CHARACTERISATION OF THE FLEXURAL SANDWICH STRUCTURES BEHAVIOUR OF ALUMINIUM FOAM COMPOSITE. Millicent Styles

Transcription

1 CHARACTERISATION OF THE FLEXURAL BEHAVIOUR OF ALUMINIUM FOAM COMPOSITE SANDWICH STRUCTURES Millicent Styles A thesis submitted for the degree of Doctor of Philosophy of The Australian National University February, 2008

2 DECLARATION This thesis is an account of research undertaken between September 2004 and February 2008 at The Department of Engineering, Faculty of Engineering and Information Technology, College of Engineering and Computer Science, The Australian National University, Canberra, Australia. This thesis contains no material which has been accepted for the award of any other degree or diploma in any university. To the best of the author s knowledge, it contains no material previously published or written by another person, except where due reference is made in the text. Signed Millicent Styles February 2008 i

3 PUBLICATIONS JOURNAL PAPERS 1. M. Styles, P. Compston and S. Kalyanasundaram, Finite Element Modelling of Core and Skin Thickness Effects in Aluminium Foam/Composite Sandwich Structures under Flexural Loading, Composite Structures, Volume 86, Issues 1-3, November 2008, pages M. Styles, P. Compston and S. Kalyanasundaram, The effect of core thickness on the flexural behaviour of aluminium foam sandwich structures, Composite Structures, Volume 80, Issue 4, October 2007, pages Paul Compston, Millicent Styles, and Shankar Kalyanasundaram, Low Energy Impact Damage Modes in Aluminium Foam and Polymer Foam Sandwich Structures, Journal of Sandwich Structures and Materials, Sept 2006; 8: CONFERENCE PAPERS 1. M. Styles, P. Compston, S. Kalyanasundaram, Flexural behaviour of aluminium foam/composite structures, Sandwich Structures 7: Advancing with Sandwich Structures and Materials, Proc. of the Seventh International Conference on Sandwich Structures (ICSS-7), Aalborg, Denmark, August Springer. Ed Thomsen OT, Bozhevolnaya E, Lyckegaard A. 2. P.Compston, M. Styles, S. Kalyanasundaram, A comparison of low energy impact behaviour in aluminium foam and polymer sandwich structures, Sandwich Structures 7: Advancing with Sandwich Structures and Materials, Proc. of the Seventh International Conference on Sandwich Structures (ICSS-7), Aalborg, Denmark, August 2005, Springer. Ed Thomsen OT, Bozhevolnaya E, Lyckegaard A. 3. M. Styles, P. Compston, S. Kalyanasundaram, The effect of core thickness on the flexural behaviour of aluminium foam sandwich structures, 13th International Conference of Composite Structures (ICCS- 13), Melbourne, Australia, November M. Styles, P. Compston, S. Kalyanasundaram, Finite Element Modelling of Core and Skin Thickness Effects in Aluminium Foam/Composite Sandwich Structures under Flexural Loading, 14th International Conference of Composite Structures (ICCS-14), Melbourne, Australia, November 2007 ii

4 ACKNOWLEDGEMENTS I would like to thank my co-supervisors Dr. Paul Compston and Dr. Shankar Kalyanasundaram for the opportunity to undertake this varied project that combined an unusual material, a significant but temperamental experimental technique and the arduous yet rewarding world of FEA research. Their experience, support and advice on the experimental and modelling aspects, respectively, was gratefully received. I would also like to thank the technical staff of the Engineering department for their assistance in sample preparation and equipment use. For their random conversations, help and distractions I must thank my fellow students. In particular, James, and Joel and Luke for their shared battle experiences with Aramis and LS-Dyna. Thanks also to Aase Reyes and Professor Odd Sture Hopperstad of the Norwegian University of Science and Technology for their useful material modelling communications. I would like to thank my friends for their enduring optimism, diversions and amusements throughout; whether I was grumpy or receptive. I am very grateful for the encouragement and confidence my parents have always shown me and thank them for their ongoing support and love. Finally thanks to Dan, for always believing in me and showing such understanding, patience and humour to help get me here and beyond. iii

5 ABSTRACT Aluminium foam has a range of properties that are desirable in many applications. These properties include good stiffness and strength to weight ratios, impact energy absorption, sound damping, thermal insulation and non combustibility. Many of these characteristics are particularly attractive for core materials within sandwich structures. The combination of aluminium foam cores with thermoplastic composite skins is easily manufactured and has good potential as a multifunctional sandwich structure useful in a range of applications. This thesis has investigated the flexural behaviour of such structures using a combination of experimental and modelling techniques. The development of these structures towards commercial use requires a thorough understanding of the deformation and strain mechanisms of the structure, and this will, in turn, allow predictions of their structural behaviour in a variety of loading conditions. The experimental research involved the use of an advanced 3D optical measuring technique that produces realtime, full-field strain evolution during loading. This experimental characterisation of strain evolution in this class of sandwich structure under flexural loading is the first of its kind in the world. The experimental work studied the sandwich structure undergoing four-point bend testing. Initial studies compared the behaviour of the aluminium foam structure with a more traditional polymer foam sandwich structure. The aluminium foam structure was found to have equivalent or improved mechanical properties including more ductile deformation and an enhanced energy absorption. An investigation was conducted on the effect of core and skin thickness on the metal structure and a range of flexural behaviours were observed. Analysis of the strain distribution showed a complex development including localised effects from the non-uniform cellular structure of the material. An understanding of the variation with size is important in establishing design methods for utilising these structures. In particular, it is desirable that finite element simulations can be used to predict behaviour of these structures in a diverse range of loading conditions. This aspect was considered in the second half of this study. An existing constitutive model for aluminium foam, developed for use in compression energy absorption studies, was used to investigate finite element simulations of the flexural behaviour of the sandwich structure. The FE model was able to predict the general deformation behaviour of the thinner skinned structures although the magnitude of the load-displacement response was underestimated. It is suggested this may be related to the size effect on the input iv

6 Abstract parameter characterisation. The strain distribution corresponded well with the experimental strain measurements. It was found a simple increase in the material model input parameters was able to more closely match the magnitude of the load-displacement response while maintaining the appropriate strain distribution. The general deformation shape of the model with the thicker skin corresponded reasonably well with the experimental observations. However, further work is necessary on the element failure criterion to capture the shear cracking observed. The strain distributions of the model predicted this failure with high strain concentrations matching those of the experimental contours. The last part of the thesis describes a parametric study on the effect of the foam material model input parameters on the flexural behaviour of the sandwich structure model. An important conclusion of this work is that this material model for aluminium foam can, with some development, be utilized to provide a viable method for simulating aluminium foam composite sandwich structures in flexural loading situations. v

7 NOMENCLATURE The following is a list of the most commonly used symbols in this work. ρ Density g/cm 3 ρ * Total density of cellular material g/cm 3 ρ s Density of cellular wall material g/cm 3 b Sandwich beam width mm f Sandwich beam skin thickness mm c Sandwich beam core thickness mm d Sandwich beam skin centroids spacing mm F Force kn σ Stress MPa ε Strain -- E Young s Modulus N/m 2 D Flexural rigidity N.mm 2 τ Shear stress MPa M Maximum bending moment N.m P max Maximum bending load kn l Support span mm s Loading span mm σ p Plateau stress MPa ε D Densification strain -- σˆ Equivalent stress MPa εˆ Equivalent strain -- σ vm von Mises equivalent stress MPa σ m Mean stress MPa α Yield surface shape parameter -- υ p Plastic coefficient of contraction -- α 2 Yield surface shape parameter MPa γ Yield surface shape parameter MPa β Yield surface shape parameter -- v(t) Velocity field mm/ms T Total time of loading ms d max Maximum displacement mm vi

8 TABLE OF CONTENTS Declaration... i Publications...ii Acknowledgements...iii Abstract... iv Nomenclature... vi Table of Contents...vii List of Figures... x Chapter 1 Introduction Scope and Objectives Thesis Structure... 6 Chapter 2 Background and Literature Review Cellular Solids Sandwich Structures Theory Failure Modes Polymer foam core sandwich structures Foam and skin materials Current Research Metal foam core sandwich structures Aluminium Foam Mechanical characterisation of bulk foam Bonded metal skins Integral metal skins Alternative skin materials Metal foam with composite skins Modelling Constitutive models Summary Chapter 3 Experimental Methods Materials Manufacture Flexural Testing Full-field strain measurement Literature review of strain mapping Optical strain measurement Sample preparation System specification Data analysis Chapter 4 Comparison of Flexural behaviour in polymer and metal foam sandwich structures Flexural behaviour review Experimental method vii

9 Contents cont Sample manufacture Flexural test procedure Flexural results Failure behaviour of Al foam sandwich structure Failure behaviour of polymer foam sandwich structure Mechanical properties Summary Chapter 5 Flexural behaviour of Aluminium foam sandwich structure Introduction Materials and manufacture Flexural test procedure Core thickness Load displacement curves Energy curves Mechanical properties Strain behaviour Skin thickness Load displacement curves Mechanical properties Energy curves Strain behaviour Summary Chapter 6 Investigation of bulk foam behaviour for modelling Compression testing Sample manufacture Test conditions Compression testing results Load-displacement curves Energy plots Strain distribution Section line plots Tensile testing Modelling Numerical implementation of Deshpande-Fleck model Curve fitting Finite element model Compression modelling results Deformation behaviour Strain distribution Summary Chapter 7 FE Modelling of Flexural behaviour of Aluminium foam sandwich structure Introduction Finite element model Material models viii

10 Contents cont Element and Contact definitions Load application Results and Discussion Deformation behaviour of 20mm core structure Strain distribution of 20mm core structure Deformation behaviour of 5mm core structure Strain distribution of 5mm core structure Deformation behaviour of 20mm core structure with 4ply skin Strain distribution of 20mm core structure with 4ply skin Summary Chapter 8 Parametric Study of Aluminium foam Material Model Design of experiment study Factors Levels Quality measures Factor effects Load displacement behaviour Strain contours Strain section line plots Summary Chapter 9 Conclusions and Future Work Thesis Conclusions Experimental Work Modelling work Future work Appendix References ix

11 LIST OF FIGURES Figure 1.1: Alporas foam in use as a sound absorbing material on the underside of an elevated expressway [2]... 3 Figure 1.2: Crash boxes with front cross beam [3]; Prototypes of crash absorbers using aluminium extrusions filed with aluminium foam [4]... 3 Figure 1.3: Prototype of a BMW engine mount using metal foam core with cast outer surface [4]... 4 Figure 1.4: Foam panels in the Ariane 5 rocket: cone segment showing details of flange and upper edge [7]... 5 Figure 2.1: Geometry of a sandwich beam Figure 2.2: Example polymer foam/ composite sandwich structure applications: LM 61.5 P Wind turbine[16], Mundal Båt AS Fishing Vessel [17] Figure 2.3: Typical open cell metal foam; Duocel by ERGAerospace [30] Figure 2.4: Example metal foam closed cell structures: a) Alulight foam by Alulight International GmbH [31], b) FORMGRIP foam by University of Cambridge [32], and c) AFS by Karmann [4] Figure 2.5: Typical Alporas cell structure Figure 2.6: Alporas production method using foaming agent [12] Figure 2.7: Typical metal foam compression stress strain curve [37] Figure 3.1: Typical through thickness cell structures for Alporas foam panels with thicknesses of (a) 5 (b) 10 and (c) 20mm Figure 3.2: Sandwich component materials, before and after consolidation Figure 3.3: Sandwich Structure lay up Figure 3.4: Four-point flexural testing geometry Figure 3.5: Photo showing (a) patterned sample in 4-point bend test, and (b) higher magnification of typical patterned foam surface Figure 3.6: Image showing stereo cameras capturing four-point bend test Figure 3.7: Diagram of the geometry used to transform image coordinates from the stereo camera images to object points on the measurement surface [101] Figure 3.8: A typical Aramis image showing user defined start points in red and computed facets in green Figure 3.9: A typical calculated strain distribution overlayed on a camera image from an Aramis project Figure 3.10: An example strain distribution Figure 4.1: Polymer foam sandwich lay up Figure 4.2: A comparison of the metal and polymer foam core cellular structures Figure 4.3: Schematic of four-point bend test and Aramis measuring volume Figure 4.4: Typical load-displacement curve for the aluminium foam structure, showing load a) at yield, b) at 6.5mm and c) at 10mm Figure 4.5: Typical damage observed in the 10mm aluminium foam structure x

12 List of Figures cont. Figure 4.6: Typical 4pt bend Alporas strain maps at (a) 5mm, (b) 6.5 mm, (c) 10mm crosshead displacement, and (d) showing 3D contours at 10mm crosshead displacement Figure 4.7: Typical load-displacement curve for the polymer foam structure, showing load a) at 3mm, b) at yield, and c) at 4.5mm Figure 4.8: Typical damage observed in 10mm Divinycell polymer sandwich structure Figure 4.9: Typical 4pt bend Divinycell strain maps at (a) 3 mm, (b) 3.5 mm, (c) 4.5 mm crosshead displacement, (d) showing 3D contours at 4.5 mm crosshead displacement Figure 4.10: Typical 4pt bend Divinycell strain map at 10mm crosshead displacement Figure 4.11: Direct comparison of typical load-displacement curves for the two core materials Figure 5.1: Typical load-displacement plot for each core thickness Figure 5.2: Energy absorbed calculated from area under load-displacement curves for each core thickness Figure 5.3: Typical deformation behaviour of sample with 5mm core; (a) Final deformed shape (b) Strain distribution at peak load, displacement 8mm, (c) Strain distribution at 10mm displacement Figure 5.4: Typical deformation behaviour of sample with 10mm core; (a) Final deformed shape (b) Strain distribution at peak load, displacement 4.5mm, (c) Strain distribution at 10mm displacement Figure 5.5: Typical deformation behaviour of sample with 20mm core and 1 ply skins; (a) Final deformed shape, (b) Strain distribution at peak load, displacement 2.7mm, (c) Strain distribution at 10mm displacement Figure 5.6: Strain contour showing position of 5 section planes Figure 5.7: Section strain line plots showing the typical strain distribution of the 5mm structure at a) peak load, 8mm displacement (stage 93) and b) 10mm displacement (stage120) Figure 5.8: Section strain line plots showing the typical strain distribution of the 10mm structure at a) peak load, 4.5mm displacement (stage 55) and b) 10mm displacement (stage 120) Figure 5.9: Section strain line plots showing the typical strain distribution of the 20mm structure at a) peak load, 2.7mm displacement (stage 33) and b) 10mm displacement (stage 120) Figure 5.10: Section strain line plots showing the typical progressive strain distribution of Section 2 (centre plane) across a displacement range of mm for a) 5mm structure, b) 10mm structure and c) 20mm structure Figure 5.11: Typical Epsilon X strain distribution at 10mm displacement for sample with 20mm core Figure 5.12: Typical Epsilon Y strain distribution at 10mm displacement for sample with 20mm core Figure 5.13: Typical load-displacement plot for each skin thickness Figure 5.14: Energy absorbed calculated from area under load-displacement curves for each skin thickness xi

13 List of Figures cont. Figure 5.15: Typical deformation behaviour of sample with 20mm thick Alporas core and 4 ply Twintex skins; (a) Final deformed shape, (b) Strain distribution at peak load, displacement 4.5mm, (c) Strain distribution at 10mm displacement Figure 5.16: Typical deformation behaviour of sample with 20mm thick core and 4 ply skins focussing on the shear crack; (a) detail of crack, (b) Strain distribution at peak load, displacement 5.7mm, (c) Strain distribution at 10mm displacement, (d) Strain distribution at 20mm displacement Figure 5.17: Section strain line plots showing the typical strain distribution of the 20mm structure with 4ply skins for the region between the load rollers at a) peak load, 4.5mm displacement (stage 55) and b) 10mm displacement (stage 120) Figure 5.18: Section strain line plot showing the typical progressive strain distribution of Section 2 (centre plane) across a displacement range of mm for the 20mm structure with 4ply skins, for the region between the load rollers Figure 5.19: Section strain line plots showing the typical strain distribution of the 20mm structure with 4ply skins for the shear crack region at a) peak load, 5.7mm displacement (stage 35) and b) 10mm displacement (stage 60) Figure 5.20: Section strain line plot showing the typical progressive strain distribution in the shear crack region of Section 2 (centre plane) across a displacement range of mm for the 20mm structure with 4ply skins Figure 6.1: Cube compression sample Figure 6.2: Diagram showing orientation labels for cubes cut from bulk foam panel Figure 6.3: Cube compression test in progress Figure 6.4: Typical deformed sample under compression loading, at 6mm crosshead displacement Figure 6.5: Typical load-displacement plot for each sample orientation Figure 6.6: Typical energy absorbed during compression for each sample orientation Figure 6.7: Typical compression strain distributions for each sample orientation at two crosshead displacements; x-orientation at a) 1.3mm and b) 2.7mm, y- orientation at c) 1.3mm and d) 2.7mm, z-orientation at e) 1.3mm and f) 2.7mm Figure 6.8: Cube strain contour showing position of 5 section planes Figure 6.9: Section strain line plots of Z-direction sample at a) 1.3mm (stage 20) and b) 2.7mm (stage 40) Figure 6.10: Section strain line plot of the Z-direction sample showing the typical progressive strain distribution of Section 3 across a displacement rang of 0.7-4m Figure 6.11: Typical tensile test illustrating a propagating crack Figure 6.12: Typical failed tensile sample Figure 6.13: Typical tensile stress strain curve Figure 6.14: Typical tensile strain distribution for progressive crosshead displacements at a) 0.7mm (stage 20), b) 1mm (stage 40) and c) 1.3mm (stage 60) xii

14 List of Figures cont. Figure 6.15: Deshpande Fleck yield surface curve fit of experimental compression data Figure 6.16: Typical cube compression mesh geometry Figure 6.17: Deformation of foam cube model after 13mm of top plate displacement Figure 6.18: von Mises Stress-strain response of single element compared with experimental data Figure 6.19: Typical z-orientation strain distributions from the experiment and model data respectively at crosshead displacements of a) and b) 0.76mm, c) and d) 1.76mm, e) and f) 3.4mm and g) and h) 5.75mm Figure 7.1: Typical mesh geometry for sandwich structure FE model Figure 7.2: Deshpande Fleck yield surface curve fit of experimental compression data used for flexural modelling Figure 7.3: Typical deformation in the 20mm core structure; a) FE model and b) observation from experimental work Figure 7.4: Comparison of the load-displacement curve from FE model with the curve from experimental work for the 20mm core structure Figure 7.5: Comparison of the load-displacement curves after modifying material parameters (plateau stress (σ p ), γ and α 2 magnitude) for the 20 mm thick aluminium foam core in the FE model Figure 7.6: Load-displacement curves for the 20mm core structure after modifying Young s modulus for the composite skin in the FE model Figure 7.7: Typical strain distribution at peak load (~2.7mm displacement) for the 20mm core structure; a) FE model and b) real-time experimental measurement Figure 7.8: Typical strain distribution at 10mm displacement for the 20mm core structure ; a) FE model and b) real-time experimental measurement Figure 7.9: Schematic showing the position of sections taken through the model strain contour for strain line plots Figure 7.10: Section von Mises strain line plot for 20mm 1ply model at crosshead displacements of a) peak load 2.7mm and b) 10mm Figure 7.11: Deformation shape for the 5mm core structure; a) FE model and b) observation from experimental work Figure 7.12: Load-displacement curves for the 5mm core structure; from the experimental work, the initial FE model, and after modifying material parameters (plateau stress (σ p ), γ and α 2 magnitude) for the aluminium foam core in the FE model Figure 7.13: Typical strain distribution at 10mm displacement for the 5mm core structure; a) FE model and b) real-time experimental measurement Figure 7.14: Section von Mises strain line plot for 5mm 1ply model at crosshead displacements of 1.5mm Figure 7.15: Section von Mises strain line plot for 5mm 1ply model at crosshead displacements of a) peak load 8mm and b) 10mm Figure 7.16: Typical deformation in the 20mm 4ply core structure; a) FE model and b) observation from experimental work Figure 7.17: Comparison of the load-displacement curve from FE model with the curve from experimental work for the 20mm core 4ply structure xiii

15 List of Figures cont. Figure 7.18: Typical strain distribution at 10mm displacement for the 20mm core 4ply structure centred on the load rollers; a) FE model and b) real-time experimental measurement Figure 7.19: Typical strain distribution at 10mm displacement for the 20mm core 4ply structure centred on the shear crack; a) FE model and b) real-time experimental measurement Figure 7.20: Section plot for 20mm 4ply model central region at crosshead displacements of a) around peak load 4.5mm and b) 10mm Figure 7.21: Schematic showing the position of sections taken through the model strain contour for strain line plots centred on the shear crack Figure 7.22: Section plot for 20mm 4ply model crack region at crosshead displacements of a) around peak load 4.5mm and b) 10mm Figure 8.1: Effect of parameters on strain-hardening curve [104] Figure 8.2: Load-displacement curves from each run of the L16 array Figure 8.3: Factor effect level plots for the peak load for a) plateau stress, b) α 2, c) γ, d) β, and e) ε D Figure 8.4: Factor effect level plots for the displacement at peak load for a) plateau stress, b) α 2, c) γ, d) β, and e) ε D Figure 8.5: Typical von Mises strain contour for each of the 16 runs Figure 8.6: Strain section line plots for each run at 2.7mm displacement before peak load, showing the centre section for the region bordered by the load rollers Figure 8.7: Strain section line plots for each run at a displacement of 10mm, showing the centre section for the region bordered by the load rollers Figure 8.8: Factor effect level plots for the strain in the centre section at x-position 7.5mm at a displacement of 2.7mm for a) plateau stress, b) α 2, c) γ, d) β, and e) ε D Figure 8.9: Factor effect level plots for the strain in the centre section at x-position 7.5mm at a displacement of 10mm for a) plateau stress, b) α 2, c) γ, d) β, and e) ε D xiv