The Fabrication and Mechanical Properties of Continuous Fiber Composite Lattice Structures

Contents

Abstract

Acknowledgements

Declaration and Copy Right

List of publications

List of Figures

List of Tables

Nomenclature

Chapter 1: Introduction
1.1 Overview
1.2 Thesis Objective
1.3 Thesis Outline
1.4 Sandwich Panel Design Concept
1.5 Cellular materials
1.5.1 Stochastic cellular materials
1.5.2 Periodic cellular materials
1.6 Manufacture
1.6.1 Autoclave molding
1.6.2 Filament winding
1.6.3 Resin transfer molding
1.7 Vacuum Assisted Resin Transfer Molding (VARTM) process
1.7.1 Variations of the VARTM process
1.7.2 VARTM process and quality of composite
1.8 Elastic and strength properties of composite materials
1.8.1 Elastic properties of composite materials
1.8.2 Strength properties of composite materials
References

Chapter 2: Experimental procedures
2.1 Introduction
2.2 Lattice fabrication
2.2.1 Consumable materials
2.2.2 Constituent materials
2.2.3 Preparation Process
2.2.4 Infusion Process
2.2.5 Post infusion process
2.3 Hybrid core sandwich panel studies
2.3.1 Overview
2.3.2 Materials and Manufacturing
2.3.3 Compression tests
2.3.4 Interfacial fracture tests
2.4 Vertical, pyramidal, and octet lattice studies
2.4.1 Overview
2.4.2 Materials and fabrication
2.4.3 Compression tests
2.5 BCC, BCCz, FCC and F2BCC lattice studies
2.5.1 Overview
2.5.2 Materials and fabrication
2.5.3 Compression tests
2.6 Other lattice structures
References

Chapter 3: Analytical Modeling
3.1 Introduction
3.2 Elastic properties of parent material
3.3 Elastic values
3.4 Strength values
3.5 Analytical model of the compressive response
3.5.1 Analytical predictions for the response of composite pyramidal truss core
3.5.2 Analytical predictions of the vertical column core response
3.5.3 Analytical predictions for the response of the modified pyramidal truss core
3.5.4 Summary
3.5.5 Analytical predictions of the response of the octahedral lattice core
3.5.6 Analytical predictions of the response of the BCC core
3.5.7 Analytical predictions of the response of the FCC core
3.5.8 Analytical predictions of the response of the BCCz core
3.5.9 Analytical predictions of the response of the F2BCC core
References

Chapter 4: Finite Element Analysis
4.1 Introduction
4.2 ANSYS FE package
4.3 Constitutive models for the composite material
4.3.1 Elastic response
4.3.2 Damage initiation & progression model for the fiber reinforced composites
4.4 Quasi-static Finite element modelling
4.4.1 Modelling of lattice core sandwich structures
4.5 Numerical analysis results
4.5.1 Vertical lattice
4.5.2 Pyramidal lattice
4.5.3 Modified pyramidal lattice
4.5.4 BCC lattice
4.5.5 BCCz lattice
4.5.6 FCC lattice
4.5.7 F2BCC lattice
4.6 Conclusions
References

Chapter 5: Results and Discussion
5.1 Introduction
5.2 Resin flow and post-manufacture visual assessment
5.2.1 Hybrid GFRP/PET core
5.2.2 Vertical, pyramidal and octet lattice
5.2.3 BCC, BCCz, FCC and F2BCC lattice
5.3 Compression tests
5.3.1 Hybrid GFRP/PET core
5.3.2 Vertical, pyramidal and octet lattice
5.3.3 BCC, BCCz, FCC and F2BCC lattice
5.4 Skin-core Interfacial fracture toughness
5.4.1 Hybrid GFRP/PET core
References

Chapter 6: Conclusions and Future Work
6.1 Introduction
6.2 Conclusions
6.3 Recommended future work
References

Appendix A

Appendix B

Appendix C

Abstract

Hassan Ziad Jishi, “The Fabrication and Mechanical Properties of Continuous Fiber Composite Lattice Structures”, PhD. Thesis, PhD in Engineering, Department of Aerospace Engineering, Khalifa University, United Arab Emirates, May 2016.

The primary aim of this research work is to examine the mechanical properties per weight density of novel core materials for use in sandwich panels. Composite lattice core sandwich structures with relative densities in the range of 3% to 35% were manufactured and tested under quasi-static compression loading conditions. Collapse strength, failure mechanisms and energy absorption characteristics of the lattice structures have been evaluated.

Since these core material shapes are unique, research involved developing suitable manufacturing methods. The study started by looking at introducing ‘simple through thickness lattice’ structure into PET foam cores. This was achieved by drilling the foam material, glass fibers were then inserted into the perforations. The panel was then infused with resin using the vacuum assisted resin transfer molding process. This was then extended to look at the possibility of removing the ‘core’ by adopting a-lost mold manufacturing procedure that would leave a free-standing lattice structure. This involved inserting reinforcing fiber tows through holes in wax blocks. Following infusion with an epoxy resin and subsequent post curing, the preforms were heated to a temperature above that required to melt the wax, leaving well-defined lattice structures based on vertical, pyramidal, modified-pyramidal, octet configurations and others based on what are termed BCC, BCCz, FCC and F2BCC designs.

Compression tests showed that the strength of individual struts and the corresponding cores increases with strut diameter and fiber volume fraction. Smaller diameter struts failed in buckling, whereas the larger diameter columns failed in a crushing mode involving high levels of energy absorption. Truss core structures with 4 mm diameter columns, based on 28% fiber volume fractions offered specific energy absorption values above 70 kJ/kg. Compression tests on the four lattice structures based on BCC, BCCz, FCC and F2BCC designs indicated that the F2BCC lattice offered the highest compression strength of approximately 12 MPa. Although, when normalized by relative density, the BCCz lattice structure out-performed the three remaining structures. The specific energy absorption values of the lattices were relatively high, ranging from 44 kJ/kg for the BCC lattice to 80 kJ/kg for the BCCz structure. Similarly, the specific compression strengths of some of the lattices have been shown to be superior to those of more traditional core materials. An examination of the samples during testing highlighted a number of failure mechanisms, including strut buckling, fracture at the strut-skin joints and debonding of the reinforcing members at the central nodes.

The compression strength properties of the various lattice structures have been compared to currently available engineering materials, where it is noted that the properties of these lattice structures can be further increased using higher fiber volume fractions.

Micromechanical based analytical expressions for predicting the through thickness elastic properties and compression collapse strengths of all lattice structures manufactured using the lost mold technique are presented. Finally, the properties of the various lattice structures considered here were also predicted using finite element modeling techniques for comparison with analytical calculations and experimental results. The finite element predictions showed excellent agreement with the analytical calculations which validate the analytical derivations.

Indexing Terms: Lattice structures, Sandwich structures, Mechanical properties, Resin infusion, Finite Element, Composites, VARTM, Unidirectional fiber.

Acknowledgements

A special word of thanks goes to my family for their continuous support and encouragement. My father Ziad Jishi, May God give him mercy, would have been extremely proud of what I have accomplished. My mother, Laila Arslan has been very encouraging and proud and of course, this work would not have been possible without the help and patience of my wife Laila Othmane. I was also fortunate enough to be blessed with two daughters, Eleen and Mila during the period of this work.

I also would like to acknowledge my advisors Prof. Wesley J. Cantwell and Dr. Rehan. Umer for their help, support and outstanding guidance. I thank Jimmy Thomas and Bitu Scaria for their help in preparing the test specimens. Thanks to Dr. Zuheir Barsoum for his assistance in running the FE simulations.

Last but not least, the research carried out was made possible by Mubadala Aerospace and Khalifa University through funding the Aerospace Research and Innovation Center and by Khalifa University for providing a full PhD scholarship.

Declaration and Copy Right

I declare that the work in this thesis was carried out in accordance with the regulations of Khalifa University of Science, Technology and Research. The work is entirely my own except where indicated by special reference in the text. Any views expressed in the thesis are those of the author and in no way represent those of Khalifa University of Science, Technology and Research. No part of the thesis has been presented to any other university for any degree.

Author Name: Hassan Ziad Jishi

Author Signature: Hassan Ziad Jishi Date: 25 May 2016

Copyright ©

No part of this thesis may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, without prior written permission of the author. The thesis may be made available for consultation in Khalifa University of Science, Technology, and Research Library and for inter-library lending for use in another library and may be copied in full or in part for any bona fide library or research worker, on the understanding that users are made aware of their obligations under copyright, i.e. that no quotation and no information derived from it may be published without the author's prior consent.

List of publications

Published papers:

1. H. Z. Jishi, R. Umer and W. J. Cantwell, SkinǦcore debonding in resinǦinfused sandwich structures, Polymer Composites, 2015.

2. H. Z. Jishi, R. Umer and W. J. Cantwell, The fabrication and mechanical properties of novel composite lattice structures, Materials & Design, vol. 91, pp.286-293, 2016. Under review:

1. H. Z. Jishi, R. Umer, K. Ushijima and W. J. Cantwell, The mechanical properties of composite lattice structures. Submitted to Journal of Composite Structures, 2016. In preparation for submission:

1. H. Z. Jishi, F. Almehairi, R. Umer and W. J. Cantwell, A lost mold technique for manufacturing novel lattice structures based on natural fibers.

2. H. Z. Jishi, R. Umer, Z. Barsoum and W. J. Cantwell, Numerical simulation of continuous fibers composite lattice structures.

Published conference papers:

1. H. Z. Jishi, R. Umer, Z. Barsoum and W. J. Cantwell, The mechanical properties of sandwich structures based on composite column cores, in the 20th International Conference on Composite Materials (ICCM20), Copenhagen, Denmark, 2015.

2. H. Jishi, R. Umer and W.J. Cantwell, Investigation of Skin-Core Adhesion in Resin Infused Sandwich Panels, 12th International conference on Flow Processes in Composite Materials (FPCM12), Enschede, The Netherlands, 2014.

List of Figures

Figure 1.1: Materials used in the Boeing 787[2]

Figure 1.2: Modified Ashby materials property charts for (a) Young’s modulus and (b) Compression strength for engineering materials[10]. Composite lattice structures could fill the gap area in the low density - high stiffness and strength region

Figure 1.3: Cellular materials in nature: (a) cork, (b) balsa wood, (c) sponge, and

Figure 1.4: Three dimensional cellular material (a) open-cell polyurethane (b) closed-cell polyethylene[13]

Figure 1.5: Schematic diagram of an idealized cell representative of an open-cell foam[13]

Figure 1.6: Unit cell edges undergoing bending due to an applied compressive force[13]

Figure 1.7: Typical compressive stress-strain trace of a bending-dominated foam structure

Figure 1.8: (a) m < 0, if the joints are rigid the configuration becomes a bending dominated structure, (b) m=0, stretch dominated structure and (c) m > 0, over constrained structure[19]

Figure 1.9: Cellular material topologies [10, 24]

Figure 1.10: Hexagonal honeycombs manufactured using an expansion process[24]

Figure 1.11: Elastic and shear modulus of hexagonal honeycombs and open cell foams vs. relative density[15]

Figure 1.12: Schematic diagram of the slotting procedure for creating prismatic cores[26]

Figure 1.13: Sandwich panels based on 3D Kagome’ trusses metallic lattice structures[10]

Figure 1.14: Tetrahedral truss structures created through a metal forming technique[24]

Figure 1.15: Sandwich panels based on tetrahedral trusses metallic lattice structures with a unit cell size of 10 mm[10]

Figure 1.16: Sandwich structures based on copper textile cores configured at (a) 0/90o and (b) ±45 orientations[24]

Figure 1.17: A Non-weave approach for manufacturing cellular core structures from solid wires or hollow tubes[24]

Figure 1.18: (a) Pyramidal lattice structure fabricated using the hot press mold and (b) adhesively bonded between skins to for the sandwich panel[30]

Figure 1.19: a) Truss member are water jet cut from laminate sheets, b) truss members are snap-fitted together forming the pyramidal lattice configuration. c) The truss were fitted and adhesively bonded in milled facesheet pockets[31]

Figure 1.20: An Ashby strength versus density map for engineering materials[31]

Figure 1.21: Schematic diagram illustrating the manufacturing procedure of the stretch- bend-hybrid hierarchical composite pyramidal lattice cores[34]

Figure 1.22: Stretch-stretch-hybrid hierarchical composite pyramidal lattice cores[35]

Figure 1.23: a) Manufactured Lattice core based on carbon fiber reinforced poly-ethylene terephthalate (CPET). b) Sandwich panel with a lattice truss core bonded to stringer reinforced face sheets[32]

Figure 1.24: EDM Pyramidal carbon fiber reinforced epoxy lattices having a core relative density of 4.95%[34]

Figure 1.25: Finished semi-WBK composite core[36]

Figure 1.26: a) The hybrid CFRP pyramidal lattice core sandwich panel assembly, b) Photograph of manufactured sample and c) x-ray image showing the interior core structure of the panel[37]

Figure 1.27: a) Unit cell of an octahedral lattice configuration. b) Stress-strain curve of a stretch dominated structure[19]

Figure 1.28: Variation of relative modulus with relative density for various cellular materials. The line of slope 1 represents stretch-dominated structures, while slope 2 corresponds to bending-dominated materials[19]

Figure 1.29: Variation of relative strength with relative density for various cellular materials. Stretch dominated structures lie along a trajectory of slope 1; bending dominated structures along line of slope 2[19]

Figure 1.30: layup assembly for autoclave molding of composite laminates[2]

Figure 1.31: Schematic of filament winding process[48]

Figure 1.32: Schematic of the RTM process[2]

Figure 1.33: Schematic of VARTM process[48]

Figure 1.34: Aerospace components manufactured using the VARTM process[61]

Figure 1.35: Schematic of a typical SCRIMP process[64]

Figure 1.36: Schematic of the VAP setup[61]

Figure 1.37: Schematic of the CAPRI setup and processing steps[61]

Figure 1.38: Schematic of compaction pressure variation during VARTM infusion[51]. . 52 xvi

Figure 1.39: Matrix splitting (brooming)

Figure 1.40: a) Initial buckling of fibers, b) development of cracks on the lower edge and c) a fully-formed kink band[83]

Figure 1.41: Elastic micro-buckling modes: (a) Initial configuration (b) Shear mode and (c) Extensional mode

Figure 1.42: a) Kink band geometry and b) kink band failure in unidirectional carbon-epoxy composite[88]

Figure 2.1: Four lattice structures (progressing from simple to complex) that have been manufactured. (a) Vertical column, (b) modified pyramidal truss, (c) BCCz lattice and (d) an octet structure

Figure 2.2: (a) Wax block showing threading pattern of carbon fiber (b) Perforated PET foam core with holes reinforced with glass fibers

Figure 2.3: Threaded samples showing fibers extending over the skins through the holes

Figure 2.4: Perforated foam core with holes reinforced with glass fiber tows

Figure 2.5: Photograph illustrating laboratory set-up of the VARTM infusion process

Figure 2.6: Schematic of the VARTM process used to infuse the skins and core

Figure 2.7: Summary of the step-by-step procedures used in the VARTM process and lost mold technique

Figure 2.8: Hybrid composite core structure consisting of a unidirectional GRFP lattice with PET foam configured as the core of a sandwich panel with glass fiber composite face sheets

Figure 2.9: (a) Materials B and D unit cell with vertical truss arranged in a 25.4mm square pattern (b) Materials C and E with truss positioned in a 12.7mm square pattern

Figure 2.10: (a) Schematic of the configuration of sandwich panels investigated in this study. (b) Schematic of the patterns for the through-thickness fiber reinforcement in (i) Materials D and E and (ii) Material F

Figure 2.11: Schematic of the VARTM manufacturing set-up

Figure 2.12: Stacking procedure completed in preparation for vacuum bagging and infusion

Figure 2.13: The hybrid core under compression loading

Figure 2.14: Schematic of the three point bend test used to characterize the interfacial fracture toughness of the sandwich structures

Figure 2.15: Plot of compliance against the cube of crack length of the specimen from (a) Material B, (b) Material C

Figure 2.16: Schematic diagram showing the locations of the 2, 2.5, 3, and 4 mm diameter holes in the test samples. The edge lengths of the squares is nominally 30 mm. All dimensions are in mm

Figure 2.17: Schematic drawings of the two procedures used to thread the samples

Figure 2.18: Schematic of the VARTM process used to infuse the skins and core

Figure 2.19: Idealized images of (a) a pyramidal structure and (b) a modified pyramidal structure, reinforced with a central vertical member

Figure 2.20: Computer generated image of an octet truss structure

Figure 2.21: Schematic of the compression test used to characterize the axial strength of the manufactured core structure

Figure 2.22: Schematic of the unit cell topologies: (a) the BCC unit cell and (b) the BCCz unit cell (c) the FCC unit cell and (d) the F2BCC lattice

Figure 2.23: (a) Schematic drawings of the procedure used to thread the samples. The fibers extend through the holes and then between the wax core and the skins. (b) Threaded samples showing fibers extending over the skins through the holes

Figure 2.24. Schematic of the VARTM process used to infuse the lattice structures

Figure 3.1: Unidirectional fiber-reinforced composite[1]

Figure 3.2: Randomly distributed fibers in the cross-section of a strut with Vf =51%

Figure 3.3: Fiber tows through the core oriented at an angle

Figure 3.4: Estimated longitudinal modulus for materials having various fiber volume fractions. Experimental results are based on the 3-point bend test performed on rods having circular cross-sections

Figure 3.5: Schematic of a unit cell of the 4-legged pyramidal core

Figure 3.6: Schematic of (a) unit cell (b) deflection of a single truss of the pyramidal core upon application of a uniaxial compressive load (c) the free-body diagram of a truss subjected to compression and shear

Figure 3.7: Schematic diagram of a vertical column core

Figure 3.8: Schematic of (a) unit cell (b) deflection of single column within the core upon application of a uniaxial compressive load

Figure 3.9: Sketch of a unit cell of the 4-legged pyramidal core

Figure 3.10: Schematic of (a) unit cell (b) deflection of a single inclined truss and the vertical truss of the pyramidal core upon application of a uniaxial compressive load (c) the free-body diagram of a truss subjected compression and shear

Figure 3.11: Structure of an octahedral lattice core. The red struts represent the octahedron core

Figure 3.12: Schematic of a BCC unit cell

Figure 3.13: Schematic showing (a) deflection of a BCC cell upon application of a uniaxial compressive load (b) the free-body diagram of a strut subjected to compression and shear (c) due to symmetry the BCC resembles the pyramidal lattice unit cell

Figure 3.14: Schematic of a FCC unit cell

Figure 3.15: Schematic of a BCC-z unit cell

Figure 3.16: Schematic showing (a) deflection of a BCCz core upon application of a uniaxial compressive load (b) the free-body diagram of a strut subjected to compression and shear (c) the free-body diagram of half a vertical strut subjected

Figure 3.17: Schematic of a F2BCC unit cell

Figure 4.1: Single strut illustrating fiber orientation

Figure 4.2: BEAM188 element geometry[8]

Figure 4.3: Loading direction, boundary conditions and assembly of the pyramidal lattice core

Figure 4.4: The FE mesh for the BCC unit cell

Figure 4.5: Typical mesh generated for the numerical analysis

Figure 4.6: Failure stress and CPU time are plotted against element size for the pyramidal pin-jointed lattice core having a strut diameter of 3 mm and a Vf =

Figure 4.7: Failure stress and CPU time are plotted against element size for the F2BCC lattice

Figure 4.8: Failure stress and CPU time are plotted against step size for the end-clamped pyramidal lattice core

Figure 4.9: The failure stress and CPU time are plotted against step size for the F2BCC lattice

Figure 4.10: An imperfection sensitivity analysis study for the pyramidal lattice model

Figure 4.11: An imperfection sensitivity analysis study for the BCCz lattice model

Figure 4.12: Numerical and micro-mechanical predictions of the elastic modulus of the vertical lattice core

Figure 4.13: Strength predictions based on Euler buckling and plastic micro-buckling failure modes and FE models

Figure 4.14: Initial elastic modulus of the pyramidal lattice based on numerical and analytical models. The modulus increases linearly with increasing relative density

Figure 4.15: Numerical and analytical predictions of the pin-jointed pyramidal lattice compression strength

Figure 4.16: FE model and analytical predictions of the rigid-jointed pyramidal lattice compression strength

Figure 4.17: FE model and analytical predictions for the initial stiffness of a modified pyramidal lattice core

Figure 4.18: Strength predictions for the pin-jointed modified pyramidal core. The failure mode shifts from elastic buckling to plastic microbuckling for cores having a relative density above 0.04%

Figure 4.19: Strength predictions based of edge-clamped modified pyramidal model. For relative densities above 0.009 the core fails due to plastic micro-buckling

Figure 4.20: Initial stiffness predictions based for a BCC lattice constructed from pin- jointed and rigid-jointed struts

Figure 4.21: Compression strength of a BCC lattice with rigid-jointed struts

Figure 4.22: Compression strength of a BCC lattice with pin-jointed struts

Figure 4.23: FE model and analytical predictions for the initial stiffness of the BCCz lattice structure

Figure 4.24: Strength predictions for the pin-jointed BCCz core. The failure mode shifts from elastic buckling to plastic microbuckling for cores having a relative density above 0.045%

Figure 4.25: Strength predictions based on the rigid-jointed BCCz lattice model

Figure 4.26: Numerical and micro-mechanical predictions of the elastic modulus for an FCC lattice. The initial modulus increases linearly with increasing relative density 190 Figure 4.27: Strength predictions based on a rigid-jointed FCC lattice model. The failure mode shifts from elastic buckling to plastic micro buckling for cores having a relative density above 0.045%

Figure 4.28: Strength predictions for the pin-jointed FCC core. At relative densities over 0.16%, the core fails due to plastic microbuckling

Figure 4.29: Numerical and micro-mechanical predictions of the Elastic modulus

Figure 4.30: Strength predictions based on Euler buckling and plastic micro-buckling failure modes compared to FE model results

Figure 4.31: Strength predictions based on a rigid-jointed F2BCC structure. Elastic buckling of the struts is the predicted failure mode for relative densities below 0.07. At relative densities above 0.30, the struts fail due to plastic micro-buckling

Figure 4.32: Numerical predictions for the specific initial stiffness of the various lattice core configurations

Figure 4.33: Numerical predictions for the specific compression strength of the various lattice core configurations

Figure 5.1: (a) Top face sheet with in-plane flow, (b) Bottom face sheet with in-plane and radial flow through the holes from top to bottom

Figure 5.2: Cross-sections of manufactured samples with filled holes. (a) Materials B, (b) Materials C, (c) Material D-D, (d) Material D-S, (e) Material E-D, (f) Material E-S, (g) Material F-D, (h) Material F-S

Figure 5.3: The unit cell of a column truss core based on an array of 4 mm diameter columns

Figure 5.4: Photograph of a 6 x 6 column core based on 2.5 mm diameter struts

Figure 5.5: Photographs of (a) a pyramidal structure and (b) a modified pyramidal structure, reinforced with a central vertical member

Figure 5.6: (a) Various views of a structure based on three octet unit cells, (b) A photograph of an octet truss unit cell structure

Figure 5.7: Optical micrographs of individual columns (a) 2 mm diameter, Vf = 0.51 (b) 2.5 mm diam. Vf = 0.28 (c) 3 mm diam. Vf = 0.28, (d) 4 mm diam. Vf =

Figure 5.8. Photographs of the BCCz, the F2BCC, the BCC and FCC lattice structures following manufacture

Figure 5.9: Axial compression stress strain-curves for Materials A, B, and C

Figure 5.10: Axial compression response of Materials A, D-S, E-S and F-S

Figure 5.11: Summary of the compression strengths of the core materials

Figure 5.12: Schematic drawings of the two procedures used to thread the samples

Figure 5.13: Stress-strain traces for individual columns (a) 2.5 mm diameter and (b) 3 mm diameter. Vf = 0.42. Dashed line = Configuration A and Solid line = Configuration B

Figure 5.14: Stress-strain traces of individual columns of 4 mm diameter. Vf = 0.28. Dashed line = Configuration A and Solid line = Configuration B

Figure 5.15: Variation of specific compression strength with slenderness ratio for single columns. The samples are based on Configuration B

Figure 5.16: Stress-strain traces for multiple columns (a) 3 mm diameter and (b) 4 mm diameter. Vf = 0.28. Dashed line = Configuration A and solid line = Configuration B

Figure 5.17: The variation of specific compression strength with slenderness ratio for the truss cores. Vf =

Figure 5.18: Stress-strain traces for multiple columns (i) 2 mm diameter and (ii) 4 mm diameter. Vf = 0.28. Dashed line = experiment and solid line = FE model

Figure 5.19: The variation of SEA as a function of slenderness ratio for the truss cores

Figure 5.20: Typical stress-strain traces following compression tests on single columns based on different fiber volume fractions (a) 3 mm diameter columns (b) 4 mm diameter columns

Figure 5.21: Photographs of individual 3 mm diameter columns at various stages of testing: (i) neat resin, (ii) Vf = 8% and (iii) Vf = 12%

Figure 5.22: Photographs of individual 4 mm diameter columns during testing:

Figure 5.23: The variation of failure stress with fiber volume fraction for the 3 and 4 mm diameter columns. The solid lines correspond to the predictions of Euler buckling theory based on the properties at a given fiber volume fraction

Figure 5.24: Typical stress-strain traces following compression tests on core structures based on arrays of columns with diameters of 2.5, 3 and 4 mm

Figure 5.25: Stages of deformation in truss core based on 3 mm diameter columns. The crosshead displacement is shown under each figure

Figure 5.26: Stages of deformation in truss core based on 3mm diameter columns

Figure 5.27: The variation of compression strength with slenderness ratio for the truss cores. The solid line corresponds to the prediction offered by Euler theory

Figure 5.28: The variation of the compression strength of the core structures with column slenderness ratio

Figure 5.29. Summary of the specific strengths of the pyramidal and modified pyramidal structures. The photos show plain and modified samples during testing. Open columns = experiment and hatched columns = FE modeling

Figure 5.30: Photographs of an octet truss structure (a) prior to testing and (b) following compression testing. The sample height is 56 mm

Figure 5.31. (a) Stress-strain traces for the BCC lattice structure (b) photographs showing the deformation modes with increasing strain

Figure 5.32. (a) Stress-strain traces for the BCCz lattice structure (b) photographs showing the deformation modes with increasing strain

Figure 5.33. (a) Stress-strain traces for the FCC lattice structure (b) photographs showing the deformation modes with increasing strain

Figure 5.34. (a) Stress-strain traces for the F2BCC lattice structure (b) photographs showing the deformation modes with increasing strain

Figure 5.35. Summary of the Young’s modulus properties of the four lattice structures. Included in the figure are the experimentally-determined values of modulus as well as those predicted by the analytical and FE models,

Figure 5.36. (a) Comparison of the compression strengths of the four lattice structures and (b) comparison of the specific compression strengths (experimental data) of the lattices

Figure 5.37. Summary of the specific energy absorption values of the four lattice structures

Figure 5.38: Typical load-displacement traces for Materials A, B and C

Figure 5.39: Fracture surfaces of Materials A, B, and C following interfacial failure

Figure 5.40: Typical load-displacement traces for Materials D-D, E-D and F-D

Figure 5.41: Photograph of the edge of Material F-D during interfacial fracture testing

Figure 5.42: Typical load-displacement traces for Materials D-S, E-S and F-S

Figure 5.43: Fracture surfaces of Materials D-D, E-D and F-D following interfacial failure. 246 Figure 5.44: Summary of the interfacial fracture properties of the sandwich structures ... 248 Figure 6.1: An Ashby diagram of strength versus density for engineering materials. The measured compression strengths of the various lattice cores are included[1]

Figure 6.2: An Ashby diagram including the FE model predictions for compression strengths of the various lattice cores made from a material having a 51% fiber volume fraction[1]

Figure 6.3: An Ashby diagram including the FE model predictions for the elastic modulus of the various lattice cores made from a material having a 51% fiber volume fraction[1]

Figure B.1: a) Top view of a single skin sandwich structure (S[4]), b) skin free side of the S[4]structure, c) lattice wheel d) Natural fiber reinforced airfoil and Carbon fiber reinforced airfoil

Figure C.1: Photographs showing (a) Jute fibers passing through the holes in the wax mold in a continuous fashion, (b) Natural fiber sheets forming the airfoil skin placed around the mold, (c) airfoil stack sealed in a vacuum back in preparation for the infusion process (d) and flow front on one side of the airfoil during the VARTM process

Figure C.2: Snapshots showing the progression of resin through the reinforcement with the blue and red colors indicating dry and resin rich regions respectively

List of Tables

Table 1.1: Resin infusion patents overview[62]

Table 2.1: Summary of hole separation, fiber volume fraction in the perforations and overall core density for the various materials

Table 3.1: Constituent materials elastic properties

Table 3.2: Elastic properties for materials having three different fiber content

Table 3.3: Summary of the strength characteristics for materials having 28% and 42% fiber volume fraction

Table 3.4: Pyramidal lattice elastic and strength properties

Table 4.1: Summary of elastic properties of CFRP materials manufactured at three different fiber volume fractions

Table 4.2: Summary of strength characteristic data for the CFRP materials (*Assumption)

Table 4.3: Summary of the fracture energy data for the truss material (lower bound and upper bound values correspond to materials having Vf = 0.14 and Vf = 0.48 respectively)

Table A.1: Summary of the mechanical properties used in this study (a) elastic properties and (b) strength characteristics

Nomenclature

Abbildung in dieser Leseprobe nicht enthalten

Chapter 1: Introduction

1.1 Overview

Despite the development of highly efficient turbofan and turboprop engines with lower emissions and the improvements achieved in fuel efficiency through the adoption of advanced aircraft technology, the increase in air traffic volume is overshadowing all the above improvements and resulting in a net increase in pollution emission coming from the aviation sector. The reduction of structural weight of future aircraft provides one avenue to achieve significant reduction in fuel consumption and an increase in payload, as a result, there is a growing drive in the aerospace sector to develop increasingly lightweight, high performance load-bearing, multifunctional structures. In addition for the structure to be light weight, other properties such as high stiffness, high strength and multifunctional capability are important, especially for aerospace applications. Materials, such as aluminum alloys and titanium, have been the favorite choice of aerospace structural materials for many years due to their high stiffness to weight ratio[1]. However, the advent of relatively newly developed materials such as fiber reinforced composites are causing a paradigm shift in favor of these new materials for aerospace structural applications, due to their ability to achieve significant weight reductions, while maintaining superior mechanical properties, in comparison to their metallic counterparts. Commercial aircraft, military craft, helicopters, business jets, general aviation aircraft and space craft all make substantial use of composites. As a result, there is a growing drive in the aerospace sector to develop increasingly lightweight, high-performance load-bearing, multifunctional structures. The recent introduction of the Boeing 787 represents an excellent example, with composites representing fifty percent (by weight) of the aircraft structure. Another example is the Airbus A350XWB, making more extensive use of advanced composite components than its predecessors.

illustration not visible in this excerpt

Figure 1.1: Materials used in the Boeing 787[2].

Traditionally, many lightweight aircraft components have been based on sandwich structures, consisting of composite skins bonded to honeycomb or foam cores. More recently, there has been a growing interest in the potential offered by lattice core structures in the design and manufacture of ultra-light sandwich panels for high-performance engineering applications. The stiffness and strength properties of these lattice structures depend on the materials of which they are made and their topology. Metallic lattice structures, based on architectures such as the Kagome’ structure[3], pyramidal designs[4]and the octet truss configuration[5]have been examined. A number of manufacturing techniques have been used to produce these metallic structures including a rapid processing and brazing procedure[6], investment casting[7] and selective laser melting[8].

Subsequent mechanical testing has shown that many of these structures offer a range of attractive mechanical properties [3-9]. Recently, attention has focused on developing composite lattice structures that should, in principle, out-perform their metallic counterparts. Here, a new manufacturing technique is developed to fabricate ultra-light composite lattice structures and hybrid foam reinforced with composite lattice structures in addition to characterizing their mechanical properties mainly in compression and develop analytical models to predict their mechanical properties for comparison with numerical predictions and experimental results. These new composite lattice structures offer the potential to fill the gap between the currently available engineering materials and the unattainable material space. This is illustrated in the existing gap within the modified Ashby diagrams for strength vs. density and stiffness vs. density shown in Figure 1.2. The goal here is to develop a manufacturing technique that will enable the fabrication of composite based lattice structures with properties that can fill these observed gaps.

illustration not visible in this excerpt

Figure 1.2: Modified Ashby materials property charts for (a) Young’s modulus and (b) Compression strength for engineering materials[10]. Composite lattice structures could fill the gap area in the low density - high stiffness and strength region.

1.2 Thesis Objective

The primary objective of this work is (1) to investigate the possibility of fabricating millimeter size, all composite lattice core sandwich panels with superior specific strength/ stiffness properties; (2) to develop a viable method for manufacturing these lattice based core structures; (3) to investigate their mechanical properties and failure mechanism as a function of the constituent material properties and core geometry; (4) to develop analytical models for predicting the elastic stiffness and collapse strength of these structures and (5) to carry out numerical simulations for comparison with experimental results and for validating the analytical models.

The potential significance of this work is that it will enable the manufacture of composite lattice structures of various complexity. Given the potential of these composite structures in filling the gap area in the low density - high stiffness and strength region in Figure 1.2, their performance will be experimentally determined. s

1.3 Thesis Outline

The remainder of this thesis is organized as follows:

Chapter 1: Literature Review; continues to examine the sandwich panel concept based on cellular materials, their mechanical properties and manufacturing techniques including the vacuum assisted resin transfer molding (VARTM) process. Chapter 2: Experimental Procedure; presents the lost mold technique for manufacturing the lattice core structures and includes details of the experimental procedures used in measuring the mechanical properties.

Chapter 3: Analytical Modeling; develops the micromechanical models for the mechanical performance of the lattice structures in response to compression loading. Chapter 4: Finite Element Analysis; provides details about relevant aspects involved in developing the finite element models the results of which are then compared with the analytical predictions.

Chapter 5: Results and Discussion; includes discussion of the results of all lattice structures considered in this study.

Chapter 6: Conclusions and Future Work; then discusses the significance of these results in the context of the goals of this work and provides an outline for future work.

1.4 Sandwich Panel Design Concept

Sandwich construction is emerging as the structural design of choice, due to its ability to provide excellent mechanical properties at minimal weight. A sandwich panel consists typically of three layers; a lightweight core between two relatively thin face-sheets. The core material being low in density plays a fundamental role in providing a strong, stiff and lightweight sandwich structure design when placed between two face-sheets. Typically, cores are made of metallic or non-metallic honeycomb, cellular foams, balsa wood, and trusses while commonly-used materials for face-sheets are laminated composites and metals[2]. The task of the face-sheets is to carry almost all of the bending and in-plane loads in addition to providing high surface quality and good impact performance. The mechanical requirement of the core is to prevent the movement of the face-sheets relative to each other and stabilize them against wrinkling or buckling while defining the flexural stiffness, out of plane shear and compressive properties. Additional functions of the core include thermal and acoustic insulation and energy absorption during impact. This task distribution in the sandwich construction enables high stiffness and strength for lightweight panels and parts. A wide range of core materials for use in sandwich composites are available. Each core material provides particular properties suitable in various conditions. Currently, there is a strong interest in developing lightweight, high-performance structures for enhanced aerospace design. More recently, there has been a growing interest in the use of foldcore structures and lightweight lattice architectures for use in aerospace design. The unique and attractive properties offered by cellular materials based on lattice truss topologies have, in recent years, been investigated by a number of authors [3, 5-7, 11, 12]. Previous work has shown that such lattices exhibit stiffness and strength properties that scale linearly with density, ρ. This is in contrast to polymer and metal foams, whose strength and stiffness properties scale as ρ³ /² and ρ² respectively. A brief review of cellular materials follows.

1.5 Cellular materials

A cellular material consists of an interconnected network of solid struts or plates that make up the faces and edges of the cell[13]. The properties of the cellular structure depend directly on the shape and structure of the cell. The most important structural characteristic of such structures is relative density, ρ, defined as the density of the cellular structure divided by the density of the solid of which it is made[13]. Light weight structures characterized by a low density cellular material configured as the core with a denser outer surface are very common in nature[14]. Few examples include cork, wood, sponge, plant stems, trabecular bone and bird beaks[14]. Cork and balsa wood consists of closed cells resembling a honeycomb, Figure 1.3 (a) and (b). Others, such as sponge and bone are an open network of struts with multi-node connection. This naturally-occurring construction allows for structures with good mechanical properties at low weight. They are essentially stiff, strong, lightweight and multifunctional structural form of a sandwich construction. If it were not for this design, trees for example, would not be able to withstand the bending loads from wind and would collapse under its own weight.

illustration not visible in this excerpt

Figure 1.3: Cellular materials in nature: (a) cork, (b) balsa wood, (c) sponge, and (d) trabecular bone[13].

Inspired by the lessons learned from nature, synthetic cellular materials have evolved. Currently, a wide range of cellular solids are being manufactured including foams, honeycombs, prismatic materials, and truss structures. All cellular solids are generally categorized as being open cell or closed cell with stochastic or periodic topologies[15].

1.5.1 Stochastic cellular materials

Figure 1.4 illustrates two examples of man-made stochastic cellular structures. They are foam structures that are characterized by having a random microstructure distribution or pattern. Two sub-types can be distinguished, open cell and closed cell stochastic architecture. In the first, the material has been formed into struts that join at vertices forming the cell edges as in Figure 1.4a. In the second, the cell faces are sealed by a solid membrane (Figure 1.4b).

illustration not visible in this excerpt

Figure 1.4: Three dimensional cellular material (a) open-cell polyurethane (b) closed-cell polyethylene[13].

Foam materials are typically made from diverse materials such as polymers, metals, ceramics, glasses and composites. Cellular metals for example are manufactured by foaming of liquid metal by injecting a gas or by the decomposition of a gas releasing particles[16]. Polymeric foams are produced in a process that involves the nucleation and growth of gas bubbles in a polymer matrix[17]. Due to the random nature of the manufacturing process, statistical variations in cell size and shape exist leading to nonuniform distribution of material in the cell walls/edges. This leads to considerable density and mechanical properties fluctuation within the foam structure[16].

Generally, factors influencing the structural properties of cellular material properties are found to be dependent on relative density, properties of the solid of which the cellular structure is made, cell type (open/closed), shape and topology [16, 18]. Gibson and Ashby [13]derived the micromechanical response of an open-cell foam using an idealized unit cell. The model was based on a cubic array with edges of length L and square cross-section of side t (Figure 1.5).

illustration not visible in this excerpt

Figure 1.5: Schematic diagram of an idealized cell representative of an open-cell foam[13]. With t<<L, the relative density of the cell in terms of the unit cell key geometric dimensions is given by:

illustration not visible in this excerpt

is the density of the foam and ߩ௦ is the density of the parent material of which it isכwhere ߩ made. When a compressive force, F, is applied at the unit cell mid-point as shown in Figure 1.6, the edges bend with a deflection, δ. Using standard beam theory; the elastic deflection δ is proportional to [illustration not visible in this excerpt] where ܧ௦ is the elastic modulus of the material of ݐସ.ןthe beam and I is the second moment of area of the beam and is given by [illustration not visible in this excerpt]

Figure 1.6: Unit cell edges undergoing bending due to an applied compressive force[13]. The applied force F is related to the remote compressive stress ߪ by [illustration not visible in this excerpt]. Usingןcompressive strain ߳ sustained by the unit cell is related to displacement by ߳ the above relations, it follows that the elastic modulus [illustration not visible in this excerpt] of a foam with a bending dominated behavior is given as[13]:

illustration not visible in this excerpt

Using a similar approach, the collapse strength of an open cell foam structure can be approximated as[13]:

illustration not visible in this excerpt

This bending dominated behavior can be extended to most closed-cell foam materials with resulting stiffness and strength predictions that follow the same scaling laws as Equations 1.3 and 1.4[18]. This arises from the fact that the cell faces are very thin relative to the cell struts. Consequently, the cell membranes fail at very low stresses with little contribution to stiffness and strength, leaving the cell edges to carry the majority of the load[18]. Equations 1.2 and 1.3 demonstrate that a decrease in relative density in foam materials is accompanied by a rapidly decreasing strength and stiffness, since they scale as ρ³ /² and ρ² respectively. A typical compressive stress-strain curve for a bending-dominated foam is illustrated in Figure 1.7. The initial elastic behavior is dictated by the bending of the cell edges. Once the elastic limit is reached, the cell edges begin to fail either by elastic buckling, plastic yielding or brittle fracture, depending on the nature of the cell material. This failure continues at a constant rate, as observed in the long collapse plateau stress portion of the curve. Once the collapse process is almost complete, the opposing cell walls come into full contact and continued loading compresses the solid material, resulting in a rapid increase in stress.

illustration not visible in this excerpt

Figure 1.7: Typical compressive stress-strain trace of a bending-dominated foam structure [19].

The material is not fully utilized in bending-dominated cellular materials such as foams. Therefore, such materials exhibit lower specific stiffness and strength properties compared to stretch-dominated structures[20]. However, the long flat plateau stress in their stress-

strain curves is an attractive property for energy-absorbing applications[19]. Foam is the material of choice for the main impact-absorbing element of the motorcycle helmet[13].

The struts in Figure 1.5 are arranged in a way that allows them to bend under an applied load resulting in reduced stiffness and strength properties. They can be reconfigured to become optimally constrained in a way that prevents bending, resulting in a stretchdominated structure. This can be explored through an understanding of Maxwell’s Criterion of structural rigidity[21]. A structure constructed from b struts joined by j frictionless joints is said to be statically and kinematically determinate when the following condition for a two dimensional structure is met:

[illustration not visible in this excerpt] (1.4)

In three dimensions, the equivalent condition is:

[illustration not visible in this excerpt] (1.5)

Figure 1.8(a) illustrates an example for the case when ܯ ൏ Ͳ, the truss will fold up when loaded, making it a mechanism without stiffness or strength. If the joint were rigid, the bars would bend when loaded as in the configuration of the idealized cell model in Figure 1.5. The truss configuration in Figure 1.8(b) is an example for the case of ܯ ൌ Ͳ in which the truss members would carry tension or compression when loaded, making a stretch- dominated structure. This would be the case whether the hinges were free to rotate or rigid. Rigid hinges have little influence because slender structures are much stiffer when stretched rather than when bent[19]. For this reason, stretch-dominated structures have a high structural efficiency; bending-dominated structures have lower efficiency[19].

Figure 1.8: (a) m<0, if the joints are rigid the configuration becomes a bending dominated structure, (b) m=0, stretch dominated structure and (c) ܯ ൐ Ͳ, over constrained structure[19].

Figure 1.8c is an over-constrained truss configuration with ܯ ൐ Ͳ. If the horizontal truss is elongated or shortened, the truss configuration would be in a state of self-stress, even in the absence of external loads. Maxwell’s criteria given in Equations 1.4 and 1.5 is a necessary but generally not a sufficient condition for rigidity, as it doesn’t account for the possibility of states of self-stress and of mechanism [19]. The generalized form of Maxwell’s equation in three dimensions is given by[22]:

[illustration not visible in this excerpt](1.6)

where s is the number of self-stress states and m is the number of mechanisms. A frame is considered statically and kinematically-determinate (rigid) when ݏ ൌ ݉ ൌ Ͳ. An examination of Equation 1.6 reveals that a vanishing left-side only indicates that the number of mechanisms and states of self-stress are equal, not that each equals zero. This explains the nature of Maxwell’s rule as a necessary rather than sufficient condition. However, Maxwell’s criterion gives a prescription for designing a stretch-dominated structure.

1.5.2 Periodic cellular materials

Microstructures of periodic architecture include either three dimensional micro-truss assemblies referred to as, a lattice structure, or two dimensional periodic channels, referred to as prismatic materials or honeycombs[23]. Generally, periodic cellular materials have a highly porous structure with 20% or less of their interior volume occupied by solid[24]. They are characterized by an ordered structure of repeating a unit cell geometry. Periodic materials can be divided into three main groups, namely honeycomb, prismatic and lattice cellular structures as shown in Figure 1.9.

illustration not visible in this excerpt

Figure 1.9: Cellular material topologies [10, 24]

An advantageous property of periodic cellular materials is that they are often stretch- dominated structures, in which the stiffness and strength scale linearly with relative density. Synthetic honeycombs are based upon the efficient design of a honeybee’s nest[15]. It is a structure made up of regular arrays of prismatic hexagonal open cells. It represents a two dimensional cellular solid as the hexagonal unit cells pack to fill a plane in two dimensions.

Honeycombs can be made from square, triangular, or hexagonal shaped unit cells in addition to other variations Figure 1.9 (a, b and c). Part of a sandwich panel construction, honeycomb cores with unit cell walls arranged perpendicular to the face sheet form a closed cell structure. Honeycomb cores are manufactured from a variety of materials for sandwich structures, depending on the application. For low stiffness and strength applications (such as domestic internal doors) they are made from paper and card. For aerospace applications that require high stiffness, and strength with minimum weight, they are constructed from Nomex paper or aerospace grade aluminum. Hexagonal honeycombs are manufactured using an expansion process (Figure 1.10). In this process large thin sheets of the material are printed with alternating parallel thin strips of adhesive and the sheets are stacked in a heated press while the adhesive cures. The stack of sheets is then sliced through the thickness and these slices are gently stretched and expanded to form the sheet of continuous hexagonal cell shapes. This in-plane expansion process results in two of the six cell walls having double thickness, consequently, the honeycomb will have different mechanical properties in the 0o and 90o directions of the sheet[13]. Another approach involves the assembly of slotted strips of material to create square or triangular honeycombs that are less anisotropic than their hexagonal counterpart[25].

illustration not visible in this excerpt

Figure 1.10: Hexagonal honeycombs manufactured using an expansion process[24]

Properties of honeycomb materials depend on the relative density, the properties of the solid of which the cellular structure is made, the cell shape and the topology [16, 18]. In general, honeycomb materials produce one of the highest strength to weight ratios of any structural material. When compressed in-plane, the cell walls bend, giving a linear elastic behavior up to a critical load upon which the cells fail by elastic buckling, plastic yielding or brittle fracture. In tension, the cell walls bend, as in compression, up to a critical load and fractures if the cell material is brittle or plastically yields if ductile. When loaded out- of-plane, parallel to the axis of the unit cells, the cell walls will extend or compress resulting in a much higher modulus and collapse strength[13]. Figure 1.11 compares the out-of-plane performance of a hexagonal honeycomb to an open-cell foam structure. It is noted that the elastic modulus of the foam is significantly lower than the honeycomb at low relative densities. A similar trend is observed with yield strength. These differences are the result of the foam’s low structural efficiency arising from the bending-dominated behavior of the cell edges and, to a lesser degree, due to the presence of microscopic defects (depending on the manufacturing process) within the foam micro structure[15].

illustration not visible in this excerpt

Figure 1.11: Elastic and shear modulus of hexagonal honeycombs and open cell foams vs. relative density[15].

Prismatic core structures are made of plate or sheet elements that form the edges of the unit cell. They are essentially honeycomb structures, rotated 90o about their horizontal, resulting in open channels (open cell) in one direction and a closed cell structure in the remaining orthogonal directions, as observed in Figure 1.9ii. The open channels enable excellent ventilation characteristics, avoiding problems associated with water accumulation, which is common in closed cell core materials, such as honeycombs and foams. Prismatic cores come in various unit cell topologies, including triangular, diamond, navtruss or a Y-truss corrugation. Metallic corrugated cores are manufactured using a corrugation method. In this process, a thin sheet of material is continuously bent by pressing or folding to form the corrugation patterns[24]. Some metals can be corrugated through an extrusion process [24]. Alternatively, a slotting procedure is used in which sheets of the core material are cut into rectangles, cross-slotted, assembled in arrays and joined by brazing (or adhesive bonding) to construct the prismatic cells[26]. The slotting procedures can be used to fabricate prismatic metallic or composite cores, while the corrugation method is limited to metallic materials only.

illustration not visible in this excerpt

Figure 1.12: Schematic diagram of the slotting procedure for creating prismatic cores[26].

In another approach, a hot press is used to produce composite corrugated cores in which the pre-preg material is placed between upper and lower molds and cured[27]. The out-of-plane compression and shear strength of triangular and diamond corrugated cores were investigated and found to have lower specific strengths compared to square- honeycomb and pyramidal sandwich cores, due to a weak buckling mode[26]. In contrast, the longitudinal shear strength and energy-absorption capacity were comparable to square- honeycomb cores, offering significant potential for applications in sandwich panel construction[26].

Materials with a periodic microstructural architecture of micro-truss assemblies are referred to as lattice materials. They are characterized by having an open-cell architecture, since they are constructed from a regular repetition of slender beams leaving three dimensional interconnected void spaces. The slender beams or trusses can be of any cross-sectional shape, including circular, square, hollow or I-beam sections. In one study, hierarchical composite pyramidal lattice core were manufactured with struts based on foam-core sandwich struts [28]. Micro-lattice truss architectures can be configured in various arrangements, such as pyramidal[6], textile[11], tetrahedral[7], 3-D Kagome’[3], octahedral[5]and other lattice topologies.

Various methods have been developed for the manufacture of metallic-based lattice structures involving casting, forming, and textile weaving techniques[29]. In investment casting, the truss core and face-sheets are made from wax or polymer by injection molding, 3-D printing or any other rapid prototyping techniques. This pattern is then coated with a layer of ceramic shell by dipping into ceramic casting slurry. Once the ceramic coating is dried, the wax or polymer is removed by melting leaving a hollow mold that reflects the final sandwich panel configuration. This is then filled with liquid metal and after the molten metal has cooled, the ceramic mold can be broken and the casting removed. Sandwich panels based on a three dimensional Kagome’[3]and tetrahedral[7]lattice core were manufactured using the investment casting method as illustrated in Figure 1.13.

illustration not visible in this excerpt

Figure 1.13: Sandwich panels based on 3D Kagome’ trusses metallic lattice structures[10].

Metal forming techniques involve a sheet of metal that is perforated using die stamping, laser or water jet cutting and subsequently deformed by bending or folding to reflect the desired core configuration, as shown in Figure 1.14. The truss pattern is then bonded between two face-sheets.

Figure 1.14: Tetrahedral truss structures created through a metal forming technique[24]. A 6061-T6 aluminum octahedral lattice structure is illustrated in Figure 1.15. It was constructed from multiple layers of tetrahedral structure that were manufactured by metal forming techniques. The nodes were bonded using a brazing process.

illustration not visible in this excerpt

Figure 1.15: Sandwich panels based on tetrahedral trusses metallic lattice structures with a unit cell size of 10 mm[10].

In another approach, metal based truss structures were made from weaving and braiding of metallic wires[29]. It is considered a simple and cost-effective approach as it virtually does not involve any waste material. Any metal alloy that can be drawn into a wire can be utilized. The metal textiles are then stacked and bonded to create the periodic cellular core. By varying the orientation of the metallic woven fabrics, different topologies can be achieved, as illustrated in a 0/90o and േ45o configurations of copper textile core sandwich structures shown in Figure 1.16.

Figure 1.16: Sandwich structures based on copper textile cores configured at (a) 0/90o and (b) ±45o orientations[24].

Weaving of metallic tubes to form the textile layer is more difficult, as they tend to buckle when plastically bent. Alternatively, a non-weaving approach can be utilized[29]. The wires, could be hollow or solid, are stacked in a slotted tool that maintains the wire spacing and orientation. The wires or hollow tubes are bonded or welded together and to the face sheets to achieve a square or diamond lattice topologies as illustrated in Figure 1.17. Manufacturing of hollow pyramidal lattice core structures is made possible through high precision drilling methods[29]. Core configurations based on hollow trusses make for a more efficient use of the material and has been identified as the one of the strongest cores, hence, making it an attractive design[6].

illustration not visible in this excerpt

Figure 1.17: A Non-weave approach for manufacturing cellular core structures from solid wires or hollow tubes[24].

Recently, attention has focused on developing composite lattice structures that should, in principle, out-perform their metallic counterparts. Investment casting, folding, weaving and braiding methods are suitable for metallic-based lattice structures. In response, techniques for manufacturing of composite based lattice core structure have been developed. Recently, techniques such as hot press molding[30], mechanical interlocking[31]and folding and cutting flat sheets of composite material sheet[32]have been used to produce composite lattice structures of varying complexity. The hot press molding procedure involves the placement of pre-preg layers between a multi-part mold. Once the pre-preg has cured the carbon fiber composite pyramidal truss structures is removed from the mold and attached between two face-sheets using an adhesive as shown in Figure 1.18. In a similar approach called the hot-embossing method, the pre-pregs were placed in a mold with both ends embedded into the top and bottom face-sheets to form a single structure[33]. Once cured, the mold is removed, leaving a free standing pyramidal lattice core sandwich structure.

illustration not visible in this excerpt

Figure 1.18: (a) Pyramidal lattice structure fabricated using the hot press mold and (b) adhesively bonded between skins to for the sandwich panel[30].

Another fabrication method that was investigated involves pultruded composite rods that are adhesively bonded to face sheets containing a series of pre-drilled holes to form the pyramidal truss members[31]. Following this, truss patterns were cut from unidirectional sheets and adhesively bonded into milled slots in the skins. These procedures were rejected as a result of premature failure of the bonds. A third technique proved more successful. Here, a semi-continuous truss pattern was cut from 0o, 90o panels using a water-jet cutting facility. The pyramidal structure was then formed by snap-fitting the members together and the skins were then bonded. A schematic diagram of the snap fitting approach is illustrated in Figure 1.19.

illustration not visible in this excerpt

Figure 1.19: a) Truss member are water jet cut from laminate sheets, b) truss members are snap-fitted together forming the pyramidal lattice configuration. c) The truss were fitted and adhesively bonded in milled facesheet pockets[31].

The resulting pyramidal structures offered attractive mechanical properties when tested in compression[31], the results of which a plotted on an Ashby diagram of strength versus density shown in Figure 1.20. Here, although impressive, it is clear that the measured values fall below the limit associated with the unattainable materials space. This discrepancy was attributed to the inefficient use of material in the nodes and the onset of delamination from the nodal connections.

illustration not visible in this excerpt

Figure 1.20: An Ashby strength versus density map for engineering materials[31]

Stretch-bend-hybrid hierarchical composite pyramidal lattice cores were manufactured using two different core configurations[34]. In the first approach (Figure 1.21a), a flat foam core sandwich plate produced by hot pressing was cut into strips. The strips were then snap-fitted together and incorporated with face-sheets by slot insertion at the nodes and adhesively bonded. In the second approach (Figure 1.21b), corrugated foam sandwich plate was fabricated using a corrugated steel mold. Strips were then cut from the corrugated foam sandwich plate fit together by slot insertion at the pyramidal nodes.

illustration not visible in this excerpt

Figure 1.21: Schematic diagram illustrating the manufacturing procedure of the stretch- bend-hybrid hierarchical composite pyramidal lattice cores[34]

Further, the same authors manufactured what are termed stretch-stretch-hybrid hierarchical composite lattice cores, by employing a two-step approach that involved assembling pyramidal lattice sandwiches into macroscopic truss configurations[35]. The hierarchical pyramidal lattice structure is illustrated in Figure 1.22.

illustration not visible in this excerpt

Figure 1.22: Stretch-stretch-hybrid hierarchical composite pyramidal lattice cores[35].

A more recent manufacturing route for lattice truss core material is based on carbon fiber reinforced thermoplastic polymer resin to produce lattice cores in a three step procedure [32]. Initially, the corrugated plate shape is fabricated by hot forming using corrugated molds. Slots are then machined into the corrugated sheet at a predefined width and separation. Finally, the sheet is expanded into its final shape (Figure 1.23a). The fabricated core is then hot-bonded to stringer reinforced face-sheets, as illustrated in Figure 1.23b for a poly-ethylene terephthalate fiber reinforced poly-ethylene terephthalate. Experimental measurements revealed that the through thick compression strengths of these core were comparable to high end metallic cores.

illustration not visible in this excerpt

Figure 1.23: a) Manufactured Lattice core based on carbon fiber reinforced poly-ethylene terephthalate (CPET). b) Sandwich panel with a lattice truss core bonded to stringer reinforced face sheets[32].

Pyramidal carbon fiber reinforced epoxy lattices were also manufactured by means of electrical discharge machining (EDM)[30]. A flat top corrugated sheet of the composite material was manufactured by pressing in a hot mold. Near-pyramidal truss cores were created using an EDM plunge cutting technique that employed a suitably-shaped cuprite electrode. The face-sheets were finally adhesively bonded to the top and bottom of the manufactured core. Measured compression strengths were found to be lower than theoretical predictions due to debonding between the core and face sheets.

[...]