CHARACTERIZATION AND MODELING OF THE FERROMAGNETIC SHAPE MEMORY ALLOY Ni-Mn-Ga FOR SENSING AND ACTUATION DISSERTATION Presented in Partial Ful¯llment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Neelesh Nandkumar Sarawate, B.E., M.S. ***** The Ohio State University 2008 Dissertation Committee: Approved by Marcelo Dapino, Adviser Rajendra Singh Adviser Stephen Bechtel Graduate Program in Rebecca Dupaix Mechanical Engineering °c Copyright by Neelesh Nandkumar Sarawate 2008 ABSTRACT Ferromagnetic Shape Memory Alloys (FSMAs) in the Ni-Mn-Ga system are a recent class of active materials that can generate magnetic ¯eld induced strains of 10% by twin-variant rearrangement. This work details an extensive analytical and experimental investigation of commercial single-crystal Ni-Mn-Ga under quasi-static and dynamic conditions with a view to exploring the material's sensing and actua- tion applications. The sensing e®ect of Ni-Mn-Ga is experimentally characterized by measuring the flux density and stress as a function of quasi-static strain loading at various ¯xed magnetic ¯elds. A bias magnetic ¯eld of 368 kA/m is shown to mark the transition from irreversible to reversible (pseudoelastic) stress-strain behavior. At this bias ¯eld, a reversible flux-density change of 0.15 Tesla is observed over a range of 5.8% strain. A constitutive model based on continuum thermodynamics is developed to describe the coupled magnetomechanical behavior of Ni-Mn-Ga. Me- chanical dissipation and the microstructure of Ni-Mn-Ga are incorporated through internal state variables. The constitutive response of the material is obtained by restricting the process through the second law of thermodynamics. The model is further modi¯ed to describe the actuation and blocked-force behavior under a uni¯ed framework. Blocked-force characterization shows that Ni-Mn-Ga exhibits a block- ing stress of 1.47 MPa and work capacity of 72.4 kJ/m3. The model requires only ii seven parameters which can be obtained from two simple experiments. The model is physics-based, low-order and is therefore suitable for device and control design. The behavior of Ni-Mn-Ga under dynamic mechanical and magnetic excitations is addressed. First, a new approach is presented for modeling dynamic actuators with Ni-Mn-Ga as a drive element. The constitutive material model is used in conjunction with models for eddy current loss and lumped actuator dynamics to quantify the frequency dependent strain-¯eld hysteresis. Second, the magnetization response of Ni-Mn-Ga to dynamic strain loading of up to 160 Hz is characterized, which shows the response of Ni-Mn-Ga as a broadband sensor. A linear constitutive equation is used along with magnetic di®usion to model the dynamic behavior. Finally, the e®ect of changing magnetic ¯eld on the resonance frequency of Ni-Mn- Ga is characterized by conducting mechanical base excitation tests. The measured ¯eld induced resonance frequency shift of 35% indicates that Ni-Mn-Ga is well suited for vibration absorption applications requiring electrically-tunable sti®ness. Ferromagnetic shape memory Ni-Mn-Ga is thus demonstrated as a multi-functional smart material with possible applications in sensing, actuation, and vibration control which require large deformation, low force, tunable sti®ness and fast response. Other applications being investigated elsewhere such as energy harvesting further expand the application potential of Ni-Mn-Ga. The physics-based constitutive model along with the models for dynamic magnetic and mechanical processes provide a thorough understanding of the complex magnetomechanical behavior. iii ACKNOWLEDGMENTS I would like to express my sincere gratitude towards my advisor Prof. Marcelo Dapino, for his continuous guidance, understanding, and patience during my Ph.D. study. I have thoroughly enjoyed interacting with him during my stay at OSU. This research would not have been possible without his insightful suggestions, enthusiasm, and trust in me. I would also like to thank my dissertation committee, Prof. Rajendra Singh, Prof. Stephen Bechtel, and Prof. Rebecca Dupaix for their assistance in addressing several technical issues, thoroughly reviewing my proposal and providing valuable sugges- tions. The knowledge acquired through their courses has been invaluable towards my research. I am grateful to all the colleagues in Smart Materials and Structures Lab, espe- cially LeAnn Faidley, Xiang Wang, and Phillip Evans for their help in addressing various experimental and theoretical issues. I am thankful to the Mechanical Depart- ment sta® for their cooperation. I would like to thank the machine shop supervisor, Gary Gardner, for his help in completing the test setups. Finally, I would like to thank my parents and brother for their continuous love and encouragement. iv VITA November 20, 1979 . Born - Pune, India 2001 . .B.E. Mechanical Engineering, University of Pune, India 2001-2002 . Design Engineer Hodek Vibration Technologies, India 2004 . .M.S. Mechanical Engineering University of Missouri-Rolla, Rolla MO 2004-present . .Graduate Research Associate, The Ohio State University Columbus OH PUBLICATIONS Journal Publications N. Sarawate and M. Dapino, \Characterization and modeling of the dynamic sensing behavior of Ni-Mn-Ga", Smart Materials and Structures, Draft in preparation. N. Sarawate and M. Dapino, \Magneto-mechanical energy model for nonlinear and hysteretic quasi-static behavior of Ni-Mn-Ga", Journal of Intelligent Material Systems and Structures, in review. N. Sarawate and M. Dapino, \Dynamic actuation model for magnetostrictive mate- rials," Smart Materials and Structures, in review. N. Sarawate and M. Dapino, \Sti®ness tuning using bias ¯elds in ferromagnetic shape memory alloys," Journal of Intelligent Material Systems and Structures, in review. v N. Sarawate and M. Dapino, \Magnetization dependence on dynamic strain in ferro- magnetic shape memory Ni-Mn-Ga," Applied Physics Letters, Vol. 93(6), p. 062501, 2008. N. Sarawate and M. Dapino, \Magnetic ¯eld induced stress and magnetization in mechanically blocked Ni-Mn-Ga," Journal of Applied Physics. Vol. 103(1), p. 083902, 2008. N. Sarawate and M. Dapino, \Frequency dependent strain-¯eld hysteresis model for ferromagnetic shape memory Ni-Mn-Ga," IEEE Transactions on Magnetics, Vol. 44(5), pp. 566-575, 2008. N. Sarawate and M. Dapino, \Continuum thermodynamics model for the sensing ef- fect in ferromagnetic shape memory Ni-Mn-Ga," Journal of Applied Physics, Vol. 101 (12), p. 123522, 2007. N. Sarawate and M. Dapino, \Experimental characterization of the sensor e®ect in fer- romagnetic shape memory Ni-Mn-Ga," Applied Physics Letters, Vol. 88(1), p. 121923, 2006. Conference Publications N. Sarawate, and M. Dapino, \Characterization and modeling of dynamic sensing behavior of ferromagnetic shape memory alloys," Proceedings of ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, Paper #656, Ellicott City, MD, October 2008. N. Sarawate, and M. Dapino, \Dynamic strain-¯eld hysteresis model for ferromagnetic shape memory Ni-Mn-Ga," Proceedings of SPIE Smart Structures and Materials, Vol. 6929, p. 69291R, San Diego, CA, March 2008. N. Sarawate, and M. Dapino, \Electrical sti®ness tuning in ferromagnetic shape mem- ory Ni-Mn-Ga," Proceedings of SPIE Smart Structures and Materials, Vol. 6529, p. 652916, San Diego, CA, March 2007. N. Sarawate, and M. Dapino, \Magnetomechanical characterization and uni¯ed mod- eling of Ni-Mn-Ga," Proceedings of SPIE Smart Structures and Materials, Vol. 6526, p. 652629, San Diego, CA, March 2007. vi N. Sarawate, and M. Dapino, \A thermodynamic model for the sensing behavior of fer- romagnetic shape memory Ni-Mn-Ga," Proceedings of ASME IMECE, Paper #14555, Chicago, IL, November 2006. N. Sarawate, and M. Dapino, \Sensing behavior of ferromagnetic shape memory Ni-Mn-Ga," Proceedings of SPIE Smart Structures and Materials," Vol. 6170, pp. 61701B, San Diego, CA, February 2006. FIELDS OF STUDY Major Field: Mechanical Engineering Studies in: Smart Materials and Structures Prof. Dapino Applied Mechanics Prof. Dapino, Prof. Bechtel, Prof. Dupaix System Dynamics and Vibrations Prof. Dapino, Prof. Singh vii TABLE OF CONTENTS Page Abstract ....................................... ii Acknowledgments .................................. iv Vita ......................................... v List of Tables .................................... xii List of Figures ................................... xiii Chapters: 1. Introduction and Literature Review ..................... 1 1.1 Introduction and Motivation ...................... 1 1.2 Overview of Smart Materials ..................... 5 1.2.1 Ferroelectrics .......................... 6 1.2.2 Magnetostrictives ........................ 8 1.2.3 Shape Memory Alloys ..................... 9 1.3 Ferromagnetic Shape Memory Alloys ................. 14 1.3.1 Early Work ........................... 15 1.3.2 Properties and Crystal Structure ............... 18 1.3.3 Magnetocrystalline Anisotropy ................ 19 1.3.4 Strain Mechanism ....................... 20 1.4 Literature Review on Ni-Mn-Ga .................... 22 1.4.1 Sensing Behavior ........................ 23 1.4.2 Modeling ............................ 26 1.4.3 Dynamic Behavior ....................... 30 1.5 Research Objectives .......................... 33 1.6 Outline of Dissertation ......................... 33 viii 1.6.1 Quasi-static Behavior ..................... 34 1.6.2 Dynamic Behavior ......................