Design of Sandwich Structures

Design of Sandwich Structures Achilles Petras Robinson College Cambridge Sup ervisor Dr MPF Sutclie A dissertation submitted to Cambridge University Engineering Department for the degree of Do ctor of Philosophy Decemb er To my parents and b ebita Declaration This dissertation presents the results of research carried out in the Engineering Department of the UniversityofCambridge b etween Octob er and Octob er Except where sp ecic reference is made to the work of others this dissertation is the original result of myown work and includes nothing which is the outcome of work done in collab oration No part of this dissertation has been submitted for a degree at any other University This dissertation is approximately words long and contains gures Achilles Petras March Robinson College Cambridge ii Acknowledgements Iwould like to express my gratitude to my sup ervisor Dr Michael Sutclie for all his kind help encouragement and dedicated guidance without which this pro ject would not have been p ossible He gave me exibility to follow my research interests but at the same time he kept me going in the right direction His patience with pro ofreading my thesis is highly appreciated I am also grateful to Professor Norman Fleck for his invaluable advice and fruitful discussions Iwould like to thank him for supp orting nancially my pro ject US Oce of Naval Researchgrant J and my attendance at the th International Conference on Sandwich Construction in Sto ckholm I acknowledge with gratitude the generous nancial supp ort of the Greek State Scholarship Foundation IKY I would like to thank Professors Christos Panagop oulos and Constantinos Lascarides at the National Technical University of Athens and Dr Dimitris Niarchos at the National Centre for Scientic Research Demokritos in Greece for supp orting and urging me to pursue my PhD studies at Cambridge I would like to thank Nigel Ho okham and Peter Clayton from Hexcel Comp osites in Duxford for providing materials and valuable technical information I wish to ac knowledge the Cambridge University Engineering Department CUED and esp ecially the Cambridge Centre for Micromechanics CCM for use of their facilities I am also grateful to Alan Heav er and Simon Marshall for building the test rigs and helping me during my exp eriments Sp ecial thanks to the CUEDs librarians for their kindest assistance I wish to thank my friend Antonios Zervos for helping me out on compu tational mo delling topics Many thanks to Roxy Pia Ingo Sinisa Guy Dongquan Kieran Jide at the CCM for those stimulating discussions and entertaining moments when there was achance to see them due to my night shifts Sta students and fellows at Robinson College have help ed makemy time at Cam bridge really enjoyable Thanks to all my friends here in Cambridge for the enjo yable moments wehave shared during these three years Also to my friends in Athens Kostas and Stefanos for not forgetting me and for making my holidays in Greece a real fun I am extremely grateful to my parents Violetta and Alexandros for their constant understanding caring love and supp ort o o Finally but most imp ortantlyI would like to thank Georgina for her love patience and the happy life we share together Te amo iii Abstract Failure mo des for sandwich b eams of GFRP laminate skins and Nomex honeycomb core are investigated Theoretical mo dels using honeycomb mechanics and classical beam theory are describ ed A failure mo de map for loading under p oint b ending is constructed showing the dep endence of failure mo de and load on the ratio of skin thickness to span length and honeycomb relative density Beam sp ecimens are tested in p oint b ending The eect of honeycomb direction is also examined The exp eri mental data agree satisfactorily with the theoretical predictions The results reveal the imp ortant role of core shear in a sandwich b eams b ending b ehaviour and the need for a b etter understanding of indentation failure mechanism Highorder sandwich b eam theory HOSBT is implemented to extract useful infor ab out the way that sandwich beams resp ond to lo calised loads under p oint mation b ending Highorder or lo calised eects relate to the nonlinear patterns of the in plane and vertical displacements elds of the core through its height resulting from the unequal deformations in the loaded and unloaded skins The lo calised eects are examined exp erimentally by Surface Displacement Analysis of video images recorded during p oint b ending tests A new parameter based on the intrinsic material and geometric prop erties of a sandwich beamisintro duced to characterise its susceptibility to lo calised eects Skin exural rigidityisshown to playakey role in determining the way that the top skin allo ws the external load to pass over the core Furthermore the contact stress distribution in the interface b etween the central roller and the top skin and its imp ortance to an indentation stress analysis are investigated To b etter mo del the failure in the core under the vicinity of lo calised loads an Arcan typ e test rig is used to test honeycomb cores under simultaneous compression and shear loading The exp erimental measurements show a linear relationship between the out ofplane compression and shear in honeycomb cores This is used to derive a failure criterion for applied shear and compression which is combined with the highorder sandwich beam theory to predict failure caused by lo calised loads in sandwich b eams made of GFRP laminate skins and Nomex honeycomb under p oint b ending loading indenters size are p erformed on appropriately Short beam tests with three dierent prepared sp ecimens Exp eriments validate the theoretical approach and reveal the iv Abstract nature of pre and p ostfailure b ehaviour of these sandwich b eams HOSBT is used as a compact computational to ol to reconstruct failure mo de maps for sandwich panels Sup erp osition of weight and stiness contours on these failure maps provide carp et plots for design optimisation pro cedures Keywords comp osite structures sandwich structures Nomex honeycomb sandwich b eams failure mo de maps honeycomb anisotropy indentation lo calised eects highorder sandwich beam theory mixed failure criterion for honeycombs biaxial testing of honeycombs v Contents Preface and Declaration ii Acknowledgements iii iv Abstract Contents vi List of Figures viii List of Tables xi Nomenclature xii Intro duction and Overview Intro duction to Comp osite Structures olymer Comp osites Fibre Reinforced P Structural Optimisation Sandwich Structures Previous Work on Indentation Analyses Previous Work on Indentation Failure Prediction Scop e and Outline of the Thesis Failure Mo de Maps for Honeycomb Sandwich Beams Intro duction Beam Theory for Sandwich Panels Skin Failure Core Failure Honeycomb Mechanics Construction of a Failure Mo de Map A Failure Mo de Map for Beams with a GFRP Skin and Nomex Core Exp eriments Exp erimental Results vi Contents Discussion Skin Failure Core Failure Eect of Ribb on Direction Intracell Buckling Conclusions Indentation Resistance of Sandwic h Beams Intro duction HighOrder Sandwich Beam Theory Surface Displacement Analysis Eect of Spreading Stresses Contact Pressure Distribution Case Study Concluding Remarks Indentation Failure Analysis Intro duction Failure Envelop e for Nomex Honeycombs Failure Analysis with HOSBT Exp erimental Work Concluding Remarks Failure Maps using HOSBT Intro duction Reconstruction of Failure Maps Optimisation Carp et Plots Concluding Remarks Conclusions and Future Work Conclusions Future Work App endix A Exp erimental Results Bibliography vii List of Figures Sandwich construction with honeycomb core Sandwich panels with a corrugated b foam and c honeycomb core Typical hexagonal honeycomb with a set of doubled walls t is the single wall thickness and is the honeycomb cell size Test rig for indentation fatigue tests on aircraft o or panels a Simply supp orted b eam b Cross section on AA Failure mo des in the skin Failure mo des in the core Comparison of theoretical and exp erimentally measured outofplane a compressive

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