DTIC AD1005542: Quasi-static Characterization and Modeling of the Bending Behavior of Single Crystal Galfenol for Magnetostrictive Sensors and Actuators

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ABSTRACT

Title of Dissertation: QUASI-STATIC CHARACTERIZATION AND
MODELING OF THE BENDING BEHAVIOR
OF SINGLE CRYSTAL GALFENOL FOR
MAGNETOSTRICTIVE SENSORS AND
ACTUATORS

Supratik Datta, Doctor of Philosophy, 2009

Dissertation Directed By: Professor Alison B. Flatau,
Department of Aerospace Engineering

Iron-gallium alloys (Galfenol) are structural magnetostrictive materials that
exhibit high free-strain at low magnetic fields, high stress-sensitivity and useful
thermo-mechanical properties. Galfenol, like smart materials in general, is attractive
for use as a dynamic actuator and/or sensor material and can hence find use in active
shape and vibration control, real-time structural health monitoring and energy
harvesting applications. Galfenol possesses significantly higher yield strength and
greater ductility than most smart materials, which are generally limited to use under
compressive loads. The unique structural attributes of Galfenol introduce
opportunities for use of a smart material in applications that involve tension, bending,
shear or torsion. A principal motivation for the research presented in this dissertation
is that bending and shear loads lead to development of non-uniform stress and
magnetic fields in Galfenol which introduce significantly more complexity to the
considerations to be modeled, compared to modeling of purely axial loads.
This dissertation investigates the magnetostrictive response of Galfenol under
different stress and magnetic field conditions which is essential for understanding and
modeling Galfenol’s behavior under bending, shear or torsion. Experimental data are
used to calculate actuator and sensor figures of merit which can aid in design of
adaptive structures. The research focuses on the bending behavior of Galfenol alloys
as well as of laminated composites having Galfenol attached to other structural
materials. A four-point bending test under magnetic field is designed, built and
conducted on a Galfenol beam to understand its performance as a bending sensor. An
extensive experimental study is conducted on Galfenol-Aluminum laminated
composites to evaluate the effect of magnetic field, bending moment and Galfenol-
Aluminum thickness ratio on actuation and sensing performance.
A generalized recursive algorithm is presented for non-linear modeling of
smart structures. This approach is used to develop a magnetomechanical plate model
(MMPM) for laminated magnetostrictive composites. Both the actuation and sensing
behavior of laminated magnetostrictive composites as predicted by the MMPM are
compared with results from existing models and also with experimental data obtained
from this research. It is shown that the MMPM predictions are able to capture the
non-linear magnetomechanical behavior as well as the structural couplings in the
composites. Model simulations are used to predict optimal actuator and sensor design
criteria. A parameter is introduced to demarcate deformation regimes dominated by
extension and bending. The MMPM results offer significant improvement over
existing model predictions by better capturing the physics of the magnetomechanical
coupled behavior.
QUASI-STATIC CHARACTERIZATION AND MODELING OF THE BENDING
BEHAVIOR OF SINGLE CRYSTAL GALFENOL FOR MAGNETOSTRICTIVE
SENSORS AND ACTUATORS

By

Supratik Datta

Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park, in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2009

Advisory Committee:
Professor Alison B. Flatau, Chair/Advisor
Professor Abhijit Dasgupta
Professor Sung Lee
Professor Norman M. Wereley
Professor Manfred Wuttig
© Copyright by
Supratik Datta
2009
To the memory of my late grandfather
Pravash Chandra Dutta
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Acknowledgements
First and foremost, I would like to thank my advisor Dr. Alison Flatau for her
unwavering support at all times that helped me to meet several challenges in graduate
school. I am thankful to her for her confidence in me and for allowing me to pursue
several ideas in the past six years, some of which helped me towards my PhD
dissertation. She has been an excellent mentor who took active initiative in my
professional development as an independent researcher. She always encouraged me to
interact and collaborate with peers and facilitated interactions with them at many
occasions. Her guidance on public speaking helped me win accolades at many
conferences. Most importantly, I would like to thank her for being such a nice human
being and teaching me how to remain calm and keep a smile on your face no matter
how difficult a situation you are in.
I would like to thank all my committee members, Dr. Wereley, Dr. Wuttig,
Dr. Dasgupta and Dr. Lee, for their thoughtful suggestions during the oral exam and
pre-defense. I was particularly influenced by Dr. Wereley’s class on composites and
ended up using a significant amount of the knowledge gained in that course in this
dissertation. I would especially like to thank Dr. Wuttig for taking time out often to
interact with me and for introducing me to the intriguing world of material science. It
was a pleasure attending his classes on smart materials and kinetics. I am also
thankful to Dr. Dasgupta for helping me to develop an appreciation of application of
mathematical principles in unifying different engineering areas through his course on
energy methods. The opportunity to discuss my work with him at “College Perk”
completely changed my way of thinking about modeling smart materials. I would like
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to thank Dr. Inderjit Chopra whose course on smart structures taught me several
useful modeling techniques that I have used in this work. I would also like to thank
Dr. Mary Bowden for recommending me for the Wylie dissertation fellowship.
I would like to acknowledge the financial support from ETREMA Products
Inc. under contract number 05C0165 and the US Office of Naval Research under
MURI contract number N000140610530. I would also like to thank Dr. Jon
Snodgrass, Dr. Julie Slaughter and Eric Summers from ETREMA and Dr. Arthur
Clark, Dr. James Restorff and Marilyn Wun-Fogle from NSWC Carderock for
stimulating discussions and for providing me with valuable resources for my research.
I would also like to acknowledge the encouragement that I received from Dr. Thomas
Lograsso of Materials Preparation Center, Ames, during our occasional meetings at
workshops and conferences. I am also thankful to Late Dr. William Armstrong for his
criticism of my early work which motivated me to develop the coupled model
discussed in this dissertation.
I would like to thank Pat Baker, Becky Sarni, Debora Chandler, Julia John,
Rita Woodell, LaVita Williams, Peter Alexander, Otto Fandino, Kevin Lewy and all
other staff members in the Aerospace Engineering Department for making my stay at
the University of Maryland a wonderful experience. I would particularly like to thank
Rosalia for encouraging me to apply for the AIAA graduate award. Special thanks to
Howard Grosenbacher at the Engineering machine shop and David Cogswell at the
Physics machine shop for helping me with the fabrication of my experimental setup
and for sharing their insights which helped me to learn a great deal. Dr. Phil Piccoli
deserves a special mention for helping me with composition analysis using EDS and
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WDS. I would also like to thank a number of people in the Manufacturing Building
who have helped me in designing and conducting experiments. Dr. V. K. Pavlin, Dr.
Y. T. Choi, Dr. Jin-Hyeong Yoo, Dr. Suok-Min Na and Dr. Wei Hu have been of
great help at many a times. Dr. Patrick Downey and Dr. Anirban Chaudhuri have
been of immense help in teaching me a number of things in the lab and for always
coming up with useful suggestions and advice. I particularly need to thank Kunal
Kothari for sharing his design insights on the four-point bending test fixture. I would
also like to thank Luke Twarek, Mark Staley, Sarah Haack, Baran Sahin, Marie
Schroeder and Frank Graham for helping me at different times during the period of
my graduate studies.
I need to specially mention two of my colleagues, Dr. Jayasimha Atulasimha
and Chaitanya Mudivarthi. Atul has been an excellent mentor and Chaitanya has been
the best office-mate. The honest feedback and friendly advice that I received from
them deeply influenced my work. Thanks to both of you for being such great friends.
I would also like to thank my personal friends Subhamoy, Anyesha, Ayush, Theron
and Indrajit, for all their help and personal advice which made my stay at Maryland a
memorable experience.
I must thank my parents for inculcating in me the urge for advanced education
at a tender age which finally motivated me to pursue a doctoral degree. I am
particularly indebted to my father for supporting my decision to join graduate school
and for instilling in me the belief that I should do my best and leave the rest to God.
This belief helped me to overcome many uncertain times that I faced in the past six
years.
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Finally, I would like to thank my wife Ritaja for making my home and making
me the person that I am today. She is the sweetest thing I found in grad school but I
must confess that I haven’t been able to return her unconditional love because of my
pre-occupation with research. I hope she forgives me for that knowing that I could not
have completed this journey without her hand in my hand.
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Table of Contents

Acknowledgements .................................................................................................... iii
Table of Contents ...................................................................................................... vii

Chapter 1: Introduction ............................................................................................. 1
1.1. Smart structures ............................................................................................ 2
1.1.1. Applications of smart structures ........................................................... 3
1.1.2. Role of smart materials ......................................................................... 4
1.2. Overview of smart materials ......................................................................... 6
1.2.1. Introduction to ferroic materials ........................................................... 7
1.2.2. A unified view of ferroic materials ..................................................... 14
1.3. Physics of ferromagnetism .......................................................................... 16
1.3.1. Fundamental magnetic quantities ....................................................... 17
1.3.2. Demagnetization and its significance ................................................. 21
1.3.3. Electromagnetism and magnetic circuit .............................................. 23
1.3.4. Maxwell’s equations and their significance ........................................ 26
1.3.5. Classification of magnetic materials ................................................... 28
1.3.6. Magnetism at the atomic scale ............................................................ 30
1.3.7. Magnetic domains and process of magnetization ............................... 33
1.4. Phenomenon of magnetostriction ............................................................... 40
1.4.1. Magnetoelastic effects ........................................................................ 41
1.4.2. Fundamental relations in magnetostriction ......................................... 43
1.4.3. Magnetostrictive actuation and sensing .............................................. 46
1.4.4. History of the development of magnetostrictive materials ................. 50
1.5. Iron-gallium alloys (Galfenol) .................................................................... 53
1.5.1. Metallurgy of Fe-Ga alloys ................................................................. 53
1.5.2. Magnetostriction and other properties of Fe-Ga alloys ...................... 57
1.5.3. Processing of Fe-Ga alloys ................................................................. 61
1.5.4. Applications of Fe-Ga alloys .............................................................. 63
1.6. Overview of magnetomechanical models ................................................... 65
1.6.1. Constitutive material models .............................................................. 65
1.6.2. Device-level models............................................................................ 71
1.7. Objectives and organization of the dissertation .......................................... 72

Chapter 2: Experimental studies and model simulations of actuator and sensor
figures of merit .......................................................................................................... 75
2.1. Background and scope of this work ............................................................ 75
2.2. Experiment .................................................................................................. 76
2.2.1. Sample description .............................................................................. 77
2.2.2. Description of transducer .................................................................... 78
2.2.3. Instrumentation ................................................................................... 79
2.2.4. Actuator characterization under constant stress .................................. 81
2.2.5. Sensor characterization under constant magnetic field ....................... 82
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