ATOMISTIC MODELING OF THE AL AND FE2O3 MATERIAL SYSTEM USING CLASSICAL ...

291 Pages·2005·12.24 MB·English

ATOMISTIC MODELING OF THE AL AND FE O MATERIAL SYSTEM USING
2 3
CLASSICAL MOLECULAR DYNAMICS

A Dissertation
Presented to
The Academic Faculty

By

Vikas Tomar

In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy in Mechanical Engineering

Georgia Institute of Technology

December, 2005

Copyright © Vikas Tomar 2005
ATOMISTIC MODELING OF THE AL AND FE O MATERIAL SYSTEM USING
2 3
CLASSICAL MOLCECULAR DYNAMICS

Approved by:

Dr. Min Zhou, Advisor Dr. Sathya Hanagud
The George W. Woodruff School of School of Aerospace Engineering
Mechanical Engineering Georgia Institute of Technology
Georgia Institute of Technology
Dr. Naresh Thadhani
Dr. David McDowell School of Materials Science and
The George W. Woodruff School of Engineering
Mechanical Engineering Georgia Institute of Technology
Georgia Institute of Technology
Dr. Karl Jacob
Dr. Jianmin Qu School of Polymer, Textile and Fiber
The George W. Woodruff School of Engineering
Mechanical Engineering Georgia Institute of Technology
Georgia Institute of Technology
Date Approved:
October 17, 2005
To My Mom, Dad, Sister, Brother, and Jinhyun
ACKNOLEDGEMENTS

I wish to thank my advisor, Dr. Min Zhou, for his unending support as well as for a series
of ‘frank discussions’ that have helped me in achieving my professional targets as well as
in my professional development for an academic career. I am especially thankful to Dr.
David McDowell, Dr. Jianmin Qu, Dr. Farrokh Mistree, Dr. Karl Jacob, Dr. Naresh
Thadhani, Dr. Mo Li, and Dr. Sathya Hanagud for extending their support to my career as
well as to my research. This research work was supported by an AFOSR-MURI grant to
Georgia Tech and computations were carried out at NAVO, ERDC, ARL, AHPCRC, and
JPL major shared resources centers. Timely progress in this work would not have been
possible without regular discussions at MURI meetings. I earnestly appreciate prompt
administrative support of Ms. Cecelia Jones at innumerable occasions during my stay at
Georgia Tech. My life during the span of last four and a half years at Georgia Tech would
have been very difficult without wonderful colleagues and friends. I wish to thank Karel
Minnaar, Greg Ingram, John Clayton, Doug Spearot, Wuwei Liang, Jim Shepherd,
Mahesh Shenoy, Ambarish Kulkarni, Vivek Sharma, Nitin Patel, Abhijit Gogulapati, Xia
Lu, Jitesh Panchal, Haejin Choi, Abhinav Saxena, Karthik Krishnan, Nishanth Gurnani,
Jie Yang, Kai Liu, Jason Mayeur, and many other friends who were always ready to
celebrate and share trivialities of research and life with me. I cannot thank enough my
fiancée Jinhyun Lee for her patience, understanding, and support that made the coupling
between my work and my life an interesting experience.

iv
TABLE OF CONTENTS

ACKNOLEDGEMENTS iv
LIST OF TABLES viii
LIST OF FIGURES ix
SUMMARY xvi
CHAPTER 1 INTRODUCTION 1
CHAPTER 2 THE INTERATOMIC POTENTIAL FOR fcc-Al+α-Fe O MATERIAL
2 3
SYSTEM 8
2.1 Introduction 9
2.2 Functional Form of the Interatomic Potential 15
2.3 Fitting and Testing of the Potential Parameters 26
2.4 Chapter Summary and Insights 42
CHAPTER 3 THE FRAMEWORK FOR MOLECULAR DYNAMICS MODELING 44
3.1 High-Level Parallel MD Code and MD Visualization Tools 46
3.2 Generation of Nanocrystalline Structures for MD Simulations 52
3.2.1 Schemes for Generating Nanocrystalline Materials 54
3.2.1.1 Voronoi Tessellation 59
3.2.1.2 Melt Growth Method 60
3.2.1.3 Inverse Monte-Carlo Method with Voronoi Tessellation 61
3.2.2 Algorithm 63
3.3 Nanocrystalline Al after Equilibration 69
3.4 Nanocrystalline Fe O and Al+Fe O Composites after Equilibration 76
2 3 2 3
v
3.5 Algorithm for the Calculation of Quasi-static Strength 85
3.6 Shock Wave Propagation Algorithm for MD Shock Simulations 89
3.7 Equilibrium Structure of an Interface between fcc-Al and α-Fe O lattices 94
2 3
3.8 Chapter Summary and Insights 102
CHAPTER 4 MECHANICAL BEHAVIOR OF THE NANOCRYSTALLINE
MATERIALS 105
4.1 Nanocrystalline Material Systems 106
4.1.1 Experimental Characterization 113
4.1.2 Analytical Characterization 115
4.2 Characterization of the Mechanical Behavior of Nanocrystalline Materials
Using Classical Molecular Dynamics 119
4.3 Tensile and Compressive Mechanical Behavior of Nanocrystalline Al 128
4.4 Tensile and Compressive Mechanical Behavior of Nanocrystalline Fe O 147
2 3
4.5 Compressive Mechanical Behavior of Nanocrystalline 40%Al+60%Fe O and
2 3
60%Al+40%Fe O Composites 153
2 3
4.6 Hall-Petch Relation as a Function of Volume Fraction 168
4.7 Chapter Insights and Conclusions 170
CHAPTER 5 ANALYSES OF THE SHOCK WAVE PROPAGATION 175
5.1 Why Study Single Crystal Shock Using MD? 176
5.2 Some Important Results from Shock Wave Propagation Analyses in Single
Crystalline Systems 182
5.2.1 Shock Wave Profile Calculations 188
5.2.2 Interatomic Potential for Calculations of Forces 189
5.2.3 Hugoniot Calculations 191
vi
5.3 Shock Wave Propagation analyses in <100>, <110>, and <111> Oriented
Single Crystalline Al 192
5.4 Shock Wave Propagation Analyses in <0001> Oriented Single Crystalline α-
Fe O 213
2 3
5.5 Analyses of Shock Wave Propagation through an Interface of Al and Fe O 218
2 3
5.6 Chapter Insights and Conclusions 231
CHAPTER 6 SUMMARY AND CONCLUSIONS 235
CHAPTER 7 RECOMMENDATIONS 241
APPENDIX A VISUALIZATION SCRIPT FOR VMD 243
REFERENCES 246
VITA 274

vii
LIST OF TABLES

Table 2.1 Sum of squares and corresponding average errors during initial fitting for each
crystal component 31
Table 2.2 Fitted and predicted properties of fcc-Al using parameter set 32
Table 2.3 Fitted and predicted properties of bcc-Fe using parameter set 33
Table 2.4 Fitted and predicted properties of B2 Fe-Al using parameter set 34
Table 2.5 Fitted and predicted properties of α-Al O using parameter set 35
2 3
Table 2.6 Fitted and predicted properties of α-Fe O using parameter set 36
2 3
Table 2.7 Pair parameters of the potential 37
Table 2.8 Cluster and electrostatic parameters of the potential 37
Table 3.1 A survey of the average grain sizes of the nanocrystalline materials used by
various researchers 63
Table 4.1 Classification of the available techniques to synthesize nanocrystalline
materials 108

viii
LIST OF FIGURES

Figure 2.1 An illustration of the fitting procedure 28
Figure 2.2 (a) Generalized a 6 112 {111} stacking fault energy of fcc-Al, (b)
Generalized a 2 111{110}stacking fault energy of bcc-Fe 40
Figure 3.1 An illustration of the application of the slip-vector approach in (a) identifying
grain boundaries in polycrystalline Al and (b) identifying structural order in single
crystalline Fe O 50
2 3
Figure 3.2 Schematics for 3-D Voronoi tessellation cf. Chen (1995) 58
Figure 3.3 Set of nanocrystalline structures before MD equilibration 67
Figure 3.4 A comparison of the histograms of grain size distribution in the nanocrystalline
structures with the target log-normal and normal grain size distributions 68
Figure 3.5 Time history of (a) the pressure and (b) the temperature in nanocrystalline
structures during MD equilibration 69
Figure 3.6 (a) Illustration of the low-angle and high-angle grain boundary mismatches
before MD equilibration in all samples of nanocrystalline Al and (b) the slip-vector based
viewgraphs of the same samples after MD equilibration for identifying the thickness of
grain boundaries, (for ease of comparison, only the middle section is analyzed) 71
Figure 3.7 A comparison of the fraction of grain boundary atoms as a function of the
average grain size in nanocrystalline Al after MD equilibration 72
Figure 3.8 A comparison of the partial Al-Al RDFs for nanocrystalline Al with grain size
(a) 7.2 nm, (b) 4.7 nm, and (c) 3.9 nm, before and after MD equilibration 74
Figure 3.9 (a) Partial Al-Al RDFs for polycrystalline Al at all grain sizes after MD
equilibration and (b) RDF for amorphous carbon 75
ix
Figure 3.10 A section of polycrystalline Fe O with grain size (a) 7.2 nm, (b) 4.7 nm, and
2 3
(c) 3.9 nm before and after MD equilibration 77
Figure 3.11 Single Crystal Fe O , (a) before equilibration, (b) after equilibration with
2 3
periodic boundary conditions imposed, and (c) after equilibration as a cluster 78
Figure 3.12 (a) Time history of the pressure during equilibration of Fe O in various
2 3
crystalline settings and (b) time history of pressure during MD equilibration of 7.2 nm
grain size Fe O nanocrystalline structure with different number of atoms along grain
2 3
boundaries 80
Figure 3.13 an illustration of the effective range of electrostatic interaction along grain
interfaces in nanocrystalline Fe O with the average grain size 7.2 nm (red arrows signify
2 3
the effective range of electrostatic interaction along grain boundaries; white arrows
signify crystalline orientation) 80
Figure 3.14 (a) The Fe-Fe, (b) the O-O, (c) the Fe-O, and (d) the total Fe O RDF for
2 3
nanocrystalline Fe O with grain size 7.2 nm before and after the MD equilibration 82
2 3
Figure 3.15 (a) Total Fe O RDFs for nanocrystalline Fe O with all grain sizes and (b)
2 3 2 3
Total Fe O RDFs for nanocrystalline Fe O in the work of Cannas et al. (2004) for 3
2 3 2 3
different types (A, B, C) of samples 83
Figure 3.16 (a) The partial Al-Al RDFs and (b) the total Fe O RDFs for
2 3
60%Al+40%Fe O with different grain sizes 84
2 3
Figure 3.17 (a) The partial Al-Al RDFs and (b) the total Fe O RDFs for
2 3
40%Al+60%Fe O with different grain sizes 84
2 3
Figure 3.18 Set of nanocrystalline structures used during simulations after the MD
equilibration 85
Figure 3.19 A comparison of the stress-strain relations with fixed stretching time period
and different equilibration time periods 87
Figure 3.20 Illustration of three primary methods for generating shock waves: (a)
symmetric impact, (b) shrinking periodic boundaries, and (c) momentum mirror (piston
velocity u , shock velocity u ), cf. Holian et al. (1999). 90
p s
x