MARINE COMPOSITE PANELS UNDER BLAST LOADING A Dissertation Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Dushyanth Sirivolu August, 2016 MARINE COMPOSITE PANELS UNDER BLAST LOADING Dushyanth Sirivolu Dissertation Approved: Accepted: ____________________________ ____________________________ Advisor Department Chair Dr. Michelle S. Hoo Fatt Dr. Sergio Felicelli ____________________________ ____________________________ Committee Member Interim Dean of College Dr. Graham Kelly Dr. Eric Amis ____________________________ ____________________________ Committee Member Dean of the Graduate School Dr. Kwek-Tze Tan Dr. Chand Midha ____________________________ ____________________________ Committee Member Date Dr. Atef Saleeb ____________________________ Committee Member Dr. Dmitry Golovaty ii ABSTRACT Composite and composite sandwich panels are being used and considered as an alternative to metal panels in ship structures due to their high stiffness- and strength- to weight ratio, improved corrosion resistance and low radar and magnetic signatures. In such applications they may be subjected to both in-air and under-water blast loading and it is important to understand the response of composite panels to blast loading. Analytical solutions were developed to elucidate the deformation and damage initiation of composite and composite sandwich panels under blast. Three different problems were considered in this study: composite shells subjected to external pressure pulse, composite sandwich shells subjected to blast loading and composite sandwich plates subjected to air and blast loading. The response of a double-curvature, composite shell under external blast was examined using Novozhilov non-linear shell theory and Lagrange’s equations of motion. The predicted stable response of the shell was shown to compare well with FEA results from ABAQUS Explicit. The Budiansky-Roth criterion was used to examine the instability of the shell. It was shown that the dynamic pulse buckling strength of the shell could be increased by reducing the radius of curvature of the shell for a fixed span, or by increasing angular extent for fixed radius of curvature. Both these parameters triggered instability at higher buckling modes and were responsible for higher buckling strength. iii A multi-layered, analytical model was developed to study the blast response of double-curvature, composite sandwich panels with crushable, elastic-plastic PVC foam core. Plastic core crushing and energy absorption are important core properties for blast mitigation. The PVC foam core was modeled with isotropic and transversely isotropic properties. Predicted solutions using isotropic foam core was shown to be in good agreement with FEA results from ABAQUS Explicit. For sandwich shells with higher curvature and in-plane membrane resistance, lower blast resistance was found with transversely-isotropic foam core than with an isotropic foam core. The study suggested that modeling the sandwich core as an isotropic material, as is commonly done in practice, leads to non-conservative estimates in the structure’s ability to resist blast loads. A fluid-solid interaction model was developed to examine the dynamic response of a composite sandwich plate subjected to air blast/air back, water blast/water back, and water blast/water back conditions. Reflected and radiated surface traction vectors were introduced to account for the plate motions at the interface of fluid and solid. The fluid damping terms resulted in substantially reducing and slowing down the deformation of the sandwich plate. This caused higher pressure loads to induce damage in the water blast/air back and water blast/water back panels when compared to air blast/air back panel. For the thick composite sandwich plates, the panels with the high density foam was more blast resistant in air blast/air back condition, while sandwich panels with lower density foam were more blast resistant in the water blast/air back and water blast/water back conditions. For thin composite sandwich plates, sandwich panels with lower density foam were most blast resistant in all blast loading conditions. It was also shown that the core plasticity in the air blast/air back panel was primarily due to transverse shear. iv However, in the water blast/air back, it was due to combined transverse compression and shear, and in the water blast/water back case, plasticity in the core was due to hydrostatic pressure and transverse shear. v ACKNOWLEDGEMENTS I want to convey my sincere appreciation and gratitude to my advisor Dr. Michelle S. Hoo Fatt. During my studies at The University of Akron, she encouraged me to work on various research problems, provided me with an unlimited access at all times and more importantly, valuable guidance in completing this research. The accomplishment of this degree would be impossible without her consistent help and support. I would like to thank Dr. Yapa Rajapakse, Solids Mechanics Program Manager at the Office of Naval Research, for financially supporting this project under the Grant N00014-11-1-0485. I would like to thank my committee members: Dr. Graham Kelly, Dr. Kwek-Tze Tan from the Department of Mechanical Engineering, Dr. Atef Saleeb from the Department of Civil Engineering and Dr. Dmitry Golovaty from the Department of Theoretical and Applied Mathematics, for agreeing to be on my committee and providing me with valuable suggestions during the dissertation proposal. Their comments and suggestions have improved the quality of my research work. I would like to thank the staff and faculty in the Department of Mechanical Engineering for their help during my study at The University of Akron. A special thanks to Mr. Cliff Bailey and Ms. Bayaan Jundi for allowing me to use the Mechanical Engineering computer lab and patiently helping me with computer/software related vi issues. Also, I would like to thank Ms. Cortney Castleman for helping me with various office-related matters. I would also like to thank my friends and colleagues both in the Department and outside The University. I would like to thank Preethi, Isaac and Ahamed for their help during my work. Outside the lab, Kranthi, Kalyan, Sandeep, Mani Harsha, Bharat, and many others have been very supportive and made my stay enjoyable. I would like to thank my cousin Shravan Sirivolu, his wife, Roshni Sirivolu and their children for their love and support. Last but not the least, special thanks to my parents, Hari Kishan Sirivolu and Bharathi Sirivolu, and my sister Hithaswi Sirivolu. There is no way that I could have done it without their love, encouragement, patience and understanding. vii TABLE OF CONTENTS Page LIST OF TABLES ............................................................................................................ xi LIST OF FIGURES ......................................................................................................... xii CHAPTER I. INTRODUCTION .......................................................................................................... 1 II. RESPONSE OF DOUBLE CURVATURE SHELLS UNDER EXTERNAL BLAST LOADS ….................................................................................. 9 2.1 Background ......…………………………………………….................................. 9 2.2 Problem Formulation ...…………………............................................................ 13 2.2.1 Novozhilov non-linear shell theory …........................................................ 13 2.3 Nonlinear Equations of Motion …………........................................................... 16 2.4 Stable Forced Response ……………................................................................... 18 2.4.1 Solution of Lagrange’s equations of motion ............................................... 19 2.4.2 Finite element analysis ………………………………..……...................... 20 2.5 Dynamic Instability ………………………………………………...................... 24 2.5.1 Critical buckling curves .…………………………………………............. 25 2.5.2 Influence of shell geometry ...……………………………………............. 27 2.6 Summary ….……………………………………………………………............. 32 III. BLAST RESPONSE OF DOUBLE-CURVATURE SANDWICH PANELS .......... 33 3.1 Background ......……………………………………………................................ 33 3.2 Problem Formulation ...…………………............................................................ 37 viii 3.2.1 Facesheet kinematics …………………...................................................... 40 3.2.2 Core kinematics ………………………...................................................... 41 3.2.3 Transient response of shell ……………...................................................... 43 3.3 Predicted Response with Isotropic and Transversely-isotropic Core .................. 51 3.3.1 Isotropic foam core ...…………………...................................................... 53 3.3.2 Transversely isotropic foam core ….…...................................................... 57 3.4 Failure of Sandwich Shell …………................................................................... 60 3.4.1 Facesheet failure …………………...…...................................................... 60 3.4.2 Core failure ………………………...…...................................................... 61 3.5 Influence of Transverse Isotropy ...………………………………...................... 62 3.6 Summary …….…………………………………………………………............. 65 IV. WATER BLAST RESPONSE OF COMPOSITE SANDWICH PLATES ……...... 66 4.1 Background ……….............................................................................................