Nghiên cứu động lực phân tử lỗ rỗng trong đồng - Luận án tiến sĩ Đại học California San Diego

UC San Diego UC San Diego Electronic Theses and Dissertations Title A molecular dynamics study of void initiation and growth in monocrystalline and nanocrystalline copper Permalink https://escholarship.org/uc/item/6905g1rt Author Traiviratana, Sirirat Publication Date 2008 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA, SAN DIEGO A Molecular Dynamics Study of Void Initiation and Growth in Monocrystalline and Nanocrystalline Copper A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Engineering Sciences (Mechanical Engineering) by Sirirat Traiviratana Committee in charge: Professor David J. Benson, Chair Professor Marc A. Meyers, Co-Chair Professor Eduardo M. Bringa Professor Petr Krysl Professor Vlado A.

Lubarda Professor Vitali F. Nesterenko 2008 Copyright Sirirat Traiviratana, 2008 All rights reserved. The dissertation of Sirirat Traiviratana is ap- proved, and it is acceptable in quality and form for publication on microfilm: Co-Chair Chair University of California, San Diego 2008 iii DEDICATION To my passed father, Mr. Prasert Traiviratana To my passed brother, Master Sergeant 1st Class Sirisak Traiviratana To my patient mother, Mrs.

Pranorm Traiviratana To the Royal Thai Navy Lieutenant Sirirat Traiviratana iv TABLE OF CONTENTS Signature Page. iv Table of Contents. v List of Figures. viii List of Tables.

xiii Vita and Publications. xiv Abstract of the Dissertation .1 Simple Continuum Models for Void Expansion .2 Continuum Models for Material with Porosity .3 Single Crystal Studies .4 Outline of the Problems .5 Objectives of Research. 26 2 Molecular Dynamics Fundamentals .1 The Molecular Dynamics Simulation Process .2 Equilibrium and Relaxation .2 Molecular Dynamics Codes, LAMMPS .3 The Embedded Atom Method .4 Single-crystalline and Bi-crystalline Structure Generation .2 Single Crystalline Structure .3 Bi-crystalline Structure .5 Polycrystalline Structure Generation .2 Vectors and Planes .3 Coordinate Rotation and Orientation .4 Euler Angles and Euler Parameters .5 Search and delete algorithm .6 Periodic Boundary Conditions. 46 3 Results and Discussion .1 Void Growth in Single-crystal - Hydrostatic expansion .2 Void Growth in Bicrystal Structure .3 Compression and Expansion of Nanocrystalline Nickel .4 Void Growth in a Single-Crystal Structure - Uniaxial expansion .3 Interpretation and Calculation .5 Calculation of Dislocation Interactions .1 In Plane Dislocation and Interactions .2 Biplanar Dislocation and Interactions .6 Void Growth Kinetics .7 Density of Geometrically Necessary Dislocations .8 Void Growth in Single Crystals with Different Loading Orientations 101 3.

112 vi 4 Algorithm for dislocation information extraction .1 Filtering out non-defect particles .2 Search boxes generation .3 Neighbor particles search .4 Filter for the Dislocation Planes .5 Normal of plane of dislocation .6 Leading and Trailing Edge of Dislocation .7 The Length of Dislocation and Dislocation Density .8 The Velocity of Dislocation .1 Algorithms for Dislocation Information Extraction .2 Atomistic Model for Void Growth Compared to Current Continuum Models .4 Molecular Dynamics Simulation of Nanocrystal Copper .1 Base Crystalline Structure, BCC, FCC .4 Voids in Polycrystalline Structure .1 LAMMPS Input File .3 Nanocrystalline Structure Simulation .4 LAMMPS Dump File Processing. 179 vii LIST OF FIGURES Figure 1.1: Stress-strain curve for general description of elasticity and plasticity.2: Plastically deformed zone around a void, (a) TEM by Christy et al. [8]; (b) SEM by Ahn et al.3: Evidence of slip around growing voids from Meyers and Ai- mone [7].4: Plastic region round a spherical cavity expanded by uni- formly distributed internal pressure.5: The normalized stress σ/E vs. expanded void radius R/R0 , with Y /E = 3/500 and two values of Poisson’s ratio ν = 1/3 (lower curve) and ν = 1/2 (upper curve)(from Lubarda and Meyers [20]).6: Dislocation models for void growth from (a) Meyers and Ai- mone [7], (b,c,d) Stevens and Davison [21].7: Geometrically necessary dislocation around a rigid particle in softer material, from Ashby [40], (a) undeformed model, (b) de- formed model, (c) shear loop dislocations, and (d) prismatic loop dislocations.8: Dislocation loops postulated by Lubarda et al.

[41] with the direction of dislocation motion marked by arrows.9: Void-size prediction from growth through vacancy diffusion along dislocations (Cuitiño-Ortiz model); void sizes reached in 100 s at the three temperatures of 300, 400, and 600 K marked.10: Growing void developed into an octahedron shape defined by slip planes.11: Growing voids developed into geometric shapes from (a) Mey- ers and Aimone [7] and (b) Christy et al.12: Growing void developed into geometric shape from Stevens and Davison [21].1: Flow chart of general MD simulation.2: A space lattice according to Barrett and Massalski [84] .3: (a) Lattice axes, interaxial angles and unit cell [84] and (b) configuration of atoms for the Face Centered Cubic structure with the lattice size of a, created by Bas Zoetekouw (bas@zoetekouw.5: Plane and Normal vector sketch .6: Euler rotation using (a) Euler angles and (b) Euler parameters 40 viii Figure 2.7: Distribution of rotated bases by Euler angles and Euler pa- rameters.8: Generated polycrystalline structure with average grain size of 5nm.9: Relaxed polycrystalline structure colored by centrosymmetry parameter.10: 12 nearest neighbor atoms surrounding a center atom, with the 3 dashed atoms belong in plane A, the 7 atoms belong in plane B and the last 3 atoms belong in plane C, in the FCC plane ABC configuration.11: Illustration of the geometry of slip in crystalline material.1: Sketch diagram of simulation setup for single crystal cubic domain and hydrostatic strain .2: Growth of voids from very high strain rate(2.88×1011 ) under hydrostatic expansion. The thin slab enables us to see defect atoms within the simulation box. The color bar (purple, blue, cyan, green, yellow and red) represents the values of centrosymmetry parameter from low to high.3: Growth of void from 3.01267 × 108 s−1 strain rate: dislo- cation generation and motion, and shape changing of void under hydrostatic expansion (a,b,c are slabs of small ∆z which is perpen- dicular to [001].4: Diagram of simulation setup for bicrystal domain with (a) cylindrical void and (b) spherical void.5: Dislocations emanating from cylindrical void (loading axis z) 56 Figure 3.6: Dislocation loops emanating from spherical void (loading axis z) .7: Sequence of loop nucleation and growth in the bicrystal sim- ulation.8: Sequence of loop nucleation and growth in the bicrystal sim- ulation(continued).9: Shear loops and their interaction in bicrystal simulation with initial void at grain-boundary (uniaxial strain).10: Lateral stresses generated when loading is applied in direc- tion ZZ.11: Plot of pressure against time.12: Plot of shear stress versus strain for nanocrystal Ni (d = 5 nm).13: Sequence of nanocrystalline nickel (d=5 nm) under 38 GPa loading. Note the disappearance of most dislocations after unloading.14: Plot of pressure against time for nanocrystal sample with voids.15: Plot of shear stress versus strain of nanocrystal sample with voids.16: Sequence of nanocrystal nickel under 23 GPa loading with sample containing voids.17: Sequence of nanocrystal nickel under 38 GPa loading with sample containing voids .18: Diagram of simulation setup for a single crystal cubic domain and uniaxial strain.19: Plot of stresses against strain for different strain rates while fixing void size at 1.20: Plot of stresses against strain for different strain types while fixing void size at 1.0 nm radius and strain rate at 108 s−1 .21: Plot of stresses against strain for different void size at fixed strain rate of 108 s−1 .22: Normalized critical stress against normalized void size; (a) with models; (b) on log-log scale with α = 0.23: Plots of von Mises critical stress (yield stress) from additional simulations in collaboration with Eduardo M.24: Initiation of plastic flow at void surface (at 590ps); (a) ren- dered atoms from MD; (b) diagram of (11̄1̄) and (1̄1̄1̄) slip planes intersecting sphere surface at 45◦ ; (c) rendered atoms from (a), ro- tated to show two loops; (d) diagram showing leading partial dislo- cations.25: Continued loop expansion; (a) rendered atoms from MD (591ps); (b) corresponding sketched diagram; (c) rendered atoms from MD (595ps); (d) corresponding sketched diagram.26: Later growth and interaction of shear loops emanating from void: (a) 597 ps; (b) 598 ps; (c) 599 ps.27: In-plane dislocation interactions; (a) before interaction; (b) onset of interaction; (c) interactions and reaction; (d) uniform ex- pansion of loops leaving dislocation segments behind.28: Plane (111) on principal directions.29: Plane (111) with in-plane partial dislocations interactions.30: Top view of two perfect dislocations.31: Top view of partial dislocations.32: Damage vs Time; (a) comparison of MD simulations and Cocks-Ashby equation (b) predictions from Cocks-Ashby equation (n is exponent in power-law constitutive equation).33: Volume increment generated in void by the expansion of two shear loop rings.34: Calculated density of geometrically-necessary dislocations as a function of the ratio k = Rr .35: Schematic showing traces of two slip planes intersecting void at 45◦ : loading axis ([110]) marked by arrows.36: Sequence of shear loop nucleation and growth for [110] load- ing direction.

Note directions and planes in (d) as well as second loop forming (loading direction perpendicular to plane of paper for Figs. 3(a-c) and marked in Fig.37: Sequence of loop nucleation and growth for loading along [100] (loading direction perpendicular to the plane of paper). Note two loops reacting and forming biplanar loop.38: Sequence of loop nucleation and growth for loading along [111] (loading direction perpendicular to the plane of paper). Note the formation of loops on three planes in (b).39: Plane and directions labeled for [111] loading direction; (a), schematic illustration and (b), MD simulation.40: Plot of stresses against strain for different loading orienta- tions for R = 2 nm.1: Atom rendered with a centrosymmetry parameter filter show- ing dislocation planes and grain boundary.2: Atom colored by number of neighbors showing outward nor- mal vector.3: Separated dislocation planes and average plane normals, each with a distinct color.4: Stereographic triangle showing normal directions of dislo- cation planes from a simulation of a void between two crystals of copper undergoes uniaxial expansion.2, spherical void configuration.5: Leading and trailing edge extraction and curve fitting.

Note: the centroid is at (0,0), the local x-axis goes from -65 to 65. 120 xi LIST OF TABLES Table 2.1: The crystal systems [84] .1: Table of different potentials used for copper.2: Table of simulation configurations for void growth under uni- axial expansion.3: Table of Schmid factor calculation for three loading directions. 105 xii ACKNOWLEDGEMENTS Financial support from LLNL grant B558558, ILSA contract number W-7405- Eng-48 and NSF EVO CBET-0742730 Program is gratefully acknowledged. I would like to thank Hussam Jarmakani and Paul Erhart for help with nanocrys- talline samples of nickel, Eduardo Bringa for his help and guidance on molecular dynamics, Prof.

Meyers for encouraging me to take a class of “Imperfections in solids” and last but not least, Prof. Benson for providing, time and time again, incredible practical solutions to many problems throughout my research. Sections in the chapter 3 concerning void growth in single crystalline copper including the calculations of dislocation interactions were published as an article in Acta Materialia, vol 56 (2008), page 3874-3886 with the co-authors Eduardo M. Benson and Marc A.

Sections in the chapter 3 concerning void growth in single crystalline copper with uniaxial loading direction along [110] and [111] and their analysis are in preparation for publication. xiii VITA April 10, 1976 Born, Samut Songkhram, Thailand, 1995 Armed Force Academy Preparatory School, Bangkok, Thailand, 2000 B., Royal Thai Naval Academy, Samut Prakarn, Thailand, 2002-2003 Teaching assistant, Department of Mechanical Engi- neering, Oregon State University, 2003 M., Oregon State University, Corvallis, OR, USA, 2004-2008 Teaching and Research assistant, Department of Me- chanical and Aerospace Engineering, University of Cal- ifornia, San Diego, 2008 Ph., University of California, San Diego, La Jolla, CA, USA PUBLICATIONS D. “Void Growth and Coalescence Nanocrystalline Metals: Molecular Dynamics Modeling, Continuum Modeling, and Experiments. Nguyen, editors, Shock Compression of Condensed Matter, number 1, pages 343-346.

15th APS Tropical Conference, American Insti- tute of Physics, 2007. “Void growth in metals: Atomistic calculations.” Acta Materialia, vol 56: pages 3874-3886, 2008. xiv ABSTRACT OF THE DISSERTATION A Molecular Dynamics Study of Void Initiation and Growth in Monocrystalline and Nanocrystalline Copper by Sirirat Traiviratana Doctor of Philosophy in Engineering Sciences (Mechanical Engineering) University of California San Diego, 2008 Professor David J. Benson, Chair Professor Marc A.