The Plasticity Of Metals At The Sub-micrometer

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The Plasticity Of Metals At The Sub-micrometer

Transcript Of The Plasticity Of Metals At The Sub-micrometer

THE PLASTICITY OF METALS AT THE SUB-MICROMETER SCALE
AND DISLOCATION DYNAMICS
IN A THIN FILM
A DISSERTATION SUBMITTED TO THE DEPARTMENT OF MATERIALS SCIENCE AND
ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
Seok Woo Lee September 2011

© 2011 by Seok Woo Lee. All Rights Reserved. Re-distributed by Stanford University under license with the author.
This work is licensed under a Creative Commons AttributionNoncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/tf313qt3147
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I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.
William Nix, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.
Wei Cai, Co-Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.
David Barnett
Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education
This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives.
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Abstract
Nanotechnology has played a significant role in the development of useful engineering devices and in the synthesis of new classes of materials. For the reliable design of devices and for structural applications of materials with micro- or nano-sized features, nanotechnology has always called for an understanding of the mechanical properties of materials at small length scales. Thus, it becomes important to develop new experimental techniques to allow reliable mechanical testing at small scales. At the same time, the development of computational techniques is necessary to interpret the experimentally observed phenomena. Currently, microcompression testing of micropillars, which are fabricated by focused-ion beam (FIB) milling, is one of the most popular experimental methods for measuring the mechanical properties at the micrometer scale. Also, dislocation dynamics codes have been extensively developed to study the local evolution of dislocation structures. Therefore, we conducted both experimental and theoretical studies that shed new light on the factors that control the strength and plasticity of crystalline materials at the sub-micrometer scale.
In the experimental work, we produced gold nanopillars by focused-ion beam milling, and conducted microcompression tests to obtain the stress-strain curves. Firstly, the size effects on the strength of gold nanopillars were studied, and “Smaller is Stronger” was observed. Secondly, we tried to change the dislocation densities to control the strength of gold nanopillars by prestraining and annealing. The results showed that prestraining dramatically reduces the flow strength of nanopillars while annealing restores the strength to the pristine levels. Transmission electron microscopy (TEM) revealed that the high dislocation density (~1015 m-2) of prestrained nanopillars significantly decreased after heavy plastic deformation. In order to interpret this TEM observation, potential dislocation source structures were geometrically analyzed. We
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found that the insertion of jogged dislocations before relaxation or enabling cross-slip during plastic flow are prerequisites for the formation of potentially strong natural pinning points and single arm dislocation sources. At the sub-micron scale, these conditions are most likely absent, and we argue that mobile dislocation starvation would occur naturally in the course of plastic flow.
Two more outstanding issues have also been studied in this dissertation. The first involves the effects of FIB milling on the mechanical properties. Since micropillars are made by FIB milling, the damage layer at the free surface is always formed and would be expected to affect the mechanical properties at a sub-micron scale. Thus, pristine gold microparticles were produced by a solid-state dewetting technique, and the effects of FIB milling on both pristine and prestrained microparticles were examined via microcompression testing. These experiments revealed that FIB milling significantly reduces the strength of pristine microparticles, but does not alter that of prestrained microparticles. Thus, we confirmed that if there are pre-existing mobile-dislocations present in the crystal, FIB milling does not affect the mechanical properties. The second issue is the scaling law commonly used to describe the strength of micropillars as a function of sample size. For the scaling law, the power-law approximation has been widely used without understanding fundamental physics in it. Thus, we tried to analyze the power-law approximation in a quantitative manner with the well-known single arm source model. Material parameters, such as the friction stress, the anisotropic shear modulus, the magnitude of Burgers vector and the dislocation density, were explored to understand their effects on the scaling behavior. Considering these effects allows one to rationalize the observed material-dependent power-law exponents quantitatively.
In another part of the dissertation, a computational study of dislocation dynamics in a free-standing thin film is described. We improved the ParaDiS (Parallel Dislocation Simulator) code, which was originally developed at the Lawrence Livermore National Laboratory, to deal with the free surface of a free-standing thin film. The spectral method was implemented to calculate the image stress field in a thin film. The faster convergence in the image stress calculation were obtained by employing Yoffe’s image stress, which removes the singularity of the traction at the intersecting point between a threading
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dislocation and free surface. Using this newly developed code, we studied the stability of dislocation junctions and jogs, which are the potential dislocation sources, in a free standing thin film of a face-centered-cubic metal and discussed the creation of a dislocation source in a thin film.
In summary, we have performed both microcompression tests and dislocation dynamics simulations to understand the dislocation mechanisms at the sub-micron scale and the related mechanical properties of metals. We believe that these experimental and computational studies have contributed to the enhancement of our fundamental knowledge of the plasticity of metals at the sub-micron scale.
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Acknowledgements
Many people have contributed to the work presented in this dissertations and I would like to express my gratitude to all of them.
First and foremost, I would like to thank my GREAT research advisor Professor William D. Nix for his guidance, advice and encouragement. I have come to know him as a person with a rare talent and great enthusiasm for both teaching and research. He is always full of new and interesting ideas and is never too busy to make time for his student. It has been both a pleasure and a privilege to work for him.
Secondly, I would like to thank for my co-advisor Professor Wei Cai for introducing me into the computation world which I have never experienced before. I will never forget many of private discussions to understand dislocation behavior. It has been also a great pleasure to learn ParaDiS from him.
I would also like to extend my gratitude to Professors David. M. Barnett, Reinhold H. Dauskardt and Curtis W. Frank for serving on my oral examination committee. I thank them for their many helpful suggestions and comments. Especially, I would like thank Prof. Dauskardt for giving me a chance to teach his class. Teaching students was one of the best experiences for my five years at Stanford University.
It has been a great pleasure to work with many talented group members who have given me indispensable assistance. I enjoyed the interactions and the discussions with the former and present Prof. Nix group members, including Arief S. Budiman, Aileen Maloney, Seung Min J. Han, Ill Ryu, Lucas A. Berla and Björn Backes. In particular, I want to specially thank Lucas and Ill for all their kind help and all the discussion that we had. He has been a close friend, classmate, and a colleague to whom I am deeply
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indebted. Furthermore, I also enjoyed the useful discussion with Prof. Cai group members, including Christopher R. Weinberger, Keonwook Kang, Eunseok Lee, Harkbum Lee, Jie Yin, Seunghwa Ryu, William Cash, William Kuykendall, Sylvie Aubry.
It has been a great pleasure to collaborate with many other people inside and outside of Stanford University. Dan Mordehai in Technion, Israel, kindly provided the Au microcrystal samples for compression tests. Working with Ashwini Bharathula was so fun since a metallic glass is one of my favorite research topics. Ann Marshall always kindly helped me to obtain great transmission electron microscope images at Stanford Nanocharacterization Laboratory. I also appreciate Richard Chin teaching how to use the focused-ion beam machine and the Omniprobe.
I enjoyed taking classes from the Materials Science and Engineering faculty members, and I would like to thank them for making the learning experience invaluable. I would like to thank the MSE staff, including Billie Kader, Fi Verplanke, Doris Chan and Jane Edwards. All of them have been very supportive and have facilitated my graduate studies career.
Finally, I would like to thank my family and friend who have encouraged me and supported me during my studies. All of my friends in MSE and also KMSE have made my years at Stanford enjoyable, and I want to thank them for all the memorable moments that we shared. I would like to specially thank my beautiful wife, Kyunga and my cute daughter, Claire. Their love and support was the biggest energy for me to pursue this Ph.D. work. I have been always happy during my Stanford life due to their beautiful smiles.
Support for this work by the U.S. Department of Energy, Grant number DEFG02-04ER46163, NSF CMS-0547681, AFOSR FA9550-07-1-0464, Army High Performance Computing Center at Stanford University is gratefully acknowledged.
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Table of Contents
Abstract......................................................................................................................... v Acknowledgements ............................................................................................. viii Table of Contents .................................................................................................... x List of Tables .......................................................................................................... xvi List of Figures ....................................................................................................... xvii
Chapter 1 Introduction
1.1. General overview ..................................................................................................... 1 1.2. Micro-mechanical testing at small length scales ..................................................... 4
1.2.1 Development in experimental techniques.......................................................... 4 1.2.2. Features of mechanical properties at small length scales ................................. 6 1.3. Line dislocation dynamics simulation at small length scales ................................ 10 1.4. Outline of the dissertation ...................................................................................... 14 1.4.1 Outstanding issues when this dissertation work began.................................... 14 1.4.2. The scope of the dissertation........................................................................... 15 1.5. References.............................................................................................................. 18
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DissertationPropertiesStrengthFilmFib Milling