Material Characterization, Constitutive Modeling and Finite Element Simulation of Polymethyl methacrylate (PMMA) for Applications in Hot Embossing Doctoral Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Kamakshi Singh, B.E. Graduate Program in Mechanical Engineering ***** The Ohio State University 2011 Dissertation Committee: Rebecca B. Dupaix, Advisor Jose M. Castro Amos Gilat Allen Yi ABSTRACT Polymethyl methacrylate (PMMA) is an amorphous thermoplastic used in various industrial applications. PMMA is compatible with human tissues and allows high resolution features to be embossed onto a surface, thus making it highly desirable for use in bio-medical, micro-optics, micro-fluidic devices, electronics, micro-electro-mechanical systems (MEMS), etc. The processes used to fabricate these devices capitalize on the fact that the mechanical behaviour of the polymers changes drastically around the glass transition temperature (Tg). The polymer is deformed at temperatures above the Tg where the material is more fluid-like and then cooled below the Tg where it behaves more like a solid. The changes in physical properties make this temperature regime highly favourable for these warm-temperature deformation processes. The same rationale also makes it more difficult to develop a continuum model which accurately predicts the polymer behaviour with temperature and strain rate dependence across the glass transition temperature. Most of the existing constitutive models do not achieve this task; they either work below or above glass transition, but not in both these regions. Hence, there is a greater need to develop a constitutive model for the polymer that can capture the material behaviour across the glass transition temperature (Tg - 20 to Tg + 60) relevant for hot ii embossing applications. The aim of this thesis is to develop such a material model for PMMA. First, material characterizations experiments were conducted on PMMA well across its glass transition temperature (Tg). This experimental data along with the existing data in the Dupaix lab was used in developing the material model. In order to develop the new material model for application in hot embossing that will work across the wide range of temperature and strain rates, two existing constitutive models on the polymer PMMA were studied: the Dupaix-Boyce model and the Dooling-Buckley-Rostami-Zahlan model. From the aforementioned study, a new continuum model was developed to capture the mechanical behavior over a wider range of temperature across the glass transition. Experimental data was also collected from hot embossing experiments on the polymer PMMA across its glass transition temperature. This was done to better understand the process conditions of hot embossing and thus identify the vital parameters essential that the new developed material model must be able to capture. Finally, hot embossing simulations were performed on ABAQUS using the new material model. These results were used to validate the new material model. The new model worked extremely well for large strain deformations capturing the strain rate and temperature dependence, as well as stress relaxation of the material. The model was less accurate in capturing stress relaxation for small strain deformations. The strengths and weaknesses of the current model are discussed for future work improving the constitutive model. iii DEDICATION To my parents, Prof. H. B. Singh and Mrs. Usha Singh iv ACKNOWLEDGEMENTS First of all, I would to thank my advisor Dr. Rebecca B. Dupaix for being the most wonderful advisor I could possibly imagine. Her guidance, encouragement and support throughout my graduate school has made my stay at The Ohio State University a very fulfilling experience. I genuinely appreciate the fact that she managed to find time to have our weekly meetings and discussions even with her new triplets. I would also like to thank my committee members Prof. Amos Gilat, Prof. Jose M. Castro and Dr. Allen Yi for being part of my committee and giving their invaluable time and suggestions. In addition, I wish to thank Prof. Gary L. Kinzel, Assistant Chair of the Department of Mechanical Engineering and Ms. Judith Ann Brown, Graduate Program Coordinator of Department of Chemistry for giving me an opportunity to be a teaching assistant (TA) in their respective departments. Being a TA was a very enriching experience and helped me grow as both a student and a person. I wish to thank my lab mates Arindam, Greg and Bill who’s work I followed; Guru for teaching me how to conduct experiments in our lab and for being a good friend; Parth, Tom, Nimet, Srinath, Sarah, Ann, Jason, Sushma and all my friends and colleagues at OSU. In particular, I am grateful to have known Venuka, Yashas and Shubham, they have been more like a family than friends. v I believe I am blessed indeed to have a family like mine, my parents have always supported me and have had faith and trust in my judgment; irrespective of their opinions on what they considered was the right thing for me. My sister, Dr. Namrata Singh, has been a pillar of strength in my life. She is my best friend, confidant, guardian and everything. Last but not the least; I would like to thank my husband Dr. Navneet Singh for bearing with all my frustrations and complains regarding graduate school and otherwise , and for making me believe that I am a better person than I actually am. I am really, really looking forward to finishing graduate school and spending all our future times together. And finally, no more travelling over the weekends! vi VITA January 1984…….……….……………………………………………BORN: Basti, India July 2005 – January 2006…………………………………………….….....Inplant Trainee Larsen and Toubro Limited Mumbai, India August 2002 - June 2006……….……………………………...…Bachelor of Engineering University of Mumbai Mumbai, India January 2007 – June 2007……………………….…………...Graduate Teaching Assistant Department of Chemistry The Ohio State University, Columbus September 2007 – June 2008………….……………………..Graduate Teaching Assistant Department of Mechanical Engineering The Ohio State University, Columbus July 2008 – March 2011…..…….…………………….……..Graduate Research Assistant Department of Mechanical Engineering The Ohio State University, Columbus FIELDS OF STUDY Major Field: Mechanical Engineering vii TABLE OF CONTENTS Page Abstract ………………………………………………………………………………... ii Dedication ……………………………………………...…………………………........ iv Acknowledgements …………………………………...……………………………….. v Vita …………………………………………………………………………………….. vii List of Tables ……………………………………………………………………….…. xii List of Figures …………………………………………………………………………. xiii Chapter 1: Introduction ……………………………………...………………………… 1 1.1 Introduction ………………………………………...……………………… 1 1.2 Summary of Work …………………………………………………………. 3 Chapter 2: Literature Review ………………………………………………………….. 5 2.1 Experiments ……………………………………………………………..… 5 2.2 Constitutive Modeling ….…………………………………………………. 11 2.3 Hot Embossing Experiments ………………………………………………. 26 2.4 Hot Embossing Simulation ………………………………………………... 31 Chapter 3: Compression Experiments ………………………………………………… 34 viii Page 3.1 Introduction ……………………………………………………………….. 34 3.2 Material ……………………………………………………………………. 35 3.3 Experimental Set-up and Procedure ……………………………………….. 36 3.3.1 Experimental Set-up .……………………………………………. 36 3.3.2 Test Procedure …………………………………………………... 38 3.3.3 Limitations of plane strain compression fixture ………………… 40 3.3.4 Experimental Errors ……………………………………………... 41 3.4 Experimental Results ……………………………………………………… 45 3.5 Discussion …………………………………………………………………. 56 Chapter 4: Existing Constitutive Model ………………………………………………. 59 4.1 Introduction ……………………………………………………………….. 59 4.2 Dupaix-Boyce (DB) Model ……………………………………………..… 60 4.2.1 Details of Constitutive Model …………………………………… 60 4.2.2 Optimization of Material Constants …………………………….. 67 4.2.3 Comparison with Experimental Data ……………………………. 69 4.3 Dooling-Buckley-Rostami-Zahlan (DBRZ) Model ………………………. 73 4.3.1 Details of Constitutive Model …………………………………… 73 4.3.2 Replication of the DBRZ Model ………………………………… 79 4.3.3 Optimization of Material Constants …………………………….. 80 4.3.4 Comparison with Experimental Data ……………………………. 82 ix Page 4.4 Discussion …………………………….…………………………………… 87 Chapter 5: New Constitutive Model …………………………………………………... 90 5.1 Introduction …………………………………………………………….…. 90 5.2 Modifications to Dupaix-Boyce Model …………………………………… 91 5.2.1 Additional Molecular Relaxation Network ……………………… 91 5.2.2 Additional Transition Slope Constant …………………………… 95 5.2.3 New Model ………………………………………………………. 98 5.3 Results …………………………………………………...………………… 98 5.4 Discussion …………………………………………………………………. 106 Chapter 6: Hot Embossing Experiments ………………………………………….…… 110 6.1 Introduction ……………………………………………………………….. 110 6.2 Experimental Details – Material and Test Set-up …………………….…… 113 6.3 Experimental Results and Discussion ……………………………….…….. 115 6.4 Conclusion ……………………………………………………………….... 131 Chapter 7: Hot Embossing Simulations ………………………………….……………. 134 7.1 Introduction ……………………………………………………………….. 134 7.2 Finite Element Model ……………………………………………………... 136 7.3 Hot Embossing Simulations ……………………………………………….. 139 7.4 Analysis of New Model ...…………………………………………………. 148 7.5 Suggestions for New Model ……………………………………………..… 156 x Page 7.6 Conclusion ………………………………………………………………… 161 Chapter 8: Conclusion & Future Work ………………………………….…………….. 163 8.1 Conclusion ……………………………………………………………….... 163 8.2 Future Work ……………………………………………………………….. 166 References ……………………………………………………………………………..