development and modeling of mechanical alloying for ...copper-matrix composites reinforced with...

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

ii

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

iv

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

reduction and more efficient milling.

Keywords: copper; composite; powder; mechanical alloying; finite element method; isopropyl alcohol

vi

Agradecimentos

Em primeiro lugar, quero agradecer ao meu orientador, Professor Alberto Ferro, pela confiança,

exigência e apoio durante todo o trabalho e pelo exemplo de pedagogia e ciência desde os anos da

licenciatura.

Ao meu orientador Professor Ricardo Baptista, quero agradecer a ajuda durante todo o processo e os

preciosos conselhos na utilização do Abaqus.

Um agradecimento especial à Professora Mafalda Guedes, pela sua ajuda na parte experimental e

pela sua simpatia, disponibilidade e dedicação, sem os quais este trabalho teria sido muito mais

difícil.

Agradeço igualmente ao Doutor António Gonçalves pela disponibilidade e ajuda na realização de

ensaios de difracção de raio-X no CTN e ao Doutor Carlos Nogueira pela sua atenção na utilização

do aparelho CILAS no LNEG.

Quero agradecer a amizade de quem me acompanhou durante estes anos, em particular ao António

Alvarenga, à Ana Cláudia e ao Francisco Faria.

À minha namorada, Ana Ferreira, quero agradecer a compreensão, paciência e alegria que sempre

me transmite.

É com orgulho que agradeço à minha família por me ter proporcionado todas as condições para que

pudesse realizar o meu percurso académico. Um obrigado especial à minha avó Adelina e ao meu

avô Carlos por todo o carinho e apoio, ao meu pai pelo desafio e inspiração e à minha mãe, cujo

amor e dedicação pelo filho foram inexcedíveis e indispensáveis durante todo este caminho.

Tomás

viii

Acknowledgments

I would first like to thank my supervisor, Professor Alberto Ferro, for the trust, challenge and support

during this thesis project and for his example of pedagogy and science.

To my supervisor, Professor Ricardo Baptista, I would like to thank the help during all the process and

the precious advices regarding Abaqus.

A special thanks to Professor Mafalda Guedes, for her help on the experimental part of the work and

for her kindness and availability, which were crucial for this work.

I would also like to thank Doctor António Gonçalves for his availability and help in the X-ray diffraction

experiments and to Doctor Carlos Nogueira for his help in using CILAS.

I would like to thank the friendship of those who have stood by me these years, in particular António

Alvarenga, Ana Cláudia and Francisco Faria.

To my girlfriend, Ana Ferreira, i would like to thank the understanding, patience and joy that she

always brings to my life.

I proudly thank my family for giving me the conditions to finish my degree. A special thank you to my

grandmother Adelina and to my grandfather Carlos for all the care and support, to my father for the

challenges and inspiration and to my mother, whose love and dedication for her son have been

limitless and indispensable throughout my life.

Tomás

x

Contents

1. Introduction ..................................................................................................................... 1

2. State of the Art ................................................................................................................. 3

2.1. Copper-matrix composites ................................................................................... 3

2.1.1. Alumina reinforcement .......................................................................................... 4

2.1.2. Graphite reinforcement ......................................................................................... 4

2.1.3. Carbon nanotubes reinforcement ......................................................................... 4

2.2. Mechanochemical processing .............................................................................. 5

2.2.1. High-energy ball milling ........................................................................................ 5

2.2.2. Process parameters .............................................................................................. 6

2.3. Modeling .............................................................................................................. 7

2.3.1. Introduction to ball mill modeling .......................................................................... 7

2.3.2. Finite element method .......................................................................................... 8

2.3.3. Computer modeling of ball milling ........................................................................ 9

2.3.4. Constitutive equations for materials in ball milling impacts .................................. 9

3. Experimental method and techniques ..........................................................................11

3.1. Ball milling ..........................................................................................................11

3.1.1. Materials ............................................................................................................. 11

3.1.2. Sample identification – pure copper ................................................................... 12

3.2. Powder compaction ............................................................................................13

3.3. Ball mass variation and pictures of the surface ...................................................13

3.4. Density measurement of powder pellets .............................................................14

3.5. X-ray diffraction (XRD) ........................................................................................14

3.6. SEM....................................................................................................................16

3.7. Particle size distribution ......................................................................................16

3.8. Hardness measurement ......................................................................................16

3.8.1. Indentation Size effect ........................................................................................ 17

3.9. Clarifications .......................................................................................................17

3.9.1. Sampling challenges ........................................................................................... 17

3.9.2. Contamination from vial wall and milling balls .................................................... 18

3.9.3. Simultaneous mechanisms ................................................................................. 18

3.9.4. Analysis............................................................................................................... 18

4. Pure copper - influence of media size and process control agents ...........................19

4.1. Dry conditions, large balls (DL) ...........................................................................19

4.1.1. Mass variation and ball images .......................................................................... 19

4.1.2. SEM images and particle size ............................................................................ 20

4.1.3. XRD - Scherrer ................................................................................................... 22

4.2. Dry conditions, small balls ..................................................................................23



4.2.3. XRD - Scherrer ................................................................................................... 26

4.3. Isopropyl alcohol, large balls ...............................................................................26



4.3.3. XRD - Scherrer ................................................................................................... 29

4.4. Isopropyl alcohol, small balls ..............................................................................30

xi



4.4.3. XRD .................................................................................................................... 33

4.5. Systems comparison ..........................................................................................34

4.5.1. Mass variation ..................................................................................................... 34

4.5.2. Particle size and morphology ............................................................................. 36

4.5.3. XRD - Scherrer ................................................................................................... 41

4.6. Mechanical testing ..............................................................................................42

4.6.1. Powder microhardness ....................................................................................... 42

4.6.2. Green density and hardness .............................................................................. 43

5. Copper composites – Influence of annealing temperature .........................................47

5.1. XRD ....................................................................................................................48

5.2. Powder microhardness .......................................................................................48

6. Modeling – FEM ..............................................................................................................51

6.1. Model set up .......................................................................................................51

6.1.1. 2D model and parts ............................................................................................ 51

6.1.2. Motion ................................................................................................................. 52

6.1.3. Materials ............................................................................................................. 52

6.1.4. Mesh ................................................................................................................... 53

6.1.5. Simulation time ................................................................................................... 55

6.2. Simulations .........................................................................................................56

6.3. Results ...............................................................................................................57

6.3.1. Von Mises stress ................................................................................................ 58

6.3.2. Plastic equivalent strain (PEEQ) ........................................................................ 61

6.3.3. Conclusions ........................................................................................................ 65

7. Summary .........................................................................................................................67

7.1. Conclusions ........................................................................................................67

7.1.1. Pure copper ........................................................................................................ 67

7.1.2. Copper composites ............................................................................................. 67

7.1.3. FEM simulations ................................................................................................. 68

7.1.4. Comparison ........................................................................................................ 68

7.2. Future work .........................................................................................................68

8. References ......................................................................................................................69

xii

Figure Index

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

xiii

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

............................................................................................................................................................... 42

Fig. 35 - Density - pressure curve for pure not-milled copper ............................................................... 43

Fig. 36 – HV1 (left axis) and Relative density (right axis) for powder pellets as a function of milling time

............................................................................................................................................................... 45

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

HD03S simulation .................................................................................................................................. 62

Fig. 47 - PEEQ as a function of simulation time for element 1of particles of 1, 2, 3, 4 and 10 of HD03S

simulation............................................................................................................................................... 63

Fig. 48 – Detail (model center) of the stress distribution for FD10L simulation .................................... 63

xiv

Table Index

Table 1 – Contaminant batch values for starting copper powder .......................................................... 12

Table 2 – Pure copper powder sample denomination ........................................................................... 13

Table 3 – Peaks used for XRD analysis and calculations ..................................................................... 15

Table 4 – Copper powder composites sample denomination ............................................................... 47

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

xvi

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

xvii

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

ε̇ Strain rate

ε ̇ Normalizing strain rate �� Strain at fracture �� Equivalent plastic strain ��̇ Equivalent plastic strain rate matrix

θ Angle between incident ray and scattering planes

λ Wavelength of incident radiation � Equivalent stress

σ0 Strength of the wrought material

σp Strength of the porous material

σ Average of normal stresses

σ�� Von Mises equivalent stress

[K] Matrix of properties

{F} Vector of actions

{u} Vector of behavior

a Lattice spacing

A Johnson-Cook empirical model parameter

B Johnson-Cook empirical model parameter

C Johnson-Cook empirical model parameter

D Crystallite size

D1 Johnson-Cook fracture empirical parameter


xviii



d10 length for which 10% of the particles, in volume, have lower diameter



f(p) function of porosity/density

f1 Function of strain hardening

f2 Function of strain rate strengthening

f3 Function of thermal softening

h Miller plane index

k Miller plane index

K Scherrer geometric factor

l Miller plane index

n Johnson-Cook empirical model parameter

S Stress matrix

sm microstrain

1

1. Introduction

This work aims to be an introduction to the use of the finite element method (FEM) as a modeling tool

for mechanical milling processes. FEM models can provide insight into the milling mechanisms and

show predictive capability. A reliable model is therefore desirable for confirming hypothesis and saving

experimental time and resources. When establishing a model, experimental data is key for validating

and assuring the accuracy of the modeling results. In this work, FEM results are compared with

experimental results in a copper-copper-copper system. Copper composites are widely used for the

production of electromechanical components in several industries and understanding how process

parameters influence the final material properties can be valuable.

The main body of this work can be divided into three different parts. The first part studies the ball

milling of a copper-copper-copper system and the influence of process parameters. Since ball milling

is a process mainly used for producing powder composites, the second part deals with the analysis of

copper-matrix composite powders, namely the characterization of copper-alumina, copper-graphite,

copper-alumina-graphite and copper-carbon nanotubes composites, and the effect of annealing

temperature on powder properties. The first two parts present the analysis of the experimental data

necessary to assess the merit of the FEM model. The third and final section consists of a FEM study

of the ball milling process.

This thesis is divided in 7 sections. This introduction is section 1. In section 2 - State of the Art, a brief

literature review of the production processes, properties and applications of copper-matrix powders is

presented. The basics of mechanochemical processing and modeling, specifically FEM modeling, are

also reviewed in this section. Section 3 - Experimental method, serves as an introduction to the

experimental techniques and materials used. In section 4 - Pure copper - influence of media size and

process control agents, the experimental results of the copper-copper-copper millings are presented

and analyzed and in section 5 - Copper composites – Influence of annealing temperature, the same is

done for the copper-composite powders. Section 6 - Modeling – FEM presents the set-up of the FEM

model and the simulation results. Finally, in section 7 - Summary, experimental and simulation data

are compared, the conclusions of the work are summarized and future work possibilities are proposed.

3

2. State of the Art

In this section, the production processes, properties and applications of copper-matrix powders are

introduced. The basics of mechanochemical processing and modeling, specifically FEM modeling, are

also reviewed.

2.1. Copper-matrix composites

A metal matrix composite (MMC) is a composite with a continuous metallic matrix reinforced with at

least a few percent of another material by volume [1]. The reinforcement is often nonmetallic (usually

ceramic), as to provide the composite material with different properties and more attractive

engineering attributes [2][3]. Research on this type of composites had its inception in the 1960’s,

seeing sustained interest of the scientific and industry sectors since the 1980’s [1][2]. MMC’s are used

in the space[4], automotive[5][6][7], electrical and welding industry [5] and are mainly produced by

either casting [8][9][10] or by powder metallurgy methods. [11]

Copper’s high thermal and electric conductivity, in addition to its high melting point and corrosion

resistance, makes it the metal of choice for several applications including electrical and cooled heat

conductors, such as resistance welding electrodes, nozzle and combustion chamber liners [12],

electrical contacts and electronic packaging [13]. However, copper and its alloys’ relatively high

ductility [14], low wear resistance and low high-temperature strength [15] restrict the possible uses of

these materials in applications requiring higher mechanical strength. To solve this problem, copper

may be reinforced with micro or nano-sized ceramic particles, yielding a copper-matrix composite with

improved room and high-temperature strength as well as better wear resistance [13]. This

reinforcement also has a positive effect on other properties such as the Young’s modulus [15],

preventing the sliding of grain boundaries [14] and impeding grain growth via kinetic pinning [16].

These composites usually present increased hardness values due to a combination of both the

smaller grain size (Hall-Petch effect) and Orowan strengthening. [16] [17]

Popular ceramic reinforcements include carbon fiber [18], carbides such as NbC[19] WC[20], TiC[21]

and SiC[13] and oxides such as ZrO2 [22], SiO2 [23] and Al2O3 [24], which is one of the reinforcements

used in this work. Cumulatively with these hardening reinforcements, graphite is also a useful addition

to achieve improved composite properties [13], and its influence on copper matrix composite was also

studied in the work. Other more novel reinforcements include graphene [25] and carbon nanotubes

(CNT’s) [26]. In this work, the effects of alumina, graphite and carbon nanotubes as reinforcements

are studied.

4

2.1.1. Alumina reinforcement

Copper-alumina composites are an example of how oxide dispersion strengthening improves the

mechanical properties of the material. Most copper-alumina composites are prepared by mechanical

alloying [27], the same technique used in this work, with hardening of the material being attributed, as

previously mentioned, to both Hall-Petch and Orowan mechanisms [28]. To maintain good

conductivity, the volume percentage of alumina should be kept low (low single digits) [29]. On the

other hand, using most common processes such as powder metallurgy, especially if the Al2O3 particles

are too small, it is difficult to distribute and tightly bind the alumina in the copper matrix [12]. As

expected, an increase in alumina content leads to lower conductivity and higher hardness [29]. A

decrease in particle size, to nano-sized Al2O3 also leads to increased hardness [30].

2.1.2. Graphite reinforcement

Copper-graphite composites add the properties of graphite, namely small thermal expansion

coefficient and solid lubricating to the excellent thermal and electrical conductivity of copper [31],

making these composites ideal for use in systems involving transmission of electrical current and

sliding movement [32]. Copper-graphite composites exhibit improvements in both anti-friction and

wear properties [33]. Wear resistance is affected by volume fraction, increasing until a fraction at

which the wear mechanisms approach those of pure graphite [33]. For high loads and high graphite

content, delamination can occur, leading to three-body wear mechanisms and increased wear rate

[13]. Zhan et al. demonstrated how graphite could be incorporated as a second addition to an already

reinforced metal-matrix composite, in this case Cu-SiC, showing how a graphite-rich mechanically

mixed layer improved the tribological properties of the hybrid composite. Hybrid composites of

Cu/Al2O3/C (graphite) will be studied in this work. Mechanical alloying of copper-graphite composites

possibly leads to the formation of metastable solid solutions, resulting in an increase of the lattice

parameter of copper with carbon concentration [34].

2.1.3. Carbon nanotubes reinforcement

Carbon nanotubes have also been used as reinforcement in metal-matrix composites to improve

mechanical, thermal and electrical properties [35] [36], with several processing difficulties still

associated with the dispersion of the CNT’s in the metal matrix [26]. In this work, copper reinforced

with multi-walled carbon nanotubes is studied.

5

2.2. Mechanochemical processing

The powders studied in this work were processed in high-energy ball mills. This process can be

divided into mechanical milling (MM) where one powder of a given composition is milled, with no

material transfer being required for homogenization and mechanical alloying (MA) where different

powders are milled together, with material transfer being involved to produce, in this work’s case, a

metal-matrix composite [37]. These processes induce several defects (dislocations, vacancies) and

can be used to synthesize nanostructured materials and metallic glasses [38]. The particle size as well

as crystallite size vary, for most cases, logarithmically with processing time, as is shown schematically

in Fig. 1. The steady-state is reached faster if the ball-to-powder ratio (BPR) or milling energy are

increased or if the temperature is lowered (welding less favorable). [39] When considering MA and

MM, a comprehensive review can be found in reference [39], Mechanical alloying and milling, an

article by Suryanarayana, 2001.

2.2.1. High-energy ball milling

MA and MM processes start off by loading the powder (a powder mix in the case of MA) into the mill

vial with the milling medium, to be milled for a desired length of time. In this work, a planetary ball mill

was used. In these mills, the vial rotates around its axis and around the center axis of the mill, in

opposite directions, causing the milling balls to run down the inside wall of the vial. Several types of

interactions occur within the ball mill, including friction (between balls and between balls and vial

surface) [39], compression (weight of the ball compresses the powder particle), shear (ball moves over

another powder covered ball or the wall of the vial) and impact (ball impacts another powder covered

ball or the wall of the vial) [40]. Impact phenomena, as is detailed in section 2.3.1, are,

overwhelmingly, the most prominent contributors to fracture and welding processes [39]. With

increasing rotating speed, the motion shifts from cascading (A) to cataracting (B) to centrifugal (C)

(Fig. 2). For maximum impact energy, the velocity must be set as to achieve a cataract motion [41]. In

all cases, most energy, over 99% of it, is lost in the form of heat.

Fig. 1 – Schematic representation of the evolution of particle and crystallite size with milling time. [39]

6

When the balls collide with one another or with the vial wall, the powder particles trapped in between

are subjected to high stresses, proportional to the impact energy. There are two cases of milling in this

work: ductile-ductile, for the copper-copper-copper milling, and ductile-brittle, in the case of the

copper-matrix composites.

Fig. 2 - Types of motion in a ball mill: A) cascading; B) cataracting and C) centrifugal [41]

Milling of ductile powders can be divided in three stages. In the first stage, the ductile particles are

flattened by the ball impacts, with some material getting weld onto the ball and vial surfaces. In the

second stage, the platelet-shaped particles are cold welded into a lamellar structure, with particle size

increasing. Further milling results in work hardening and convolution of the ductile particles, leading to

the third stage. The work-hardened and embrittled particles fragment and particle size is reduced, until

a steady-state is reached, with the rate of welding and fracturing balancing out.[39]

In the first stages of MA with ductile and brittle components, soft particles are flattened by the ball

impacts and weld together into lamellae, while the brittle components get fragmented and trapped

along the interlamellar spacings. It is during these early stages that reinforcement particles are to be

incorporated in the ductile matrix. Further milling results in work hardening, convolution and

fragmentation of the powder. With powder size reduction and lamellar refinement, the interlamellar

spacing decreases and the brittle particles get uniformly dispersed in the matrix.

2.2.2. Process parameters

Parameters such as the type of mill, container materials, milling time and speed, size of the milling

media, ball-to-powder ratio, milling atmosphere, presence of process control agents (PCA) and

temperature influence the milling process and the characteristics of the powder. In this work, milling

time, the size of the milling medium and the presence of a PCA were varied. Other milling parameters

were kept constant for all millings.

According to literature, the longer the milling time, the more homogenous the mixture in MA, as the

particles have more time to be dispersed in the matrix. However, milling times should be restricted to

the time necessary to achieve steady-state, as to save energy and avoid unnecessary contamination.

As for the size of the milling medium, larger, heavier balls usually increase the milling efficiency since

7

more energy is transmitted to the powders, with reported cases of different phases being formed

simply by increasing the diameter of the balls [42]. PCA are added to the powder mixture to reduce the

effect of cold welling. These PCA are more often organic compounds such as alcohols, with lubricant

properties. Increasing quantities of PCA result in a smaller particle size, sometimes even orders of

magnitude smaller [42]. The effect of these parameters on the particle size, morphology is studied in

this work.

2.3. Modeling

2.3.1. Introduction to ball mill modeling

Mechanical milling and alloying are solid-state powder processing techniques involving extensive

plastic deformation and repeated welding, fracturing and rewelding of powder particles, usually in a

high-energy ball mill [39]. It is an intricate and complex process and, therefore, the models so far

developed are not comprehensive or predictive [40]. A finite element method (FEM) simulation of

mechanical alloying will necessarily be limited in the number of parameters and variables it considers,

resulting in an approximate prediction. The FEM simulations in this work consider primarily mechanical

behavior and response.

A clear and concise overview of mechanical alloying (MA) modeling was carried out by Courtney in

1995 [40]. In this article, several studies which deal with the mechanics and dynamics of MA and their

effect on alloying kinetics and characteristics of processed powders are summarized. The reasons for

which exact answers are unattainable are detailed:

Elasto-plastic constitutive equations that describe with precision the mechanical behavior of

the material under high strain and strain rate conditions common to MA are not available.

Frequency and velocity of effective impacts can only be approximately ascertained.

Thickness of powder trapped between the media during impacts in only approximately known.

Simultaneous need for sophisticated computing of both deformation response of powder

particles and of welding and fracture events.

Courtney concludes that a good model identifies variables that importantly affect the process outcome

leading to a possible reduction in empirical studies and better chance at process optimization, dividing

the modeling of MA into two categories: global modeling and local modeling.

Global modeling is useful for studying the influence of process parameters such as milling speed or

vial size and for improving device efficiency. High speed cinematography and global modeling both

identify two main types of media interaction, direct impacts and ball sliding, as detailed in section

2.2.1. Direct impacts are high velocity collisions between milling balls and ball sliding corresponds to

low velocity collisions due to different rotational velocities between adjacent columns or rows of milling

balls [43]. Global modeling provides valuable insight into collision efficiency as a function of impact

velocity and angle. Studies in which the coefficient of restitution of balls was measured have

8

determined that most collisions (more than 50%) result in very low energy dissipations (10% of

maximum one) and that most effective deformation, fracture and welding phenomena are only verified

in head-on collisions, in which the velocity is approximately the maximum velocity. This conclusion

greatly simplifies the collision dynamics to be used in local modeling.

In local modeling, a single collision involving powder trapped between milling media is analyzed. To

develop a local model, the powder properties, such as density, initial particle size, shape and the

material constitutive equations for high strain and strain rate conditions, must be known. Furthermore,

process parameters such as the machine’s specific frequency, the velocity of collisions and the BPR,

which in turn affects the coating powder thickness, are necessary to develop an accurate model.

These process parameters can be obtained through experimental or global modeling results. With all

these input parameters, the deformation of the particles, the probability of particle coalescing and of

particle fracture can be determined for a specific collision. By calculating several collisions, particle

characteristics such as shape, size and hardness can be determined as a function of milling time

(number of collisions).

2.3.2. Finite element method

Even though the use of a competent software, in this case ABAQUS, may not demand a complete and

direct knowledge of the theory of finite element method (FEM), it is important to understand the basis

of these solutions and their advantages and disadvantages.

The principle of the FEM is the decomposition of the spatial domain into a set of elements of a given

shape and size, called mesh. The elements are connected at points called nodes, which are used to

construct the approximation of the functions for the whole domain, in a process called interpolation. It

is at these points that the value of the functions is to be calculated, restricting the degrees of freedom

to a finite number, instead of an infinite number when considering a continuum. The problem is then

reduced to a set of algebraic equations, considering a governing equation of the problem and the

boundary conditions, which can be summarized by the matrix equation ( 1 ):

[�]{ } = { } ( 1 )

In this equation, {u} is a vector of the behavior verified when a vector of actions {F} is applied to a

domain with a [K] matrix of the properties. In an elastic problem, for example, [K] would be the

stiffness matrix, {u} the displacement and {F} the forces. The quantity is interpolated by a polynomial

over an element and, after solving the equations and obtaining the variables at the nodes, the

equation can be inverted to obtain a solution [44].

The big advent of FEM occurred in the 1960’s, with the first book on the subject being published in

1967 by Zienkiewicz and Chung [45] and most software packages, including Ansys and Abaqus, were

developed in the following decade. The biggest advantages of FEM are its versatility and applicability

to a variety of engineering problems (from solid mechanics to heat and electrostatic problems), the

9

complexity of the geometry it allows for (unlike the more restrictive finite difference or finite volume

method) and the ability to handle complex loading (in both time/frequency and space, allowing for

loads to be applied both to the nodes and to the element as a whole). As to the method’s

disadvantages, those include the inability to achieve an exact solution, adding to the inevitable

numerical difficulties associated with the software and the susceptibility to user based mistakes such

as choosing wrong element type and size, leading to convergence problems [44]. Standard text books

on the FEM are available [46], some of them dedicated to its application to Materials’ Science [44].

2.3.3. Computer modeling of ball milling

Several models have been developed for global modeling (as described in section 2.3.1) of ball

milling, intent on tuning and perfecting the milling parameters for more efficient milling. The models

developed are either mathematical predictive models based on kinematic equations [47][48][49][50] or

developed by the distinct (discrete) element method (DEM). DEM modeling for this approach is aptly

summarized by McCormick and Dallimore in Distinct Element modeling of Mechanical Alloying in a

Planetary Ball Mill [51] but one can understand the method as a simplification of FEM where all

elements are separated parts. DEM models were developed for both SPEX/shaker [52] [53] and

planetary ball mills [54] [55].

No models were found for local modeling, as local data for global modeling was estimated from

experimental results. In this work, focus will be given on the FEM modeling of the local problem,

particularly the impact and deformation processes to which the powder particles are subjected.

2.3.4. Constitutive equations for materials in ball milling impacts

Ball milling is a dynamic process, involving impact and severe deformation of the powders particles.

When simulating such process, the material’s constitutive equations need to be defined in both elastic

and plastic regimes and require a fracture/failure criterion.

For the elastic regime, the properties required to construct the material model are general properties,

namely the mass density, Young’s modulus and Poisson’s ratio.

For the plastic regime, given the high strain rates and the natural influence of strain hardening,

common plastic deformation models derived from uniaxial or biaxial testing would be inaccurate. A

more appropriate model is the Johnson-Cook five-parameter empirical model. This model is highly

used in hypervelocity impact and explosively driven fracture [56]. It is therefore expected to fit the high

strain rates of the mechanical milling and alloying process better than other more widely used models.

The model represents the flow stress σ as a function of strain hardening (f1), strain rate strengthening

(f2) and thermal-softening (f3). The resulting function ( 2 ) therefore yields:

10

σ (��, ε̇) = (��) ε̇ = ( + �� ) + ln ε̇ ε ̇⁄ ( 2 )

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]

11

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

12

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.

13

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




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 )

14

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.

15

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



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

16

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

17

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

18

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

19

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)

20

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)


25

30

35

40

45

0 1 2 3 4 5 6 7 8

Crystallite

size (nm)


23

4.2. Dry conditions, small balls

In this section, the samples produced in dry conditions and with small balls (DS) are characterized.


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(%)


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.


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)


26


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.


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)


-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(%)


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.


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


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)


15

20

25

30

35

40

45

0 1 2 3 4 5 6 7 8

Crystallite

size (nm)


30

4.4. Isopropyl alcohol, small balls

In this section, the samples produced in wet conditions and with small balls (WS) are characterized.


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(%)


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.


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)


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)


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 (%)


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)


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


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)


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


0

50

100

150

0 20 40 60

HV0,012


0

50

100

150

0 20 40 60

HV0,012


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


D) WS

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

the annealing temperature is 800o C

Table 4 – Copper powder composites sample denomination

Annealing temperature

Composition

(-%)

No heat

treatment 600o C 700o C 800o C 900o C

Cu_st Cu_st Cu_st_600 Cu_st_700 Cu_st_800 Cu_st_900

Cu Cu_nht Cu_600 Cu_700 Cu_800 Cu_900

Cu-2G Cu-2G_nht Cu-2G_600 Cu-2G_700 Cu-2G_800 Cu-2G_900

Cu-2A Cu-2A_nht Cu-2A_600 Cu-2A_700 Cu-2A_800 Cu-2A_900

Cu-2G-2A Cu-2G-2A_nht Cu-2G-2A_600 Cu-2G-

2A_700

Cu-2G-

2A_800

Cu-2G-

2A_900

Cu-2CNT Cu-2CNT_nht Cu-2CNT _600 Cu-2CNT

_700

Cu-2CNT

_800

Cu-2CNT

_900

48

5.1. XRD

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:

4 (ball velocities) × 2 (ball sizes) × 3 (particle distances) = 24 (total simulations).

The simulations (in bold) and the number of nodes per simulation and are identified in Table 9. The

elements are plane stress elements: CPS3 (3.node linear) and CPS4R (4-node bilinear).

Table 9 - Simulation identification and number of nodes

Ball velocity (m/s)

1 3 6 10

Small

balls

(S)

No distance (ND) ND01S 36202 ND03S 43146 ND06S 43146 ND10S 43146

Half distance (HD) HD01S 36202 HD03S 36202 HD06S 38726 HD10S 40619

Full distance (FD) FD01S 36202 FD03S 34309 FD06S 36202 FD10S 36202

Large

balls

(L)

No distance (ND) ND01L 38770 ND03L 46446 ND06L 54319 ND10L 60629

Half distance (HD) HD01L 43286 HD03L 45810 HD06L 51795 HD10L 54950

Full distance (FD) FD01L 34330 FD03L 39505 FD06L 44854 FD10L 48009

6.3. Results

Two output variables are analyzed to assess the deformation and stress solicitation of the particles:

Von Mises stress (VMS), which is described by equation (11), where <S,S> is the internal

product of the stress matrix (S) by itself. [75]

� = √ < , > (11)

58

Equivalent plastic strain (PEEQ), which is described by equation (12), where < ��̇ , ��̇ > is the

internal product of the equivalent plastic strain rates matrix (�� ̇ by itself. The plastic strain

rates are calculated according to the Johnson-Cook model. [75]

= √ < ��̇ , ��̇ > (12)

6.3.1. Von Mises stress

In this section, the von Mises stress distribution and values are presented.

6.3.1.1. Von Mises distributions

The von Mises stress distributions give information on the von Mises stress of

the elements and on the deformation of the particles.

The color legend for stress distributions is Fig. 42, with the scale in Pa. First, to

clarify the general evolution of powder deformation and stress distribution with

impact time, the example of the second particle of the FD10L simulation, is given

(Fig. 43). This simulation is chosen due to the high deformations and clear

powder shape changes involved.

Upon impact (4 µs), an “X” shaped high-stress zone forms, with the highest

located in the middle of the particle. With further deformation (12 µs, 24 µs),

around the “X” diagonal that moves from the top-left to the bottom-right a band

of high stress is formed. This diagonal corresponds to the radial direction of the

impacting ball. The ball is applying stress in the top-down direction but also in the left-to-right direction,

resulting in the diagonal band. Once the ball begins to recede, the stress decreases (40 µs). The

particle is then subjected to a residual stress and strain field.

Fig. 43 – von Mises stress distribution for particle 2 of FD10L as a function of simulation time

Stres distributions were taken at the instant of maximum von Mises stress for each simulation. Fig. 44

shows the effect of the three variables on the stress distribution and powder shape during impact.

Fig. 42 - color legend for stress

maps(Pa)

59

Fig. 44 - von Mises stress distribution for all simulation conditions at the instant of respective maximum von Mises stress

60

When comparing the simulations with small and large balls, the difference resides primarily on the

number of impacted powder particles. Large balls impact more particles due to their larger surface but

do not appear to influence significantly the powder shape.

Ball velocity also influences the number of impacted particles, with higher velocities corresponding to

more affected particles. Ball velocity affects stress distribution and powder shape. Higher velocities

lead to higher maximum stresses and to increasingly flatter powder shape. This effect of ball velocity

on powder shape is less clear for the ND (no distance) simulations.

With increasing distance between particles, the number of affected particles decreases. Higher

maximum stress and more deformed particles are verified for greater distance between particles.

6.3.1.1. Von Mises stress values

Table 10 presents the maximum von Mises stress for each simulation condition. The table cells are

colored to allow a quick overview of the lower (colder colors) and higher stress values (warmer colors).

Information from the table corroborates the initial visual analysis of Fig. 44. Ball size seems to

influence the maximum stress for lower velocities (1 m/s, 3 m/s) but not for higher velocities. Higher

ball velocity and more distance between particles lead to higher stresses. The highest stress

corresponds to the FD10L simulation and the lowest stress corresponds to the ND01S simulation.

These maximum and minimum results are in accordance with the identified general trend of the effect

of the variables.

Table 10 - maximum von Mises stress values for all simulation conditions

Maximum von Mises

stress (MPa) 1 m/s 3 m/s 6 m/s 10 m/s

S

ND 317 358 395 395

HD 324 402 423 433

FD 327 423 436 441

L

ND 332 380 395 410

HD 350 412 423 438

FD 374 429 438 447

Table 11 shows the instants for which the maximum von Mises stress was verified for each simulation.

As a tendency, higher velocities correspond to earlier instants of maximum stress (iMS). The ball

impacts the surface at an earlier time, with the maximum stress occurring for shorter times. Distance

between particles appears to have no clear influence on iMS. Larger ball size corresponds to later

iMS. Observing the simulation history frame-by-frame, these later iMS are due to the deformation of

61

the vial. A larger ball, with more energy, is able to deform the vial, prolong the impact and lead to later

iMS. For the 10L simulations, the instant of maximum stress occurs later than expected because the

high energy involved results in a very wide affected area. This effect widens the stress distribution and

allows for higher stresses to be reached at longer times.

Table 11 - Instant of maximum von Mises stress for each simulation condition

Instant of maximum von

Mises stress (µs)

Ball velocity (m/s)

1 3 6 10

Small

balls

(S)

No distance (ND) 30 18 12 6

Half distance (HD) 32 18 12 12

Full distance (FD) 30 18 14 10

Large

balls

(L)

No distance (ND) 36 22 12 22

Half distance (HD) 40 24 14 18

Full distance (FD) 44 20 16 12

6.3.2. Plastic equivalent strain (PEEQ)

Three mesh elements of the particle, with locations specified in Fig. 45, were defined as of particular

interest to study the particle deformation and strain:

element 1 - close to the center of the circle

element 144 – top surface element in contact with the impacting ball

element 288 – lateral surface element

Fig. 45 - Element location in particle

62

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 20 40 60 80 100

PEEQ

Simulation time (microseconds)

Particle 10

element 1

element 144

element 288

6.3.2.1. Element choice

To determine the value of the information for each element, PEEQ was calculated for the three

defined elements (1, 144 and 288) for particles 1 and 10, counting from the center of the model, for

the HD03S simulation (Fig. 46).

As it can be observed, PEEQ is initially 0, increasing rapidly at the moment of impact and then

stabilizing at a constant value for each element and both particles. The increase in strain occurs first

for particle 1, since impact occurs first for particles closer to the center of the model. The increase in

strain occurs initially for element 144 since it is a top surface element, suffering the impact first. Strain

of element 288 is ten and twenty times lower than that of elements 144 and 1 respectively. For that

reason, in following analysis, the focus will be on elements 1 and 144.

PEEQ of element 1 suffers a decrease from particle 1 to particle 10 (from 0.43 to 0.36) while PEEQ of

element 144 remains approximately the same. This constancy of PEEQ for element 144 indicates that

the strain of top elements is approximately the same for every deformed particle of a given simulation

condition.

Fig. 46 – PEEQ as a function of simulation time for elements 1, 144 and 288 of particles of 1 and 10 of HD03S simulation

6.3.2.2. Particle choice

In each simulation, several particles are affected. To determine which particle should be studied,

PEEQ was calculated for element 1 of particles 1, 2, 3, 4 and 10, counting from the center of the

model, for the HD03S simulation (Fig. 47).

Particle 1 is the closest to the diameter of the milling ball and to the center of the model (Fig. 48). This

influences the desired symmetry of the simulation, yielding a lower PEEQ than for particles 2, 3 and 4

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 20 40 60 80 100

PEEQ


Particle 1

element 1

element 144

element 288

63

after 12 µs of simulation. For these three particles, the PEEQ is approximately the same, for every

instant. PEEQ decreases for particles further from the center of the model. This is observed for

particle 10, which displays a lower PEEQ than other particles. Considering this, PEEQ for particle 2,

counting from the center of the model, was defined as the strain parameter for comparison between

different simulation conditions. PEEQ comparisons are carried out for the last PEEQ value, as the

strain stabilizes after impact.

Fig. 47 - PEEQ as a function of simulation time for element 1of particles of 1, 2, 3, 4 and 10 of HD03S simulation

Fig. 48 – Detail (model center) of the stress distribution for FD10L simulation

6.3.2.3. Particle 2 – PEEQ

Table 12 presents the PEEQ for element 1 of particle 2 for each simulation condition. The table cells

are colored to allow a quick overview of the lower (colder colors) and higher PEEQ values (warmer

colors).

0

0,1

0,2

0,3

0,4

0,5

0,6

0 20 40 60 80 100

PEEQ


particle 1

particle 2

particle 3

particle 4

particle 10

64

Table 12 – Last PEEQ values for element 1 of particle 2 for all simulation conditions

PEEQ – element 1

1 m/s 3 m/s 6 m/s 10 m/s

S

ND 0.05 0.13 0.15 0.17

HD 0.10 0.45 0.59 0.68

FD 0.13 0.55 0.68 0.75

L

ND 0.08 0.12 0.14 0.17

HD 0.25 0.52 0.64 0.74

FD 0.31 0.65 0.74 0.81

Table 13 - Last PEEQ values for element 144 of particle 2 for all simulation conditions

PEEQ – element 144

1 m/s 3 m/s 6 m/s 10 m/s

S

ND 0.13 0.13 0.13 0.13

HD 0.14 0.14 0.15 0.21

FD 0.14 0.15 0.31 0.26

L

ND 0.13 0.13 0.13 0.13

HD 0.14 0.14 0.15 0.22

FD 0.14 0.18 0.25 0.24

Larger ball size, higher velocities and larger distance between particles leads to an increase in PEEQ.

The influence of ball size is greater for lower velocities and larger distance between particles. The

effect of velocity is more visible when velocity is increased from 1 m/s to 3 m/s and for larger distance

between particles. The most significant variable which affects strain is the distance between particles.

When increasing the distance between particles from ND (no distance) to HD (half distance), there is a

clear increase in PEEQ for all velocities and ball size. There is a 100% increase in strain from ND01S

to HD01S and a 335% increase in strain from ND10L to HD10S. When increasing the distance from

HD to FD (full distance), there is also an increase in PEEQ, but not as significant. The increase in

strain from HD01S to FD01S is of 30% and from HD10L to FD10L it is of 9%. This is in accordance

with Fig. 44. With HD, the particles deform and, for the conditions used, do not touch. This means that

the deformation was not limited by the contact with another particle, as is the case for ND simulations.

This change in limitation from ND to HD is what accounts for the great increase in PEEQ.

65

The highest PEEQ corresponds to the FD10L simulation and the lowest PEEQ corresponds to the

ND01S simulation. These maximum and minimum results are in accordance with the identified general

trend of the effect of the variables and to the values of maximum von Mises stress.

Table 13 presents the PEEQ for element 144 of particle 2 for each simulation condition. The PEEQ for

element 144 are much lower than for element 1. For this top surface element, ball size and ball

velocity do not influence PEEQ in a clear manner. Distance between particles appears to have an

effect on PEEQ for element 144, albeit less than for element 1, particularly for higher velocities. The

increase in strain from ND01S to FD01S is of only 8% for element 144, compared to 160% for element

1. The increase in strain from ND10L to FD10L is of 88% for element 144, compared to 376% for

element 1. Fig. 44 and, as detail, Fig. 48 show that, for high velocities and full distance between balls,

the shape of the top of the particle stops being flat and assumes an angle. That change is what

explains the increase of PEEQ with ball distance.

6.3.3. Conclusions

Larger balls, higher ball velocities and greater distance between the balls lead to greater stress and

strain. That increase in strain and stress is visible when comparing the two extreme conditions –

ND01S and FD10L. Strain (PEEQ) increases from 0.05 to 0.81 and the maximum von Mises stress

increases from 317 MPa to 447 MPa. Increasing the space between particles from ND to HD is the

parameter change with greatest influence on strain values. Evolution of particle shape, stress and

strain during impact is similar for all particles, with the exception of particle 1. The zone of greatest

stress is a diagonal band following the radial direction of the milling ball.

67

7. Summary

In this section, the work’s conclusions are presented as well as suggestions for future work.

7.1. Conclusions

Conclusions for each individual part of the work are presented and a comparison between

experimental and simulations results is established.

7.1.1. Pure copper

In this work, the effect of ball size, isopropyl alcohol and milling time on powder morphology and

properties was studied:

Isopropyl alcohol prevents welding to the surface of the milling balls. When milling with smaller balls,

increased impacts per area lead to quicker work-hardening and fracture. This leads to a possible

rejuvenation phenomenon of the ball’s surface, in both wet and dry conditions.

Copper powder loses its original dendritic shape and its size decreases for early times (30 minutes) in

wet systems, where the isopropyl alcohol prevents welding and promotes deformation and fracture

phenomena. For dry systems, particle size reduction occurs slower. After four hours, powder for all

systems assumes a flake shape. For longer times (8 hours) there is a clear decrease in particle size

for all systems. Smaller balls and wet systems lead to smaller particle size. Between these two

parameters, isopropyl alcohol seems to be the main particle size controlling factor for longer times.

Similar conclusions can be extracted for crystallite size. Crystallite size reduction is much faster and

more severe in wet conditions. Smaller balls also lead to slightly smaller crystallite sizes.

For dry systems and longer milling times, compacted powder pellets collapsed during hardness

measurements. This indicates that flat powder of larger size and expected higher hardness may lead

to lower green strength. Powders milled in wet conditions appear to circumvent the work-hardening

issue and lead to a stronger, albeit not very dense, compact.

7.1.2. Copper composites

In addition, the effect of annealing on copper powder composites was analyzed. Milled composite

powders suffer considerable crystallite size growth after annealing at 900o C. All systems, after

annealing, display similar crystallite sizes, close to that of the copper powder prior to milling. Milled

powders display higher hardness values for all annealing temperatures. This increased hardness may

be attributed to the reinforcement of the milled copper by exogenous added graphite and alumina

particles from the vial and balls.

68

7.1.3. FEM simulations

FEM simulations to model the impact during milling were carried out. Larger balls, higher ball

velocities and greater distance between balls lead to greater stress and strain. Increasing the space

between particles from ND (no distance) to HD (half distance, one particle radius) is the parameter

change with greatest influence on strain values, leading to increases of strain up to 350%. Evolution of

particle shape, stress and strain during impact is similar for most particles and the zone of greatest

stress is a diagonal band following the radial direction of the milling ball.

7.1.4. Comparison

When comparing the simulation results with the properties of the milled powder, the effects of a major

variable can be confirmed.

In the simulations, presence of a PCA is translated into spacing between the particles. Comparing

simulations with no distance to simulations with some distance between particles, the strain and stress

values are considerably higher for the latter case. Strain values can suffer three-fold increases for

some simulation conditions. Isopropyl alcohol prevents welding and assures that powder particles

have more space to deform. This leads to more severe changes in powder shape and increased work-

hardening. Increased work-hardening is linked to fracture phenomena and smaller particle size. The

milled and analyzed powder may support these assumptions. Powder milled in wet conditions suffers

severe deformation for early times and displays a smaller particle size.

7.2. Future work

To further the understanding of copper powder composites and to establish a better connection with

FEM models, these suggestions for future work are proposed:

Pre-seiving and determining particle size before CILAS analysis

Nanohardness measurements on the set powders to determine work-hardening

Pressure-density curves for pellets of each milling condition

XRD analysis of the composite powders annealed at intermediate temperatures of 600, 700,

800o C

FEM simulations of several impacts and layers of particles

69

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