at failure
Figure 4-16. A plot of milling efficiency as a function of milling time for the 1.5 mm at varying rotational rates.
113
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1000 10000 100000
Milling time (sec)
Milli
ng e
ffici
ency
, η (
%)
1.5 mm media, 2000 rpm
1.5 mm media, 1500 rpm
1.5 mm media, 1000 rpm
Figure 4-17.A plot of milling efficiency at failure, right side of Figure 4-13 used for comparison of efficiencies as a function of rotational rate.
Table 4-11.Milling efficiency as a function of percent amount of strain the material has experienced at 1000 rpm and varying media size. The 1.5 mm media reaches over 60 % of the maximum strain while milling at 37% efficiency. The last few percent of the maximum strain result in the most inefficient milling.
Percent of total strain Mill efficiency Percent of total strain Mill efficiency Percent of total strain Mill efficiency23 8 37 14 64 3750 2 57 9 76 1769 0.8 76 3 83 491 0.4 92 1 91 2
0.5 mm media 1.0 mm media 1.5 mm media
114
Table 4-12. Experimental design for central composite design 1. Factor 1 Factor 2 Response
Run A: Rotation rate (rpm) B: Media size (mm) Strain at failure
1 1500 1.5 2.89
2 1000 1 2.41
3 2000 1.5 2.72
4 1500 1 1.95
5 1000 1 2.26
6 1500 0.5 2.70
7 2000 0.5 2.31
8 2000 1 2.17
9 2000 1 1.88
10 1000 1.5 3.04
11 1000 0.5 2.36
12 1500 0.5 2.63
Table 4-13. Analysis of variance for the central composite design 1 described in Table 4-12. Sum of Degrees of Mean F p-value
Source Squares Freedom Square Value Prob>F
Model 1.222 5 0.244 7.141 0.0165
A: Rotation rate 0.123 1 0.123 3.579 0.1074
B: Media Size 0.261 1 0.261 7.613 0.0329
AB 0.018 1 0.018 0.532 0.4931
A^2 0.009 1 0.009 0.276 0.6182
B^2 0.812 1 0.812 23.715 0.0028
115
1000 1250 1500 1750 2000
0.50
0.75
1.00
1.25
1.50Strain at failure
2.17
2.34
2.34
2.52
2.52
2.702.88
Rotation rate (rpm)
Med
ia si
ze (m
m)
1000 1250 1500 1750 2000
0.50
0.75
1.00
1.25
1.50Strain at failure
2.17
2.34
2.34
2.52
2.52
2.702.88
Rotation rate (rpm)
Med
ia si
ze (m
m)
Figure 4-18.Contour plot for central composite design 1, a minimum strain of 2.17 can be seen at approximately 0.9 mm milling media.
116
1000 1250
1500 1750
2000
0.50
0.75
1.00
1.25
1.50
1.9
2.2
2.5
2.8
3.1
A: Rotation rate
a size Media size (mm)
Rotation rate (rpm)
Stra
in a
t fai
lure
1000 1250
1500 1750
2000
0.50
0.75
1.00
1.25
1.50
1.9
2.2
2.5
2.8
3.1
A: Rotation rate
a size Media size (mm)
Rotation rate (rpm)
Stra
in a
t fai
lure
Figure 4-19. Surface response for central composite design 1, a trough exists at the 1.0 mm media size.
117
1000 1250
1500 1750
2000
0.50
0.75
1.00
1.25
1.50
0.094
0.11075
0.1275
0.14425
0.161
Media size Media size (mm)
Rotation rate (rpm)
Stan
dard
err
or (u
nits
of s
train
)
1000 1250
1500 1750
2000
0.50
0.75
1.00
1.25
1.50
0.094
0.11075
0.1275
0.14425
0.161
Media size Media size (mm)
Rotation rate (rpm)
Stan
dard
err
or (u
nits
of s
train
)
Figure 4-20. Standard error associated with central composite design 1, error increases at the limits of the study.
118
Table 4-14. Experimental design for central composite design 2. Factor 1 Factor 2 Response
Run A: Rotation rate (rpm) B: Media size (mm) Strain at failure
1 1000 1 2.41
2 1000 1 2.26
3 1500 1.5 2.98
4 1500 2 2.55
5 2000 2 2.39
6 2000 1.5 2.72
7 1000 2 2.50
8 1500 1 1.95
9 2000 1 1.88
10 2000 1 2.17
11 1000 1.5 3.04
Table 4-15. Analysis of variance for the central composite design 2 described in Table 4-10. Sum of Degrees of Mean F p-value
Source Squares Freedom Square Value Prob>F
Model 1.216 5 0.243 11.921 0.008
A: Rotation rate 0.106 1 0.106 5.175 0.072
B: Media Size 0.230 1 0.230 11.254 0.020
AB 0.011 1 0.011 0.546 0.493
A^2 0.005 1 0.005 0.265 0.629
B^2 0.717 1 0.717 35.129 0.002
119
1000 1250 1500 1750 2000
1.00
1.25
1.50
1.75
2.00Strain at failure
2.152.33
2.50
2.50
2.68
2.68
2.85
Med
ia s
ize
(mm
)
Rotation rate (rpm)
1000 1250 1500 1750 2000
1.00
1.25
1.50
1.75
2.00Strain at failure
2.152.33
2.50
2.50
2.68
2.68
2.85
Med
ia s
ize
(mm
)
Rotation rate (rpm)
Figure 4-21. Contour plot for central composite design 2, shows a maximum at approximately the 1.6 mm media.
120
1000 1250
1500 1750
2000
1.00 1.25
1.50 1.75
2.00
1.9
2.2
2.5
2.8
3.1
A: Rotation rat B: Media size Media size (mm) Rotation rate (rpm)
Stra
in
1000 1250
1500 1750
2000
1.00 1.25
1.50 1.75
2.00
1.9
2.2
2.5
2.8
3.1
A: Rotation rat B: Media size Media size (mm) Rotation rate (rpm)
Stra
in
Figure 4-22. Surface response for central composite design 2, a peak can be seen at intermediate media size.
121
B: Media size
1000 1250 1500 1750 2000
Interaction
1.70
2.05
2.40
2.75
3.10
Rotation rate (rpm)
Stra
in a
t fai
lure
2.0 mm milling media1.0 mm milling media
B: Media size
1000 1250 1500 1750 2000
Interaction
1.70
2.05
2.40
2.75
3.10B: Media size
1000 1250 1500 1750 2000
Interaction
1.70
2.05
2.40
2.75
3.10
Rotation rate (rpm)
Stra
in a
t fai
lure
2.0 mm milling media1.0 mm milling media
Figure 4-23. A plot of the interaction between the media size and rotation rate, it can be seen that there is only a slight interaction at low.
122
1000
1250
1500
1750
2000
1.00
1.25
1.50
1.75
2.00
0.073
0.08675
0.1005
0.11425
0.128
A: Rotation rate B: Media size Media size (mm) Rotation rate (rpm)
Stan
dard
err
or (u
nits
of s
train
)
1000
1250
1500
1750
2000
1.00
1.25
1.50
1.75
2.00
0.073
0.08675
0.1005
0.11425
0.128
A: Rotation rate B: Media size Media size (mm) Rotation rate (rpm)
Stan
dard
err
or (u
nits
of s
train
)
Figure 4-24. Standard error associated with central composite design 2.
123
Figure 4-25. Transmission electron microscope image of “as received” aluminum particle.
124
Figure 4-26. Diffraction pattern obtained from particle in Figure 4-20.
125
Figure 4-27. Transmission electron microscope image of sectioned flake after 4 hours of milling.
126
Figure 4-28. Single crystalline diffraction pattern of sectioned flake after 4 hour sof milling.
127
CHAPTER 5 CASE STUDY: MATERIAL SELECTION AND DEVELOPMENT FOR INFRARED
OBSCURANTS
Introduction
U.S. Army has used obscurant smokes and clouds as a defense against spectral targeting
for many years. Recent advancements in technology have led to communication and detection
systems functioning in the infrared and microwave region of the electromagnetic spectrum and
new obscurant materials are needed to meet these wavelengths. According to
“globalsecurity.org”, virtually all nations have access to sensors and guided munitions utilizing
the infrared portion of the electromagnetic spectrum. The widespread availability of these
devices has led the United States Military to search for the best countermeasures to mitigate their
effectiveness.
Janon Embury measured the mass extinction coefficients of many materials and later
theoretically calculated the extinction coefficients for materials depending on their shape and
size [7, 8, 79-82]. The calculations indicated that electrically conductive high aspect ratio
particles with the minor dimension in the nanometer size range and the major dimension of about
1/3rd the wavelength of light would exhibit many fold improvement over the materials currently
available. The method of choice for this purpose is to disperse fine metal flakes or rods into the
atmosphere between friendly forces and the enemy. With higher obscuration efficiency, less material
will be required, thus reducing the weight or volume of obscurant munitions carried by soldiers
or combat vehicles. Attenuation by a particulate cloud follows Beer-Lambert law, Equation 5-1,
where Io and I are incident and attenuated light intensities, α is the extinction coefficient, C is the
concentration of the particles in the light path of length L.
128
lno
I C LI α⎛ ⎞ = − ⋅ ⋅⎜ ⎟⎝ ⎠
5-1
In Equation 5-1, α is dependant on size and optical properties of the particles and its units may
be expressed on either mass or volume basis with the use of corresponding concentration and
path length units.
The goal of this study was to obtain a four fold improvement over the existing IR
obscurant material. In order to achieve this goal the army uses Equation 5-2 to gauge the
performance of the obscurant.
Figure of Merit = FoM = Y Pα ρ⋅ ⋅ ⋅ 5-2
In Equation 5-2, α is the extinction coefficient on the mass basis, ρ is the material density, Y is
the yield factor that is a measure of the ease of a material to be disseminated and is the ratio of
the mass of particulates successfully disseminated and the total mass of the material in a grenade.
The factor P is the packing factor that measures the mass fraction of material in the fill volume.
From these terms it can be seen that the figure of merit is a function of the type of material,
material properties, loading of the grenade and dissemination of the powder in the grenade. The
Particle Engineering Research Center applied a systems approach to achieve this goal by
improving every factor in the figure of merit equation (FOM). However, this study will only
focus on the selection and development of obscurant materials, for example, thinner flakes will
be used that will increase the area of coverage at a cost of less material. The other aspects of the
FOM equation can be found in a thesis by Tedeschi [64].
Development of New Obscurant Materials
In order to achieve the improvement goal, the FOM has to increase four fold. The right
hand terms in the Equation 5-2 are not mutually exclusive. First, the α is dependant on the
material. Higher α values are achieved by using high aspect ratio and electrically conductive
129
particles. Based on previous work, metal flakes and rods were expected to be ideal candidates [7,
8, 79-82]. The best shape and size of materials are flakes and rods with a major dimension
greater then 3 μm and a minimum dimension of less than 100nm and lower the better. These
high aspect ratio materials (major/minor dimension) are difficult to manufacture. The cost of the
material and processing into desired shape and dimensions must be minimized to reduce the
overall cost of the grenade. Metal nanorods with these dimensional requirements are difficult and
expensive to produce. Entanglement of fibers also results in poor dispersion and dissemination.
On the other hand, flakes nearing these dimensions have been manufactured in large quantities
for decades by milling. Metal ductility plays a significant roll in the aspect ratio of the flake that
can be produced. It is possible to obtain a higher aspect ratio with softer materials, which means
that softer materials can be made thinner, thus increasing the aspect ratio. Higher density
materials have been shown to have greater dissemination efficiencies, resulting in higher
performance. It was possible then to construct a chart of relevant material properties (ductility,
electrical conductivity, and density) to aid in the selection of candidate materials.
The relative magnitudes of density, ductility, and conductivity for several materials can be
seen in Figure 5-1. Theoretically, a material with high values in each of these areas would be and
ideal infrared obscurant. The figure shows that one such material is copper, which has a high
ductility, conductivity and density. Another possible candidate would be silver; however, silver
is a precious metal and is expensive. Aluminum is also a good candidate with respect to
conductivity and ductility; however, its low density will hurt its overall performance on a volume
basis. It is also possible to use alloys of some of these materials to increase performance.
As shown above the data presented in Figure 5-1 is a useful tool for selecting possible
materials, however, density, ductility, and conductivity are not the only material properties that
130
are important to material selection. As mentioned earlier, cost of the raw and processed material
is also important. Aluminum has been found to be pyrophoric, which means that it is possible to
ignite the aluminum powder. Copper powder does not form a passivation later, which means it
will eventually oxidize to copper oxide which will reduce its conductivity. There are also
environmental concerns for all the materials. Additional work in coating the material also being
performed in this project, however, this work is beyond the scope of this specific study.
Several materials were selected for processing from Figure 5-1. A comparison of the
experimentally measured performance of different materials is shown in Figure 5-2. This figure
shows that copper gives the highest performance followed by silver-coated copper and
aluminum. The reason for the high performance of copper is due to its high ductility, high
density and high conductivity. The performance of aluminum is relatively low because of its low
density (roughly a third that of copper). Even though tin has a high ductility and high density, it
has a low performance due to it low electrical conductivity.
A wet stirred media milling process was used to produce high aspect ratio flakes from the
raw material. This is the same process that was the focus of this dissertation, however, it was
found that milling just beyond the point of particle breakage gave the best obscurant material,
this result will be discussed later in this chapter. The milling equipment and procedures for this
study are the same that were used in the dissertation work with the exception that most of the
experiments in the case study involved longer milling times. Several of the characterization
techniques discussed in Chapter 3 were developed specifically for the measurements of the
figure of merit of the materials. However, the next section will give a brief review of these
techniques and how they were used to calculate FOM.
131
Material Characterization and Obscurant Performance Measurement Method
Particle size characterization was performed on the samples using the Coulter LS Model
13320 laser diffraction particle sizer. The specific surface area measurements are obtained from a
Quantachrome NOVA 1200 gas sorption instrument. Images of the particles were taken using a
JEOL 6330 field emission scanning electron microscope.
The FOM values were calculated from transmission data obtained from the FTIR using a
dual pass transmission (DPT) cell and from measurement of the amount of material per area. In
this measurement the powder was dispersed onto DPT slides and the transmission of IR light
through the slide was measured in a reflection mode. By this method the degree of dispersion
and material performance could be evaluated. The amount of powder used was within the
measurement error of lab balance so for a higher degree of accuracy Inductively Coupled Plasma
Spectroscopy (ICP) was used and is described in detail below. This allowed the accurate
measurement of masses well below those seen for these experiments. The material performance
was determined based on the material FOM, or the improvement of the new materials compared
to a standard material (brass flakes) supplied by the US Army.
The standard procedure used for FOM measurements is as follows. The dry powders were
dispersed in a Galai® vacuum dispersion chamber onto a glass microscope slide and a DPT
slide. The powder was allowed to settle for forty five minutes after which the DPT slide was
placed in the FTIR for measurement. The glass microscope slide was placed in a Nalgene®
bottle with a 1M HCL acid solution to dissolve the metal in order to accurately measure the
concentration using the ICP. Mass was calculated by measuring the concentration of Al in
solution, and normalized by the area of the glass slide.
The Perkin-Elmer Plasma 3200 Inductively Coupled Plasma Spectroscopy (ICP) system is
equipped with two monochromators covering the spectral range of 165-785 nm with a grated
132
ruling of 3600 lines/mm. The ICP operates on the principle of atomic emission by atoms ionized
in the argon plasma. Light of specific wavelengths is emitted as electrons return to the ground
state of the ionized elements, quantitatively identifying the species present. The system is
capable of analyzing materials in both organic and aqueous matrices with a detection limit range
of less than one part per million. This detection limit is well below the concentrations used in
these experiments and therefore allowed accurate measurement of the material mass
disseminated.
Production of Infrared Obscurant
In this project several metallic materials were measured, their FOM was compared with the
current obscurant material brass which has a FOM of 1. This study evolved over a several years,
the first material chosen to work with was the current brass material. Further milling was used to
improve the current material. The starting material was brass flake obtained from US Bronze.
The flake was produced by dry ball milling with the addition of stearic acid to prevent oxidation.
The stearic acid coating also aids in the dispersion of the brass by making the brass surface
hydrophobic.
A screening design of experiment (DOE) was followed to determine the effects of media
loading and rotational rate on the massed based FOM of brass. The milling media used in all
experiments was high-density yttria stabilized zirconia with a mean particle size of 500 microns.
The rotational rate was varied from 700, 2000, and 3300 rpm. The experimental parameters for
this study can be found in Table 5-1.
The results of the initial screening design can be seen in Figure 5-3. It was determined that
rotational rate had very little effect on FOM value and showed that as media loading increased
FOM increased. It should be noted that the effect of rotational rate on FOM is similar to that
observed in the theoretical study of deformation of aluminum. An increase of 25% in the FOM
133
was obtained from the screening design. The DOE determined that larger media loading
increased the FOM. Using the information obtained form the DOE, Figure 5-4 gives FOM for
the “as received” material, and that milled with a media volume of 480 ml of milling media. It
can be seen in Figure 5-4 that a much larger FOM is obtained when the media volume was
increased. However, it can also be seen that at high wavelengths the FOM value for high media
loading decreases more rapidly. The decrease at high wavelengths is due to the reduction in
particle size form milling. When the particle sizes become less than 1/3 the size of that
wavelength no longer scatters light at the wavelength [7, 8]. This design enabled future
experiments to set the media loading at a high concentration.
The second design used in this study was a full factorial (22) design; this involves choosing
two factors (rotational rate and media size) and two levels per factor for a total of 4 experiments.
Table 5-2 is a list of the milling parameters used in the 22 statistical design. The media loading in
this experiment was fixed at 300 ml, which is the maximum capacity of the mill. This design
measured responses of FOM and particle size at milling times of 6,12, 18, and 24 hrs. The
surface response of figure merit versus the design factors can be seen in Figure 5-5. At
increasing media sizes the figure merit increased. It was determined that the 1.5 mm media
resulted in the highest figure of merit. The increase in the FOM is due to the increased
deformation of particles.
It is important to note that particle sizes roughly 1/3 the wavelength of IR light do not
effectively scatter light at that wavelength [8]. Particle breakage in the mill can reduce the
effectiveness of the material at longer wavelengths. Figure 5-6 gives the effect of milling time on
the particle size distribution of brass. As received brass has a mean particle size of 10 μm with a
nearly normal distribution and as milling time increases the particle size decreases. The particle
134
size distribution becomes bi-modal, which is indicative of a breakage mechanism. After 24 hr the
mean particle size was approximately 2.3 μm. This means that the flakes should no longer
effectively scatter light above 7 μm. Figure 5-7 is a plot of FOM versus wavelength at varying
milling times. As milling time increased the FOM increased, this is due to increase in particle
deformation. At a milling time of 18 hrs the FOM begins to decrease at the higher wavelengths,
due to particle breakage, the affect of particle breakage on the decrease in more dramatic at 24
hrs of milling time. At 24 hrs the particle size is 2.3 μm and the wavelength where the FOM
begins to decrease is 7 μm, this agrees with the calculations made by Embury. The combination
of these designs and the theoretical studies established a basis for empirically relating milling
parameters to FOM. The designs determined that high media loadings and that the 1.5 mm
grinding media resulted in the highest performing flake. Rotation rate was found to have only a
minimal affect on FOM. These results correlate with the theoretical study of particle
deformation.
Media density was not investigated in the study of deformation of aluminum particles,
however, density is a component of all the models. Theoretically media density should affect the
stress acting on the particle and in turn affect particle deformation. Experiments were performed
to mill copper with stainless steel, zirconia, and tungsten carbide grinding media (densities of
9.8, 6.0, and 16 g/cc, respectively), Figure 5-8 gives these results. Tungsten carbide media
results in the largest amount of deformation before breakage, followed by stainless steel, and
zirconia. That indicates the highest density media, tungsten carbide density (16 g/cc), performed
the best and, zirconia, the lowest density media (6 g/cc) was the worse.
135
Summary
The above studies proved that is possible to improve the obscuration properties of existing
materials and to produce new and improved obscurants by stirred media milling. It was found
that high aspect ratio flakes could be produced by milling soft metals, that the softer the metal
the thinner the flake that could be produced. A relationship based on fundamental material
properties was derived for selecting materials that would produce the best infrared obscurant.
The relationship suggested that copper, aluminum, and silver would yield the best flakes from
milling. The study found that larger media produced a larger thinner flake; the results indicate
that the smaller media fractured the materials causing the materials to have a lower aspect ratio
that was detrimental to their performance. Denser media yield higher aspect ratio in shorter
milling time. The shorter milling times would ultimately result in economic saving if the process
was scaled up. Milling speed did not appear to have any effect on the quality of the product;
however, greater rotational rate resulted in much faster deformation. Greater rotational rates
would result in energy and time saving if the process was scaled up. During this study particle
size was closely monitor by sample from the milling during the experiments. All the experiments
showed and initial increase in the particle size at short milling times due to deformation followed
by a decrease due to particle breakage. This study found that a final optimum particle size of
approximately 5 μm yielded the highest performing obscurant.
136
Iron
Tita
nium
Tung
sten
Zinc Ti
n
Bra
ss
Al-B
ronz
e
Alu
min
um
Cop
per
Silv
er
Densi t y ( g/ cc)
Conduct i vi t y *10^-7 ( ohm-cm)
Duct i l i t y ( %)
0
10
20
30
40
50
60Density (g/cc) Conductivity *10 -̂7 (ohm-cm) Ductility (%)
Figure 5-1.A chart of relevant material properties of materials for use as an infrared obscurant.
High values in each property are preferred for candidate materials.
137
Figure 5-2. The performance of various milled metals, the copper has the highest performance to
due to the properties being the highest in all the desired area.
Table 5-1. Experimental parameters used in the statistical design of experiment used to
determine milling parameters.
Experiment Media volume (ml) Rotation rate (rpm)1 0 20002 40 7003 40 3300
4a 60 20004b 60 20004c 60 20005 120 7006 120 33007 160 2000
138
Rotation rate (rpm)Media volume (ml)
Figu
reof
Mer
it
Rotation rate (rpm)Media volume (ml)
Figu
reof
Mer
it
Figure 5-3. The results of the initial design of experiment, indicating that higher media loading
increase the performance of the material.
139
0.7
0.9
1.1
1.3
1.5
1.7
1.9
3 5 8 10 13 15wavelength (um)
Figu
re o
f Mer
it
Brass As ReceivedRun 8 (480ml/700rpm)As received brassMedia volume of 480 ml
0.7
0.9
1.1
1.3
1.5
1.7
1.9
3 5 8 10 13 15wavelength (um)
Figu
re o
f Mer
it
Brass As ReceivedRun 8 (480ml/700rpm)As received brassMedia volume of 480 ml
Figure 5-4. Plot of FOM for as received and ground brass at specific milling condition of 480ml
media volume and 700 rpm rotational speed
Table 5-2. Experimental parameters used in the full 2 factorial (22) statistical design of
experiment. Experiment Media size (mm) Rotation rate (rpm)
1 0.5 5002 0.5 1500
3a 1.0 10003b 1.0 10004 1.5 5005 1.5 1000
140
1.67
2.04
2.40
2.78
3.13
500
7501000
12501500
0.50
0.75
1.00
1.25
1.50
Media size (mm)Rotation rate (rp
m)
Figu
re o
f Mer
it
1.67
2.04
2.40
2.78
3.13
500
7501000
12501500
0.50
0.75
1.00
1.25
1.50
1.67
2.04
2.40
2.78
3.13
500
7501000
12501500
0.50
0.75
1.00
1.25
1.50
Media size (mm)Rotation rate (rp
m)
Figu
re o
f Mer
it
Figure 5-5. The results of the affect of varying media size and rotation rate on the performance of
a milled brass flake.
141
0
1
2
3
4
5
6
7
8
0.1 1 10 100
Particle diameter (μm)
Volu
me
perc
ent (
%)
As Received (10.3um)6hr (7.5um)12h (5.4um)r18hr (3.4um)24hr (2.3um)
Figure 5-6. Differential volume particle size distribution at increasing milling times.
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
3 5 7 9 11 13 15
Wavelength(μm)
Mas
s ex
tinct
ion
(m^2
/g)
6hr
12hr
18hr
24hr
Figure 5-7. Figure of merit versus IR wavelength for increasing milling times.
142
0
5
10
15
20
25
30
0 5 10 15 20
Milling time (hr)
Mea
n pa
rticl
e di
amet
er ( μ
m)
Tungsten Carbide Stainless Steel Zirconia
Figure 5-8. Mean particle size as a function of milling time for different density milling media,
zirconia (6 g/cc), stainless steel (9.8 g/cc), and tungsten carbide (16 g/cc).
143
CHAPTER 6 SUMMARY, CONCLUSIONS, AND FUTURE WORK
Summary and Conclusions
The goal of the study was to develop a fundamental and predictable understanding of
particle deformation during stirred media milling. This study confirmed that particle deformation
during stirred media milling is a complex phenomenon. It is difficult to understand and predict
the interaction of milling parameters with each other and the material being processed. Novel
characterization techniques and methods were used to understand the deformation process.
Statistical analysis and design of experiments were used to interpret data, develop predictive
models, and develop screening experiments for determining the most significant milling
parameters and their effect on deformation. Relationships between milling parameters, particle
deformation, and milling efficiency were established based on the fundamental theories of
contact mechanics and mechanical behavior of materials. Finally, knowledge gained from this
study was then used to develop a material for the US Army to obscure infrared light.
In order to achieve the goals of this study a systematic approach was used to study the
process including:
• Development of characterization techniques and sample preparation methods capable of measuring high aspect ratio particles
• Determine the milling parameters that have the most significant affect on particle deformation
• Establish a relationship, based on fundamental theories between, milling parameters and particle deformation
• Calculate milling efficiency with respect to milling parameters
• Develop milling models capable of predicting particle deformation
To achieve these objectives it was necessary to develop particle sizing techniques capable
of measuring high aspect particles. The predominate characterization technique used in this study
144
to measure particle size was light scattering, which was designed for measuring spherical
particles. The results proved that light scattering was capable of measuring the major dimension
of high aspect ratio particles.
The case study required the ability to measure the capability of metallic flakes to obscure
IR light. The measurement needed to be representative of how the metallic flakes would perform
in an aerosolized cloud in a combat environment. In order to obtain this measurement three
challenges had to be addressed:
• Obtain a dry dispersible powder • Disperse powder • Characterize the dispersed powder
A dry powder was obtained through supercritical drying. This technique involved the
exchange of the solvent (alcohol) to liquid carbon dioxide. Following the solvent exchanges, the
sample was then dried using the supercritical drying technique described in Chapter 3, this
method yielded an easily dispersible powder. The sample was then disseminated onto a dual pass
transmission slide and placed into and FTIR for characterization. These procedures allowed for a
measurement of grenade performance that closely relates to that observed in the field.
Several statistical designs of experiments were performed in this study. Preliminary
designs were used to determine which milling parameters were significant and required a more
rigorous study and which variables could be held constant. The preliminary designs determined
that a maximum media loading was important for causing the maximum amount of particle
deformation. The early designs also showed that rotation rate and media size could affect media
loading and required further investigation to determine their exact behavior. Milling studies at
varying media size and rotation rate showed that the 1.5 mm milling particles resulted in the
highest amount of deformation. Rotation rate was found to affect the rate of particle deformation
145
and had little to no influence over the maximum attainable deformation. Hertz’s theory was used
to explain the relationship between rotation rate, media size and particle deformation.
Hertz’s theory was used to determine the stress acting on the media, the theory was then
expanded to determine the stress acting on the particle by calculating the number of particles in
the contact area between colliding milling media. The data indicated that as media sizes
decreased the stress acting on the particle increased. The 1.5 mm media resulted in the highest
amount of deformation, due to the stress being close to the yield stress of the aluminum material.
The media sizes smaller than 1.5 mm caused stresses greater than the yield stress and thus
resulted in an early onset of particle breakage. Models that describe media frequency of contacts
failed to describe the rotation rate effects on deformation observed in this study. New models
were derived that demonstrated that media size had no effect on the number of times that
particles were stressed during the experiment. The new models also determined that rotation rate
effect the number of times a particle was stressed during the milling experiments. The empirical
data agreed with the results of the rotational rate models, however, further experimentation
would be required to obtain a strong validation of the rotation rate models.
The strain energy was calculated from assumptions of the conservation of volume of the
particles during deformation. For the first time it was possible to calculate milling efficiency
based on the strain energy. The study found that milling efficiency was the greatest for the 1.5
mm media and that efficiency decreased with milling time. A rotation rate of 2000 rpm resulted
in the highest efficiency at the point of particle breakage. The study also determined the reasons
for inefficiency during the milling processes. Previous studies had proposed that viscous friction
and heat generated in the milling process were the leading cause of inefficiency. This study
found that elastic collision which resulted in no deformation led to the inefficiency.
146
Statistical design of experiment was used to develop an empirical model capable of
predicting particle deformation during milling based on rotation rate and media size. The model
also validated the fundamental theories used to explain the behavior of milling parameters on
deformation. The statistical design showed that the interactions between media size and rotation
rate had a minimal effect on deformation. This result was also obtained by the fundamental
theory based on contact mechanics which showed the stress acting on the particle only varied
slightly with rotation rate. The statistical design predicted that a media size of 1.5 mm would
yield the most strain in the particle.
For the first time relationships between particle deformation and milling parameters based
on fundamental theories were established using Hertz’s theory and collision frequency. The
relationship between milling parameters and the stress acting on the particle could be used as a
scaling parameter to improve and design milling processes. Results of this investigation showed
that it was possible to predict milling efficiency, which could be directly applied to many milling
operations currently in use. The case study proved that the understanding developed in this study
could be directly applied to developing products used in real world applications.
Future Work
This study developed a knowledge base for milling processes where particle deformation is
desired. However, most milling processes involve particle breakage, a suggestion for future work
would be to determine correlation between the models developed in this study and the particle
breakage models. An example of this is that many researches have recognized the non linear
breakage rate kinetics in a milling process [83, 84]. A similar relation would exist between stress
acting on a particle and particle size as a function of milling time. As particle size decreases in a
breakage process, the number of particles in the contact area would increase, thus decreasing the
stress acting on the particle. It is also known that as particle size decrease the number of defects
147
in the particle also decreases, requiring higher stress to fracture the particle. These results could
be the reason that a so called “grinding limit” is observed in many milling process. One method
of testing the applicability of the models developed in this study to breakage processes would be
to reduce the number concentration of particles during the milling process, thus maintaining a
constant level of stress acting on the particles.
Another area of interest for future work would be to investigate the effect of media density
on particle deformation. Density has a direct effect on the stress acting on the particle, it would
be interesting to determine if the effect on deformation is as predicted by the models. One area,
which requires more study, is that of the frequency of media and particle contacts. The results
obtained in this study were not sufficient and conclusive enough to make up a significant theory.
More empirical data and short sampling intervals would be required to obtain a more robust
model capable of describing the effect of media size on frequency of particle contact.
One of the most novel aspects of this study was the ability to obtain an actual value for
milling efficiency. It is possible to test this method of measuring milling efficiency by
manipulating other milling variables such as viscosity and determine the effect on energy
utilization. It would also be interesting to further investigate the mechanisms of milling
efficiency such as the result of elastic collisions and their effect on inefficiency. Further work is
needed to construct milling models that are capable of predicting deformation of materials based
on milling parameters and material properties.
Finally, the goal of this study was to develop a fundamental understanding of particle
deformation during milling and develop a predictive model. In most respects this goal was
accomplished, however, it is important to develop a model that includes a time parameter. It may
148
also be possible to construct a model that includes a material property parameter and properties
of milling media, such as, media density, and hardness.
149
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BIOGRAPHICAL SKETCH
Rhye Garrett Hamey was born in Medina, Ohio. He attended Cloverleaf High
School. After high school he obtained a degree in chemical engineering at The Ohio State
University. While at Ohio State, Rhye attended a class on particle technology instructed
by visiting Professors Brian Scarlett and Dr. Brij Moudgil. Through continued contact
with Professor Scarlett, Rhye became interested in particle technology and chose to
pursue a graduate degree from the Department Materials Science and Engineering at the
University of Florida. He performed his study while working at the Particle Engineering
Research Center. In 2005, Rhye obtained a Master’s degree in Materials Science and
Engineering. After receiving his Master’s Rhye decided to continue his Ph.D. study under
the supervision of Dr. Hassan El-Shall.