Molecular Dynamics Studies on the Prediction of Interface Strength of

Cu (Metal)-Cu50Zr50 (Metallic glass) Metal Matrix Composites

A THESIS IN PARTIAL FULFILMENTS OF REQUIREMENTS FOR THE AWARD OF
THE DEGREE OF

Master of Technology (Dual Degree)

Submitted to
NATIONAL INSTITUTE OF TECHNOLOGY, ROURKELA

by
Rakesh Nalla
710MM1126

Under the Guidance of

Dr. Natraj Yedla

DEPARTMENT OF METALLURGICAL & MATERIALS ENGINEERING

NATIONAL INSTITUTE OF TECHNOLOGY
ROURKELA-769008
INDIA
2015

i
 CERTIFICATE

This is to certify that the thesis entitled Molecular Dynamics Studies on the Prediction of

Interface Strength of Cu (Metal)-Cu50 Zr50 (Metallic glass) Metal Matrix Composites by

Rakesh Nalla in partial fulfilment of the requirements for the award of Master of

Technology (Dual Degree) in Metallurgical and Material Science Engineering at National

Institute of Technology, Rourkela, is an authentic work carried out by them under my

supervision and guidance. To the best of my knowledge, the matter embodied in the thesis

has not been submitted to any other university/institute for the award of any Degree or

Diploma.

Dr. Natraj Yedla

Dept. of metallurgical Engineering

National Institute of Technology

ii
 ACKNOWLEDGEMENT

I take this opportunity to express my deep gratitude to Dr. Natraj Yedla, my guide, who
provided me the initial motivation to work in this field. He kept on encouraging and
inspiring me all through, sacrificing his valuable time & energy.

Also I express my sincere thanks to Mr. Pradeep Gupta (Phd scholar) who guided me
throughout in running the simulations and also in producing the results.

I also express my sincere thanks to the Department of Metallurgical and Materials

Engineering for all the help and coordination extended by the department.

I am also greatly thankful to all the staff members of the department and all my well-
wishers.

Date:22-05-2015

Place:Rourkela

Rakesh Nalla

Roll No: 710MM1126

Dept. of Metallurgical and Materials Engineering

National Institute of Technology, Rourkela

iii
 ABSTRACT

The aim of this investigation is to predict the interface strength of metal (Cu-matrix)–
metallic glass (Cu50Zr50-reinforcement) composites via molecular dynamics (MD)
simulations. Simulation box size of 100 Å (x) × 110 Å (y) × 50 Å (z) is used for the
investigation. At first Cu–Cu50Zr50 crystalline model is constructed with the bottom layer
(Cu) of 50 Å and the top layer of 60 Å (Cu50Zr50) in height along y–direction. Thereafter,
Cu50Zr50 metallic glass is obtained by rapid cooling at a cooling rate of 4 × 10 12 s-1. The
interface model is then equilibrated at 300 K for 500 ps to relieve the stresses. EAM
(Embedded Atom Method) potential is used for modelling the interaction between Cu–Cu
and Cu–Zr atoms. The fracture strength of Cu–Cu50Zr50 model interface is determined by
tensile (mode–I) and shear (mode–II) loading. Periodic boundary conditions are applied
along z–direction for shear while along x– and z–directions for tensile tests. A timestep of
0.002 ps is used for all the simulations. Tensile and shear tests are carried out at varying
strain rates (108 s-1, 109 s-1 and 1010 s-1) and temperatures (100K, 300 K and 500 K). The
interface model is allowed for full separation under both the deformation modes. It is found
that tensile as well as shear strength decrease with increase in temperature and increase with
strain rate, as expected. Further, the maximum stress in shear is smaller than that in tensile at
all strain rates and temperatures. Critical observations of the obtained results on Cu–Cu50Zr50
composites indicate better shear strengths as compared to the results of metal (matrix)-
ceramic (reinforcement) composites available in the literature. Hence it can be concluded
that metallic glass acts as a better reinforcement material than the popular ceramic
reinforcements.

Key words: Molecular dynamics, tensile, shear, strain rate, temperature, interface.

iv
 Contents
Certificate ......................................................................................................................... ii
Acknowledgement ...........................................................................................................iii
Abstract ........................................................................................................................... iv
List of figures ................................................................................................................... 1
List of tables ..................................................................................................................... 2

CHAPTER ONE................................................................................................................. 3
1.1 Inroduction ................................................................................................................. 3
1.1.1 Composite ............................................................................................................ 3
1.1.2 Types of composites ............................................................................................. 3
1.1.2.1 Metal Matrix composites(MMCs) .................................................................. 3
1.1.2.2 Polymer Matrix composites(PMCs) ............................................................... 4
1.1.2.3 Ceramic Matrix composites(CMCs) ............................................................... 4
1.1.3 Applications of composites ................................................................................... 4
1.1.4 Interface ............................................................................................................... 4
1.1.5 Methods for studying the strength of the interface ................................................ 5
v
 1.1.5.1 Indentation hardness test ................................................................................ 5
1.1.5.2 3-Point Bending Test ..................................................................................... 5
CHAPTER TWO ............................................................................................................... 6
2.1 Literature Survey ........................................................................................................ 6
2.2 Gaps in the literature ................................................................................................... 8
2.3 Objectives of the work ................................................................................................. 9
CHAPTER THREE ......................................................................................................... 10
3.1 Modeling procedure .................................................................................................. 10
3.2 LAMMPS ................................................................................................................. 11
3.3 Input script file for creating sample ........................................................................... 12
3.4 Input script file for mode 1 (Tensile) deformation without crack ............................... 14
3.5 Input script file for mode 2 (Shear) deformation without crack .................................. 16
3.6 Input script file for mode 1 (Tensile) deformation with crack .................................... 18
3.7 Input script file for mode 2 (Shear) deformation with crack ....................................... 20
3.8 Work Plan ................................................................................................................ 22
CHAPTER FOUR ............................................................................................................ 23
4.1 Results and Discussions ............................................................................................ 23
4.2 Deformation (Tensile and Shear) studies of the Cu –CuZr interface .......................... 23
4.3 Effect of strain rate on the interface strength ............................................................. 24
4.3.1 Atomic positions snap shots (Mode I without crack) ........................................... 26
4.3.2 Atomic positions snap shots (Mode I with crack) ................................................ 28
4.3.3 Atomic positions snap shots (Mode II without crack).......................................... 30
4.3.4 Atomic positions snap shots (Mode II with crack) .............................................. 32
4.4 Effect of temperature on interface strength ................................................................ 33
CONCLUSIONS .............................................................................................................. 37
REFERENCES ................................................................................................................. 38

vi
 List of Figures
Fig No. Caption Page
Atomic snapshot of interface (a) without crack, (b)
1 with crack 24

Stress-Strain plot for Mode-I without crack, Cu50Zr50

2 metallic glass reinforced in Cu Metal matrix. 25

Atomic snapshot at different strains of the model

3a without crack under Mode-I deformation 26
Atomic snapshot at different strains of the model
3b without crack under Mode – I deformation. 26
Stress-Strain plot for Mode-I with crack, Cu50Zr50
4 metallic glass reinforced in Cu Metal matrix. 27
Atomic snapshot at different strains of the model with
5a crack under Mode-I deformation. 28
Atomic snapshot at different strains of the model with
5b crack under Mode-I deformation. 29
Stress-Strain plot for Mode-II without crack,
6 Cu50Zr50 metallic glass reinforced in Cu Metal 30
Atomic snapshot at different strains of the model
7a without crack under Mode –II deformation. 31
Atomic snapshot at different strains of the model
7b without crack under Mode – II deformation. 31
Stress-Strain plot for Mode-II with crack, Cu50Zr50
8 metallic glass reinforced in Cu Metal matrix. 32
Atomic snapshot at different strains of the model with
9a crack under Mode-II deformation. 33
Atomic snapshot at different strains of the model with
crack under Mode-II deformation. 33
Stress-Strain plot for Mode-I without crack, Cu50Zr50
10 metallic glass reinforced in Cu Metal 34
Stress-Strain plot for Mode-I with crack, Cu50Zr50
11 metallic glass reinforced in Cu Metal 35
Stress-Strain plot for Mode-II without crack,
12 Cu50Zr50 metallic glass reinforced in Cu Metal 36
Stress-Strain plot for Mode-II with crack, Cu50Zr50
13 metallic glass reinforced in Cu Metal 37
 List of Tables

1 Details of studies 22

2
CHAPTER 1

1.1 INTRODUCTION
1.1.1 COMPOSITE
Composite is a blend of two materials, where one of the materials is called the reinforcing
phase, made up of particles or fibers that are embedded in the matrix phase. The second
phase is called matrix phase. The function of the matrix phase is to transfer stress
between the reinforcement phases [1]. Composite is a heterogeneous mixture of two or
more materials where the individual properties of the materials are preserved unlike an
alloy. Composite is a combination of two or more phases, one phase is stronger and is
called reinforcement and the other is a weaker phase called the matrix. The reinforcing
phase is normally used to increase the stiffness and strength of the matrix phase.

1.1.2 TYPES OF COMPOSITES

1.1.2.1 METAL MATRIX COMPOSITES (MMCs)
The composite material where at least one constituent is metal and the other material may be
either metal or any other material. These metal matrix composites are made by dispersion of
reinforcing material in the metal matrix. In structural applications, lighter metals are used as
matrix providing support to the reinforcements [2]. Cobalt and nickel alloy matrix is used for
high temperature applications.
3
1.1.2.2 POLYMER MATRIX COMPOSITES (PMCs)
These composites consist of polymer matrix with glass, aramid and boron fibers as reinforcing
materials. Polymer matrix materials in comparison to MMC’s and CMC’s are manufactured with
ease. The secret of their wide application lies in the ease of their production and their light
weight. Glass fiber reinforced polymers is most widely used composite materials. One of the
main drawbacks of the PMCs’ is low service temperature[3].

1.1.2.3 CERAMIC MATRIX COMPOSITES (CMCs)

These polymers have ceramic materials as the matrix with any other reinforcing materials.
Ceramic materials have high strength, good high-temperature properties and low density. The
use of ceramic materials is limited because of certain drawbacks[4]. They cannot withstand
tensile loading because of poor ductility and low plasticity. Ceramics materials are brittle. This is
because of the inability to dissipate energy. So in order to increase the toughness of these
materials, ceramic matrix composites are used.

1.1.3 APPLICATIONS OF COMPOSITES

Composites are used in the manufacture of variety of products like sports goods, rockets,
missiles, spacecraft, satellites and various automobile components. Carbon fiber reinforced
plastic is used in cases of limb deformity. Chemical industry uses the composites for valves,
containers, pressure vessels etc. Lightweight, high-strength carbon, kevlar and glass-fiber
composites are used in military aircrafts [5]. Extensively composites are used in sports goods
industry in the form of cricket bats, surfing boards, bicycles, tennis rackets etc. The use of
composite materials has significantly increased in the recent times.

1.1.4 INTERFACE
The surface between the matrix phase and the reinforcing phase is called interface. Interface is a
boundary through which the different properties of the materials such as elastic modulus,
density, and concentration change, etc change. The properties of the composite materials
depends on the i) matrix phase, ii) reinforcing phase and iii) interface between the matrix and the
interface. The interface plays a vital role in determining the mechanical properties of the
composite. This is because of the large surface area occupied by the interface. Therefore the
interface between the matrix and the reinforcement plays a crucial role in determining the

4
resultant properties of the composite and the strength of the composite depends on the strength of
the interface.

1.1.5 METHODS FOR STUDYING THE STRENGTH OF THE INTERFACE

1.1.5.1 INDENTATION HARDNESS TEST

Indentation hardness tests are utilized as a part of mechanical building to focus the hardness of a
material to distortion. A few such tests exist, wherein the analysed material is indented until an
impression is framed; these tests can be performed on a naturally visible or tiny scale. At the
point when testing metals, space hardness corresponds sprightly with tractable strength. This
connection allows financially imperative non-destructive testing of mass metal conveyances with
lightweight, even compact hardware, for example, hand-held Rockwell hardness analysers.

1.1.5.2 3-POINT BENDING TEST

The 3-point bending test enables the calculation of young's modulus in bending, flexural stress,
stress-strain behaviour of the material. The fundamental favourable position of a three point
flexural test is the simplicity of the sample preparation and testing. Then again, this system has
additionally a few drawbacks: the after effects of the testing strategy are touchy to sample and
stacking geometry and strain rate.

5
CHAPTER 2

2.1 LITERATURE SURVEY

Composite consists of a strong phase (reinforcement) and a weak phase (matrix). So the strength
of the composite depends on the degree of compatibility between the two regions. Depending on
the extent of bonding and the interface thickness between these two phases, the deformation
behavior varies. In this work, the interface is modeled using finite element method to analyse the
behavior of metal matrix composites under deformation. A thin layer of interface is modeled
using an artificial material. Different samples of the material with different stiffness and different
volume fractions are used to vary the interaction at the interface. It is found that the composite
provides greater strength than the traditional materials. This is significantly realized for higher
volume fraction of reinforcement and large area of the interface. The flow curves match with the

experimental curves [6]. The enhancing use of metal matrix composites in different areas of

interest makes it necessary for the prediction of mechanical properties from the known
parameters. In this work investigation of the effect of interface strengths on the mechanical
behavior of composite at different loading conditions is done. Failure mechanisms during the
loading process: ductile failure in metal matrix, brittle failure in SiC particles and interface
debonding between matrix and particles. The damage models are developed to simulate the
failure in the composite. The simulation results show that particle arrangements plays little role
in the stress–strain relationships before damage initiates. However, the particle arrangements in
the micromechanical models do play a significant role in the maximum strengths and
6
corresponding failure strain of MMC. Under uniaxial tensile loading, the strength of weak
interface is higher than that of strong interface, while the failure strains with weak interface are
lower than that with strong interface [7]. In the recent years, the use of materials made up of
metals and ceramics significantly increased because of their versatile properties which makes
them suitable for application in various ways. Despite the increasing use of these materials, the
mechanical properties of metal-ceramic interfaces is not properly understood. In this work, a
cohesive law is established for metal-ceramic interfaces using Vander Waal’s force. Equations
for calculation of shear and tensile stresses are derived from the grain size, volume density and
also from the parameters in Vander Waal’s force. The cohesive law is governed by tensile
cohesive stress, shear cohesive stress and cohesive energy. This helps in understanding the
interface strength of metal ceramic composites. This law is very helpful for the interfaces which
have Vander Waal’s force as the predominant mechanism of interaction [8]. The interface
between the matrix and reinforcement plays a crucial role in deciding the resultant properties of
composite. Strong interface ensures efficient load transfer from reinforcement to matrix which
affects properties such as stiffness, creep and fatigue. Here, a cohesive zone law is modelled by
MD simulations in order to generate traction-separation law for ductile brittle interface in Mode I
and Mode II deformations at elevated temperatures. It is found that the traction-separation law is
consistent with the existing models [9]. With the advancement of modern technology, the need
for new engineering materials for automobile industries became necessary leading to the
development of MMC’s. Aluminium particularly has very high strength to weight ratio. The
interface is the critical region in determining the properties of composites. The problem with the
interface is the improper wettability of the reinforcement with the matrix. Coating of the
reinforcements is one of the technique to improve the interfacial bonding. This work coating on
reinforcements such as carbon/graphite, showed improvement in the interactions at the interface.
The metal coatings improved the wettability of the matrix and reinforcement. It is economical
but leads to change in the composition of the matrix. Ceramic coatings reduce the wettability of
the reinforcement with matrix and most of them are quite expensive [10]. Metallic glasses have a
unique set of properties including high yield strength and large elastic limit and also good
resistance to corrosion. Taking these properties into consideration, the metallic glasses can be
used as reinforcements in metal matrix composites (MMCs), which are blend of high-strength
glassy phase and a soft metallic matrix. The mechanical properties of Al-based composites
reinforced with different volume fractions of Fe49.9Co35.1Nb7.7B4.5Si2.8 glassy particles are
7
investigated under tensile loading [11]. Metallic glasses are assessed to be good structural
materials. Although they have restricted applications in comparision with conventional
materials, their outstanding properties make them useful for wide range of applications like in
micro electro-mechanical system devices. They are made to perform better at high temperatures,
designed to have better mechanical and thermal fatigue and creep resistance. MMc’s in
comparision to PMC’s have amazing resistance to flame, moisture and hence can withstand high
temperatures [12]. The solubility of carbon in copper is less at high temperatures. Hence the
wettability of carbon fibres with copper is low. This low wettability does not allow proper
fabrication of composite. Thus taking this into consideration, studies of the interfaces by using
the Metallic Glasses as reinforcement materials is done and it is found that there is improvement
in bond strength at the interface.[13]

2.2 GAPS IN THE LITERATURE

A significant progress is made in the usage of composite materials in the recent times. However,
in comparison to all other composites, the research on metal-metallic glass composites has drawn
less attention. There are seldom experimental and simulation deformation studies reported on the
metal-metallic glass composites. So, in view of this, the present study is broadly aimed to study
the following:
a) Interface strength of the metal (Cu)-metallic glass (Cu50Zr50) composite interface by
performing molecular dynamics (MD) simulations.
b) Crack behaviour along the Cu-CuZr interface subjected to different loading conditions
and temperatures.

8
2.3 OBJECTIVES OF THE WORK

a) To create Cu (metal)-CuZr (metallic glass) model interface.

b) To carry out Mode I (tensile) and Mode II (shear) deformation studies of the Cu (metal)-
CuZr(metallic glass) interface .

c) To investigate the crack propagation behaviour at the Cu (metal)-CuZr (metallic glass)

interface.

d) To carryout mode-I (tensile) and mode-II (shear) deformation studies of Cu (metal)-CuZr

(metallic glass) interface with crack.

e) To study the effect of temperature (100 K, 300 K, 500 K ) and strain rates (10 8 s-1, 109 s-
1
, and 1010 s-1 ) on the interface strength during mode-I and mode-II loading conditions.

9
CHAPTER 3

3.1 MODELING PROCEDURE [12 ]

Molecular dynamics is a simulation technique where the positions of a set of interacting atoms
and molecules of a system is determined by using the equations of motion. The atoms and
molecules of the system are allowed to interact for the period of time giving a view of their
motion. The trajectories of the interacting particles are determined by solving Newton's
equations of motion where forces between the particles and the potential energy are defined by
molecular mechanics force fields. The Newton's equation of motion can be expressed as follows:

F=miai ............................................................(1)
ai =d2ri/dt2.......................................................(2)
where F is the force between the interacting particles, mi = mass of each particle ( considering the
homogenous system, mass of each particle is same), ai = acceleration of each particle and ri =
particle position.

Given an initial set of positions and velocities, the subsequent time evolution through which the
particle interaction and movement takes place can be completely determined. During simulations
atoms and molecules will 'move' in the computer, bumping into each other during interaction,
vibrating about a mean position (if constrained), or wandering around (if the system is fluid),
oscillating in waves in concert with their neighbours, perhaps evaporating away from the system
if there is a free surface, and so on, in a way similar to what real atoms and molecule would do.

The initializations of MD simulations starts with initializing the positions and velocities of atoms
and after that the total energy is being calculated which include bond energy, torsional energy,

10
bond angle energy, non-bond energy. Then the forces on the atoms are calculated. Subsequently,
atoms are moved and Newton's equation of motion is integrated to obtain the atomic trajectory.

Since any molecular system contains a large number of micro-particles, atoms or molecules. It is
quite impractical and most of the times impossible to characterize the properties of such a vast
system analytically. In this case MD simulation comes handy to solve this problem by using
numerical methods. In order to get the simulation results to be error free, calculation are carried
out by the machine (computer) selecting a proper algorithm implemented in a suitable
programming language. In this way, complexity can be introduced and more realistic systems
can be investigated, achieving a better understanding of real experiments. Due to its important
commercial applications, this simulation technique is now gaining much more popularity.

3.2 LAMMPS

 LAMMPS is an acronym for Large scale Molecular Massively Parallel Simulator.

This is the basic code required to do materials simulation.
 LAMMPS consists of potentials for soft materials and solid-state materials and
many more kind of materials
 LAMMPS can be used to model atoms or as a parallel particle simulator.
 For computational efficiency LAMMPS uses neighbour lists to keep track of nearby
particles.
 This code is written with the help of c++. The designing structure of the code is so
flexible that it can be easily modified and extended with new applications.
 A set of pre and post-processing tools are also packaged with LAMMPS, some of
which can convert input and output files to/from formats used by other codes.
 OVITO is a molecular visualizations/graphics program designed for the display and
analysis of molecular assemblies.
 OVITO can display any number of structures using a wide variety of rendering
styles and coloring method.

In this project work, all the simulations have been performed using LAMMPS and resulting
models and structures have been analyzed and processed using OVITO Visualization program.

11
3.3 INPUT SCRIPT FILE FOR CREATING SAMPLE

# Cu-CuZr interface studies

units metal
echo both
atom_style atomic
dimension 3

12
boundary ppp
region box block 0 100 0 110 0 50 units box
create_box 3 box

lattice fcc 3.61

region Cu block 0 100 0 50 0 50 units box
create_atoms 1 region Cu units box
group solid region Cu

lattice fcc 3.61

region CuZr_glass block 0 100 60 110 0 50 units box
create_atoms 2 region CuZr_glass units box
set region CuZr_glass type/fraction 3 0.5 12393

group glass region CuZr_glass

group entire union solid glass

timestep 0.002

pair_style eam/fs
pair_coeff * * Cuzr_mm.eam.fs Cu Cu Zr

thermo 1000
velocity all create 300 8728007 rot yes mom yes dist gaussian

# Energy Minimization
minimize 1.0e-3 1.0e-4 10000 10000

13
thermo_style custom step temp vol press pe ke etotal

dump 1 all atom 40000 dump.Cu-CuZr_interface.lammpstrj

dump_modify 1 scale no
log logCu-CuZr_interface.data

fix 1 glass npt temp 300 2000 0.01 iso 0.0 0.0 0.1

run 10000
unfix 1

fix 1 glass npt temp 2000 2000 0.01 iso 0.0 0.0 0.1

run 50000
unfix 1

fix 1 glass npt temp 2000 270 0.01 iso 0.0 0.0 0.1
run 100000
unfix 1

3.4 INPUT SCRIPT FILE FOR MODE I (TENSILE) DEFORMATION WITHOUT

CRACK

# 3d metal tensile simulation

units metal
boundary ssp
echo both
atom_style atomic

read_data cuzr.dat

pair_style eam/fs
pair_coeff * * CuZr_mm.eam.fs Cu Cu Zr
14
#region

region 1 block -3 103 -3 30 -2 52 units box

region 2 block -3 103 60 114 -2 52 units box

group lower region 1

group upper region 2
group boundary union lower upper
group mobile subtract all boundary

compute csym all centro/atom fcc

compute peratom all pe/atom

# Energy Minimization

minimize 1.0e-9 1.0e-9 1000 10000

# equilibrate

velocity mobile create 100.0 5812775

fix 1 all nvt temp 100 100 0.01
fix 2 boundary setforce 0.0 0.0 0.0

timestep 0.002

# shear

velocity upper set 0.0 0.003 0.0

velocity mobile ramp vy 0.0 0.003 y 30 60 sum no units box

# output

dump 1 all custom 100 dump1.tensile_check2*.lammpstrj id type x y z

# stress calculation

compute 10 mobile stress/atom

compute 20 mobile reduce sum c_10[2]

#large 150000 vol;

15
variable stress equal c_20/(3*150000)

variable stress_MPa equal v_stress/10

#log file

log logcu_cuzr5050_tensile_ramp_check2.dat

thermo 1000
thermo_style custom step temp v_stress v_stress_MPa

run 500000

3.5 INPUT SCRIPT FILE FOR MODE II (SHEAR) DEFORMATION WITHOUT

CRACK

# 3d metal shear simulation

units metal
boundary ssp
echo both
atom_style atomic

read_data cuzr.dat

pair_style eam/fs
pair_coeff * * CuZr_mm.eam.fs Cu Cu Zr

#region
16
region 1 block -3 103 -3 30 -2 52 units box
region 2 block -3 103 60 114 -2 52 units box

group lower region 1

group upper region 2
group boundary union lower upper
group mobile subtract all boundary

#region my cylinder z 50 50 10 0 54 units box

#delete_atoms region my

compute csym all centro/atom fcc

compute peratom all pe/atom

# Energy Minimization

minimize 1.0e-4 1.0e-4 1000 10000

# equilibrate

velocity mobile create 300.0 5812775

fix 1 all nvt temp 300 300 0.01
fix 2 boundary setforce 0.0 0.0 0.0

timestep 0.002

# shear

velocity upper set 0.01 0.0 0.0

velocity mobile ramp vx 0.0 0.01 y 30 60 sum no units box

# output

dump 1 all custom 100 dump1.shear_10^8_check2*.lammpstrj id type x y z

# stress calculation

compute 10 mobile stress/atom

compute 20 mobile reduce sum c_10[4]

17
#large 150000 vol;

variable stress equal c_20/(3*150000)

variable stress_MPa equal v_stress/10

variable strain equal (xhi-104)/104

#log file

log logcu_cuzr5050_shear_10^8_check2.dat

thermo 2500
thermo_style custom step temp v_stress v_stress_MPa v_strain

run 500000

3.6 INPUT SCRIPT FILE FOR MODE I (TENSILE) DEFORMATION WITH CRACK

# 3d metal tensile simulation

units metal
boundary ssp
echo both
atom_style atomic

read_data cuzr.dat

pair_style eam/fs
pair_coeff * * CuZr_mm.eam.fs Cu Cu Zr

#region

region 1 block -3 103 -3 30 -2 52 units box

region 2 block -3 103 60 114 -2 52 units box

group lower region 1

18
group upper region 2
group boundary union lower upper
group mobile subtract all boundary

region my cylinder z 50 50 10 0 54 units box

delete_atoms region my

compute csym all centro/atom fcc

compute peratom all pe/atom

# Energy Minimization

minimize 1.0e-9 1.0e-9 1000 10000

# equilibrate

velocity mobile create 100.0 5812775

fix 1 all nvt temp 100 100 0.01
fix 2 boundary setforce 0.0 0.0 0.0

timestep 0.002

# tensile

velocity upper set 0.0 0.003 0.0

velocity mobile ramp vy 0.0 0.003 y 30 60 sum no units box

# output

dump 1 all custom 100 dump1.tensile_check2*.lammpstrj id type x y z

# stress calculation

compute 10 mobile stress/atom

compute 20 mobile reduce sum c_10[2]

#large 150000 vol;

variable stress equal c_20/(3*150000)

19
variable stress_MPa equal v_stress/10

#log file

log logcu_cuzr5050_tensile_ramp_check2.dat

thermo 1000
thermo_style custom step temp v_stress v_stress_MPa

run 500000

3.7 INPUT SCRIPT FILE FOR MODE II (SHEAR) DEFORMATION WITH CRACK

# 3d metal shear simulation

units metal
boundary ssp
echo both
atom_style atomic

read_data cuzr.dat

pair_style eam/fs
pair_coeff * * CuZr_mm.eam.fs Cu Cu Zr

#region

region 1 block -3 103 -3 30 -2 52 units box

region 2 block -3 103 60 114 -2 52 units box

group lower region 1

group upper region 2
group boundary union lower upper
group mobile subtract all boundary
20
region my cylinder z 50 50 10 0 54 units box
delete_atoms region my

compute csym all centro/atom fcc

compute peratom all pe/atom

# Energy Minimization

minimize 1.0e-4 1.0e-4 1000 10000

# equilibrate

velocity mobile create 300.0 5812775

fix 1 all nvt temp 300 300 0.01
fix 2 boundary setforce 0.0 0.0 0.0

#fix 3 lower temp/rescale 10 300.0 300.0 10.0 1.0

timestep 0.002

# shear

velocity upper set 0.01 0.0 0.0

velocity mobile ramp vx 0.0 0.01 y 30 60 sum no units box

# output

dump 1 all custom 100 dump1.shear_10^8_check2*.lammpstrj id type x y z

# stress calculation

compute 10 mobile stress/atom

compute 20 mobile reduce sum c_10[4]

#large 150000 vol;

variable stress equal c_20/(3*150000)

variable stress_MPa equal v_stress/10

variable strain equal(xhi-104)/104

#log file
21
log logcu_cuzr5050_shear_10^8_check2.dat

thermo 2500
thermo_style custom step temp v_stress v_stress_MPa

run 500000

Deformation studies in both cases Mode I and Mode II (with crack & without crack) are carried
out at different strain rates (108 s-1 , 109 s-1 , 1010 s-1 ) and different temperatures (100K, 300K,
500K) using the above codes.

3.8 WORK PLAN

The following Table 1 gives the details of the simulation studies that will be carried out on Cu-
Cu-Zr interface.

Table 1: Details of studies

Alloy Mode of Strain Temperature
model deformation rate
Cu-Cu-Zr Mode-I 108 s-1 100 K , 300 K, 500 K
109 s-1 100 K , 300 K, 500 K
10 -1
10 s 100 K , 300 K, 500 K
Cu-Cu-Zr Mode-II 108 s-1 100 K , 300 K, 500 K
9 -1
10 s 100 K , 300 K, 500 K
1010 s-1 100 K , 300 K, 500 K
With center crack at the interface
Cu-Cu-Zr Mode-I 108 s-1 100 K , 300 K, 500 K
9 -1
10 s 100 K , 300 K, 500 K
1010 s-1 100 K , 300 K, 500 K
8 -1
Cu-Cu-Zr Mode-II 10 s 100 K , 300 K, 500 K
109 s-1 100 K , 300 K, 500 K
10 -1
10 s 100 K , 300 K, 500 K

22
CHAPTER 4

4.1 RESULTS AND DISCUSSIONS

MD simulations of Mode-I and Mode-II studies on the Cu- Cu50Zr50 interface with crack and
without crack have been studied. The tests were conducted at varying strain rates (1 × 108 s-1, 1×
109 s-1 and 1 × 1010 s-1) and temperatures (100K, 300K and 500K) to investigate the deformation
behaviour and response on the mechanical properties such as yield point, and maximum load the
interface can withstand.

4.2 DEFORMATION (TENSILE AND SHEAR) STUDIES OF THE Cu (METAL)-CuZr

(METALLIC GLASS) INTERFACE
The model was deformed along Y-axis (Tensile, Mode-I) and X-axis (Shear, Mode-II). The
deformation was done at different strain rates i.e., 1 × 108 s-1, 1 × 109 s-1 and 1 × 1010 s-1 and at
different temperatures in the range of 100 K-500 K to understand the stress-strain behaviour and
response to the mechanical properties. Fig 1 shows the atomic snapshot of the Interface without
crack (Fig. 1a) and with crack (diameter 10 Å) (Fig.1b).

23
4.3 EFFECT OF STRAIN RATE ON THE INTERFACE STRENGTH
To study the strain rate effect, three different strain rates are used in the simulation, which will
predict the different properties of the interface. Stress-strain plot are plotted to examine the
behaviour of the interface strength. Fig. 2 shows the (Mode-I without crack) stress-strain curves
of interface at 100 K (Fig. 2a), at 300 K (Fig 2b) and 500 K (Fig 2c) and at three strain rates, i.e.
108 s-1, 109 s-1 and 1010 s-1. All the curves show a linear elastic and plastic behaviour. Yielding
occurs by sudden drop in the stress. With further straining the stress-strain curves are serrated
and are more prominent with decreasing strain rate and increasing temperature. With increasing
strain rate, yield strength increases and decreases with increasing temperature.

24
 Figure. 2. Stress-Strain plot for Mode-I without crack, Cu50Zr50 metallic glass reinforced in Cu Metal
matrix at varying strain rate from a to c; (a) 100K, (b) 300K, (c)500K.

4.3.1 Atomic positions snap shots (mode I deformation without crack)

The following Figs. 3a and 3b shows the atomic position snap shots of the model interface at
different strains and deformed at stain rate of 1010 s-1 and 109 s-1. The plastic deformation
initiates by slip in the crystalline region and by diffusive movement of atoms in the glassy
region. With further straining (10%) a void is generated at the interface resulting in sudden drop
in the stress.

25
 Figure. 3a: Atomic snapshot at different strains of the model without crack under Mode-I deformation
strained at strain rate of 1×1010s-1.

Figure. 3b: Atomic snapshot at different strains of the model without crack under Mode-I deformation
strained at strain rate of 1×109 s-1.

Fig. 4 shows the (Mode-I with crack) stress-strain curves of interface at 100 K (Fig. 4a), at 300 K
(Fig 4b) and 500 K (Fig 4c) and at three strain rates, i.e. 108 s-1, 109 s-1 and 1010 s-1. All the curves
show a linear elastic and plastic behaviour. Yielding occurs by sudden drop in the stress. With
further straining the stress-strain curves are serrated and are more prominent with decreasing
strain rate and increasing temperature. With increasing strain rate, yield strength increases and
decreases with increasing temperature.
26
Figure. 4: Stress-Strain plot for Mode-I with crack, Cu50Zr50 metallic glass reinforced in Cu Metal matrix
composite at varying strain rate from a to c; (a) 100K, (b) 300K, (c) 500K.

4.3.2 Atomic positions snap shots (mode I deformation of interface with crack)
The following Figs. 5a and 5b shows the atomic position snap shots of the model interface with
crack at different strains and deformed at stain rate of 10 10 s-1 and 109 s-1. The plastic
deformation initiates by slip in the crystalline region and by diffusive movement of atoms in the
glassy region. The void enlarges with progress of deformation and separation of the interface
occurs at strain of 0.16.

27
 Figure 5a: Atomic snapshot at different strains of the model with crack under Mode-I deformation
strained at strain rate of 1×1010 s-1.

Figure 5b: Atomic snapshot at different strains of the model with crack under Mode-I deformation
strained at strain rate of 1×109 s-1.

Fig. 6 shows the (Mode-II without crack) stress-strain curves of interface at 100 K (Fig. 6a), at
300 K (Fig 6b) and 500 K (Fig 6c) and at three strain rates, i.e. 108 s-1, 109 s-1 and 1010 s-1. All the
curves show a linear elastic and plastic behaviour. Yielding occurs by sudden drop in the stress.

28
With further straining the stress-strain curves are serrated and are more prominent with
decreasing strain rate and increasing temperature. With increasing strain rate, shear yield strength
increases and decreases with increasing temperature.

Figure. 6. Stress-Strain plot for Mode-II without crack, Cu50Zr50 metallic glass reinforced in Cu Metal
matrix at varying strain rate from a to c; (a) 100K, (b) 300K, (c)500K.

4.3.3 Atomic positions snap shots (mode II deformation of interface without crack)
The following Figs. 7a and 7b shows the atomic position snap shots of the model interface at
different strains and deformed at stain rate of 10 10 s-1 and 109 s-1. The plastic deformation
initiates by slip in the crystalline region and by diffusive movement of atoms in the glassy
region. With progress of deformation amorphization of crystalline region occurs close to the
interface at strain rate of 109 s-1.

29
 Figure 7a: Atomic snapshot at different strains of the model without crack under Mode-II deformation
strained at strain rate of 1×1010 s-1.

Figure 7b: Atomic snapshot at different strains of the model without crack under Mode-II deformation
strained at strain rate of 1×109 s-1.

Fig. 8 shows the (Mode-II with crack) stress-strain curves of interface at 100 K (Fig. 8a), at
300 K (Fig 8b) and 500 K (Fig 8c) and at three strain rates, i.e. 108 s-1, 109 s-1 and 1010 s-1. All the
curves show a linear elastic and plastic behaviour. Yielding occurs by sudden drop in the stress.

30
With further straining the stress-strain curves are serrated and are more prominent with
decreasing strain rate and increasing temperature. With increasing strain rate, shear yield strength
increases and decreases with increasing temperature.

Figure. 8: Stress-Strain plot for Mode-II with crack, Cu50Zr50 metallic glass reinforced in Cu Metal matrix
at varying strain rate from a to c; (a) 100K, (b) 300K, (c) 500K.

31
4.3.4 Atomic snap shots with crack (mode II deformation of interface with crack)

The following Figs. 8a and 8b shows the atomic position snap shots of the model interface at
different strains and deformed at stain rate of 10 10 s-1 and 109 s-1. The plastic deformation
initiates by slip in the crystalline region and by diffusive movement of atoms in the glassy
region. The regions near the void act as source of dislocations. With progress of deformation
closure of the void occurs.

Figure 9a: Atomic snapshot at different strains of the model with crack under Mode-II deformation
strained at strain rate of 1×1010 s-1.

Figure 9b: Atomic snapshot at different strains of the model with crack under Mode-II deformation
strained at strain rate of 1×109 s-1.

32
4.4 Effect of temperature on interface strength
Fig. 10 shows the (Mode-I without crack) stress-strain curves of the model interface at 108 s-1
(Fig.10a), at 109 s-1 (Fig 10b) and 1010 s-1 ( Fig 10c) and at three different temperature, i.e.,
100K, 300K and 500K. As the temperature increases the yield strength decreases. Flow softening
is observed at all strain rates and temperatures.

Figure 10: Stress-strain plot for Mode-I deformation of model interface without crack, at varying
temperature from a to c (a) 1×108s-1, (b) 1 ×109s-1, (c) 1×1010s-1.

33
Fig. 11 shows the (Mode-I with crack) stress-strain curves of the model interface at 108 s-1
(Fig.11a), at 109 s-1 (Fig 11b) and 1010 s-1 ( Fig 11c) and at three different temperature, i.e.,
100K, 300K and 500K. As the temperature increases the yield strength decreases. Flow softening
is observed at all strain rates and temperatures.

Figure 11: Stress-strain plot for Mode-I deformation of model interface with crack, at varying
temperature from a to c (a) 1×108s-1, (b) 1 ×109s-1, (c) 1×1010s-1.

34
Fig. 12 shows the (Mode-II without crack) stress-strain curves of the model interface at 108 s-1
(Fig.12a), at 109 s-1 (Fig 12b) and 1010 s-1 (Fig 12c) and at three different temperature, i.e., 100K,
300K and 500K. As the temperature increases the yield strength decreases.

Figure 12: Stress-strain plot for Mode-II deformation of model interface without crack, at varying
temperature from a to c (a) 1×108s-1, (b) 1 ×109s-1, (c) 1×1010s-1.

35
Fig. 13 shows the (Mode-II with crack) stress-strain curves of the model interface at 108 s-1
(Fig.13a), at 109 s-1 (Fig 13b) and 1010 s-1 ( Fig 13c) and at three different temperature, i.e.,
100K, 300K and 500K. As the temperature increases the yield strength decreases.

Figure 13: Stress-strain plot for Mode-II deformation of model interface with crack, at varying
temperature from a to c (a) 1×108s-1, (b) 1 ×109s-1, (c) 1×1010s-1.

36
5. CONCLUSIONS

The present study gives a significant insight on the mechanism and deformation behaviour of

the interface between Cu50Zr50 metallic glass reinforced in Cu Metal matrix composite. The stress-

strain analysis provides vital information on the performance of these materials when they are

used at different temperatures and loading conditions. The following conclusions can be drawn

from the present study.

a) Plastic deformation mechanism is by slip (evident from atomic position snap shots) in
the crystalline region and by random movement of atoms in the glassy region.
b) Yield strength increases with increase in strain rate, while decreases with increasing
temperature.
c) Mechanical properties like Yield strength, ultimate tensile strength decreases with the
presence of crack at the interface between Cu50Zr50 metallic glass reinforced in Cu
Metal matrix composite.
d) Flow softening is observed at all strain rates and temperatures.

37
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