Development and modeling of mechanical alloying for production of copper matrix composite powders reinforced with alumina and graphite Tomás Dinis Calado Seixas Thesis to obtain the Master of Science degree in Materials Engineering Supervisors: Prof. Alberto Ferro, Prof. Ricardo Baptista Examination Committee Chairperson: Prof. Maria de Fátima Reis Vaz Supervisor: Prof. Alberto Eduardo Morão Cabral Ferro Members of the Comittee: Prof. Augusto Manuel Moura Moita de Deus Dr. Marta Sofia Rosado Silva Dias December 2016
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Development and modeling of mechanical alloying for
production of copper matrix composite powders
reinforced with alumina and graphite
Tomás Dinis Calado Seixas
Thesis to obtain the Master of Science degree in
Materials Engineering
Supervisors: Prof. Alberto Ferro, Prof. Ricardo Baptista
Examination Committee
Chairperson: Prof. Maria de Fátima Reis Vaz
Supervisor: Prof. Alberto Eduardo Morão Cabral Ferro
Members of the Comittee:
Prof. Augusto Manuel Moura Moita de Deus
Dr. Marta Sofia Rosado Silva Dias
December 2016
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Resumo
Compósitos com matriz de cobre, usados para aplicações electromecânicas, são frequentemente
produzidos por moagem sinérgica (MS). Compreender a MS e a influência dos parâmetros de
moagem nas propriedades dos pós é, então, relevante. Neste trabalho, a modelação pelo método dos
elementos finitos (MEF) é usada para estudar essa influência.
Pós de cobre foram moídos durante tempos desde 10 minutos a 8 horas, num moinho planetário com
cuba e bolas de cobre. O tamanho das bolas e a presença de isopropanol foram as variáveis
analisadas. As amostras foram caracterizadas por DRX, MEV e dureza Vickers. Os pós moídos com
isopropanol, que reduz a taxa de soldadura, verificaram um mais rápido e mais significativo
decréscimo de tamanho de partícula e cristalite e mais rápidas mudanças na morfologia dos pós.
Compósitos com matriz de cobre reforçados com alumina, grafite e nanotubos de carbono, moídos
previamente durante 8 horas em cuba e com esferas de alumina, foram também caracterizados.
Recozimento destas amostras, a 900o C durante uma hora, levou a um aumento do tamanho de
cristalite mas não a uma redução de dureza.
Realizaram-se simulações pelo MEF, alterando o espaçamento entre partículas, a velocidade e o
tamanho das bolas. O espaçamento entre partículas revelou ser o factor mais significativo no
aumento da tensão e deformação nos pós.
Os resultados da análise aos pós de cobre puros e as simulações pelo MEF correlacionam-se e
podem sugerir que baixas taxas de soldadura e partículas mais separadas são o factor primordial
para uma moagem mais eficiente.
Palavras-chave: cobre; compósito; pó; moagem sinérgica; método dos elementos finitos; isopropanol
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Abstract
Copper-matrix composites, used for electromechanical applications, are often produced by
mechanical alloying (MA) in attrition mills. Understanding MA and the influence of milling parameters
on powder properties is therefore valuable. In this work, finite element method (FEM) modeling is used
as a tool to study that influence.
Pure copper powder was milled for times of 10 minutes up to 8 hours, in a in a planetary ball mill with
a copper vial and copper balls. Ball size and the presence of a process control agent, isopropyl
alcohol, were the variables analyzed. The samples were characterized by XRD, SEM and Vickers
hardness measurements. Powders milled with isopropyl alcohol, which lowers welding rates, showed
faster and more significant particle and crystallite size reduction and faster powder shape changes.
Copper-matrix composites reinforced with alumina, graphite and carbon nanotubes, previously milled
for 8 hours in an alumina vial with alumina balls, were also studied in this work. Annealing of those
samples at 900o C, in a tube furnace for one hour, lead to a significant crystallite size growth but not to
significant hardness reduction.
FEM simulations were carried out, changing spacing between particles, ball velocity and size. The
most significant factor responsible for increased stress and strain in the powders was more spacing
between particles.
Results from both pure copper milled samples and FEM simulations correlate and may suggest that
having lower welding rates and more separated particles is the overriding factor to faster particle size
Fig. 1 – Schematic representation of the evolution of particle and crystallite size with milling time. [39] 5
Fig. 2 - Types of motion in a ball mill: A) cascading; B) cataracting and C) centrifugal [41] .................. 6
Fig. 3 – SEM (SE) micrograph of the initial copper powder .................................................................. 11
Fig. 4 – Theoretical diffractogram for pure copper ................................................................................ 15
Fig. 5 – RMV of the DL balls as a function of milling time ..................................................................... 19
Fig. 6 – Photographs of the DL balls after milling. Scale bar: 16 mm. .................................................. 20
Fig. 7 – SEM-SE of DL milled copper powder. Scale bar: 100µm ........................................................ 21
Fig. 8 - Particle size (CILAS) evolution of DL powder as a function of milling time .............................. 22
Fig. 9 - Crystallite size (Scherrer equation) for DL powder as a function of milling time ...................... 22
Fig. 10 - RMV of the DS balls as a function of milling time ................................................................... 23
Fig. 11 - Photographs of the DS balls after milling. Scale bar: 8 mm. .................................................. 23
Fig. 12 - SEM-SE of DS milled copper powder. Scale bar: 100µm ....................................................... 25
Fig. 13 - Particle size (CILAS) evolution of DS powder as a function of milling time ............................ 25
Fig. 14 - Crystallite size (Scherrer equation) for DS powder as a function of milling time .................... 26
Fig. 15 - RMV of the WL balls as a function of milling time ................................................................... 26
Fig. 16 - Photographs of the WL balls after milling. Scale bar: 16 mm. ................................................ 27
Fig. 17 - SEM-SE of WL milled copper powder. Scale bar: 100µm ...................................................... 28
Fig. 18 - Particle size (CILAS) evolution of WL powder as a function of milling time............................ 29
Fig. 19 - Crystallite size (Scherrer equation) for DL powder as a function of milling time..................... 29
Fig. 20 – RMV of the WS balls as a function of milling time .................................................................. 30
Fig. 21 - Photographs of the DL balls after milling. Scale bar: 8 mm. ................................................... 30
Fig. 22 - SEM-SE of WS milled copper powder. Scale bar: 100µm ...................................................... 32
Fig. 23 - Particle size (CILAS) evolution of DL powder as a function of milling time ............................ 32
Fig. 24 - Crystallite size (Scherrer equation) for WS powder as a function of milling time ................... 33
Fig. 25- Comparison of the RMV of the balls for all systems as a function of milling time ................... 34
Fig. 26 – Comparison of particle size (CILAS) evolution of all powder systems as a function of milling
time ........................................................................................................................................................ 36
Fig. 27 - SEM-SE of 10 minutes milled copper powder. Scale bar: 50µm ............................................ 38
Fig. 28 - SEM-SE of 30 minutes milled copper powder. Scale bar: 50µm ............................................ 38
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Fig. 29 - SEM-SE of 1 hour milled copper powder. Scale bar: 50µm ................................................... 39
Fig. 30 - SEM-SE of 2 hours milled copper powder. Scale bar: 50µm .................................................. 39
Fig. 31 –SEM-SE of 4 hours milled copper powder. Scale bar: 50µm .................................................. 40
Fig. 32 - SEM-SE of 8 hours milled copper powder. Scale bar: 50µm) ................................................ 40
Fig. 33 – Comparison of crystallite size (Scherrer equation) for all powder systems as a function of
milling time. Detail a) – comparison for times under 30 min of the crystallite size for the wet systems 41
Fig. 34 – Comparison of powder microhardness (HV0.012) for all systems as a function of milling time
Fig. 37 - Powder microhardness (HV0.012) for composite powders as a function of annealing
temperature ........................................................................................................................................... 49
Fig. 38 – Assembly of the 2D FEM model, with close-up of the contact zone ...................................... 51
Fig. 39 – Scheme of the partitioned sections for the vial and milling ball ............................................. 54
Fig. 40 - Ball size comparison for the simulations ................................................................................. 56
Fig. 41 – Distance between balls comparison for the simulations ........................................................ 56
Fig. 43 – von Mises stress distribution for particle 2 of FD10L as a function of simulation time ........... 58
Fig. 42 - color legend for stress maps(Pa) ............................................................................................ 58
Fig. 44 - von Mises stress distribution for all simulation conditions at the instant of respective
maximum von Mises stress ................................................................................................................... 59
Fig. 45 - Element location in particle ..................................................................................................... 61
Fig. 46 – PEEQ as a function of simulation time for elements 1, 144 and 288 of particles of 1 and 10 of
Table 5 - Crystallite size (Scherrer equation) for composite powder systems as a function of annealing
temperature ........................................................................................................................................... 48
Table 6 – Materials parameters and properties to be introduced in Abaqus ........................................ 52
Table 7 – Evolution of maximum von Mises Stress and logarithmic deformation with element size .... 53
Table 8 - Evolution of maximum von Mises stress, logarithmic deformation and contact pressure with
element size. * - maximum von Mises stress is verified in a different particle ...................................... 55
Table 9 - Simulation identification and number of nodes ...................................................................... 57
Table 10 - maximum von Mises stress values for all simulation conditions .......................................... 60
Table 11 - Instant of maximum von Mises stress for each simulation condition ................................... 61
Table 12 – Last PEEQ values for element 1 of particle 2 for all simulation conditions ......................... 64
Table 13 - Last PEEQ values for element 144 of particle 2 for all simulation conditions ...................... 64
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Acronyms
BCP Bulk copper density
BPR Ball-to-powder ratio
CNT Carbon nanotubes
CPU Central processing unit
D Dry conditions
DEM Discrete element method
FD Full distance
FEM Finite element method
GD Green density
HD Half distance
HV Vickers hardness
iMS Instant of maximum stress
ISE indentation size effect
L Large balls
MA Mechanical alloying
MaM Total ball mass after milling
MbM Total ball mass before milling
MM Mechanical milling
MMC Metal matrix composite
ND No distance
PEEQ Plastic equivalent strain
PCA Process control agent
RD Relative density
RMV Relative mass variation in percentage
rpm Rotations per minute
S Small balls
SE Secondary electron
SEM Scanning electron microscopy
VMS Von mises stress
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W Wet conditions
WD Working distance
XRD X-ray diffraction
Symbols
β Peak broadening measured at half the maximum intensity
θ Angle between incident ray and scattering planes
In this function and those following, σ is the equivalent stress, �� is the equivalent plastic strain, ε̇ is
the strain rate and ε ̇ is the normalizing strain rate, with A, B, C and n being the empirical model
parameters.[57]
A failure criterion ( 3 ) can also be established on the basis of the same model:
�� = [ + exp ( σσ��)] [ + D ln ε̇ ε ̇⁄ ] ( 3 )
Where �� is the strain at fracture, σ is the average of the normal stresses and σ�� is the von Mises
equivalent stress, with D1, D2, D3 and D4 again being the empirical parameters determined by Johnson
and Cook. [57]
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3. Experimental method and techniques
In this section, the techniques used to produce and characterize the samples are detailed. In addition
to that, the produced samples are identified and clarifications on protocol are provided.
3.1. Ball milling
For the pure copper powders (non-composite) milled specifically for this work, a copper-copper-copper
system was defined. This means that the copper powders were milled in a copper vial with copper
media (balls).
The copper vial has a volume of 250 ml. Balls of two different sizes were used: 8 mm and 15 mm in
diameter. BPR of 20 and 2 g of copper powder were use. For smaller balls, 8 balls, of a total ball mass
of around 37.5 g, were used. For the large balls, 3 balls were enough, yielding, in this case, a total
mass of around 47.3 g. 2 g of isopropyl alcohol (C3H8O) were also introduced in the wet milling.
Each set of 8 or 3 balls was weighed, as was the powder and, for the wet millings, the alcohol. In that
same order, they were placed in the vial. For the longer time of 8 hours, an interval of 15 minutes, to
cool the mill, was set for the 4 hours mark.
After the millings performed under wet conditions, the vial was placed inside a kiln, at 80o C, until the
alcohol had evaporated. The powder was scraped off the vial walls using a plastic spatula (to avoid
scratching the vial and prevent metallic contamination). After removing the powder, the vial was
thoroughly cleaned with ethanol and allowed to dry before the next milling. For the dry millings, the
same protocol was followed with the evaporation step.
The mill used was a Retsch PH100 and the dedicated copper vial weighed 4.78 kg. The milling speed
for all runs was 400 rpm (rotations per minute).
3.1.1. Materials
Electrolytic copper powder from Merck, of dendritic particle shape (Fig. 3), was used as a starting
material. The information from the supplier guarantees particle size under 63 µm and the
contamination values are condensed in Table 1.
Fig. 3 – SEM (SE) micrograph of the initial copper powder
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Table 1 – Contaminant batch values for starting copper powder
Elements and substances Batch values (%)
Substances insoluble in nitric acid Max. 0.02
P Max. 0.001
Ag Min 0.002
As Max. 0.0005
Fe Max. 0.005
Mn Max. 0.001
Pb Min 0.01
Sb Max. 0.001
Sn Max. 0.01
Extensive information on the materials used for the production of the composites analyzed in this
work, particularly graphite and alumina, is present in reference [58].
3.1.2. Sample identification – pure copper
Millings were conducted in both dry and wet conditions, referred to respectively as dry and wet milling.
Dry millings were carried out without any lubricant or liquid agent in the vial. In wet milling, isopropyl
alcohol, with same mass as the powder (2g), was added to the batch. In addition to that, two different
ball sizes were tested - both larger balls, 15mm in diameter, and smaller balls, 8mm in diameter. The
third variable considered was the milling time: mills ran for 10 minutes, 30 minutes and 1, 2, 4 and 8
hours.
Combining these variables, a total of 24 (2 × 2 × 6) different powder samples were produced. The
identification for each sample is explained in Table 2.
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Table 2 – Pure copper powder sample denomination
Mill conditions
Dry milling (D) Wet milling (W)
Mill time Large balls (L) Small balls (S) Large balls (L) Small balls (S)
10 min DL_10min DS_10min WL_10min WS_10min
30 min DL_30min DS_30min WL_30min WS_30min
1h DL_1h DS_1h WL_1h WS_1h
2h DL_2h DS_2h WL_2h WS_2h
4h DL_4h DS_4h WL_4h WS_4h
8h DL_8h DS_8h WL_8h WS_8h
3.2. Powder compaction
Milled powder was compacted into pellets for density and hardness measurements. Due to the low
quantities, 13 mm diameter powder pellets were compacted with half the powder from each sample.
The die was lubricated with camphor between each compaction, a plastic divider was inserted as to
assure that the powders corresponding to different samples did not mix. After pouring the powder into
the die, the divider was removed and the lubricated punch inserted. The powder mass of each sample
used varied with the quantity of available powder, from 0.5 to 1 g per sample. The powders were
pressed with a nominal compression stress of 750MPa in a manual press.
3.3. Ball mass variation and pictures of the surface
The milling balls provide important insight into the milling process. The balls were photographed and
weighed after milling to determine mass variations. The information regarding the evolution of the
weight of the balls is summarized in the form or relative mass variation, in percentage, by equation ( 4
), where RMV is the relative mass variation in percentage, MbM is the total ball mass before milling
and MaM is the total ball mass after milling
� % = (� � − � �� � ) × ( 4 )
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The balls were weighed with a ±1 mg precision before and after milling. This provided information on
the mass transfer to and from the ball surface.
3.4. Density measurement of powder pellets
The pellets were divided in half with a metal punch, as to assess each sample’s density. The weight of
each half on air measured using a digital scale with a ±1 mg. The scale was then zeroed and the
sample was put in a plate inside water as to measure the weight of the displaced water. Using
equation ( 5 ), based on the Archimedes’ principle, the green density was calculated.
� � = � � × � � � ℎ� � � ℎ − �� � � � ℎ ( 5 )
3.5. X-ray diffraction (XRD)
X-ray diffraction (XRD) was been used in this work to determine crystallite size, residual strains and
lattice parameters. To calculate lattice spacing, a, equation ( 6 ), derived from Bragg’s law was used,
where , λ is wavelength of the incident radiation, θ is the angle between incident ray and scattering
planes and h, k and l are the Miller plane indices [59]. .
= √ ℎ + + × � × sin � ( 6 )
To determine strain, the Scherrer equation ( 7 ) was used, relating crystallite size (D) to the peak
broadening (β), measured as peak width at half the maximum intensity. This equation provides a lower
limit for crystallite size, since the influence of factors such as microstrain and dislocations on peak
broadening is not taken into account. It is, therefore, more valuable to analyze tendencies than
absolute values. This analysis is more precise for peaks with high intensity [59] and was therefore
applied to peak 1 in Table 3. In this equation, K is a geometric factor approximated to K = 0.9 [59]
= � �� cos � ( 7 )
The Williamson-Hall equation ( 8 ) was also used to try and determine crystallite size and microstrain
(sm). A linear extrapolation is carried out for the most intense the peaks, (1, 2 and 3 in Table 3) and the
parameters are taken from the line equation. �g � 2 = � �� �g � × i � + 6 ( 8 )
Both Scherrer and Williamson-Hall equations estimate the crystallite size, with the Williamson-Hall
approach, using several peaks yielding usually more accurate results. The Scherrer equation provides
more qualitative, yet valuable, data, especially when comparing peaks for a system and different
conditions.
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Table 3 – Peaks used for XRD analysis and calculations
Peak number Plane miller index [60]
Peak location – 2θ (o) [60]
Equations to be applied
1 (111) 43.32 Scherrer & Williamson-Hall
2 (200) 50.45 Williamson-Hall
3 (311) 89.94 Williamson-Hall
4 (222) 95.15 Williamson-Hall
5 (331) 136.51 Bragg’s law – lattice parameter
6 (420) 144.71 Bragg’s law – lattice parameter
Fig. 4 – Theoretical diffractogram for pure copper
A PANalytic X’Pert PRO diffractometer was used, with the current set at 35 mA and the voltage at 40
kV. Since high intensity peaks (lower 2θ) were necessary to determine crystallite size and microstrain
and higher 2θ peaks were needed to obtain a good estimate of the lattice parameter, the initial
diffractogram range used was from 30o to 150o. Due to the high noise of the measurements using
shorter acquisition times (1 s or 2 s), the time was increased to 8 s for a 0.04o step, which lead to an
average of 8 hours of measurement time per sample. To decrease acquisition time maintaining the
step (lower noise), three shorter intervals were defined, concerning important regions of the
diffractogram: 38o to 55o for the intense first two peaks of Cu; 85o to 100o for the fourth and fifth peaks
and 130o to 150o for the two high 2θ peaks. Due to time limitations, XRD analysis was not performed
for all powder samples. Table 3 summarizes which peaks are used for which calculations and Fig. 4 is
a theoretical diffractogram for pure copper [60].
Four out of six samples were picked for each system described in section 3.1.2, after analyzing the
SEM micrographs and estimating at which milling times the size variation would be most noticeable.
To prepare the sample for the diffractometer, powder was set on a 0 signal silicon wafer and a drop of
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acetone (CH3H6O) was used to agglomerate the powder. The silicon wafer was then immediately
stirred to spread the powder at an even height. Capillary effects maintain the powder in place.
The diffractograms were analyzed using the peak fitting software Fityk 0.9.8 and the functions were
fitted with PseudoVoigt functions (partially Gauss and partially Lorentz curves). [61]
3.6. SEM
Scanning electron microscopy was used to characterize the powder size and morphology evolution
during milling. In order to form a topographical image of the sample, secondary electron (SE) imaging
was used. [62]
SEM – Hitachi S2400 was used with working distance (WD) WD = 17 mm for loose powder samples
with a voltage of 20 kV. Micrographs were taken at defined amplifications of 200x (for loose powders),
500x and 2000x.
3.7. Particle size distribution
Particle size distribution analysis was carried out using a CILAS 1064 particle size analyzer with a
0.04 to 500 µm range and two laser diodes with wavelengths of 635 and 830 nm [63]. This equipment
uses laser diffraction to estimate particle size. The larger the particle, the smaller the angle at which
light is scattered relative to the laser beam. The scattering density is analyzed to calculate the size of
the particles, with the size being reported as a volume equivalent ball diameter. As size is evaluated
as an equivalent ball diameter, the measurements are less precise for particles far from an
axisymmetric shape. [64]
The CILAS 1064 offers the equivalent ball diameters d10, d50 and d90, which are the diameters for
which, respectively, ten, fifty and ninety percent of the particles have lower diameters. d50 is the
median.
The powder samples were prepared, mixing the powders with distilled water and a surfactant
(common detergent or Tiron) to disperse the particles. The dispersion was introduced in the CILAS
and sonicated for 90 seconds, for further dispersion, before particle size analysis.
3.8. Hardness measurement
Hardness is a measure of the local resistance of a material to plastic flow. Even though it is not a
fundamental material property, hardness values can be compared when variables such indenter
shape, load and duration are fixed.[65]
For specimens with dimensions (particularly thickness) in the order of the micrometer (tens to
hundreds) such as powders, one must resort to microhardness, applying loads in the 0.01 - 1 kgf
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range. The most commonly used indenter is the Vickers indenter [65]. Due to the size of the grains,
low loads were necessary (under 25 g) for the plastic and elastic zone of the indentation to be
completely contained inside the grain.
In this work, hardness measurements were carried out on the set powders using a SHIMADZU
Vickers microhardness indenter using loads of 12 g for 10 seconds. Vickers hardness measurements
were also carried out on the cold pressed powder pellets with a 1 kg force for 15 seconds.
3.8.1. Indentation Size effect
Vickers hardness number is mostly independent of the load until the indenter depth reaches a
minimum threshold value is material dependent. Beyond this value, indentation size effect (ISE) is
verified, usually leading to higher apparent hardness.
For the loads used (below 12 g), the indentation measured depth was always above the critical value
reported in literature for ISE to take place [66]. However, for the harder materials, the indentation
depth was close to such threshold.
While deep indentations (most microhardness measurements) fit strain gradient plasticity models,
shallow indentations (nanoindentation) result in a bilinear behavior [67]. The most common model
used to explain ISE is the Nix-Gao Model [68], which attributes the effect to a limitation of dislocation
sources. When the contact volume is not large enough, the dislocation sources activated (discrete in
nature) are insufficient to accommodate the plastic deformation, leading to a higher hardness [69].
ISE is also very susceptible to sample preparation, since changes in surface topography influence the
measured hardness. There are also rarer instances of a reverse effect, leading to lower measured
hardness [69].
3.9. Clarifications
In order to better understand the results in this work, it is important to first explain some of the
particularities and difficulties encountered. Some of these issues were understood after the
observation of the results of the analysis techniques but, to postpone the clarifications until after
presenting the results would be detrimental to the understanding of the overall conclusions of the
work.
3.9.1. Sampling challenges
Vial, balls and powder are all made of the same material, copper. Thus, welding of the powder to the
vial walls and milling balls is enhanced in some milling conditions. This means that there is a part of
the powder sample which in inaccessible after milling. The powder that is welded or mechanically
fixated to both the balls and the vial walls is not removed for analysis and therefore does not influence
the results of the analysis techniques used. Nevertheless, it is possible, by calculating the mass
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variation of the milling balls, to confirm this phenomenon and to take it into account when analyzing
the results.
3.9.2. Contamination from vial wall and milling balls
Since the vial and balls are made of copper, the same material as the powder, chemical contamination
is not an issue in this system. However, the material from the milling balls introduced into the system
at later milling stages has a different deformation history than the milled powder. Thus, the analyzed
material is a mixture of the sample intended to be produced and a powder with a different deformation
history. The prevalence of this contamination cannot be estimated through the used analytical
methods. However, study of the mass variation of the balls and of its surface enables to infer whether
there is a possibility of significant contamination in the analyzed powder material. If there is significant
mass loss from the balls and the surface shows craters, contamination may be a more prevalent
factor. The presence of this material with a different milling history may influence the results and
originate a divergence from the theoretically expected outcome.
3.9.3. Simultaneous mechanisms
During milling, deformation, fracture and welding are occurring simultaneously. The milling parameters
and history of the milling balls and powders define the dominant phenomena at a given instant.
However, due to the factors described previously (contamination and sampling) the influence of the
dominant phenomena may not be revealed by the analysis techniques. The dominant phenomena
may affect primarily the not-removed powder (which is, by definition, not analyzed) or be compensated
by contamination from the ball surface.
3.9.4. Analysis
Given the problems identified, a systematic experimental protocol was defined in order to attain more
accurate results. Firstly, the mass variation of the balls and the pictures of the milling balls are
analyzed. This initial analysis of the weight of the balls and their surface provides indications whether
the non-removed portion of the powder is significant and if there are contaminants derived from the
milling balls. Then, the SEM results are examined, to obtain information on the shape and size of the
removed powder. Next, the particle size (CILAS) is analyzed, to obtain quantitative results for the
powder size distribution. Analyzing the CILAS results in light of the SEM images provides insight on
whether the particle size analysis, in CILAS, is efficient at accounting particles of all sizes, namely
larger particles. The X-ray diffraction results are then analyzed, followed by the evaluation of the green
density and Vickers hardness
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4. Pure copper - influence of media size and
process control agents
This section reports the study on the influence of media size and process control agents (in this case,
isopropyl alcohol) on the hardness, crystallite size, particle size and morphology of pure copper
powders. This study is of particular interest as it yields experimental results in controlled conditions for
comparison and tuning of the FEM model proposed. In these millings, three variables were changed:
Milling in dry or wet (with isopropyl alcohol) conditions
Size of the milling balls
Milling time
Each system (column in Table 2), where the samples are identified) will be analyzed separately to
study the influence of milling time. An overview and comparison of all systems follows.
4.1. Dry conditions, large balls (DL)
In this section, the samples produced in dry conditions and with large balls (DL) are characterized.
4.1.1. Mass variation and ball images
Fig. 5 – RMV of the DL balls as a function of milling time
Fig. 5 shows that millings carried out with large balls in dry conditions, display small mass variation for
the times below two hours, with a negative variation of -0.13% for 1 hour. However, these variations
are small when compared with the larger trend of weight loss for longer milling times, 4 and 8 hours.
During the initial two hours of milling, the phenomena of welding onto the ball and of loss of material
from the ball surface seem to even out. For longer milling times, the greater number of ball impacts
leads to a possible work-hardening of the surface, with ensuing embrittlement, favoring loss of
material. To verify the presumed work-hardening of the ball, micro-hardness measurements with loads
of 12 g were carried out on ball cross sections. However, the lateral spatial resolution was not enough
-2
-1,5
-1
-0,5
0
0,5
-0,8
-0,6
-0,4
-0,2
0
0,2
0 1 2 3 4 5 6 7 8
Mass
variation (g) RMV(%)
Milling time (hours)
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to provide a significant hardness profile for the balls. Instead, ultramicro-hardness measurements
might be performed on the outer layer of the ball.
Photographs of the balls (Fig. 6) also show that, despite some surface modifications for early times
(up to 1 hour), only for the longer times does the surface attain a patterned rougher morphology (as is
visible in the 8 hours balls). Nevertheless, the mass variations must always be taken as a balance
between the material welded to and the material removed from the ball. This means that, even though
there is no significant gain of weight by the ball, some areas of the surface of the ball can still be
coated with welded powder.
Fig. 6 – Photographs of the DL balls after milling. Scale bar: 16 mm.
4.1.2. SEM images and particle size
Fig. 7 shows that for 10 and 30 milling minutes, there are no significant changes in the powder size
and shape, which retains its dendritic morphology. For one and two hours of milling, some few
particles appear to have suffered severe impacts, leading to great strain, taking up the visible flake
shape. Four hours mark a visible significant change in the micrographs. Powder assumes complete
flake morphology and a large size. The amount of deformation of the powders and the number and
type of collisions induce significant welding and powders with dendritic morphology are no longer
visible. With further milling, after 8 h, the large flake particles fragment. The 8 hours micrograph also
presents a tighter size distribution. This suggests that, for this system, only after four hours of milling
does the fracture mechanism begin to play a dominant role in size reduction and size distribution
narrowing.
The median particle size measured on CILAS (Fig. 8), displays a quick reduction of about 4 µm (from
60 to 56 µm) in the first hour of milling. A steady median particle size follows up to 4 h. From 4 to 8
hours, a relatively significant reduction of about 10 µm (from 55 to 45 µm) takes place. However, in the
particle size measurements using CILAS, there is no evidence of the large flakes observed in the SEM
micrograph for the 4 hours. This disparity can be attributed to some of the following causes. The large
21
flakes observed in SEM are not in enough number to move the particle size median upwards. For
every large flake there are several small flakes (visible in the SEM micrographs) and, in the CILAS
counts, the effect of the various small flakes obscures the rarer large flakes. Another possible cause is
that the ultrasound efficiency of the CILAS may not be enough to keep the particles dispersed due to
the weight of the large flakes. A non-dispersed particle is not counted by the detector and the larger
the particles, the harder to disperse. This theory is further supported by the fact that, after the first
measurements, the plastic tubes of the CILAS were somewhat covered by the copper particles. To
perform a more accurate particle size measurement, pre-sieving the powder or an instrument with
larger ultrasound and dispersion power, more apropriate for these metallic and heavier particles,
would be necessary.
Fig. 7 – SEM-SE of DL milled copper powder. Scale bar: 100µm
22
Fig. 8 - Particle size (CILAS) evolution of DL powder as a function of milling time
4.1.3. XRD - Scherrer
Fig. 9 - Crystallite size (Scherrer equation) for DL powder as a function of milling time
Fig. 9 shows that for DL powder samples there is a slow crystallite size evolution for the first two
hours. This is consistent with the negligible change in particle shape in the micrographs. The removed
powder has not been subjected to great deformation and, therefore, crystallite size remains
approximately constant. Between the 2 and 4 hour mark, there is a substantial reduction in crystallite
size (of about 27% of initial crystallite size) corresponding to the formation of flakes and high
deformation visible in the SEM images. Substantial milling, up to eight hours, manages to reduce
crystallite size an additional 9% of initial crystallite size. This suggests, for this system, that the period
during which the powders are subjected to greater strain and crystallite size reduction is between the 2
and 4 hour mark.
40
45
50
55
60
65
0 1 2 3 4 5 6 7 8
Median
particle
size (µm)
Milling time (hours)
25
30
35
40
45
0 1 2 3 4 5 6 7 8
Crystallite
size (nm)
Milling time (hours)
23
4.2. Dry conditions, small balls
In this section, the samples produced in dry conditions and with small balls (DS) are characterized.
4.2.1. Mass variation and ball images
Fig. 10 - RMV of the DS balls as a function of milling time
Fig. 11 - Photographs of the DS balls after milling. Scale bar: 8 mm.
Fig. 10 shows that for DS samples, the higher impact frequency of the balls and lower contact surface
area leads to an initial substantial welding of particles to the balls (for 30 minutes and 1 hour of milling
time) leading to an increase of around 1.5% in weight of the milling balls. It can be postulated that
some powder may also weld to the walls of the vial. As the milling time is raised, the number of
accumulated impacts of the balls increases, leading to work-hardening and embrittlement of the
surface of the ball. The embrittlement of the surface leads to faster material loss, (significant at the 4 h
mark). This significantly higher rate of material loss may result in an, at least partial, rejuvenation of
the surface by removal of a work-hardened layer of copper. Due to the stochastic nature of the impact
phenomenon, even though the rejuvenated surface is, by definition, more ductile, it is still rough and
-2
-1,5
-1
-0,5
0
0,5
1
-4
-3
-2
-1
0
1
2
0 1 2 3 4 5 6 7 8
Mass
variation (g)
RMV(%)
Milling time (hours)
24
irregular, as the photographs (Fig. 11) show, with some areas on the ball surface more prone to be
sites of particle welding. This means that the rejuvenated surface possibly acts as a favorable site for
welding, resulting in a weight gain from the 4 h to the 8 h mark.
The photographs of the milling balls (Fig. 11) corroborate this view of the evolution of the milling
process, with the apparent roughness of the balls increasing until one hour (welding), decreasing until
the four hour mark (loss of material) and then increasing again (re-welding). To verify and confirm the
conditions of the surface of the balls, SEM observations of ball surface cross sections and of the
craters as well as systematic roughness measurements would provide valuable data.
As is asserted by the high weight gains of the milling balls, 0.65 g of a initial powder mass of 2 g, it is
essential to bear in mind that the removed loose powder does not represent the state of the milled
powder at that time. A significant portion of the powder is fixated or welded to the milling balls (over
25%), and possibly onto the vial walls as well.
4.2.2. SEM images and particle size
SEM images and CILAS results analyze removed loose powder. Fig. 12 shows that after 10 and 30
minutes of milling, the observed powder appears to retain its dendritic morphology. The welded and
flake-shape powder is, for these times, probably welded to the ball, so no significant changes are
observable. As for the median particle size measured on CILAS (Fig. 13), there is some fluctuation in
the first half-hour of milling, which can be attributed to different degrees of dispersion in the CILAS.
After one hour of milling time, the particles seem to lose their dendritic shape and after two hours,
powders with dendritic morphology are no longer visible in the micrographs, giving way to flake-
shaped particles. This may correspond to flakes which were previously welded to the ball surface
being introduced into the system, becoming observed sample. That hypothesis is sustained by the
significant mass variation of the balls for that time – 2 hours. In the particle size analysis, a size
reduction is visible from the half-hour mark to 2 hours of 14 µm (from 62 to 48 µm) due to comminution
of the powder. In the micrographs, the particle (flake) size appears to remain approximately the same
after two hours. This observation is in line with the particle size measured, which, between two hours
and four hours, increases 7 µm. The particle size decreases, from 54 to 42 µm (a 12 µm dip), from 4
to 8 hours.
25
Fig. 12 - SEM-SE of DS milled copper powder. Scale bar: 100µm
Fig. 13 - Particle size (CILAS) evolution of DS powder as a function of milling time
40
45
50
55
60
65
0 1 2 3 4 5 6 7 8
Median
particle
size (µm)
Milling time (hours)
26
4.2.3. XRD - Scherrer
Fig. 14 - Crystallite size (Scherrer equation) for DS powder as a function of milling time
Fig. 14 shows that for DS samples a significant crystallite size reduction occurs for the first two hours
of milling time (40% of initial crystallite size). The SEM micrographs and CILAS particle size analysis
also identify the initial two hours of milling as the period during which the most significant modifications
occur, after which the powders are mostly in flake form. Additional milling, after the 2 hours, causes a
crystallite size reduction of only 7%. This is in line with the marginal changes in powder morphology.
For this system, the crystallite size seems to be reduced in the first two hours of milling, and more
dramatically in the first.
4.3. Isopropyl alcohol, large balls
In this section, the samples produced in wet conditions and with large balls (WL) are characterized.
4.3.1. Mass variation and ball images
Fig. 15 - RMV of the WL balls as a function of milling time
20
25
30
35
40
45
0 2 4 6 8 10
Crystallite
size (nm)
Milling time (hours)
-0,2
0
0,2
0,4
0,6
0,8
-0,5
0
0,5
1
1,5
2
0 1 2 3 4 5 6 7 8
Mass
variation (g)
RMV(%)
Milling time (hours)
27
Fig. 16 - Photographs of the WL balls after milling. Scale bar: 16 mm.
In the presence of isopropyl alcohol, welding is avoided. As long as the PCA is active, the favored
mechanisms are deformation and fracture, with the welding rate being negligible. Fig. 15 indicates that
for WL samples, there is only weight gain after 4 hours. Locally generated heat may lead to the
evaporation of some isopropyl alcohol, which has a boiling point of 82.6o C [70]. Due to particle size
reduction and alcohol evaporation, the PCA quantities may become insufficient to coat all the surface
of the balls, leading to some welding. Welded powder is visible on the less reflective surface of the 8
hours milling ball, as seen in Fig. 16.
4.3.2. SEM images and particle size
Fig. 17 shows that for WL samples, the powders are already severely deformed after ten minutes. The
SEM observations for 30 minutes and one hour of milling are similar. The CILAS median particle size
(Fig. 18) decreases until the hour mark (from 60 to 40 µm). Both SEM micrographs and particle size
measurements are consistent with a stage of deformation and fracture which, in the presence of
sufficient isopropyl alcohol are the dominant mechanisms.
For two, four and eight hours, the micrographs show more flake-like particles. The size reduction at
the hour mark leads to a natural increase in surface area. Due to this increase in surface area and
heat generated during milling, the amount of PCA may be insufficient to cover all the area of the
powder particles, leading to some welding. This welding is reflected by an increase in median size for
samples milled for two and four hours and in the flake morphology visible in the micrograph. During
this time, the fracture and welding mechanisms almost balance out, still favoring welding mechanisms
slightly.
The eight hour micrograph shows a more refined particle size which is corroborated by a sharp
decrease in particle size in CILAS (to 13 µm) after eight hours of milling. This can be explained by
28
accumulated number of impact, which, through work-hardening and embrittlement of the flakes, leads
to an increase in fracture rate.
Fig. 17 - SEM-SE of WL milled copper powder. Scale bar: 100µm
29
Fig. 18 - Particle size (CILAS) evolution of WL powder as a function of milling time
4.3.3. XRD - Scherrer
Fig. 19 - Crystallite size (Scherrer equation) for DL powder as a function of milling time
Fig. 19 shows that for WL samples, crystallite size is reduced very quickly - 30% in the ten initial
minutes. The presence of a PCA prevents welding and promotes work-hardening and deformation of
the powders, leading to this immediate crystallite size reduction. This initial decrease of crystallite size
is corroborated by the loss of the powder dendritic morphology for the 10 minutes SEM micrographs.
The crystallite size continues to decrease steadily, until the eight hour mark, decreasing an additional
27%. This crystallite size reduction occurs hand in hand with overall particle size reduction verified
from 1 hour to 8 hours.
For this system, the crystallite size reduction verified in just the first 10 minutes of milling is of the
same magnitude as the reduction verified for the other 470 minutes of milling time. This fact clarifies
the importance of the isopropyl as a PCA, which allows more energy from ball impacts to be spent on
plastic deformation of the powders.
0
10
20
30
40
50
60
70
0 2 4 6 8 10
Median
particle
size (µm)
Milling time (hours)
15
20
25
30
35
40
45
0 1 2 3 4 5 6 7 8
Crystallite
size (nm)
Milling time (hours)
30
4.4. Isopropyl alcohol, small balls
In this section, the samples produced in wet conditions and with small balls (WS) are characterized.
4.4.1. Mass variation and ball images
Fig. 20 – RMV of the WS balls as a function of milling time
Fig. 21 - Photographs of the DL balls after milling. Scale bar: 8 mm.
In the presence of isopropyl alcohol, welding is avoided. As long as the PCA is in sufficient quantity,
the favored mechanisms are deformation and fracture, with the welding rate being negligible. Fig. 20
shows that for times up to two hours, there is no weight gain and no welding is visible on the surface
of the balls (Fig. 21). As the milling time is raised, the number of accumulated impacts of the balls
increases, leading to work-hardening and embrittlement of the surface of the ball. The embrittlement of
the surface results in faster material loss which is significant for 4 h. The 4 h ball surface, which
appears clearly rougher, may also be a confirmation of the loss of material verified by the mass
variation measurements.
This material loss may result in a, at least partial, rejuvenation of the surface by removal of a work-
hardened layer of copper, preventing further fracture and material loss. Similar to what was described
-1,6
-1,2
-0,8
-0,4
0
-4
-3
-2
-1
0
0 1 2 3 4 5 6 7 8
Mass
variation (g) RMV(%)
Milling time (hours)
31
for previous conditions, in section 4.3.1, for a milling time inferior to some threshold between four and
eight hours, the PCA is enough to avoid significant welding to the milling balls. What is likely to be
occurring, being corroborated by the particle size data to be seen in section 4.4.2, is that, due to a
particle size reduction for longer times, the PCA quantities become insufficient to coat all surface area
which leads to some welding to the milling balls. This welding is reflected in the weight gain and
photograph of the surface for the 8h milling ball, showing a very irregular surface.
4.4.2. SEM images and particle size
Fig. 22 shows that, for WS samples, the powders are already severely deformed with few dendritic
particles remaining, after 10 - 30 minutes. The CILAS median particle size (Fig. 23) decreases sharply
for the first thirty minutes of milling (from 60 to 29 µm). This is consistent with a stage of deformation
and fracture which, in the presence of active isopropyl alcohol are the dominant mechanisms. The size
reduction at the half-hour mark leads to an increase in surface area. Due to this increase in surface
area, the amount of isopropyl alcohol may be insufficient to cover all the area of the powder particles.
Insufficient PCA favors welding phenomena, causing the increase in particle size in CILAS
measurements, from the half-hour to the two hour mark. This is reflected in the micrographs which, for
the one, two and four hour millings, show more flake-like particles. Between the two and four hours of
milling time, the fracture and welding mechanisms approximately even out, leading to a steady median
particle size. The eight hours micrographs depict more refined particles, corroborated by the CILAS
analysis which shows a sharp decrease in particle size (to 10 µm). This may be attributed to work-
hardening and embrittlement of the powder particles, which favors fracture mechanisms.
32
Fig. 22 - SEM-SE of WS milled copper powder. Scale bar: 100µm
Fig. 23 - Particle size (CILAS) evolution of DL powder as a function of milling time
0
10
20
30
40
50
60
70
0 1 2 3 4 5 6 7 8
Median
particle
size (µm)
Milling time (hours)
33
4.4.3. XRD
Fig. 24 - Crystallite size (Scherrer equation) for WS powder as a function of milling time
Fig. 24 shows that for WS samples, crystallite size reduction occurs at a fast rate, with the crystallite
size being reduced 30% in the first half-hour. The presence of the PCA prevents welding and
promotes work-hardening of the powders, leading to this substantial crystallite size reduction. This
initial change in crystallite is corroborated by the loss of the powder dendritic morphology for the 10
and 30 minutes in the SEM micrographs, similarly to what was described for the previous system in
section 4.4.3. The crystallite size continues to decrease steadily, until the eight hour mark, decreasing
an additional 27% of crystallite size.
For this system, the crystallite size reduction verified in the first half-hour is approximately the same
verified for the other seven and a half hours of milling time. This fact clarifies the importance of the
isopropyl as a PCA which allows for more energy from ball impacts to be spent on plastic deformation
of the powders for short times, as also concluded in section 4.3.3.
To confirm the rate of crystallite size reduction for times between 30 minutes and 8 hours, additional
diffractograms are necessary. These diffractograms would allow a better study of the evolution of
crystallite size with milling time.
15
20
25
30
35
40
45
0 1 2 3 4 5 6 7 8
Crystallite
size (nm)
Milling time (hours)
34
4.5. Systems comparison
In this section, each variable is analyzed simultaneously for all systems, as to provide a broader view
of the results.
4.5.1. Mass variation
Fig. 25- Comparison of the RMV of the balls for all systems as a function of milling time
Fig. 25 shows that there is no general trend that governs the weight variation over time for all milling
conditions, with clearly several mechanisms responsible for mass variation. The basic mechanisms for
weight variation are the adhesion and welding of particles to the milling balls, increasing their weight,
and the loss of material, by fracture or wear, from the ball or from powder previously welded to the ball
surface, which results in a weight decrease.
When considering the welding of particles to the milling ball, the presence of isopropyl alcohol is
responsible for lowering the welding rate, resulting in a smaller increase of mass. As for the weight
loss mechanisms, the more work-hardened the surface of the ball is, the more brittle and susceptible
to impact fracture it will be. High energies and, more importantly, higher ball impact frequencies lead
to greater work-hardening and brittleness.
The difference between possible ball contacts when comparing the millings with larger and smaller
balls is significant. Accounting only for the possibilities of contact between two balls, the number of
possible different contacts (mathematical combinations) for the larger balls (3 balls in the vial) is three,
whereas for the smaller balls (8 balls in the vial) the number is 28, an increase of almost ten times.
The surface area of the large ball is also 3.5 times larger than the small ball’s surface area. This
means that the impacts are 3.5 times more concentrated for the smaller balls. This 3.5 times impact-
per-area increase and the near ten-fold augment in possible ball-to-ball impacts is what supports the
conjecture of the greater work-hardening for millings with smaller balls. Taking into account these
numbers, it is plausible to infer that millings with greater number of balls will result in more work-
hardened ball surfaces, promoting material loss mechanisms. In this case, the phenomenon of impact
between two balls will be more significant than for the millings with larger, fewer balls, in which wear
-5
-4
-3
-2
-1
0
1
2
0 1 2 3 4 5 6 7 8
RMV (%)
Milling time (hours)
DL
DS
WL
WS
35
due to the movement of the softer milling balls surface against the vial wall, plays a more noteworthy
part. Additionally, for millings with large balls, as ball-vial wear is a more prominent weight loss
mechanism, the lubricating effect of the isopropyl alcohol in lowering the wear rate could result in less
weight loss for the milling ball.
For shorter milling times, below two hours, there is no significant weight variation for any sample
except for the DS balls, for which there is a mass increase. This suggests that, for the shorter milling
times, for both large and small balls, there are not enough impacts to work-harden and embrittle the
surface, leading to very few fracture events. For the wet-milled samples, the isopropyl alcohol
prevents significant welding for the lower milling times, impeding mass increase. For the DS balls, the
higher impact frequency leads to an initial substantial welding of particles to the balls (for 30 minutes
and 1 hour of milling time).
As the milling time increases, the number of accumulated impacts of the balls increases for all milling
conditions, leading to increased work-hardening and embrittlement of the surface of the ball. The
higher impact frequency for the smaller balls leads to quicker embrittlement and ensuing fracture,
resulting in a larger relative weight loss (visible at the 4 h mark). This significantly higher rate of
material loss results in a partial rejuvenation of the surface by removal of a work-hardened layer of
copper. Due to the stochastic nature of the impact phenomenon, even though the surface is more
ductile, it is still rough and irregular (much more than the original machined surface, before any
milling), with some areas on the ball surface more prone to be sites of particle adhesion and welding.
The major difference in the breakdown of these weight variation data for the large and small balls may
be the rejuvenation phenomenon. It essentially entails that the analysis of the millings with the small
balls has to take into account the formation of a new ductile rough ball surface, less prone to fracture
and more prone to welding. Flakey particles more easily weld to the rejuvenated surface, resulting in a
gain of weight from 4 h to 8 h.
The insufficient number of impacts-per-area of the large balls hinders the rejuvenation process. The
weight variation is more straightforwardly dictated by the balance of the weight gain (welding to the
surface) and the weight loss mechanisms. In wet conditions, longer milling times induce an increase in
surface area due to the reduction of particle size. Additionally, local temperatures upon impact can
theoretically reach the few hundreds of degrees Celsius. This may lead to some evaporation of the
isopropyl alcohol, whose boiling point is 82.6 oC [70]. Both these factors may lead to a shortage of
PCA, promoting welding onto the ball surface and causing the large balls to gain weight. In dry
conditions, the absence of PCA, which also acts as a lubricant, means that the wear rate is higher and
cannot be overcome or compensated by the welding phenomena. Higher wear rates cause weight
loss from four to eight hours of milling.
To summarize this approach to the balls’ weight variation, it is important to understand:
the mechanisms involved in weight gain (welding) and weight loss (wear and fracture on
impact)
36
that both ball size/number and the presence of a PCA have significant effect on the ball’s
weight gain and surface topology
the fact that increased work-hardening can lead to a rejuvenation of the surface and a
dramatic shift to the mechanisms’ rates.
A study of the wear mechanisms, with wear tests being performed on the surfaces of different strain
history, could provide valuable information to confirm the proposed relation between wear rates.
4.5.2. Particle size and morphology
The analysis of the properties of the milled powder must bear in mind that, as referred a portion of the
milled powder, up to approximately 30%, is weld and adherent to the milling balls (and some to the vial
walls). For short milling times, it is possible that samples analyzed by SEM and CILAS were of mostly
unaffected and not-deformed powder and that the affected powder, which suffered deformation and
welding phenomena, was mostly welded to the milling balls and vial walls. After further milling time,
with work-hardening and embrittlement of the milling ball surface, material loss from the milling ball
begins to occur. Only after significant material loss from the balls begins, which happens after 1 hour
for the small balls and after 2 hours for the larger balls, do the picked up samples represent more
accurately the status of the milled powder.
Fig. 26 – Comparison of particle size (CILAS) evolution of all powder systems as a function of milling time
Observing Fig. 26, there is a decrease in particle size for the wet systems which is not observed for
the dry systems. In the SEM micrographs, the dendritic shape of the powder is lost for the earliest of
milling times – 10 minutes (Fig. 27). This is attributed to the presence of isopropyl alcohol, preventing
welding and promoting the deformation and fracture of some powder particles. The expected initial
increase in particle size for the dry systems, for which welding of particles is promoted, is not verified
in CILAS and in SEM micrographs. This might be due to the sampling issues explained in the previous
0
10
20
30
40
50
60
70
0 1 2 3 4 5 6 7 8
Median
particle
size (µm)
Milling time (hours)
DL
DS
WL
WS
37
paragraph. A way to account for the larger particles which are not identified in CILAS would be pre-
sieving the powder samples. For early times, until 1 hour , fracture dominates for the systems with
isopropyl alcohol and welding dominates for the dry systems.
The dry system with large spheres seems to have a slower evolution, not exhibiting any significant
changes for the first two hours of milling (Fig. 28, Fig. 29 and Fig. 30). After two hours, material loss
mechanisms from the ball surface become more prominent than the welding phenomena. The material
removed from the ball surface comes in the form of flakes as is visible in the 4 h micrograph (Fig. 31).
Those work-hardened flakes suffer fracture and their size is reduced from the four to the eight hour
mark (Fig. 32). The reasons why the large flakes seen in SEM micrographs for 4 hours are not visible
in CILAS analysis were discussed in section 4.1.1.
For all systems except the DL, there is a visible increase in particle size in the CILAS analysis. This
increase is more significant for the WS system and less significant for the DS system and corresponds
to a welding of the powders and the formation of flake-like particles, as confirmed in the micrographs.
For these intermediate times (1-4 hours), welding rates are higher than for short times in the systems
with isopropyl alcohol probably due to a shortage of the alcohol which can no longer cover the entire
surface of the powder.. For intermediate times, between 1 and 4 hours, welding phenomena are
favored, tending to balance out with fracture phenomena.
For the last milling time (8 hours) there is a clear decrease in particle size for all systems as is visible
in the CILAS results. After the four hour mark, fracture appears to be the central mechanism for all
systems. The effect of ball size is visible, with the smaller balls leading to a smaller size. For the wet
systems, the increased work-hardening of the particles favors fracture mechanisms, leading to a lower
equilibrium particle size. The ball size influence is dwarfed by the influence of the isopropyl alcohol
which, for these longer times, seems to be the main particle size controlling factor. Further millings,
with longer times are required to assert if any of the systems, particularly those with isopropyl alcohol,
have reached a plateau of particle size – steady-state.
38
Fig. 27 - SEM-SE of 10 minutes milled copper powder. Scale bar: 50µm
Fig. 28 - SEM-SE of 30 minutes milled copper powder. Scale bar: 50µm
39
Fig. 29 - SEM-SE of 1 hour milled copper powder. Scale bar: 50µm
Fig. 30 - SEM-SE of 2 hours milled copper powder. Scale bar: 50µm
40
Fig. 31 –SEM-SE of 4 hours milled copper powder. Scale bar: 50µm
Fig. 32 - SEM-SE of 8 hours milled copper powder. Scale bar: 50µm)
41
4.5.3. XRD - Scherrer
Fig. 33 – Comparison of crystallite size (Scherrer equation) for all powder systems as a function of milling time. Detail a) – comparison for times under 30 min of the crystallite size for the wet systems
Fig. 33 shows that crystallite size reduction is much faster in wet conditions. Isopropyl alcohol cools
the system and prevents welding. When comparing the wet systems, larger balls lead to a faster early
crystallite size reduction for the 10 minute mark (detail a) in Fig. 33). In dry conditions, small balls lead
to a smaller crystallite size for all times. Smaller balls lead to a greater decrease in crystallite size for
longer times in both wet and dry conditions. This can be attributed to the higher number of effective
impacts per unit area. Wet milled samples show smaller crystallite size than dry milled samples. The
presence of isopropyl alcohol is the factor which comes through as the most important for more
significant crystallite size reduction.
4.5.3.1. Parameter determination and Williamson-Hall fitting
The fitting of high 2θ peaks for lattice parameter determination yielded poor results due to the low
intensity of the peaks. The acquisition time was long and the step was small as to achieve better
resolution and higher intensities, but still not enough for lattice parameter determination.
Applying the Williamson-Hall equation to the most intense peaks of each sample yielded poor results,
with negative values for crystallite size of some samples and complex (imaginary) values for
microstrain. Different fittings were performed but did not resolve this issue.
15
20
25
30
35
40
45
0 1 2 3 4 5 6 7 8
Crystallite
size (nm)
Milling time (hours)
DL
DS
WL
WS
25
30
35
40
45
0 0,5
a)
42
4.6. Mechanical testing
In this section, the overall results of microhardness, hardness and density measures are analyzed for
all systems.
4.6.1. Powder microhardness
A) DL B) DS
C) WL D) WS
Fig. 34 – Comparison of powder microhardness (HV0.012) for all systems as a function of milling time
Fig. 34 shows an overall view of the powder microhardness (HV0.012) of the samples. For samples
with milling times longer than 1 hour (and also for the sample milled with large balls in dry conditions
for one hour) no hardness values are presented; due to the small size of the powders, no proper
indentation could be produced with the minimum load available in the microindenter (12 g). Even when
an indentation could be produced, its size was large compared to the cross section area of the
powders, leading to poor significant results. As a consequence, standard deviations are high and
results can only be considered as trends. Unfortunately, the few results obtained presented no
valuable information and no tendency is established within or between the different systems.
To avert the accuracy problems and allow for more indentations per area, nanoindentation tests
should be performed on the set powders. Analyzing the nanoindentation results in the light of the
0
50
100
150
0 20 40 60
HV0,012
Milling time (minutes)
0
50
100
150
0 20 40 60
HV0,012
Milling time (minutes)
0
50
100
150
0 20 40 60
HV0,012
Milling time (minutes)
0
50
100
150
0 20 40 60
HV0,012
Milling time (minutes)
43
theory of ISE, introduced in section 3.8.1, would provide more valuable results to study the evolution
of hardness with milling time.
4.6.2. Green density and hardness
Given the impossibility, in the scope of this work, of obtaining microhardness results of individual
powders, powder from each sample was compacted into pellets and green density was measured.
The primary goal was to assess the hardness and work-hardening of the individual powders by taking
into account the remaining porosity. From those normalized results, the degree of work-hardening of
the powder for each milling time and system could be estimated. The compaction pressure is a key
factor in compact density. To study which compaction pressure would yield a compact of significant
density, a density vs compaction pressure curve was produced for pure, not-milled copper. The curve,
depicted in Fig. 35, shows that for around 750MPa the relative density appears to plateau at slightly
above 90%. Relative density (RD) is defined as a function of green density (GD) and bulk copper
density (BCD) by equation ( 9 ): % = ÷ × ( 9 )
Fig. 35 - Density - pressure curve for pure not-milled copper
Due to work hardening, powder shape and powder size distribution, the relative densities obtained for
the milled systems varied significantly (Fig. 36) and were consistently below 90%, down to 60% for
some samples.
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500 600 700 800
Relative
density (%)
Pressure (MPa)
44
Strength-density models of porous materials were used to determine σ0 (strength of the wrought
material) as an estimate for powder hardness, from σp (strength of the porous material) and a function
of porosity/density, f(p), using equation (10). [71]
� = �� �⁄ (10)
However, for some dry-milled pellets, the density and consistency of the green was not sufficient for
hardness measurements, with the pellet collapsing. Exponential and polynomial models, relating
porosity and compact strength, were fitted to the data from all the systems. However, as seen in Fig.
36, there is no clear tendency on how density influences the measured hardness of the samples.
Fitting of the data was carried out with all values and with the values divided into groups by milling
time and by individual system, as to determine an appropriate function for each set of data. The used
models provided a poor fitting for the experimental data. The strength (and therefore hardness) of the
porous material depends strongly on other factors besides hardness of the individual powders and the
compact density. As these strength-density models are based solely on strength, they cannot account
for variables such as size and powder shape, which vary greatly from sample to sample.
The density, and hardness, of a powder compact can be affected by many properties, intrinsic and
extrinsic to the powder. The hardness, the work hardening rate, surface friction and chemical bonding
between particles are important extrinsic variables and powder size, shape and lubrication are
important intrinsic factors. [71]
To evaluate the influence of these factors, pressure-density curves could be performed for each
sample. After determining those curves for each sample, pellets could be compacted with different
compact pressures as to obtain the same density. With pellets with the same density, that effect could
be normalized and others effects analyzed.
From these results, one conclusion to be extracted is that for the wet systems, the pellets never
collapsed during hardness measurements (Fig. 36 C and D), unlike the powder from dry systems and
longer times (Fig. 36 A and B). This may indicate that the larger size and expected higher hardness of
these powders leads to greens with lower strength. The smaller size of the powders milled in wet
conditions appears to circumvent the work-hardening issue and lead to a stronger, albeit not very
dense, compact.
45
Fig. 36 – HV1 (left axis) and Relative density (right axis) for powder pellets as a function of milling time
0
20
40
60
80
100
20
40
60
80
100
120
0 1 2 3 4 5 6 7 8
Relative
density (%)
HV1
A) DL
0
20
40
60
80
100
20
40
60
80
100
120
0 1 2 3 4 5 6 7 8
B) DS
0
20
40
60
80
100
20
40
60
80
100
120
0 1 2 3 4 5 6 7 8
C) WL
0
20
40
60
80
100
20
40
60
80
100
120
0 1 2 3 4 5 6 7 8
Milling time (hours)
D) WS
46
47
5. Copper composites – Influence of annealing
temperature
The influence of process parameters in a copper-copper-copper system were analyzed in section 4. In
this section, powder composite systems are studied and compared, specifically regarding the effect of
annealing temperature on powder properties.
This section is dedicated to the study of powders already milled in a previous work [58], in a Retsch,
using a alumina vial and 7 alumina balls (7 mm in diameter) with a BPR of 10, for 8 h at a speed of
400 rpm. Samples of this milled powder were divided and annealed for one hour in a tube furnace at
600, 700, 800 and 900o C, under an Argon, 4% H2 atmosphere to avoid oxidation. Samples of not
milled powder (Cu_st) were also annealed at the same temperatures for comparison
Samples are identified in Table 4. The weight percentages of components graphite (G), alumina (A)
and multi-walled carbon nanotubes (CNT) are identified as -%, followed by the annealing temperature
in o C. For example, Cu-2G-2A_800 means the powder is 2wt% graphite and 2wt% alumina and that
XRD analysis was carried out to study the influence of annealing temperature on crystallite size. Only
samples with no heat treatment and samples annealed at 900o C were analyzed, as the highest
annealing temperature is expected to produce the highest increase in crystallite size. The Cu-2CNT
system, due to lack of material, was not analyzed. The crystallite size for the initial electrolytic powder
determined by the Scherrer equation was of approximately 44nm. The results summarized in Table 5
are better suited for a qualitative analysis.
Table 5 - Crystallite size (Scherrer equation) for composite powder systems as a function of annealing temperature
Sample (not heat
treated)
Crystallite size (nm) Sample (annealed at
900o C)
Crystallite size (nm)
Cu_nht 19 Cu_900 43
Cu-2G_nht 27 Cu-2G_900 43
Cu-2A_nht 19 Cu-2A_900 43
Cu-2G-2A_nht 24 Cu-2G-2A_900 43
It is clear that, as expected, annealing at 900o C resulted in a significant increase in crystallite size.
The samples milled with graphite, Cu-2G_nht and Cu_2G-2A_nht, have larger crystallite size than
those milled without graphite, showing that crystallite size reduction may be more effective without the
presence of graphite in the milling process.
Despite this larger size prior to annealing, all samples suffer considerable crystallite size growth and
display similar final crystallite sizes, close to the crystallite size of the pure copper powder prior to
milling. XRD analysis for the intermediate annealing temperatures 600, 700, 800o C would provide a
view of the evolution of crystallite size with annealing temperature.
5.2. Powder microhardness
Fig. 37 (A-F) details the individual HV0.012 values for each system. Some samples do not have
hardness values due to the small size of the powders, which did not have enough area for a proper
indentation with the minimum load available in the microindenter (12 g). In some of the samples in
which indentation was viable, the small particle size was still not large enough to assure that there
wasn’t a contribution by the resin to the overall hardness measured.
49
A) Cu-nm B) Cu
C) Cu-2G D) Cu-2A
E) Cu-2G-2A F) Cu-2CNT
Fig. 37 - Powder microhardness (HV0.012) for composite powders as a function of annealing temperature
This, in addition to the comments on indentation size effect made in section 3.8.1, may be responsible
for loss of accuracy and significance to the microhardness measurements. Nevertheless, some
conclusions can still be retrieved from the results.
When comparing the starting copper powder (Fig. 37 A) and the milled copper powder (Fig. 37 B), the
milled powder displays higher hardness values for all annealing temperatures. This increased
50
100
150
200
nht 600 700 800 900
HV0,012
50
100
150
200
nht 600 700 800 900
50
100
150
200
nht 600 700 800 900
50
100
150
200
nht 600 700 800 900
50
100
150
200
nht 600 700 800 900
50
100
150
200
nht 600 700 800 900
Annealing temperature (oC)
50
hardness may be attributed to the reinforcement of the milled copper with alumina particles from the
vial and balls [58]. The hardness values for all systems are similar and do not suffer significant
reductions with annealing temperature. Annealing at these temperatures is known to relieve stresses
in the copper alloys, lowering hardness [72]. Orowan strengthening due to the incorporation of alumina
particles is possibly the most important strengthening mechanism since the heat treatments do not
produce a significant reduction in measured hardness. Graphite particles may also lead to Orowan
strengthening.
To avert the accuracy problems and allow for more indentations per area, nanoindentation tests
should be performed on the set powders. Analyzing the nanoindentation results in the light of the
theory of ISE, introduced in section 3.8.1, would provide more valuable results and allow for
comparisons between the different systems.
51
6. Modeling – FEM
The modeling section of this work can be divided into three parts. The first takes on the set up of the
model. The second part consists of identifying the variables and defining the simulation conditions.
The third section is the result analysis and conclusions.
6.1. Model set up
In order to understand the local mechanisms involved in mechanical milling and alloying, it was
decided that the object of study would be individual collisions of a milling ball with a flat vial surface
covered with powder particles. The sequence of the following subsections is approximately the same
sequence in which the model was constructed in Abaqus.
6.1.1. 2D model and parts
Ideally, the finite element model for this simulation would be three-dimensional, representing the vial
as a right-angle solid, the milling ball as a ball and the powder as differently shape three-dimensional
forms. However, in order to save computing time, allowing for more simulations, and to attain clear
and significant results, simplifications were made.
The first major decision was to construct a 2D model instead of a 3D one. This simplification is justified
by the fact that practically every effective impact is a head-on (90o) collision, as is specified in section
2.3.1. Since in a 90o collision, ball movement occurs only along one direction, a 3D model can be
reduced to a 2D model. The 2D cut represents a radial view of the 3D collision, with every point in the
surface plane being defined by the distance to the axis of the direction of the ball issue (radial
symmetry). Once the modeling space is defined as 2D, the parts of the model can be built.
Since it is a radial model, the milling ball, which in a 3D space would be a ball, is reduced to a semi-
circle with the same radius as the milling ball. The vial is represented as a square. The powder
particles, which in reality have an initial dendritic shape, are built as circles on the surface of the vial. A
circle was chosen since it is necessary to have the same initial particle geometry to compare the
deformation for the various simulation conditions.
The assembly of these parts into the model is displayed, with a close-up in Fig. 38.
Fig. 38 – Assembly of the 2D FEM model, with close-up of the contact zone
52
6.1.2. Motion
The stationary model (as shown in Fig. 38) represents the initial moment of the simulation. The semi-
circle, representing the milling ball, is subjected to an initial velocity, using an uniform predefined field.
The applied velocities vary roughly from 1-10 m/s [40].
6.1.3. Materials
The powder material is copper, as are the vial and milling balls. In order to run the simulation, a model
material with the properties of copper must be constructed and assigned to the parts previously
defined. As defined in section 2.3.4, due to the high strains and strain rates of the ball milling process,
the chosen material model was the Johnson-Cook five parameter model with failure criterion, defined
by equations ( 2 ) and ( 3 ).
In our simulation, temperature influence was not considered. The material properties and parameters
for the Johnson-Cook model, introduced in Abaqus, are summarized in Table 6Table 6.
Table 6 – Materials parameters and properties to be introduced in Abaqus
Material properties Value (Unit) Reference
Density 8950 kg/m3
[73] Young’s Modulus 125 GPa
Poisson’s ratio 0.35
A 90 MPa
[74]
B 292 MPa
n 0.31
C 0.029 ε ̇ 1
D1 0.54
[57] D2 4.89
D3 -3.03
D4 0.014
53
6.1.4. Mesh
Once the parts are assigned the materials and the model is defined in abstract, the mesh, the set of
elements and nodes at which the material functions will be calculated must be defined (as explained in
section 2.3.2). Defining the mesh is a decision of compromise. Choosing an excessively coarse mesh
allows for quick simulations and less central processing unit (CPU) usage but may lead to results
which are too detached from reality. On the other hand, an extremely fine mesh may provide very
accurate results only at the expense of long simulation times and processing usage. In order to
balance the two requirements - accurate results and moderate processing time – several trial runs
were carried out to assert the most appropriate mesh size and type.
6.1.4.1. Powder particles (small circles)
Firstly, the mesh of the powder particles (small circles) was studied. These are the smallest parts in
the model and also those who suffer the greatest strain and strain rates. Defining the apropriate mesh
for these parts is critical to the accuracy of the model. The particle diameter was defined as 40 µm, in
the same range as the size of our starting powder (section 3.1.1).
Using a free mesh technique, internal elements, close to the center of the circle suffer excessive
distortion, aborting the simulation. To avoid this problem, mesh elements were defined as quad-
dominated and assigned with a sweep technique. The sweep technique guarantees roughly the same
number of elements for each circumference centered on the circle center. This mesh assignment
technique requires more CPU usage for it assigns excessive elements to the center of the circle.
However, it assures that the elements do not distort excessively, allowing for the simulation to run.
To establish the more suitable element size/number of elements, simulation runs were carried out with
a coarse automatic mesh for the milling ball and vial, ball velocity of 1 m/s and ten powder particles
with no space between them. The evolution of maximum von Mises stress values and logarithmic
strain for two time instants were studied as a function of the number of elements as to determine when
the refinement of the mesh was sufficient. The circumference was first seeded with an approximate
element size of 5 µm. The results are summarized in Table 7.
Table 7 – Evolution of maximum von Mises Stress and logarithmic deformation with element size
Seeded approximate element size
(µm)
Number of elements per
particle
Max. von Mises stress at instant 1
(GPa)
Max. logarithmic
deformation at instant 1
Max. Von Mises stress at instant 2
(GPa)
Max. logarithmic
deformation at instant 2
5 75 399.8 0.659 421.4 0.907
3 252 428.2 0.839 437.2 1.125
2 630 427.2 0.898 435.5 1.108
1.5 1092 427.2 0.912 439.1 1.064
54
The values seem to reach a plateau for seeding size of 2 µm, with no significant variations when
decreasing the mesh size to 1.5 µm. Considering this, the chosen mesh was seeded with a sweep
technique and an approximate element size of 2 µm, yielding 631 nodes per particle, 567 linear
quadrilateral elements (CPS4R) and 63 linear triangular elements (CPS3)
6.1.4.2. Vial (rectangle) and milling ball (semicircle)
The meshes of the vial and milling ball must be refined enough to suitably match the deformation of
the powder particles. Using an overly coarse mesh, local stress will never be enough to enter the
plastic domain and the mesh and vial would only be solicited elastically. As a consequence, the
deformation of powder particles would be overestimated and that of the vial and milling balls would be
underestimated.
Quick simulation runs reveal that only a layer of the ball and vial are subjected to significant stresses,
with the remainder of the volume not greatly affected. Given this evidence, the meshes for the vial and
ball feature a partition. The partitioned section is meshed with a finer mesh to account for plastic
deformation and phenomena, while a coarser mesh is attributed to the less affected section.
The partitioned section is a rectangle, sharing its top left corner with the vial, with height and width
adjustable to the simulation conditions (Fig. 39).. A simulation with a large milling ball needs a wider
section and a simulation with a greater velocity needs a deeper section. The same is applicable for the
milling ball partitioned section, where the section is defined on its left by the ball diameter and on its
lower side by the circumference of the ball (Fig. 39).
Fig. 39 – Scheme of the partitioned sections for the vial and milling ball
The same procedure detailed in section 6.1.4.1 for the element size of the powder particle was
followed for the partitioned sections of both the ball and vial, simultaneously. The results are
summarized in Table 8. An extra variable of contact pressure was studied since it is important that the
stress is not underestimated. The number of elements is not stated directly as they vary with the width
and height of the section.
For an element size of 15 µm, the stress, deformation and contact pressure values stabilize. For the
15 µm and 10 µm, the maximum von Mises stress at instant 2 is observed for a different particle
(hence the asterisk) than for the previous element sizes. This is an indication that the 15 µm mesh is
55
necessary for good spatial resolution. Further refinement of the mesh yields approximately the same
results.
For the partitioned section, the chosen mesh was seeded with a structured technique (given the
partition) and an approximate element size of 15 µm. For the non-affected section, a maximum
element size of 1 mm and minimum element size of 500 µm were defined for a free advancing front
mesh, to allow for meshing integration with the partitioned section’s mesh. If not for meshing
integration, even coarser meshes would be appropriate due to the low value variations in the section.
To assure accurate results, the height and width of the partitioned section are over dimensioned,
allowing for the outer regions of the section to already be in the low-solicitation region. By over
dimensioning, the non-affected region does not play an important part in the simulation, not
compromising the results.
Table 8 - Evolution of maximum von Mises stress, logarithmic deformation and contact pressure with element size. * - maximum von Mises stress is verified in a different particle
Seeded approximate element size
(µm)
Max. von Mises
stress at instant 1 (MPa)
Max. logarithmic deformation at instant 1
Max. contact
pressure deformation at instant 1
(GPa)
Max. von Mises
stress at instant 2 (MPa)
Max. logarithmic deformation at instant
2
Max. contact
pressure deformation at instant 2
(GPa)
50 336.7 2.992 4.768 442.8 8.975 7.177
30 341.3 3.189 4.959 415.5 8.357 6.835
20 340.5 3.171 4.95 413.1 8.598 6.454
15 343.4 3.267 4.977 410.2* 8.398 7.179
10 344 3.298 4.812 410.3* 8.182 7.073
6.1.5. Simulation time
The trial simulations performed to define mesh size also provided information on the average time of
collision. The collision time is defined from the instant at which any of the powder particles begins to
suffer strain until the instant when strain stabilizes for all particles. Calculated collision times were in
the 30-50 µs range. Knowing the average collision time allows for the stipulation of simulation times
long enough to provide information on all moments of the collision. The output simulation step was set
at 2 µs to provide temporal resolution and the maximum simulation time was set at 100 µs.
56
6.2. Simulations
After the definition of the geometrical model, mesh, simulation time and material properties, the
individual simulations were stipulated. The different parameters that were varied were:
Ball velocity
o 1 m/s; 3 m/s; 6 m/s; 10 m/s – triangular numbers
Ball size
o 4 mm radius; 8 mm radius - size of the small and large milling balls in the experiment
(Fig. 40)
Distance between powder particles (Fig. 41)
o ND – no distance: 0 µm;
o HD – half distance: 20 µm (one particle radius);
o FD – full distance: 40 µm (two particle radii)
The ball velocity influences the impact energy and therefore the strain and stress in the powder
particles, vial and milling ball. The velocity of a given impact is a function of the rotation speed and
diameter of the vial.
The ball size influences not only the weight of the sphere, and hence the impact energy, but also the
curvature of the impact surface, altering the geometrical conditions of the impact.
The distance between powder particles is a variable introduced to simulate the presence of isopropyl
alcohol in the milling. The presence of a PCA with the objective to prevent welding is transcripted into
physical separation between the particles. The simulations are run with no space between the
particles (no PCA), one radius apart (some PCA), two radii apart (excess PCA).
Fig. 40 - Ball size comparison for the simulations
Fig. 41 – Distance between balls comparison for the simulations
57
Other parameters were initially considered and could be studied in further work, such as:
Number of impacts – more impacts per particle.
o Not studied because particles did not return to the vial after impact (gravity was not
accounted for) and would increase simulation time greatly
Layers of particles – simulating real situation of multiple stacked
o Increased complexity and only viable for ND situations.
Considering the 3 variables of interest, the number of simulations is 24: