Flexural Response of Syntactic Foam Core Sandwich Structures: Effects of Graded 
Face Sheets and Interpenetrating Phase Composite Foam Core 
 
by 
 
Allen Martin Craven 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
May 9, 2011 
 
 
 
 
Keywords: sandwich structures, syntactic foam, interpenetrating phase composite, three-
point bending, digital image correlation 
 
 
 
 
Approved by 
 
Hareesh V. Tippur, Chair, McWane Professor of Mechanical Engineering 
Jeffrey C. Suhling, Quina Distinguished Professor of Mechanical Engineering 
Ruel A. Overfelt, Professor of Materials Engineering 
 
 
 
ii 
 
 
 
Abstract 
 
 
In this thesis, flexural responses of sandwich structures with different syntactic 
foam core architectures are studied.  The syntactic foam core is made by dispersing 
hollow glass microballoons in epoxy matrix at different volume fractions ranging from 
20%-40%.  The face sheets of the sandwich structures are made of thin AL6061 sheets.  
Three types of sandwich structures, first one with a regular syntactic foam core 
(identified as SFS), second one with an aluminum-syntactic foam interpenetrating core 
(identified as IPC), and third one with a syntactic foam core with graded face sheet 
(identified as SFS-b) are studied.  Static three-point bend tests are carried out on all three 
types of sandwich structures and load-deflection responses are measured.  The three 
different architectures are comparatively examined in terms of peak load, deflection at 
failure, nonlinearity of the flexural response, and strain energy absorbed.  The global 
measurements are supplemented by digital image correlation measurements in the core to 
map 2D deformations and strains.  The measured normal and shear strain fields and 
optical microscopy are used to discern failure mechanisms of the three architectures.  The 
SFS sandwiches fail predominantly due to face-core debonding with a large scatter in the 
peak load and deflection at failure.  They also show very limited nonlinearity in their 
load-deflection response.  The IPC core sandwiches show a substantial improvement in 
the deflection at failure with a slight reduction in peak load and significant nonlinearity in 
load-deflection response.  The nonlinearity in this architecture is primarily due to 
iii 
debonding between the phases of the interpenetrating core as well as face sheet yielding.  
The SFS-b sandwiches, on the other hand, show substantial improvement in both peak 
load and deflection at failure along with significant nonlinearity.  This is attributed to a 
gradual shear strain variation at the graded face-core interface, unlike the SFS 
sandwiches, resulting in face sheet yielding before failure. 
The superior material under quasi-static loading based on load, deflection, and 
energy metrics was the syntactic foam core sandwiches with graded face sheets (SFS-b).  
The only time it might not be considered the optimal choice might be when considering 
the IPC core sandwiches for their ability to use the metallic foam network to hold the 
structure together longer. 
Low velocity impact tests were also conducted on select IPC and SFS-b 
architectures in order to further expound on the failure mechanisms in the quasi-static 
case, as well as initiate dynamic characterization research.  Also, the feasibility of using 
DIC method in conjunction with high-speed digital photography to study impact behavior 
of sandwich structures is illustrated.  Contrary to the quasi-static case, IPC foam core 
sandwiches appear to outperform the SFS-b sandwiches in terms of strain energy 
absorption.  The presence of the interpenetrating phases seems to have a positive effect 
under dynamic conditions. 
 
 
 
 
 
 
 
 
iv 
 
 
 
 
 
 
Acknowledgements 
 
 
 I would first of all like to thank my advisor, Dr. Hareesh Tippur, for his expertise 
and guidance throughout my graduate and undergraduate careers.  His style of managing 
his graduate students allowed me the freedom to complete this work in a manner that was 
satisfactory to us both.  Thanks also to Dr. Jeffrey Suhling and Dr. Ruel (Tony) Overfelt 
for their input and willingness to serve as my committee members.  I would like to thank 
the U.S. Army Research Office for funding this work through grants W911NF-08-1-0285 
and ARMY-W911NF-10-1-0435.  I especially want to thank all of those involved in the 
SMART Scholarship.  This wonderful program provided me with both generous funding 
for my graduate education and a civil service job in the Air Force once my degree is 
complete.  I consider myself lucky to have received such a wonderful award. 
 My time in the Failure Characterization and Optical Techniques Lab under Dr. 
Tippur was aided and made easier by my colleagues.  Thanks to Dr. Dongyeon Lee, 
Kailash Jajam, Chandru Periasamy, Vinod Kushvaha, Robert Bedsole, and Rahul Jhaver 
for their help along the way and for helping make the day to day life in the lab a 
beneficial time in my life. 
 Finally, thanks to my family and friends.  Your unwavering support and patience 
were both crucial and greatly appreciated.  As Warren Buffet said, ?Beware of geeks 
bearing formulas.? 
 
v 
 
 
 
 
 
Table of Contents 
 
 
Abstract............................................................................................................................ ii 
Acknowledgements......................................................................................................... iv 
List of Figures................................................................................................................. viii 
List of Tables.................................................................................................................. xv 
1.  Introduction...................................................................................................... 1 
 1.1 Cellular Solids and Foams................................................................................... 1 
 1.2 Sandwich Panels with Foam Cores..................................................................... 4 
 1.3 Interpenetrating Phase Composites (IPCs) ......................................................... 5 
 1.4 Literature review ................................................................................................. 6 
 1.5 Sandwich Beam Theory.......................................................................................  10 
 1.6 Objectives............................................................................................................ 14 
 1.7 Organization of the Thesis...................................................................................  15 
2.  Material Description and Sample Preparation.......................................................... 16 
 2.1 Material Description............................................................................................ 16 
  2.1.1 Syntactic Foam.......................................................................................... 16 
  2.1.2 Aluminum Foam........................................................................................ 17 
  2.1.3 IPC Foam................................................................................................... 18 
 2.2 Specimen preparation ........................................................................................ 19 
  2.2.1 Mold Preparation....................................................................................... 19 
vi 
  2.2.2 Syntactic Foam Core Specimen Preparation............................................. 20 
  2.2.3 IPC Foam Core Specimen Preparation...................................................... 22 
  2.2.4 Syntactic Foam Core with Graded Face Sheets Specimen Preparation..... 24 
  2.2.5 Pattern Preparation for Optical Measurement........................................... 25 
3.  Flexural Characteristics of Constituents................................................................... 27 
 3.1 Aluminum Foam Sandwich................................................................................ 27 
 3.2 Syntactic Foam Sandwich .................................................................................. 32 
 3.3 Summary............................................................................................................. 46 
4. Flexural Characteristics of IPC Foam Core Sandwich Structures............................. 48 
 4.1 Experimental Setup............................................................................................. 48 
 4.2 Quasi-Static Tests............................................................................................... 49 
 4.3 Summary............................................................................................................. 69 
5. Flexural Characteristics of Syntactic Foam Core Sandwich Structures with Graded  
 Face Sheets................................................................................................................ 72 
  
 5.1 Experimental Setup............................................................................................. 72 
 5.2 Quasi-Static Tests............................................................................................... 73 
 5.3 Summary............................................................................................................. 91 
6. Full Field Deformation Measurements Using Digital Image Correlation Method..... 93 
 6.1 Digital Image Correlation (DIC) Principle ....................................................... 93 
 6.2 ARAMIS? Image Analysis Software.............................................................. 97 
 6.3 Experimental Setup........................................................................................... 99 
 6.4 Optical Measurement Results........................................................................... 100 
  6.4.1 Syntactic Foam (SFS) Results................................................................. 103 
  6.4.2 IPC Results............................................................................................... 113 
vii 
  6.4.3 Syntactic Foam (SFS-b) Results.............................................................. 123 
 6.5 Impact Tests...................................................................................................... 133 
7.  Conclusions............................................................................................................. 144 
 7.1 Comparison of Results and Conclusions .......................................................... 144 
 7.2 Future work ...................................................................................................... 153 
References..................................................................................................................... 156 
Appendix A.  Global/Local Displacement Comparisons.............................................. 159 
Appendix B.  Select ARAMIS? Images..................................................................... 164
viii 
 
 
 
List of Figures 
Figure 1.1:  Honeycomb Foam????????????????????? 1 
Figure 1.2:  Open-Celled Foam????????????????????.. 2 
Figure 1.3:  Closed-Celled Foam???????????????????? 2 
Figure 1.4:  (a) Cancellous Bone and (b) Duocel? Aluminum Foam?????.. 3 
Figure 1.5:  Sandwich Panels with Metallic Foam Core??????????? 5 
Figure 1.6:  Idealized Interpenetrating Phase Composite Network??????... 5 
Figure 1.7:  Three-Point Bending Schematic of a Sandwich Beam??????.. 10 
Figure 2.1: Open-Celled Aluminum Foam Sandwich Scaffold???????? 18 
Figure 2.2: Enlarged View of Duocel? Foam ??????????????. 18 
Figure 2.3: Silicone Specimen Mold and Demolded Specimen ???????.. 21 
Figure 2.4: Syntactic Foam Core Sandwich Structure (SFS)????????? 22 
Figure 2.5: IPC Foam Core Sandwich Structure?????????????.. 23 
Figure 2.6: Single Cast SFS-b Mold: (1) Mold, (2) AL6061 Face Sheet, and (3)  
 Brazed Aluminum Foam ?????????????????.. 24 
 
Figure 2.7: Syntactic Foam Core Sandwich Structure with Graded Face Sheets  
 (SFS-b)????????????????????????.. 25 
 
Figure 2.8: Typical Decorated Random Speckle Pattern for Optical 
 Measurements?????????????????????? 26 
 
Figure 3.1:  Photograph of Three-Point Bending Test Setup????????? 28 
 
Figure 3.2:  Camera Viewing Area??????????????????... 29 
Figure 3.3:  Quasi-static Test Experimental Arrangement?????????? 30 
ix 
Figure 3.4:  Overlay of Load-Deflection Data for 20ppi Aluminum Foam Core  
 Sandwich???????????????????????? 30 
 
Figure 3.5:  Typical Aluminum Foam Stress-Strain Response ???????.... 32 
 
Figure 3.6:  Load-Deflection Data for SFS20??????????????... 33 
Figure 3.7:  Load-Deflection Data for SFS30??????????????... 33 
Figure 3.8:  Load-Deflection Data for SFS40??????????????... 34 
Figure 3.9:  Typical SFS Face-Core Debond??????????????? 35 
Figure 3.10:  Normalized Measured Peak Load for Sandwich Structures with SF  
 Foam Core with Different Volume Fractions??????????. 37 
 
Figure 3.11:  Normalized Measured Mid-Span (Load-Point) Deflection at Failure for  
 Sandwich Structures with SF Foam Core ???????????. 38 
 
Figure 3.12:  Energy Absorbed for Sandwich Structures with SF Foam Core??? 40 
Figure 3.13:  Specific Energy Absorbed for Sandwich Structures with SF Foam  
 Core?????????????????????????? 41 
 
Figure 3.14:  (a) Failed Syntactic Foam Core Sandwich with (b) Highlighted  
 Face-core Debond ????????????????????.. 42 
 
Figure 3.15:  Compressive Response of Syntactic Foam [17]?????????. 43 
Figure 3.16:  Predicted vs. Experimental Mid-Span Deflection, SFS20?????. 44 
Figure 3.17:  Predicted vs. Experimental Mid-Span Deflection, SFS30?????. 44 
Figure 3.18:  Predicted vs. Experimental Mid-Span Deflection, SFS40?????. 45 
Figure 3.19:  Overlay of Measured Load-Displacement of Sandwich Structures  
 with Syntactic Foam Core and Different Volume Fraction of  
 Microballoons in the SF ?????????????????? 45 
 
Figure 3.20:  Face-Core Debond????????????????????.. 46 
Figure 4.1: IPC Foam Core Sandwich Structure?????????????.. 49 
Figure 4.2:  Overlay of Measured Load-Deflection Data for Three Different IPC  
 Core Sandwich Beams (IPC20)???????????????.. 50 
 
x 
Figure 4.3:  Overlay of Measured Load-Deflection Data for Three Different IPC  
 Core Sandwich Beams (IPC30)???????????????.. 50 
 
Figure 4.4:  Overlay of Measured Load-Deflection Data for Two Different IPC  
 Core Sandwich Beams (IPC40)???????????????.. 51 
 
Figure 4.5:  Typical IPC Load-Deflection Curve: Point A ? Transition Point, Point  
 B ? Crack Formation, Point C ? Loss of Load Bearing Capacity ??. 53 
 
Figure 4.6:  Undeformed, P=0 N???????????????????... 54 
Figure 4.7:  Point A: Transition Point, P=1616 N ????????????? 54 
Figure 4.8:  Point B: Crack Formation, P=3741 N ????????????.. 55 
Figure 4.9:  Point C: Loss of Load Bearing Capacity, P=782 N ???????.. 55 
Figure 4.10:  Normalized Measured Peak Load for Sandwich Structures with IPC  
 Foam Core with Different Volume Fraction of SF in the IPC ???.. 57 
 
Figure 4.11:  Normalized Measured Mid-Span (Load-Point) Deflection at Failure  
 for Sandwich Structures with IPC Foam Core ?????????.. 58 
 
Figure 4.12:  Normalized Measured Load at Transition Point for Sandwich  
 Structures with IPC Foam Core ???????????????. 59 
 
Figure 4.13:  Normalized Measured Mid-Span (Load-Point) Deflection at  
 Transition Point for Sandwich Structures with IPC Foam Core ??? 60 
 
Figure 4.14:  Energy Absorbed for Sandwich Structures with IPC Foam Core??.. 61 
Figure 4.15:  Specific Energy Absorbed for Sandwich Structures with IPC Foam  
 Core?????????????????????????? 63 
 
Figure 4.16:  (a) Failed IPC Foam Core Sandwich with (b) Yielded Bottom Face... 64 
Figure 4.17:  Magnified Images of Crack Surfaces Near the Lower Face Sheet?... 65 
Figure 4.18:  Compressive Response of IPC [17]?????????????... 66 
Figure 4.19:  Predicted vs. Experimental Mid-Span Deflection, IPC20?????. 66 
Figure 4.20:  Predicted vs. Experimental Mid-Span Deflection, IPC30?????. 67 
Figure 4.21:  Predicted vs. Experimental Mid-Span Deflection, IPC40?????. 67 
xi 
Figure 4.22:  Overlay of Measured Load-Displacement of Sandwich Structures with  
 IPC Foam Core with Different Vf of Microballoons in the SF???.. 69 
 
Figure 4.23:  Illustration of IPC (a) Before and (b) After Interphase Separation  
 between Syntactic Foam and Aluminum Ligaments ???????. 70 
 
Figure 5.1: Syntactic Foam Core Sandwich Structure with Graded Face Sheets       
 (SFS-b)????????????????????????? 73 
 
Figure 5.2:  Overlay of Measured Load-Deflection Data for Three Different SF  
 Core Sandwich Beams with Graded Face Sheets (SFSb20)????? 74 
 
Figure 5.3:  Overlay of Measured Load-Deflection Data for Four Different SF Core  
 Sandwich Beams with Graded Face Sheets (SFSb30)??????? 74 
 
Figure 5.4:  Overlay of Measured Load-Deflection Data for Four Different SF Core  
 Sandwich Beams with Graded Face Sheets (SFSb40)??????? 75 
 
Figure 5.5:  Typical SFS-b Load-Deflection Curve: Point A ? Transition Point,  
 Point B ? Failure ????????????????????? 77 
 
Figure 5.6:  Undeformed, P=0 N???????????????????... 78 
Figure 5.7:  Point A: Transition Point, P=5127 N ????????????? 78 
Figure 5.8:  Point B: Failure ?????????????????????. 79 
Figure 5.9:  Normalized Measured Peak Load for Sandwich Structures with  
 Syntactic Foam Core and Graded Face Sheets ?????????.. 80 
 
Figure 5.10:  Normalized Measured Mid-Span (Load-Point) Deflection at Failure  
 for Sandwich Structures with Syntactic Foam Core and Graded Face 
 Sheets?????????????????????????.. 81 
 
Figure 5.11:  Normalized Measured Load at Transition Point for Sandwich  
 Structures with Syntactic Foam Core and Graded Face Sheets???.. 82 
 
Figure 5.12:  Normalized Measured Mid-Span (Load-Point) Deflection at Transition  
 Point for Sandwich Structures with Syntactic Foam Core and Graded  
 Face Sheets ???????????????????????. 83 
 
Figure 5.13:  Energy Absorbed for Sandwich Structures with Syntactic Foam Core  
 and Graded Face Sheets??????????????????.. 84 
 
Figure 5.14:  Specific Energy Absorbed for Sandwich Structures with Syntactic  
 Foam Core and Graded Face Sheets?????????????.. 86 
xii 
Figure 5.15:  Failed SFS-b Specimen with (a) Side, (b) Top Face, and (c) Bottom  
 Face Views ???????????????????????. 87 
 
Figure 5.16:  Magnified Images (a), (b) of Failure Surfaces and (c) From Below ?. 88 
Figure 5.17:  Predicted vs. Experimental Mid-Span Deflection, SFSb20????... 89 
Figure 5.18:  Predicted vs. Experimental Mid-Span Deflection, SFSb30????? 89 
Figure 5.19:  Predicted vs. Experimental Mid-Span Deflection, SFSb40????? 90 
Figure 5.20:  Overlay of Measured Load-Displacement of SF Core Sandwich  
 Structures with Graded Face Sheets and Different Vf of Microballoons  
 in the SF????????????????????????.. 90 
 
Figure 6.1:  (a) Undeformed and (b) Deformed Speckle Images???????.. 94 
Figure 6.2:  Tracked Subimage for Image Correlation???????????. 95 
Figure 6.3:  Coordinate System Definition???????????????... 98 
Figure 6.4:  3x3 Point Neighborhood for 2D Strain Calculation???????. 99 
Figure 6.5:  Global/Local Displacement Comparison, FLEX-16???????. 100 
Figure 6.6:  Strain Calibration Using PMMA??????????????.. 102 
Figure 6.7:  PMMA Strain (?x) Variation Along the Height of the Beam???? 102 
Figure 6.8:  PMMA Shear Strain (?xy) Variation Along the Height of the Beam ? 103 
Figure 6.9:  ARAMIS? Results for SFS20 (FLEX-38, u)?????????? 104 
Figure 6.10:  ARAMIS? Results for SFS20 (FLEX-38, ?x)?????????.. 105 
Figure 6.11:  ARAMIS? Results for SFS20 (FLEX-38, ?xy)?????????. 106 
Figure 6.12:  ARAMIS? Results for SFS30 (FLEX-39, u)?????????? 107 
Figure 6.13:  ARAMIS? Results for SFS30 (FLEX-39, ?x)?????????.. 108 
Figure 6.14:  ARAMIS? Results for SFS30 (FLEX-39, ?xy)?????????. 109 
Figure 6.15:  ARAMIS? Results for SFS40 (FLEX-24, u)?????????? 110 
Figure 6.16:  ARAMIS? Results for SFS40 (FLEX-24, ?x)?????????.. 111 
xiii 
Figure 6.17:  ARAMIS? Results for SFS40 (FLEX-24, ?xy)?????????. 112 
Figure 6.18:  ARAMIS? Results for IPC20 (FLEX-10, u)?????????? 114 
Figure 6.19:  ARAMIS? Results for IPC20 (FLEX-10, ?x)?????????.. 115 
Figure 6.20:  ARAMIS? Results for IPC20 (FLEX-10, ?xy)?????????. 116 
Figure 6.21:  ARAMIS? Results for IPC30 (FLEX-16, u)?????????? 117 
Figure 6.22:  ARAMIS? Results for IPC30 (FLEX-16, ?x)?????????.. 118 
Figure 6.23:  ARAMIS? Results for IPC30 (FLEX-16, ?xy)?????????. 119 
Figure 6.24:  ARAMIS? Results for IPC40 (FLEX-14, u)?????????? 120 
Figure 6.25:  ARAMIS? Results for IPC40 (FLEX-14, ?x)?????????.. 121 
Figure 6.26:  ARAMIS? Results for IPC40 (FLEX-14, ?xy)?????????. 122 
Figure 6.27:  ARAMIS? Results for SFSb20 (FLEX-57, u)?????????. 124 
Figure 6.28:  ARAMIS? Results for SFSb20 (FLEX-57, ?x)?????????. 125 
Figure 6.29:  ARAMIS? Results for SFSb20 (FLEX-57, ?xy)????????? 126 
Figure 6.30:  ARAMIS? Results for SFSb30 (FLEX-59, u)?????????. 127 
Figure 6.31:  ARAMIS? Results for SFSb30 (FLEX-59, ?x)?????????. 128 
Figure 6.32:  ARAMIS? Results for SFSb30 (FLEX-59, ?xy)????????? 129 
Figure 6.33:  ARAMIS? Results for SFSb40 (FLEX-65, u)?????????. 130 
Figure 6.34:  ARAMIS? Results for SFSb40 (FLEX-65, ?x)?????????. 131 
Figure 6.35:  ARAMIS? Results for SFSb40 (FLEX-65, ?xy)????????? 132 
Figure 6.36:  Schematic of Impact Test Setup: (1) high-speed digital camera,  
 (2) drop tower impactor tup, (3) delay generator, (4) specimen,  
 (5) light sources, (6) DAQ ? drop tower, (7) DAQ ? camera,  
 (8) lamp control unit, and (9) drop tower controller??????? 134 
 
Figure 6.37:  Impact Test Setup: (1) high-speed camera, (2) drop tower impactor  
 tup, (3) specimen, and (4) light source ???????????? 135 
 
xiv 
Figure 6.38:  Camera Viewing Area??????????????????... 136 
Figure 6.39:  ARAMIS? Results for IPC30 (DYN-29, u)?????????? 137 
Figure 6.40:  ARAMIS? Results for IPC30 (DYN-29, ?x)?????????? 138 
Figure 6.41:  ARAMIS? Results for SFSb30 (DYN-35, u)?????????. 139 
Figure 6.42:  ARAMIS? Results for SFSb30 (DYN-35, ?x)?????????. 140 
Figure 6.43:  Strain Energy History, IPC30???????????????? 141 
Figure 6.44:  Strain Energy History, SFSb30???????????????. 142 
Figure 7.1:  Normalized Measured Peak Load for Sandwich Structures with SF  
 and IPC Foam Cores???????????????????. 147 
 
Figure 7.2:  Normalized Measured Mid-Point (Load-Point) Deflection at Failure  
 for Sandwich Structures with SF and IPC Foam Cores?????? 147 
 
Figure 7.3:  Normalized Measured Load at Transition Point for Sandwich  
 Structures with SF and IPC Foam Cores???????????.. 148 
 
Figure 7.4:  Normalized Measured Mid-Point (Load-Point) Deflection at  
 Transition Point for Sandwich Structures with SF and IPC Foam  
 Cores???......................................................................................... 148 
 
Figure 7.5:  Energy Absorbed for Sandwich Structures with SF and IPC Foam       
 Cores ????????????????????????? 149 
 
Figure 7.6:  Specific Energy Absorbed for Sandwich Structures with SF and IPC  
 Foam Cores ??????????????????????.. 149  
 
Figure 7.7:  20% Vf: Strain (?x) Variation Along the Height of the Sandwich  
 Core?????????????????????????.. 151 
 
Figure 7.8:  20% Vf: Shear Strain (?xy) Variation Along the Height of the Sandwich  
 Core ?????????????????????????. 152 
 
 
 
 
xv 
 
 
 
List of Tables 
Table 2.1: Syntactic Foam Constituent Properties????????????? 17 
Table 2.2: Duocel? Aluminum Foam Properties????????????? 17 
Table 3.1: Aluminum Foam Sandwich Test Results ???????????.. 31 
Table 3.2: TPB SFS20 Test Results ?????????????????? 34 
Table 3.3: TPB SFS30 Test Results ?????????????????? 34 
Table 3.4: TPB SFS40 Test Results ?????????????????? 35 
Table 3.5: Material Densities????????????????????... 41 
Table 3.6: Syntactic Foam Quasi-Static Elastic Properties [17]???????. 43 
Table 4.1: TPB IPC20 Test Results ?????????????????? 51 
Table 4.2: TPB IPC30 Test Results ?????????????????? 51 
Table 4.3: TPB IPC40 Test Results ?????????????????? 52 
Table 4.4: IPC Material Densities??????????????????? 62 
Table 4.5: IPC Quasi-Static Elastic Properties [17]????????????. 66 
Table 5.1: TPB SFSb20 Test Results ?????????????????.. 75 
Table 5.2: TPB SFSb30 Test Results ?????????????????.. 75 
Table 5.3: TPB SFSb40 Test Results ?????????????????.. 76 
Table 6.1: IPC30 Impact Test Results ????????????????? 142 
Table 6.2: SFSb30 Impact Test Results ????????????????. 142 
 
1 
 
 
 
CHAPTER 1 
INTRODUCTION 
 
1.1 Cellular Solids and Foams 
 
 A cellular solid is made up of an interconnected network of solid struts or thin 
plates that form the edges or faces of cells.  The simplest of all cellular solids is a two-
dimensional array of regular polygons that look like the cells created by honeybees.  For 
this reason they are often referred to as honeycombs.  More commonly seen are three-
dimensionally packed polyhedra which are known as foams.  If the cells connect through 
open faces with the cell edges that are solid, the foam is said to be open-celled.  On the 
other hand, if the cell faces are also solid, sealing off each cell from its neighbors, the 
foam is said to be closed-celled [1].  Figures 1.1-1.3 show images of these three foam 
types. 
 
 
Figure 1.1    Honeycomb Foam (Ref: 
http://materiali.matech.it/matech/materiali/images/okpic/CP2079.jpg) 
2 
 
 
Figure 1.2    Open-Celled Foam (Ref: http://www.grantadesign.com/images/foam.gif) 
 
 
Figure 1.3    Closed-Celled Foam (Ref: http://www.alcarbon.de/jcms/images/stories/Al-
Schaeume/ALPORAS_AC/ALPORAS.JPG) 
 
Many structural materials found in nature are cellular solids: cork, sponge, coral, 
wood, and cancellous bone.  Wood is still the most widely used structural material.  
Increasingly, man-made foams and honeycombs are being used in structural applications.  
Considering their lightweight and stiff nature, their most obvious use today is in 
sandwich panels.  From the World War II planes that used panels made from thin 
plywood skins bonded to balsa wood cores to the planes of today that use fiberglass or 
3 
carbon fiber composite skins with cores of aluminum or paper-resin honeycombs or rigid 
polymer foams, sandwich panels provide excellent specific bending stiffness and 
strength.  Sandwich panels are also found in nature.  The cuttlebone of a cuttlefish is a 
multi-layer sandwich panel.  Some types of leaves are structured much in the same 
manner as sandwich panels.  Even the human skull is composed of two layers of hard 
bone separated by a lightweight core of cancellous bone.  Figure 1.4 shows the cancellous 
bone found in the human skull compared with Duocel? open-celled aluminum foam. 
 
  
(a)           (b) 
Figure 1.4    (a) Cancellous Bone and (b) Duocel? Aluminum Foam (Ref: 
http://www.ergaerospace.com/foamproperties/aluminumproperties.htm) 
 
The single most important structural characteristic of cellular solids is relative 
density, the density of the foam divided by the density of the solid of which it is 
comprised.   
Syntactic foams (SFs) are a class of structural composite foams created by 
dispersing hollow microballoons into a metal, polymer, or ceramic matrix.  The presence 
4 
of the microballoons leads to improved properties including buoyancy, lower density, and 
higher strength.   
 
1.2 Sandwich Panels with Foam Cores 
 
Sandwich panels consist of two stiff, strong skins separated by a lightweight core.  
Separating the skins, or face sheets, increases the moment of inertia of the panel with 
little penalty in terms of weight.  This produces an efficient structure for withstanding 
bending and buckling loads.  For this reason sandwich panels are often used in situations 
where weight limitation is critical, such as in aircraft structures.  The conventional way of 
stiffening panels are with stringers: strips attached between the faces with profiles such as 
a Z, a tee, or a top hat.  In general, stringer stiffened panels offer greater specific stiffness 
(stiffness per unit weight).  The drawbacks, however, are anisotropy and cost.  Metal or 
syntactic foam cores in sandwich structures offer advantages of macroscopic material 
isotropy as well as the ability to easily and cheaply mold complex lightweight structures 
in a single operation.  For applications involving a dominant bending moment, 
attachment or honeycomb stiffened sandwich panels can offer the best specific stiffness.  
This applies only in the direction the panel has been stiffened, though.  In contrast, for 
loads about which less information is known or that have comparable magnitudes in 
multi-axial (even changing) directions, the isotropic nature of foam cored sandwich 
panels offer the greatest specific stiffness in all directions. 
 
5 
 
Figure 1.5    Sandwich Panels with Metallic Foam Core (Ref: http://www.agstaron.com) 
 
1.3 Interpenetrating Phase Composites (IPCs) 
 
Interpenetrating phase composites (IPCs) are a relatively new class of composite 
materials that has the potential for outstanding multifunctional properties.  In traditional 
composites, discrete reinforcing phases such as whiskers, fibers, or dispersed particles are 
introduced into a matrix to improve or alter the resulting properties of the matrix.  In an 
IPC, constituent phases are continuous and three dimensionally interconnected.  In their 
singular state, each constituent of an IPC would be a matrix consisting of an open-celled 
microstructure.  Hence, IPCs are uniquely different from traditional composites 
consisting of a matrix with reinforcing phases that do not experience such complete 
interpenetration.  Figure 1.5 illustrates an idealized open-celled nature of two phases of 
an IPC. 
 
 
Figure 1.6    Idealized Interpenetrating Phase Composite Network 
6 
 
An advantage of IPCs over traditional reinforced composites is that higher 
volume fractions of the reinforcing or secondary phase may be introduced more easily 
into an IPC.  Furthermore, each phase is mechanically constrained by the other resulting 
in a better structural response.  Each phase of an IPC contributes its property to the 
overall macro scale characteristics synergistically.  For example, if one constituent 
provides strength, the other might enhance stiffness or thermal stability.  Among the 
potential mechanical benefits of IPCs, the ones regarding fracture and energy dissipation 
characteristics are of interest.  In traditional composites with aligned fibers, stiffness and 
strength advantages are limited to the fiber direction as crack propagation along the fibers 
cannot be effectively resisted. On the contrary, the three dimensional interconnectivity of 
the phases in an IPC could stave off failure effectively while offering macro scale 
isotropy. 
 
1.4 Literature Review 
  
The work done by Wu et al. [2] illustrates improved mechanical properties and 
impact resistance of sandwich structures with graphite/epoxy face sheets and aluminum 
honeycomb core by first filling the honeycomb core with rigid polyurethane foam.  Low 
velocity impact tests have revealed an improvement in impact resistance, including less 
frequent debonding of the face sheet and localized core crushing.  Zarei et al. [3] 
attempted to study and optimize bending behavior due to impact loading of foam-filled 
beams.  Impact tests were conducted on aluminum tubes in order to simulate car bumpers 
7 
during crashes.  An attempt was made to optimize the tube energy absorption and tube 
design to include a metallic foam core consisting of Alporas aluminum foam.  Energy 
absorption increased between 2.5%-5.2% once the foam filler was added.  Specific 
energy absorbed also increased; however, it was less pronounced.  Seitzberger et al. [4] 
examined the effects of foam filling on axially loaded tubular columns made of steel.  
Different shapes, such as square, hexagonal, and octagonal, as well as different filling 
configurations (single tube with no foam filling, two tubes with foam in between, single 
completely filled tube) were tested.  For the square, fully filled tubes, experiments 
indicated a specific energy absorption improvement of up to 60%.  A glass fiber 
composite-foam sandwich structure was studied in bending and impact situations by 
Belingardi et al. [5].  Bending tests failed starting with 45 degree shear cracks in the core 
followed by face sheet debonding.  The modulus and Poisson?s ratio gathered from 
bending tests were approximately 25 percent below the values from tensile tests, likely 
due to the dual tensile and compressive nature of loading.  Tests conducted on the 
sandwich structure showed no strain-rate effects over the range of test conditions 
investigated in the study.  The impact response of this foam-based sandwich structure 
was successfully modeled using mechanical properties determined at static or quasi-static 
rates of strain.   
Cenosphere fly ash (waste product from burning coal) microballoons and 
aluminum were used to create syntactic foam via pressure infiltration technique by Zhang 
et al. [6].  Compression tests revealed energy absorption capacity to be 27 MJ?m-3 at 47% 
strain with a peak stress of 73 MPa.  Metal-matrix IPCs were created by Zhou et al. [7].  
Using volatile agents, an aluminum matrix was created with open porosity as high as 
8 
83%.  The aluminum matrix interpenetrating phase composites reinforced with 
continuous Al2O3-TiC ceramic phase were successfully fabricated by the vacuum high 
pressure infiltration process. 
One work by Styles et al. [8] investigates the strain distribution and failure 
mechanisms associated with aluminum foam or polymer foam sandwich structures under 
four-point bending.  Real-time strain data was collected using a 3D optical technique 
(ARAMIS?, GOM mbH, Germany).  It was determined that the energy absorbed to 
yield load for aluminum foam was approximately two times that of the polymer, and the 
total energy absorption of aluminum was about 3.5 times greater.  In a separate work by 
Styles et al. [9], core thickness effects on the flexural behavior of aluminum foam 
sandwich structures were examined.  In sandwich material with Alporas foam as the core, 
the max core stress and max facing stresses decreased as core thickness increased, 
possibly due to diminishing coupling between core and facing.  Core shear stress, 
however, remained nearly the same (approximately 1.75 MPa).  The failure of the core 
became more dominant as the core thickness increased.  McKown and Mines [10] studied 
static and impact behavior of metal foam cored sandwich beams.  The sandwich material 
consisted of Alporas core with glass fiber polypropylene matrix composite (Plytron) face 
sheets.  In quasi-static tests, the shear effects in the core increased as the total specimen 
length decreased.  The range of indenter deflections (deflections=15-30 mm on a 
specimen of length=230 mm) for the two test types were similar, indicating that strain 
rate effects essentially cancel out the core failure initiation at weak points in the structure.  
From indenter energies of 15 J up to 50 J, fraction of energy absorbed up to skin failure 
ranged from 45% down to 20%, respectively.   
9 
The work done by McCormack et al. [11] illustrated the different modes of 
sandwich beam failure under quasi-static bending.  Among face yielding, face wrinkling, 
core yield, indentation, and delamination, the most common failure modes observed were 
core yield and face yield.  Chen et al. [12] studied the plastic collapse of sandwich beams 
with Alporas? foam cores.  Four-point bending allowed the competing failure modes of 
face yield, core shear and indentation to be separated physically along the beam.  Face 
yield occurred between the inner rollers, core shear occurred between the inner and outer 
rollers, and indentation was triggered directly beneath the rollers.  The collapse 
mechanism maps were generated as a tool to predict failure type/mode, and criteria for 
each of the failure cases were generated. 
 Dukhan et al. [13] performed three-point bending tests on aluminum-
polypropylene IPC material.  Strength and flexural modulus of the IPC were compared to 
that of polypropylene.  The IPC was stiffer than both constituents, and increased with 
decreasing pore size.  When 20 ppi aluminum net was used, an increase in strength of 3-
4% and an increase in modulus of around 33% accompanied the change from 
polypropylene to IPC.  The effect of volume fraction on alumina/aluminum composites 
was investigated by Travitzky [14].  Various volume fractions of aluminum were 
interspersed into alumina.  For 12% aluminum (closest to the material presented in this 
study) the bending strength increased from about 205 to 740 MPa, a 2.5 times increase.  
The Young?s modulus increased from about 205 to 330 GPa, an increase of 60%.  Chang 
et al. [15] utilized a pressureless infiltration system to produce and characterize an 
Al(Mg)/Al2O3 interpenetrating composite.  Three-point bending tests revealed an increase 
in bending strength from approximately 5 MPa to 250 MPa once a metallic phase was 
10 
introduced to a foam of 15% relative density.  Also, a decreasing trend in IPC strength 
was observed as relative density increased. 
 
1.5 Sandwich Beam Theory 
 
 This section puts forth the theory associated with bending of sandwich structures 
applicable to linear elastic cases.  It will be shown in later chapters that both IPC foam 
core sandwiches and syntactic foam core sandwiches with graded face sheets (see 
Chapter 2 for material descriptions) may be initially linear elastic, but does not remain so 
for the entirety of its tests.  This section is comprised of such theory associated with 
sandwich beams under three-point bending (TPB) loads.   
Equations based on classical beam theory are provided by Allen [16] and are 
given below for sandwich structures.  Consider a sandwich beam subjected to three-point 
bending as shown in Figure 1.7. 
 
 
Figure 1.7    Three-Point Bending Schematic of a Sandwich Beam 
 
x 
y y 
z 
core face sheet 
11 
 Let the flexural rigidity be denoted by EI.  For stacked composite beams (e.g. 
sandwich structures), the flexural rigidity is the sum of the flexural rigidities of the two 
faces and the core.  It is generally represented by the symbol D and evaluated as follows: 
 
3
12core c
bcD E=  , 
3 2
2 12 4faces f fbt btdD E E? ?= +? ?
? ?
 , 
3 2 3
6 2 12core faces f f c
bt btd bcD D D E E E= + = + +  , 
 
where the subscripts f and c represent the face sheet and core, respectively.  Similarly, the 
equivalent shear rigidity, (AG)eq, in stacked composite beams is: 
 
ceq Gc
bdAG 2)( =  . 
 
where A and G represent the cross section area and shear modulus, respectively.  These 
rigidities are used to calculate the displacement at the midspan of a (linear elastic) beam 
as: 
3
48 4( )eq
PL PL
D AG? = +  . 
 
12 
 The first term of the deflection equation, 
3
48
PL
D , represents the contribution due to 
bending.  The second term, 4( )
eq
PL
AG , represents the contribution due to shear. 
To obtain equations for stress in a three-point symmetric loading configuration, 
we begin by recognizing that strain ?=?/E leads to: 
 
f f
My E
D? = ?   ;2 2 2 2
c h h cy y? ?? ? ? ? ? ?? ?
? ?
 , 
c c
My E
D? = ?   2 2
c cy? ?? ? ?? ?
? ?
 , 
where moment is given by, ( )
, 02 2
,2 2
Px Lx
M P x L L
x L
? ? ?
??
= ? ?
? < ?
??
 , 
 
and D represents the flexural rigidity.  (Consult Figure 1.7 for definitions of the 
geometric parameters.)  Ordinary homogeneous beam bending theory gives the 
expression for shear stress at depth, y, below the centroid in the cross-section as: 
QS
Ib? =  , 
where Q is the first moment of area, I is the second moment of area about the centroid, S 
is the shear force, and b is the beam width. For a compound beam, differing moduli for 
different elements in the cross-section must be accounted for using the modification: 
( )S QEDb? = ?  , 
13 
where ( )QE? represents the sum of the products of the first moments of area (Q) and 
moduli (E), and D is the flexural rigidity.  For the sandwich construction presented here,  
( ) 2 2 2 2cf E bbtd c cQE E y y? ?? ?= + + ?? ?? ?? ?? ??  . 
Therefore, under three-point bending configuration the shear stress experienced in 
the core can be calculated using: 
2
2
2 2 4
c
f
ES td cE y
D?
? ?? ?? ?= + ?
? ?? ?? ?? ?
? ?
 , 
where the shear force is given by, 
, 02 2
,2 2
P Lx
S P L
x L
? ? ?
??=
?
?? < ?
??
 . 
 
The following are definitions of the symbols used in this and subsequent chapters: 
(AG)eq = shear rigidity 
b = specimen width 
c = core thickness 
? = deflection at mid-span 
d = distance between facing centroids 
D = flexural rigidity 
Ec = modulus of the core 
Ef = modulus of the facings 
Gc = shear modulus of the core 
h = total specimen height 
14 
l = total specimen length 
L = support span 
P = applied load 
?rel = relative density of foam 
?f = facing stress 
?c = core normal stress 
? = core shear stress 
t  =  facing thickness 
 
1.6 Objectives 
 
 This work is aimed towards demonstrating the feasibility of a lightweight 
sandwich structure with epoxy-based syntactic foam (SF) core and graded face sheets and 
an SF-based IPC foam core sandwich for improving the flexural response relative to that 
of a similar sandwich with a simple SF core.  The specific goals for the work are: 
? Develop a method for processing sandwich structures with syntactic foam and 
IPC foam cores. 
? Obtain both global and local flexural response data of SF and IPC core sandwich 
structures. 
? Explain failure mechanisms under quasi-static three-point bending configuration. 
? Study the effect of hollow filler volume fraction in the syntactic foam (20%, 30%, 
or 40%) on flexural characteristics. 
15 
? Study the possibility of improving load-deflection and strain energy absorption 
responses of syntactic foam core sandwiches by either (a) adding a 3D 
interconnected metallic foam phase to the core or (b) tailoring the face sheets to 
prevent face-core debonding. 
? For both quasi-static and impact loading cases, demonstrate ability to make local 
displacement and strain measurements using digital image correlation method in 
sandwich structures. 
 
1.7 Organization of the Thesis 
 
 This thesis is divided into seven chapters, including this one.  The first chapter 
describes the materials to be investigated, motivation for the research, and previous work 
by others in related areas.  Material description and preparation of the syntactic foam core 
and IPC foam core sandwiches are discussed in Chapter 2.  The flexural characterizations 
of unfilled aluminum foam core sandwiches and syntactic foam core sandwiches are 
discussed in Chapter 3.  Chapter 4 contains discussion of flexural characterization of IPC 
foam core sandwiches.  Chapter 5 contains discussion of flexural characterization of 
syntactic foam core sandwiches with graded face sheets.  Chapter 6 is concerned with the 
digital image correlation method used to analyze full-field deformations.  Finally Chapter 
7 presents a comparative summary and conclusions to be drawn from this work.  There 
are appendices that show global/local measurement comparisons and images related to 
the ARAMIS? digital image correlation work. 
 
16 
 
 
 
CHAPTER 2 
MATERIAL DESCRIPTION AND SAMPLE PREPARATION 
 
2.1 Material Description 
 
 Sandwich structures with aluminum faces and syntactic foam (SF) or SF-based 
IPC foam core are processed in this work.  Pressureless infiltration techniques are 
employed to create the syntactic foam-filled IPC.  The IPC foam is created by 
introducing uncured syntactic foam into aluminum sandwich performs and curing the SF 
in situ.  
 
2.1.1 Syntactic Foam 
  
The syntactic foam used in this work is made of epoxy matrix and hollow glass 
microballoon filler.  Physical and elastic properties of the constituents of the syntactic 
foam used are shown in Table 2.1.  The epoxy used was Epo-Thin?, a low viscosity resin 
(supplied by Buehler, Inc., USA).  The advantage of the Epo-Thin? epoxy is its low 
viscosity, necessary to fill small holes and voids between microballoons.  The hollow 
glass microballoons (K-1? microballoons supplied by 3M Corp.) were of average 
diameter ~65 ?m and wall thickness ~550 nm.  The microballoons used are the most 
17 
economical hollow ceramic fillers produced by 3M Corp. and advantages of their use 
include the ability to create a good bond between epoxy and glass and it having one of 
the lowest bulk densities among the available glass microballoons. 
 
Table 2.1    Syntactic Foam Constituent Properties 
Property Neat Epoxy Microballons
Elastic Modulus (MPa) 3200 -
Bulk Density (kg/m3) 1085 125
Poisson's Ratio 0.34 -  
 
2.1.2 Aluminum Foam 
  
 The open cell aluminum foam was used as the scaffold for infusing SF into the 
core of the IPC sandwiches.  The scaffold material was Duocel? foam obtained from 
ERG Materials and Aerospace Corp.  Its properties are shown in Table 2.2.  Mean cell 
size for 20 ppi material is ~1.02mm (0.040?).  Ligament diameter is ~0.2mm (0.008?). 
 
Table 2.2    Duocel? Aluminum Foam Properties 
Material Pore Density Relative Density
Aluminum
6101 20 ppi 7%  
 
 The open-cell scaffold is made from annealed 6101 aluminum, and the face sheets 
of the sandwich structures are made from annealed 6061 aluminum.  Relevant elastic 
properties for these two alloys are the same, Young?s modulus of 69 GPa (10 Msi) and 
18 
yield strength of 552 MPa (8 ksi).  Figure 2.1 shows the open-celled aluminum foam 
sandwich scaffold, and Figure 2.2 shows an enlarged view of the open-cell Duocel? 
foam. 
 
 
Figure 2.1    Open-Celled Aluminum Foam Sandwich Scaffold 
 
 
Figure 2.2    Enlarged View of Duocel? Foam (Ref: 
http://www.ergaerospace.com/foamproperties/introduction.htm) 
 
2.1.3 IPC Foam 
 
 The IPC core sandwiches were produced by introducing uncured syntactic foam 
into the aluminum foam core scaffold and allowing the SF to cure in situ.  From the 
results and conclusions from Jhaver [17] which demonstrate IPC foam superiority over 
epoxy-based syntactic foam in compression, it was thought that using IPC as the core 
19 
material in the sandwiches would produce an improved response compared to sandwiches 
with an SF core. 
 
2.2 Specimen Preparation 
 
2.2.1 Mold Preparation 
 
The specimens used in this work were made using castable two-part thermosetting 
polymer.  Given the simplicity of geometry, the specimen was cast into a near net shape 
with minor finish machining, reducing the processing time required for individual 
experiments.  To accomplish this, a specimen blank was machined from a stock 
aluminum block.  A mold cavity was then produced by pouring silicone rubber around 
the blank to create a negative of the specimen.  Specimens were then created by casting 
the material directly into the mold cavity. 
The specific rubber product used for creating the mold was PlatSil? 73 Series 
from PolyTek Development Corporation.  This is a flexible rubber mold material that has 
high tear strength and can be vulcanized at room temperature.  It has low shrinkage, 
resulting in very good dimensional stability.  To create the mold, a cardboard barrier was 
constructed and placed on a glass substrate.  The specimen blank was placed within the 
cardboard barrier and the silicone rubber mixture was poured over the blank and allowed 
to cure for 30 hours.  After curing, the cardboard barrier and the specimen blank were 
removed resulting in a cavity for future specimen castings. 
 
20 
2.2.2 Syntactic Foam Core Specimen Preparation 
 
Epoxy-based syntactic foams with varying volume fractions (20%, 30%, and 
40%) of hollow soda-lime glass microballoons were produced.  For a given test 
specimen, the general preparation sequence was as follows.  First, the desired quantities 
of resin, hardener, and glass particles were measured out.  Next, the resin and hardener 
were mixed slowly until the mixture appeared homogeneous.  Upon achieving visible 
homogeneity, the glass particles were added to the mixture and stirred slowly until the 
mixture was once again homogeneous.  Once the mixture was visibly homogeneous, it 
was then placed into a vacuum chamber.  A vacuum pump was used to bring the chamber 
down to a pressure of approximately -80 kPa (gage).  This pressure was maintained for 
approximately 4-5 minutes and then released, returning the mixture to atmospheric 
pressure.  This process of vacuuming and releasing was repeated in order to bring trapped 
air to the surface (typically 3 times).  This ensured full degassing of the mixture.  After 
the vacuum/release process, air bubbles were skimmed from the top of the mixing 
container.  During degassing, the mixture began to separate slightly into epoxy and glass 
particle constituents.  It was briefly and slowly stirred once more until fully mixed before 
pouring into the mold.  A photograph of the mold is shown in Figure 2.3 along with a 
demolded IPC foam core specimen (to be described later on). 
 
21 
 
Figure 2.3    Silicone Specimen Mold and Demolded Specimen 
 
All castings for this work were allowed to cure at room temperature for 48 hours 
prior to removal from the mold.  Upon completion of curing, the specimens were finish 
machined using a mill.  Machining was done no less than 2 days after initial casting, and 
testing occurred no less than 7 days after the initial casting. 
To produce the Syntactic Foam Sandwich (SFS) specimens, face sheets were 
punched out of a 0.813mm thick sheet of aluminum (AL6061) and machined to precise 
size.  They were sanded on one side with coarse grit sandpaper then cleaned off with 
acetone in order to create a rougher surface for bonding.  Once the core of syntactic foam 
was fully cured and machined, each face sheet was separately adhered to the core using a 
syntactic foam mixture of the same volume fraction.  After curing, the specimen was 
once again machined to remove excess material from the face sheet application process.  
Figure 2.4 shows an example of the SFS sandwich structure.  Though there is some minor 
variation, the nominal specimen size for quasi-static testing was 127mm x 25mm x 20mm 
(5? length x 1? width x 0.8? height).  Each face sheet had a nominal thickness of 
22 
0.813mm, giving a core thickness of ~18.4mm.  The nominal specimen size used for 
dynamic testing was 127mm x 25mm x 18.5mm (5? length x 1? width x 0.73? height).   
 
  
Figure 2.4    Syntactic Foam Core Sandwich Structure (SFS) 
 
2.2.3 IPC Foam Core Specimen Preparation 
 
The open cell aluminum foam sandwich material was used as the IPC scaffold.  
The foam was cut into slightly oversized pieces compared to desired final specimen size.  
The face sheet thickness for all specimens was in an as-received state of 0.813mm ? 
0.05mm (0.032? ? 0.002?).  The aluminum was first cleaned with acetone, then coated 
with silane to act as a wetting agent and to promote adhesion between the aluminum 
scaffold and syntactic foam.  Jhaver [17] explored and confirmed the benefit of the silane 
coating prior to introducing the syntactic foam.  The silane used was A-1100 Amino 
Silane, or ?-aminopropyltriethoxysilane (H2NCH2CH2CH2Si(OCH2CH3)3), obtained from 
GE Silicones.  A 5% silane solution was created (remaining 95% portion of mixture was 
9 parts ethanol to 1 part deionized, filtered water) to coat the sample per the work of 
SF core 
Aluminum 
face sheet 
0.813mm thk 
23 
Sadler and Vecere [18].   The solution was allowed to rest for one hour after mixing 
before being used.  After the coating, the aluminum was allowed to sit and dry for 12 
hours.  The exterior/outside of the face sheets were coated with a releasing agent to easily 
be able to remove excess syntactic foam after curing.  The syntactic foam was prepared in 
the same manner as outlined in Section 2.2.2 and poured into the mold, and the aluminum 
scaffold was gently pushed down into the pool of uncured syntactic foam. 
As before, all castings for this work were allowed to cure at room temperature for 
48 hours prior to removal from the mold.  Upon completion of curing, the specimens 
were finish machined using a mill.  Testing occurred no less than 7 days after the initial 
casting.  A sample of the IPC foam core sandwich structure is shown in Figure 2.5.  Note 
that the regular diagonal marks easily observed on the aluminum are tool marks. 
 
 
Figure 2.5    IPC Foam Core Sandwich Structure 
 
 
 
 
Aluminum foam 
ligaments 
Syntactic foam 
AL6061 
face sheet 
24 
2.2.4 Syntactic Foam Core with Graded Face Sheets Specimen Preparation 
 
 The graded face sheets (see Section 4.3 and Chapter 5) were obtained from the 
same supplier as the aluminum foam core sandwiches.  The face sheets had a ~2 mm 
layer of aluminum foam brazed to the aluminum face sheets on one side.  The face sheets 
were cleaned with acetone, then coated with silane in the method described in the 
previous section.  The exterior/outside of the face sheets were coated with a mold 
releasing agent, then placed into the rubber mold as shown in Figure 2.6.  The syntactic 
foam was prepared, poured into the mold, and allowed to cure in situ.  Figure 2.7 shows 
an image of the syntactic foam core sandwich with graded face sheets (SFS-b).  Note that 
the regular diagonal marks easily observed on the face sheets are tool marks. 
 
 
Figure 2.6    Single Cast SFS-b Mold: (1) Mold, (2) AL6061 Face Sheet, and (3) Brazed 
Aluminum Foam 
 
1 2 3 
25 
  
Figure 2.7    Syntactic Foam Core Sandwich Structure with Graded Face sheets (SFS-b) 
 
2.2.5 Pattern Preparation for Optical Measurement 
 
 In order to perform local displacement and strain measurements, a stochastic 
speckle pattern was created on one side of the specimen.  The side to which the pattern 
was applied was sanded using a fine grit paper and cleaned off using acetone.  Once the 
specimen surface was clean, alternating coats of white and black spray paint were applied 
until a suitable pattern was created (approximately 4 thin coats each).  After applying the 
speckle pattern, the paint was allowed to dry for 24 hours before testing.  Figure 2.8 
shows an image of a specimen with the speckle pattern used for obtaining optical 
measurements.  Approximate speckle size was ~90 ?m.  Note that the larger black 
lines/dots on the specimen are made intentionally for spatial and scaling purposes.   
 
SF core 
AL6061 
face sheet 
Aluminum foam 
} ?graded? region 
26 
 
Figure 2.8    Typical Decorated Random Speckle Pattern for Optical Measurements 
 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
loading point 
x mm 
line of symmetry 
right support 
27 
 
 
 
CHAPTER 3 
FLEXURAL CHARACTERISTICS OF CONSTITUENTS 
 
3.1 Aluminum Foam Sandwich 
 
 Unfilled aluminum foam sandwich beams were tested in quasi-static three-point 
bending (TPB).  Although the basis of the TPB tests was ASTM C393 [19], the specimen 
size guidelines could not be strictly adhered due to material availability and cost.  Instead, 
the test specimens resemble short beams.  Again, the nominal specimen size for all quasi-
static test specimens was 127mm x 25mm x 20mm (5? length x 1? width x 0.8? height). 
An MTS QTest100 (10kN load cell) universal loading machine was used for 
flexural tests.  A cylindrical loading tip of diameter 10 mm was driven downward at a 
velocity of 0.025 in/min (0.635 mm/min) as load-displacement data was collected at a 
sampling rate of 5-10 points per second.  The beams were centrally positioned on roller 
supports, also of diameter 10 mm.  The test arrangement is shown in Figure 3.1.   
 
 
28 
 
Figure 3.1    Photograph of Three-Point Bending Test Setup 
 
In order to collect gray scale data of the speckle pattern for an open-cell foam, the 
pores had to be filled with a material that offers negligible reinforcement.  Common 
expanding insulating foam was used to cover one side (face) of the foam, creating a more 
solid and even surface on which speckles could be painted.  After the foam had time to 
cure, it was sanded down to the surface of the metal foam.  The speckle pattern was then 
applied as detailed in Section 2.2.4.  It was determined through a series of tests that the 
insulating foam would not affect the material behavior because its load bearing or 
reinforcement capacity is negligible. 
CAMERA 
LENS 
LIGHT 
SOURCE 
LIGHT 
SOURCE 
BEAM 
LOADING 
FIXTURE 
CROSSHEAD 
29 
For quasi-static tests, a camera was set up to capture the right half of the 
specimen, between the loading and support rollers.  Due to the symmetry of the beam 
about the loading axis, one half beam images were captured for subsequent deformation 
analysis.  Figure 3.2 illustrates the area captured by the camera. 
 
    
Figure 3.2    Camera Viewing Area 
 
 Since a 2D analysis was performed to determine planar surface displacements, 
only one digital camera was required to capture the specimen deformation during the 
tests.  The camera used for quasi-static testing was a Nikon D100 SLR digital camera 
fitted with a 200mm lens.  Its maximum image capture size is 3008 x 2000 pixels, but for 
this work a spatial resolution of 1504 x 1000 pixels was chosen.  The camera was 
connected to and controlled by a computer using the Nikon Capture software (Version 
4.0).  The camera was set approximately two feet from the specimen, and white light 
illumination sources were placed next to the specimen.  The response of the material was 
expected to be symmetric about the loading roller; therefore the images encompass the 
right half of the beam only, from just outside the loading roller to just outside the support 
roller.  The camera was set to automatically record images once every 2-3 seconds and 
store them on the computer for later analysis.  The arrangement for the quasi-static tests 
is shown below in Figure 3.3. 
30 
 
 
                      
Figure 3.3    Quasi-static Test Experimental Arrangement 
 
The results from the tests on the unfilled aluminum foam core sandwiches are 
shown in Figure 3.4 and summarized in Table 3.1. 
 
0
100
200
300
400
500
600
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Crosshead Displacement (mm)
Lo
ad
 (N
) FLEX-32 (ALS)
FLEX-33 (ALS)
FLEX-34 (ALS)
Material: ALS
Temperature: 70?F
Overlay
**Note that the dotted black 
line is the estimated 
behavior of FLEX-32 and 
not measured data.  The 
solid black line is measured 
data.
 
Figure 3.4    Overlay of Load-Deflection Data for 20ppi Aluminum Foam Core Sandwich 
 
 
controls camera & stores 
images 
digital 
camera 
TPB test 
Illumination 
sources 
31 
 
Table 3.1    Aluminum Foam Sandwich Test Results 
Crosshead
Specimen Speed Plateau Peak
Number Type (in/min) Load (N) Load (N)
32 ALS 0.025 391 395
33 ALS 0.10 342 346
34 ALS 0.10 391 399
NUM OF SAMPLES          3 3
AVERAGE          375 380
STANDARD DEVIATION          28 30  
 
 The unfilled aluminum foam sandwiches behave in a linear fashion at the very 
beginning before the onset of nonlinearity due to core indentation and crushing.  The load 
remains nearly constant throughout the core crushing at the so-called ?plateau load? until 
the core is free of pores and densification begins (not seen in the displacement range 
used).  Figure 3.5 shows a typical stress-strain response for aluminum foam and 
illustrates the plateau and densification regions.  For the case of a TPB test, these 
crushing and densification phenomena are observed below the load roller.  When in the 
plateau region, the aluminum foam has tremendous energy absorption capacity, 
continuing to consume energy with increasing strain (or deflection) at a nearly constant 
load.  The average plateau load for the aluminum foam core sandwich is 375 N ? 28 N. 
 
32 
  
Figure 3.5    Typical Aluminum Foam Stress-Strain Response (courtesy: ERG) 
 
3.2 Syntactic Foam Sandwich 
 
The quasi-static TPB test setup for the syntactic foam core sandwich (identified as 
SFS) specimens is the same as that detailed in Section 3.1.  In order to remove any slack 
from the loading fixtures, a pre-load of ~130 N was applied.  After this pre-load was 
applied, the load was zeroed so that the pre-loaded state is the reference (undeformed) 
state.  With failure on the order of 5,000 N, the pre-load amount considered was 
negligible. 
The measured load-deflection responses from the tests are shown in Figures 3.6 to 
3.8, and the results are summarized in Tables 3.2 to 3.4.  Note that the stair-case pattern 
observed in the test data is attributed to the data acquisition rate and software and not to 
the mechanical response of the sandwich structure.  The different materials with 20%, 
Plateau Region (Core Crushing) Densification Region 
33 
30%, and 40% volume fractions of microballoons in the SF core will henceforth be 
referred to as SFS20, SFS30, and SFS40, respectively.  
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crosshead Displacement (mm)
Lo
ad
 (N
)
FLEX-37 (SFS20)
FLEX-38 (SFS20)
FLEX-45 (SFS20)
FLEX-46 (SFS20)
FLEX-47 (SFS20)
FLEX-48 (SFS20)
Material: SFS20
Temperature: 70?F
Overlay
 
Figure 3.6    Load-Deflection Data for SFS20 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crosshead Displacement (mm)
Lo
ad
 (N
) FLEX-39 (SFS30)
FLEX-40 (SFS30)
FLEX-41 (SFS30)
FLEX-42 (SFS30)
FLEX-43 (SFS30)
FLEX-44 (SFS30)
Material: SFS30
Temperature: 70?F
Overlay
 
Figure 3.7    Load-Deflection Data for SFS30 
34 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crosshead Displacement (mm)
Lo
ad
 (N
) FLEX-23 (SFS40)
FLEX-24 (SFS40)
FLEX-36 (SFS40)
Material: SFS40
Temperature: 70?F
Overlay
 
Figure 3.8    Load-Deflection Data for SFS40 
 
Table 3.2    TPB SFS20 Test Results 
Crosshead
Specimen Speed Energy Specific Energy Peak Deflection
Number Type VF(%) (in/min) Absorbed (J) Absorbed (J/kg) Load (N) at Failure (mm)
37 SFS 20 0.025 4.78 68.5 6626 1.24
38 SFS 20 0.025 2.17 31.4 4997 0.81
45 SFS 20 0.025 5.92 84.3 7098 1.42
46 SFS 20 0.025 6.18 88.4 7155 1.45
47 SFS 20 0.025 1.72 24.9 4422 0.71
48 SFS 20 0.025 7.57 108.6 7568 1.68
NUM OF SAMPLES          6 6 6 6
AVERAGE          4.73 67.7 6311 1.22
STANDARD DEVIATION          2.33 33.2 1289 0.38  
 
Table 3.3    TPB SFS30 Test Results 
Crosshead
Specimen Speed Energy Specific Energy Peak Deflection
Number Type VF(%) (in/min) Absorbed (J) Absorbed (J/kg) Load (N) at Failure (mm)
39 SFS 30 0.025 3.53 57.1 5526 1.24
40 SFS 30 0.025 3.47 55.7 5550 1.17
41 SFS 30 0.025 4.14 65.9 5815 1.37
42 SFS 30 0.025 4.08 64.9 5758 1.27
43 SFS 30 0.025 3.29 52.5 5405 1.14
44 SFS 30 0.025 3.57 57.5 5571 1.22
NUM OF SAMPLES          6 6 6 6
AVERAGE          3.68 58.9 5604 1.24
STANDARD DEVIATION          0.35 5.3 154 0.08  
Debond initiation 
35 
 
Table 3.4    TPB SFS40 Test Results 
Crosshead
Specimen Speed Energy Specific Energy Peak Deflection
Number Type VF(%) (in/min) Absorbed (J) Absorbed (J/kg) Load (N) at Failure (mm)
36 SFS 40 0.025 2.78 48.5 5126 0.97
23 SFS 40 0.025 2.35 40.5 3598 1.24
24 SFS 40 0.025 1.76 30.6 5440 0.76
NUM OF SAMPLES          3 3 3 3
AVERAGE          2.30 39.9 4722 0.99
STANDARD DEVIATION          0.51 9.0 985 0.24  
 
The flexural response of all SFS sandwiches showed a linear elastic behavior 
initially.  Failure in the SFS sandwiches typically manifested in a face-core debond.  
Once this debond occurs, the majority of load is carried by the core causing it to fail soon 
thereafter.  To give a visual of the debond failure, Figure 3.9 shows an image captured 
soon after the debond occurred during a test.  (Analyzed digital images of this specimen 
(FLEX-30, SFS30) are shown in Section 6.4.1.) 
 
 
Figure 3.9    Typical SFS Face-Core Debond 
Face-core debonding 
36 
 
The metrics used to characterize the syntactic foam core sandwiches were the 
measured peak load, the deflection measured at failure, the total strain energy absorbed, 
and the specific strain energy absorbed (which takes into account the weight difference 
associated with the different volume fractions tested).  Both the peak load and deflection 
at failure were normalized by values from the behavior of unfilled aluminum foam 
sandwiches. 
The average value for the peak load decreases with increasing volume fraction.  
The average for SFS20 is 6,311 N, for SFS30 is 5,604 N, and for SFS40 is 4,722 N.  
Ideally, data would be normalized by a sandwich consisting of aluminum face sheets 
separated by an empty core.  Practically, the unfilled 20ppi aluminum foam core 
sandwich was used to normalize the data.  To compare to the behavior of the aluminum 
foam core sandwich, the average load at failure for the SFS sandwich is normalized by 
the plateau load experienced by the aluminum foam core sandwich (390 N).  The average 
normalized load at failure for SFS20 is 16.14, for SFS30 is 14.33, and for SFS40 is 12.08.  
In Figure 3.10 these values are shown as a histogram.  This comparison is not exact.  The 
plateau load for the aluminum foam core sandwich is the load at which the stress remains 
nearly constant while able to withstand a large increase in strain.  It is this load that is 
typically used as the desired design load.  (See Figure 3.5 for a typical stress-strain 
response of this type.)  The SFS sandwiches do not experience a similar near constant 
load, but rather a steady increase (hardening behavior) until failure.  This load at failure, 
when compared to the plateau load, is twelve to sixteen times higher than the design load 
for unfilled aluminum foam core sandwiches.  Both the plateau load for the unfilled 
37 
aluminum foam core and the peak load for the SFS sandwiches can be used as the design 
load, so, while inexact, the comparison is justified.  The SFS sandwiches show superior 
load bearing capacity compared to their unfilled aluminum foam counterpart.  The large 
error seen in the SFS20 and SFS40 samples is caused by specimens that prematurely 
failed to due an especially weak face-core bond, resulting in lowering all reported 
average values.   
 
0
5
10
15
20
25
20% 30% 40%
Volume Fraction
Pe
ak
 Lo
ad
/A
LS
 P
lat
ea
u L
oa
d
SFS
 
Figure 3.10    Normalized Measured Peak Load for Sandwich Structures with SF Foam 
Core with Different Volume Fractions 
 
The average value for the mid-span deflection at failure decreases from SFS30 to 
SFS20 to SFS40, though there is no distinguishable difference in SFS20 and SFS30.  
However, without the two poorly bonded specimens in the SFS20 group that failed 
relatively earlier, the trend would have again decreased with increasing volume fraction.  
38 
The average for SFS20 is 1.22 mm, for SFS30 is 1.24 mm, and for SFS40 is 0.99 mm.  
To compare with the behavior of the aluminum foam core sandwich, the average 
deflection at failure for the SFS sandwich is normalized by the deflection at which the 
unfilled aluminum foam core sandwich behavior deviates from linearity (deflection at 
transition, 0.2mm).  This, again, is not an exact comparison since we do not have a 
deflection at failure for comparison in the unfilled aluminum foam sandwiches.  The 
average normalized deflection at failure for SFS20 is 6.29, for SFS30 is 6.38, and for 
SFS40 is 5.11.  In Figure 3.11 these normalized deflection values are shown as a 
histogram.  Once again, the large error in the SFS20 and SFS40 samples is due to 
specimens that experienced premature failure. 
 
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
20% 30% 40%
Volume Fraction
?F
ail
ur
e/
?A
LS
, n
on
lin
ea
r 
SFS
 
Figure 3.11    Normalized Measured Mid-Span (Load-Point) Deflection at Failure for 
Sandwich Structures with SF Foam Core 
 
39 
Cellular foams are used in packing and automotive applications because of their 
ability to dissipate strain energy.  Using this lightweight sandwich material could 
hopefully offer improved mechanical characteristics while still maintaining a low weight.  
The energy absorbed during flexural experiments by a specimen was calculated using the 
area under the load-deflection curve from the measured data shown in Figures 3.6 to 3.8.  
That is, the area below the load-deflection responses were computed as, 
 
0
( )U P d
?
? ?= ? , 
 
by performing numerical integration (trapezoid method) of the measured data. 
The average values for the strain energy absorbed by different SFS samples are 
plotted in Figure 3.12 as a histogram.  The average for SFS20 is 4.73 J, for SFS30 is 3.68 
J, and for SFS40 is 2.30 J.  Unfilled aluminum foam core sandwiches have a great 
capacity for energy absorption, but the cost is that they are unable to bear very much 
load.  With these SFS sandwiches, an effort was made to understand how much energy 
could be absorbed in a material with good strength bearing abilities. 
 
40 
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
20% 30% 40%
Volume Fraction
En
er
gy
 A
bs
or
be
d (
J)
SFS
  
Figure 3.12    Energy Absorbed for Sandwich Structures with SF Foam Core 
 
In order to make comparisons for varying volume fractions (and thus the 
difference in weight), specific energy (J/kg) was calculated for each specimen.  The 
energy absorbed was divided by the mass of the particular specimen determined by the 
equation, 
 
tot core core faces facesm V V? ?= +  . 
 
The densities for the SF core and aluminum faces are shown in Table 3.5. 
 
 
 
 
41 
 
Table 3.5    Material Densities 
Density
(kg/m3)
SF20 893.0
SF30 797.0
SF40 701.0
Al 6061 (face) 2700.0
Material
 
 
Once again we see the trend of the average value for the specific energy absorbed 
decreasing with increasing volume fraction.  The average for SFS20 is 67.7 J/kg, for 
SFS30 is 58.9 J/kg, and for SFS40 is 39.9 J/kg.  Figure 3.13 shows these values as a 
histogram.  Most likely it is specific energy that applications involving typical 
lightweight sandwich structures should use as a primary design metric.   
 
0
20
40
60
80
100
120
20% 30% 40%
Volume Fraction
Sp
ec
ifi
c E
ne
rg
y A
bs
or
be
d (
J/k
g)
SFS
 
Figure 3.13    Specific Energy Absorbed for Sandwich Structures with SF Foam Core 
42 
 
 As stated earlier, the SFS sandwich failures manifested in face-core debonding.  
Figure 3.14 gives a visual of a failed SFS sandwich.  Note the lack of any residual SF 
remaining on the interior portions of the face sheets in image (b), highlighting the poor 
bond strength and ease of separation between the core and face. 
 
  
(a)      (b) 
Figure 3.14    (a) Failed Syntactic Foam Core Sandwich with (b) Highlighted Face-core 
Debond 
 
The overall behavior of SFS sandwich structure is essentially linear elastic almost 
until failure.  The response of a typical specimen at each volume fraction was compared 
to the theoretical calculations from Section 1.5.1 [16].  The load histories are used to 
calculate the theoretical displacements using geometric and elastic parameters.  To 
theoretically calculate linear elastic mid-span displacements, the quasi-static elastic 
properties used for the SF material measured by Jhaver [17] under compression were 
derived from the stress-strain responses shown in Figure 3.15.  The values are shown in 
Table 3.6.    (This was an approximation made deliberately even though sandwich beams 
experience both compressive and tensile stresses, and tensile stress-strain responses could 
43 
be different from the compression responses.)  There is good agreement between the 
theoretical and experimental mid-span displacements for all volume fractions, seen in the 
comparisons shown in Figure 3.16 to 3.18.  Finally, Figure 3.19 shows a load-
displacement overlay of the three specimens used as examples, with each containing a 
different volume fraction of SF in the core. 
 
 
Figure 3.15    Compressive Response of Syntactic Foam [17] 
 
Table 3.6    Syntactic Foam Quasi-Static Elastic Properties [17] 
Elastic Modulus
(MPa)
SF20 1595
SF30 1448
SF40 1261
Material
 
 
44 
0
1000
2000
3000
4000
5000
6000
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Displacement (mm)
Lo
ad
 (N
)
Crosshead
Elastic
Prediction
Material: SFS20
Temperature: 70?F
Specimen: FLEX-38
Cast: 12Jul2010
Test: 14Sept2010
Rate: 0.025 in/min
 
Figure 3.16    Predicted vs. Experimental Mid-Span Deflection, SFS20 
 
0
1000
2000
3000
4000
5000
6000
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Displacement (mm)
Lo
ad
 (N
)
Crosshead
Elastic
Prediction
Material: SFS30
Temperature: 70?F
Specimen: FLEX-39
Cast: 04Oct2010
Test: 26Oct2010
Rate: 0.025 in/min
 
Figure 3.17    Predicted vs. Experimental Mid-Span Deflection, SFS30 
 
45 
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Displacement (mm)
Lo
ad
 (N
)
Crosshead
Elastic
Prediction
Material: SFS40
Temperature: 70?F
Specimen: FLEX-24
Cast: 18May2010
Test: 15Jul2010
Rate: 0.025 in/min
 
Figure 3.18    Predicted vs. Experimental Mid-Span Deflection, SFS40 
 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crosshead Displacement (mm)
Lo
ad
 (N
)
20%
FLEX-38 (SFS20)
30%
FLEX-39 (SFS30)
40%
FLEX-24 (SFS40)
Material: SFS
Temperature: 70?F
Overlay
 
Figure 3.19    Overlay of Measured Load-Displacement of Sandwich Structures with 
Syntactic Foam Core and Different Volume Fraction of Microballoons in the SF 
 
SFS20 
SFS30 
SFS40 
46 
3.3 Summary 
 
 It is difficult to speak much to the flexural characteristics of the syntactic foam 
core sandwiches.  Failure in the SFS sandwiches typically manifested in face-core 
debonding, shown in Figure 3.20 where part of the top face has separated from the core.  
The separation is clean, with no SF residue on the debonded portion of the face sheet. 
 
 
 
Figure 3.20    Face-Core Debond 
 
Once this debond occurs, the majority of load is transferred to the core causing it 
to fail soon thereafter.  The idea of the sandwich structure is for both the core and faces to 
contribute to the overall behavior.  After the debond, the material no longer acted as a 
lightweight sandwich composite, but rather a syntactic foam beam with aluminum plates 
on either side.  This suggests that overcoming the shear stress jump at the face-core 
interface could prevent face-core debonding.  Perhaps the addition of a metal foam matrix 
to the core would serve to prevent debonding as well as improve the deflections (and thus 
strains) experienced through the synergistic nature of an IPC foam core.  This would also 
47 
serve to increase the energy absorbing capacity.  The metal ligaments could serve as a 
bridging agent, keeping the integrity of the sandwich structure longer. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
48 
 
 
 
CHAPTER 4 
FLEXURAL CHARACTERISTICS OF IPC FOAM CORE  
SANDWICH STRUCTURES 
 
4.1 Experimental Setup 
 
The next step was to characterize sandwich structures with aluminum-syntactic 
foam interpenetrating core architecture.  It was thought that the introduction of the 
metallic foam scaffold into the core would improve the flexural response synergistically, 
retaining the strength of the syntactic foam and gaining ductility from the aluminum 
foam.  The experimental characterization of these structures in bending are carried out 
using the same setup described for the SFS sandwiches in Chapter 3.  In this case, the 
sandwich scaffold was an unfilled aluminum foam sandwich into which uncured 
syntactic foam was introduced and allowed to cure in situ.  An image of an IPC foam 
core sandwich structure is shown in Figure 4.1. 
 
49 
 
Figure 4.1    IPC Foam Core Sandwich Structure 
 
4.2 Quasi-Static Tests 
 
The load-deflection responses measured for aluminum-syntactic foam 
interpenetrating core sandwich (identified as IPC) structures are shown in Figures 4.2 to 
4.4, and the results compiled from these tests are summarized in Tables 4.1 to 4.3.  The 
different materials with 20%, 30%, and 40% volume fractions of microballoons in the 
IPC core will henceforth be referred to as IPC20, IPC30, and IPC40, respectively.  
 
Aluminum foam 
ligaments 
Syntactic foam 
AL6061 
face sheet 
50 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crosshead Displacement (mm)
Lo
ad
 (N
) FLEX-9 (IPC20)
FLEX-10 (IPC20)
FLEX-11 (IPC20)
Material: IPC20
Temperature: 70?F
Overlay
 
Figure 4.2    Overlay of Measured Load-Deflection Data for Three Different IPC Core 
Sandwich Beams (IPC20) 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crosshead Displacement (mm)
Lo
ad
 (N
) FLEX-12 (IPC30)
FLEX-13 (IPC30)
FLEX-16 (IPC30)
Material: IPC30
Temperature: 70?F
Overlay
 
Figure 4.3    Overlay of Measured Load-Deflection Data for Three Different IPC Core 
Sandwich Beams (IPC30) 
51 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crosshead Displacement (mm)
Lo
ad
 (N
) FLEX-14 (IPC40)
FLEX-15 (IPC40)
Material: IPC40
Temperature: 70?F
Overlay
 
Figure 4.4    Overlay of Measured Load-Deflection Data for Two Different IPC Core 
Sandwich Beams (IPC40) 
 
Table 4.1    TPB IPC20 Test Results 
Crosshead
Specimen Speed Energy Specific Energy Peak Deflection Transition Transition
Number Type VF(%) (in/min) Absorbed (J) Absorbed (J/kg) Load (N) at Failure (mm) Load (N) Deflection (mm)
9 IPC 20 0.025 7.34 83.3 5366 1.96 1744 0.30
10 IPC 20 0.025 6.34 80.7 4950 1.83 1472 0.28
11 IPC 20 0.025 7.76 89.7 5880 2.08 1846 0.28
NUM OF SAMPLES          3 3 3 3 3 3
AVERAGE          7.15 84.6 5399 1.96 1687 0.29
STANDARD DEVIATION          0.73 4.6 466 0.13 193 0.01  
 
Table 4.2    TPB IPC30 Test Results 
Crosshead
Specimen Speed Energy Specific Energy Peak Deflection Transition Transition
Number Type VF(%) (in/min) Absorbed (J) Absorbed (J/kg) Load (N) at Failure (mm) Load (N) Deflection (mm)
12 IPC 30 0.025 7.46 87.9 5850 1.98 1922 0.30
13 IPC 30 0.025 7.71 93.4 5205 2.18 1557 0.28
16 IPC 30 0.025 8.49 98.9 5682 2.24 1726 0.30
NUM OF SAMPLES          3 3 3 3 3 3
AVERAGE          7.89 93.4 5579 2.13 1735 0.30
STANDARD DEVIATION          0.54 5.5 334 0.13 183 0.01  
 
52 
Table 4.3    TPB IPC40 Test Results 
Crosshead
Specimen Speed Energy Specific Energy Peak Deflection Transition Transition
Number Type VF(%) (in/min) Absorbed (J) Absorbed (J/kg) Load (N) at Failure (mm) Load (N) Deflection (mm)
14 IPC 40 0.025 5.94 89.6 4445 1.91 1521 0.30
15 IPC 40 0.025 5.11 71.3 4128 1.60 1757 0.25
17 IPC 40 0.025 3.67 64.3 4360 1.70 3861* 1.24*
NUM OF SAMPLES          3 3 3 3 2 2
AVERAGE          4.91 75.1 4311 1.74 1639 0.28
STANDARD DEVIATION          1.15 13.1 164 0.16 167 0.04
*Due to loading/reloading during testing, values may not be indicative of true material behavior  
 
In the case of the SFS sandwiches, the load-deflection behavior was essentially 
linear elastic in nature (see Chapter 3).  However, for the IPC sandwiches it shows 
pronounced nonlinearity.  There is a kink or a ?knee? in each plot beyond which 
noticeable nonlinearity prevails up to failure.  This ?knee? will be referred to as the 
?transition point? in the subsequent discussion.  To define the transition point for 
analysis, a line was fit approximately through the data before the transition and another 
was fit through the data after transition.  The point where these two fitted lines intersect is 
identified as the transition point.  Both the load and deflection at the transition point were 
recorded from the graphs.  The aluminum foam core sandwiches exhibit a similar trend of 
transition from linear to nonlinear behavior.  However, unlike with the aluminum foam 
core (which has a similar value for the transition deflection), the IPC sandwiches are able 
to support additional load while continuing to deform.  For design purposes, this 
transition point can be treated similar to a yield point.  At transition, certain parts of the 
structure are undergoing plastic deformation that can never be recovered. 
The plots and pictures shown below in Figures 4.5 to 4.9 illustrate the progression 
of the test at important points of interest.  The first photo is the undeformed specimen 
used as a reference image for the particular test.  The second photo is at point A (in the 
plot in Figure 4.5), the transition point, where the behavior deviates from its initial linear 
53 
elastic response.  The third photo is when a visible crack first appears in the core.  There 
is a short time after the initial crack that the specimen still has the ability to bear some 
reduced amount of load.  The fourth photo is at the very end of the test when no load 
bearing capacity remains in the sample.  It should be noted that although no load bearing 
capacity remains, the structure itself is still mostly intact.  This is unlike the SFS 
sandwiches which tended to fail catastrophically.  (Analyzed images of this specimen 
(FLEX-10, IPC20) are shown in Section 6.4.2.) 
 
 
0
1000
2000
3000
4000
5000
6000
0.0 0.5 1.0 1.5 2.0 2.5
Displacement (mm)
Lo
ad
 (N
)
Crosshead
Material: IPC20
Temperature: 70?F
Specimen: FLEX-10
Cast: 30Sept2009
Test: 21Apr2010
Rate: 0.025 in/min
 
Figure 4.5    Typical IPC Load-Deflection Curve: Point A ? Transition Point, Point B ? 
Crack Formation, Point C ? Loss of Load Bearing Capacity 
 
A 
B 
C 
54 
 
Figure 4.6    Undeformed, P=0 N 
 
 
Figure 4.7    Point A: Transition Point, P=1165 N 
 
55 
 
Figure 4.8    Point B: Crack Formation, P=3905 N 
 
 
Figure 4.9    Point C: Loss of Load Bearing Capacity, P=1590 N 
 
56 
The same metrics used to characterize the SFS sandwiches were used for IPC 
sandwiches (measured peak load, deflection measured at failure, total strain energy 
absorbed, and specific strain energy absorbed).  In addition, two measured values at the 
transition point (load and deflection) were used for the IPC sandwiches to identify the 
nonlinear behavior.  Both the load and deflection measurements were normalized by 
values from the behavior of unfilled aluminum foam sandwiches. 
The average value for the peak load is the highest for IPC30, with the ones for 
IPC20 and IPC40 being successively lower.  The average load at failure for IPC20 is 
5,399 N, for IPC30 is 5,579 N, and for IPC40 is 4,311 N.  To compare to the behavior of 
the unfilled aluminum foam core sandwich, the average load at failure for the IPC core 
sandwich is normalized by the plateau load experienced by the aluminum foam core 
sandwich (390 N).  The average normalized load at failure for IPC20 is 13.81, for IPC30 
is 14.27, and for IPC40 is 11.03.  In Figure 4.10 these values are shown as a histogram.   
The plateau load for the aluminum foam core sandwich is the load at which the stress 
remains nearly constant while able to withstand a large increase in strain.  It is this load 
that is typically used as the desired design load.  (See Figure 3.5 for a typical stress-strain 
response of this type.)  The IPC sandwiches do not experience a similar near constant 
load, but rather a steady increase (hardening behavior) until failure.  This load at failure, 
when compared to the plateau load, is eleven to fourteen times higher than the design 
load for unfilled aluminum foam core sandwiches.  The IPC sandwiches show superior 
load bearing capacity compared to their unfilled aluminum foam counterpart. 
 
57 
0
2
4
6
8
10
12
14
16
20% 30% 40%
Volume Fraction
Pe
ak
 Lo
ad
/A
LS
 P
lat
ea
u L
oa
d
IPC
 
Figure 4.10    Normalized Measured Peak Load for Sandwich Structures with IPC Foam 
Core 
 
The average value for the mid-span deflection at failure exhibits the same trend 
seen for the peak load in the case of the IPC sandwiches, decreasing from IPC30 to 
IPC20 to IPC40.  The average for IPC20 is 1.96 mm, for IPC30 is 2.13 mm, and for 
IPC40 is 1.74 mm.  To compare to the behavior of the aluminum foam core sandwich, the 
average deflection at failure for the IPC sandwich is normalized by the deflection at 
which the unfilled aluminum foam core sandwich behavior deviates from linearity 
(deflection at transition).  This, again, is not an exact comparison since we do not have a 
deflection at failure for comparison in the unfilled aluminum foam sandwiches.  The 
average normalized deflection at failure for IPC20 is 10.09, for IPC30 is 11.01, and for 
IPC40 is 8.96.  In Figure 4.11 these values are shown as a histogram. 
 
58 
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
20% 30% 40%
Volume Fraction
?F
ail
ur
e/
?A
LS
, n
on
lin
ea
r 
IPC
 
Figure 4.11    Normalized Measured Mid-Span (Load-Point) Deflection at Failure for 
Sandwich Structures with IPC Foam Core 
 
The average value for the load at the transition point for IPC20 is 1,687 N, for 
IPC30 is 1,735 N, and for IPC40 is 1,639 N.  As with the peak load, to compare to the 
behavior of the aluminum foam core sandwich, the average transition load for the IPC 
core sandwich is normalized by the plateau load experienced by the aluminum foam core 
sandwich.  The average normalized transition load for IPC20 is 4.32, for IPC30 is 4.44, 
and for IPC40 is 4.19.  In Figure 4.12 these values are shown as a histogram.  This is the 
best comparison that can be made between IPC foam and aluminum foam core 
sandwiches, as both have a transition point.  With the IPC foam core sandwich having a 
transition load of around 4 times greater than unfilled aluminum foam sandwiches and a 
similar transition deflection, the point at which plasticity begins to set in for the IPC 
sandwiches is greatly improved.  Also, this observation makes intuitive sense.  The IPC 
59 
core sandwiches experienced a transition load four times higher than aluminum foam 
sandwiches with a comparable transition deflection, implying that IPC foam core 
sandwiches are stiffer than unfilled aluminum foam core sandwiches, which is known to 
be true.  Evidently, there is no distinguishable difference in the transition load values 
within the experimental scatter, although IPC30 specimens show a slightly higher value 
relative to the two others.  This suggests that microcrack formation in the tensile region 
of the core is likely responsible for the early transition point in IPC foam core 
sandwiches.   
 
0
1
2
3
4
5
6
20% 30% 40%
Volume Fraction
Tr
an
sit
ion
 Lo
ad
/A
LS
 P
lat
ea
u L
oa
d
IPC
 
Figure 4.12    Normalized Measured Load at Transition Point for Sandwich Structures 
with IPC Foam Core 
 
The average for mid-span deflection at the transition point for IPC20 is 0.29 mm, 
for IPC30 is 0.30 mm, and for IPC40 is 0.28 mm.  To compare with the behavior of the 
60 
aluminum foam core sandwich, the average transition deflection for the IPC core 
sandwich is normalized by the deflection at which the aluminum foam core sandwich 
behavior deviates from linearity (0.2mm).  The average normalized transition deflection 
for IPC20 is 1.49, for IPC30 is 1.53, and for IPC40 is 1.44.  In Figure 4.13 these values 
are shown as a histogram.  As in the transition load plots, these are essentially the same 
for all volume fractions of the SF in the IPC core, showing a ~50% improvement over 
aluminum foam core sandwiches.  With the increased load bearing capacity, higher 
transition load, and a small improvement in transition deflection, the IPC foam core 
sandwiches are not only similarly stiff, but much stronger than the unfilled aluminum 
foam sandwich counterpart. 
 
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
20% 30% 40%
Volume Fraction
?T
ra
ns
itio
n/
?A
LS
, n
on
lin
ea
r
IPC
 
Figure 4.13    Normalized Measured Mid-Span (Load-Point) Deflection at Transition 
Point for Sandwich Structures with IPC Foam Core 
 
61 
Briefly comparing the IPC foam core sandwiches to the SFS sandwiches, the IPC 
seems to be the better core material.  The normalized peak load showed a small reduction 
of 14.5% for IPC20, 0.4% for IPC30, and 8.7% for IPC40.  The deflection at failure, 
though, showed a pronounced increase.  The normalized deflection at failure showed an 
improvement of 60.4% for IPC20, 72.6% for IPC30, and 75.2% for IPC40. 
As before, the strain energy (U) absorbed by a specimen was calculated using the 
area under the load-deflection curve from the measured data.  That is, 
 
0
( )U P d
?
? ?= ? . 
 
The average values for the strain energy absorbed are plotted in Figure 4.14 as 
histograms.  The average for IPC20 is 7.15 J, for IPC30 is 7.89 J, and for IPC40 is 4.91 J. 
 
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
20% 30% 40%
Volume Fraction
En
er
gy
 A
bs
or
be
d (
J)
IPC
  
Figure 4.14    Energy Absorbed for Sandwich Structures with IPC Foam Core 
62 
 
In order to make comparisons for varying volume fractions, specific energy (J/kg) 
was calculated for each specimen.  The strain energy absorbed was divided by the mass 
of the particular specimen.  The mass was determined by 
 
tot core core faces facesm V V? ?= + . 
  
The density for the IPC core was determined using a 93% syntactic foam / 7% 
aluminum foam composition.  The density of the IPC foam core for a particular volume 
fraction of syntactic foam therefore was 
 
61010.93 0.07IPC SF Al? ? ?= + . 
 
The densities for the IPC core are shown in Table 4.4.  (Refer back to Table 3.5 
for densities for the SF core and faces.)   
 
Table 4.4    IPC Material Densities 
Density
(kg/m3)
IPC20 1019.5
IPC30 930.2
IPC40 840.9
Material
 
 
The results for specific strain energy are shown in Figure 4.15.  Again the same 
trend is observed in the IPC sandwiches when comparing specific energy absorption.  
63 
The average value for the specific energy absorbed is highest for the 30% volume 
fraction.  The IPC20 and IPC40 material values are both less than the IPC30, indicating 
an optimum value for the IPC core somewhere around 30% volume fraction of 
microballoons in SF.  The average for IPC20 is 84.6 J/kg, for IPC30 is 93.4 J/kg, and for 
IPC40 is 75.1 J/kg.  Comparing the specific strain energies of IPC foam and syntactic 
foam core sandwiches (which accounts for the weight difference in adding the aluminum 
foam in the core), IPC20 had a 25% improvement over its syntactic foam core 
counterpart, IPC30 had a 59% improvement, and IPC40 had an 88% improvement.  With 
IPC foam core outperforming syntactic foam core for all volume fractions, it can be 
concluded that IPC foam core sandwiches are superior to a similar configuration with 
syntactic foam core in their energy absorbing capabilities. 
 
0
20
40
60
80
100
120
20% 30% 40%
Volume Fraction
Sp
ec
ific
 E
ne
rg
y A
bs
or
be
d (
J/k
g)
IPC
 
Figure 4.15    Specific Energy Absorbed for Sandwich Structures with IPC Foam Core 
 
64 
Failure observed in IPC core sandwich structures typically manifested in tensile 
failure of the core and lower face sheet.  The failure would begin with a crack in the core 
in the tensile region.  The bottom aluminum face would then yield in the area below the 
loading roller.  This would lead to a core to face debond in the yielded area, and finally a 
crack propagating from the debond area upwards towards the compression zone of the 
core.  Due to the spontaneous nature of failure initiation, it could not be confirmed in 
static tests if a local face-core debonding preceded and contributed to the core crack 
initiation or vice versa.  However, from observing damaged specimens and from impact 
tests (see Section 6.5), it is believed that core crack initiation in the tensile region was 
likely the first event leading to failure.  Figure 4.16 shows images of a failed IPC foam 
core sandwich.  Note that the bottom face sheet has undergone yielding underneath the 
location of the loading roller.  The whole structure remains intact more than those with 
other core types because of the metallic ligaments acting as bridging agents.  Figure 4.17 
shows some magnified images of the crack.  In image (a), slight face-core and interphase 
separation are observed as well as a slight crack in the face moving outward from the 
core interface.  In image (b) an aluminum ligament has yielded and failed in the tensile 
zone.  Image (c) shows some of the aluminum ligaments that have separated from the SF, 
but serve as bridging agents, holding the structure together. 
 
  
(a)      (b) 
Figure 4.16    (a) Failed IPC Foam Core Sandwich with (b) Yielded Bottom Face 
65 
 
   
(a)    (b)    (c) 
Figure 4.17    Magnified Images of Crack Surfaces Near the Lower Face Sheet 
 
The behavior of IPC core sandwich structure resembles a bilinear response.  At 
the transition point, the behavior deviates from the initial linear elastic region to the 
nonlinear portion.  The response of a typical specimen at each volume fraction is 
compared to the theoretical mid-span displacement calculation from Section 1.5.1 [16].  
The load histories are used to calculate the theoretical displacements, along with 
geometric and elastic parameters.  To theoretically calculate linear elastic mid-span 
displacements, the quasi-static elastic properties used for the IPC material measured by 
Jhaver [17] under compression were derived from the stress-strain responses shown in 
Figure 4.18.  The values are shown in Table 4.5.  These comparisons of predicted elastic 
behavior and experimental mid-span deflection are shown in Figure 4.19 to 4.21. 
 
66 
  
Figure 4.18    Compressive Response of IPC [17] 
 
Table 4.5    IPC Quasi-Static Elastic Properties [17]  
Elastic Modulus
(MPa)
IPC20 2123
IPC30 1852
IPC40 1702
Material
 
 
0
1000
2000
3000
4000
5000
6000
0.0 0.5 1.0 1.5 2.0 2.5
Displacement (mm)
Lo
ad
 (N
)
Measured
Elastic
Prediction
Material: IPC20
Temperature: 70?F
Specimen: FLEX-10
Cast: 30Sept2009
Test: 21Apr2010
Rate: 0.025 in/min
 
Figure 4.19    Predicted vs. Experimental Mid-Span Deflection, IPC20 
67 
 
0
1000
2000
3000
4000
5000
6000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Displacement (mm)
Lo
ad
 (N
)
Measured
Elastic
Prediction
Material: IPC30
Temperature: 70?F
Specimen: FLEX-16
Cast: 15Apr2010
Test: 09Jun2010
Rate: 0.025 in/min
 
Figure 4.20    Predicted vs. Experimental Mid-Span Deflection, IPC30 
 
0
1000
2000
3000
4000
5000
0.0 0.5 1.0 1.5 2.0 2.5
Displacement (mm)
Lo
ad
 (N
)
Measured
Elastic
Prediction
Material: IPC40
Temperature: 70?F
Specimen: FLEX-14
Cast: 07Oct2009
Test: 21Apr2010
Rate: 0.025 in/min
 
Figure 4.21    Predicted vs. Experimental Mid-Span Deflection, IPC40 
 
68 
 The theoretical and experimental values deviate from each other very early on for 
all volume fractions of microballoons in the SF.  The predictions exhibit greater stiffness 
than measurements.  Note that since the theoretical response is only for the linear elastic 
case, the response after the transition point cannot be compared.  Furthermore, the 
deviations in the elastic region are possibly due to the fact that the elastic modulus for 
IPC foam core is assumed to be the same in tension as in compression.  The elastic 
stiffness of IPC foam under tension is likely lower than the compression counterpart due 
to relatively weak bonding between aluminum ligaments and the SF foam.  Furthermore, 
the lower stiffness of the structure from early on in the loading history suggests that SF 
and aluminum ligaments debond in the tensile region quite early on, causing the 
nonlinear behavior.  Yet, the global integrity of the core continues until much later on in 
the loading history.  Figure 4.22 shows a load-displacement overlay of the three 
specimens used as examples, with each containing a different volume fraction (Vf) of 
microballoons in the SF.  The transition point is virtually the same for all three cases.  
After the transition, nonlinear behavior is similar across the three different cases, with the 
30% Vf having both the greatest energy and specific energy absorbtion capacity.  The 
transition point can be considered comparable to a yield point, beyond which 
irrecoverable plastic deformation occurs. 
 
69 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crosshead Displacement (mm)
Lo
ad
 (N
)
20%
FLEX-10 (IPC20)
30%
FLEX-16 (IPC30)
40%
FLEX-14 (IPC40)
Material: IPC
Temperature: 70?F
Overlay
 
Figure 4.22    Overlay of Measured Load-Displacement of Sandwich Structures with IPC 
Foam Core with Different Vf of Microballoons in the SF 
 
4.3 Summary 
 
 While the IPC foam core sandwiches experienced slightly lower load levels than 
their syntactic foam core counterparts (comparisons are discussed in Chapter 7), the 
deflection at failure was greatly improved, thus improving the overall strain energy 
absorption.  There was also the new addition of plastic nonlinear behavior in the IPC core 
sandwiches that was not seen in the SFS sandwiches.  Also of note is that these sandwich 
beams did not fail abruptly, but rather developed a core crack and face sheet yielding.  
The aluminum foam ligaments acted as bridges holding the SF and hence the sandwich 
together, even when it could no longer take any significant load.  This could be important 
from an overall structural aspect, as one would not want a structure to catastrophically 
IPC30 
IPC40 
IPC20 
70 
fail after, say, being struck by a projectile or flying debris.  It would be better to have a 
weakened area on an intact structure than to have a catastrophic rupture in that structure. 
Considering that part of the reason for IPC core sandwich failure resides in the 
IPC itself and that the sandwiches with SF core typically failed due to face-core 
debonding, it was considered that if we were somehow able to improve the face-core 
bonding while using syntactic foam in the core, a superior material might emerge.  Using 
syntactic foam in the core rather than IPC would prevent the interphase separation that 
acts as microcracks.  This interphase separation in the tensile region is illustrated in 
Figure 4.23. 
 
   
(a)      (b) 
Figure 4.23    Illustration of IPC (a) Before and (b) After Interphase Separation between 
Syntactic Foam and Aluminum Ligaments 
 
In order to achieve this improved bonding, similar aluminum face sheets were 
used with one important difference: each face sheet had ~2mm of brazed aluminum foam 
on one side.  This narrow (thin) layer of aluminum foam would act as an extremely 
roughed surface for bonding, acting like little fingers gripping the core and hopefully 
SF Alum foam Interphase debond 
71 
preventing a premature face-core shear failure allowing the SF to perform its role of 
keeping the two faces apart for effective flexural performance.  This new type of face 
sheet is referred to as a ?graded? face sheet and will be discussed in the next chapter. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
72 
 
 
 
CHAPTER 5 
FLEXURAL CHARACTERISTICS OF SYNTACTIC FOAM CORE  
SANDWICH STRUCTURES WITH GRADED FACE SHEETS 
 
5.1 Experimental Setup 
 
This part of the research explored sandwich structures with SF foam core and 
graded (or tailored) face sheets.  Experimental characterization in bending was carried 
out using the same setup described for structures with syntactic foam core and IPC foam 
core in Chapter 3 and 4, respectively. 
The 0.813mm thick face sheets had a ~2 mm layer of brazed aluminum foam on 
one side to act as a ?roughened face? that would more readily dig into the SF core to 
transfer the load throughout the specimen.  This new type of face sheet would also 
hopefully prevent the face-core debond that caused premature failure seen in the earlier 
syntactic foam core sandwiches.  Additionally, there would not be a great amount of 
metallic foam, as the failure mechanisms in the IPC foam core stemmed from the 
interphase separation between the SF and aluminum ligaments.  Figure 5.1 shows an 
image of the syntactic foam core sandwich with graded face sheets (identified as SFS-b 
hereafter).  Note that the regular diagonal marks easily observed on the face sheets are 
tool marks. 
73 
 
  
Figure 5.1    Syntactic Foam Core Sandwich Structure with Graded Face Sheets (SFS-b) 
 
5.2 Quasi-Static Tests 
 
Flexural tests similar to those described in the previous chapters were carried out 
for syntactic foam core sandwiches with graded face sheets and load-deflection responses 
were measured.  The tests were aimed towards investigating how a tailored or graded 
face sheet could prevent premature shear separation between the face and the core.  The 
load-deflection responses for SFS-b sandwiches are shown in Figures 5.2 to 5.4, and the 
results compiled from these tests are summarized in Tables 5.1 to 5.3.  The different 
materials with graded face sheets and 20%, 30%, and 40% volume fractions (Vf) of 
microballoons in the SF core will henceforth be referred to as SFSb20, SFSb30, and 
SFSb40, respectively.  The ?b? is simply a labeling convenience, with no greater 
significance.  The first type of syntactic foam sandwich face sheet (sanded)/SF core 
combination is identified simply as ?SFS?, and the second type of face sheet (graded)/SF 
core combination is identifed as ?SFS-b?.   
SF core 
AL6061 
face sheet 
Aluminum foam 
0.813mm 
~2mm 
74 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crosshead Displacement (mm)
Lo
ad
 (N
)
FLEX-57
(SFSb20)
FLEX-58
(SFSb20)
FLEX-61
(SFSb20)
Material: SFSb20
Temperature: 70?F
Overlay
 
Figure 5.2    Overlay of Measured Load-Deflection Data for Three Different SF Core 
Sandwich Beams with Graded Face Sheets (SFSb20) 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crosshead Displacement (mm)
Lo
ad
 (N
)
FLEX-55
(SFSb30)
FLEX-56
(SFSb30)
FLEX-59
(SFSb30)
FLEX-60
(SFSb30)
Material: SFSb30
Temperature: 70?F
Overlay
 
Figure 5.3    Overlay of Measured Load-Deflection Data for Four Different SF Core 
Sandwich Beams with Graded Face Sheets (SFSb30) 
75 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crosshead Displacement (mm)
Lo
ad
 (N
)
FLEX-63
(SFSb40)
FLEX-64
(SFSb40)
FLEX-65
(SFSb40)
FLEX-66
(SFSb40)
Material: SFSb40
Temperature: 70?F
Overlay
 
Figure 5.4    Overlay of Measured Load-Deflection Data for Four Different SF Core 
Sandwich Beams with Graded Face Sheets (SFSb40) 
 
Table 5.1    TPB SFSb20 Test Results 
Crosshead
Specimen Speed Energy Specific Energy Peak Deflection Transition Transition
Number Type VF(%) (in/min) Absorbed (J) Absorbed (J/kg) Load (N) at Failure (mm) Load (N) Deflection (mm)
57 SFSb 20 0.025 11.59 145.4 8173 2.18 5876 0.95
58 SFSb 20 0.025 11.57 144.7 8156 2.16 5551 0.85
61 SFSb 20 0.025 11.47 143.1 8027 2.18 5960 0.98
NUM OF SAMPLES          3 3 3 3 3 3
AVERAGE          11.54 144.4 8119 2.18 5796 0.93
STANDARD DEVIATION          0.06 1.2 80 0.01 216 0.07  
 
Table 5.2    TPB SFSb30 Test Results 
Crosshead
Specimen Speed Energy Specific Energy Peak Deflection Transition Transition
Number Type VF(%) (in/min) Absorbed (J) Absorbed (J/kg) Load (N) at Failure (mm) Load (N) Deflection (mm)
55 SFSb 30 0.025 11.16 152.5 7581 2.21 5885 0.98
56 SFSb 30 0.025 11.85 160.8 7469 2.41 5618 1.03
59 SFSb 30 0.025 12.21 167.6 7570 2.39 5738 0.98
60 SFSb 30 0.025 12.81 175.2 7505 2.49 5658 0.98
NUM OF SAMPLES          4 4 4 4 4 4
AVERAGE          12.01 164.0 7531 2.37 5725 0.99
STANDARD DEVIATION          0.69 9.7 54 0.12 118 0.03  
76 
 
Table 5.3    TPB SFSb40 Test Results 
Crosshead
Specimen Speed Energy Specific Energy Peak Deflection Transition Transition
Number Type VF(%) (in/min) Absorbed (J) Absorbed (J/kg) Load (N) at Failure (mm) Load (N) Deflection (mm)
63 SFSb 40 0.025 10.57 157.3 6916 2.26 5137 0.89
64 SFSb 40 0.025 11.22 168.4 6328 2.44 4964 0.91
65 SFSb 40 0.025 11.04 166.4 6738 2.36 5222 0.91
66 SFSb 40 0.025 10.76 163.2 6479 2.34 5035 0.91
NUM OF SAMPLES          4 4 4 4 4 4
AVERAGE          10.90 163.8 6615 2.35 5090 0.91
STANDARD DEVIATION          0.29 4.8 263 0.07 113 0.01  
 
In the case of the SFS sandwiches, the load-deflection behavior was essentially 
linear elastic in nature (see Chapter 3) with face-core debonding leading to premature 
ultimate failure.  Moreover there was also substantial scatter in peak load and deflection 
at failure.  However, the SFS-b sandwiches clearly do not show any face-core debonding, 
primarily attributed to the graded/tailored faces penetrating the core over a small spatial 
distance adjacent to the face sheet, muting the intensity of shear stresses.  This allows the 
sandwich structure in general and the SF core in particular to contribute to the overall 
integrity.  These can be observed by the nonlinear load-deflection responses in Figures 
5.2 to 5.4.  Similar to the case with IPC core sandwiches, there is a kink or a ?knee? in 
each plot (the transition point) beyond which noticeable nonlinearity prevails up to 
ultimate failure.  To find the transition point, a line was fit through the data before 
transition and another was fit through the data after transition.  The point where these two 
fitted lines intersect is identified as the transition point.  Both the load and deflection at 
the transition point were recorded from the graphs.  The aluminum foam core sandwiches 
exhibit a similar trend of transition from linear to nonlinear behavior.  However, unlike 
the unfilled aluminum foam core sandwiches, the SFS-b sandwiches are able to absorb 
additional load while continuing to deform. 
77 
The plots and pictures shown below in Figures 5.5 to 5.8 illustrate the progression 
of the test at important points of interest.  The first photo is the undeformed specimen 
used as a reference image for the particular test.  The second photo is at point A (in the 
plot in Figure 5.5), the transition point, where the behavior deviates from its initial linear 
elastic response.  The third photo is at the very end of the test once the sample has 
fractured.  (Analyzed images of this specimen (FLEX-59, SFSb30) are shown in Section 
6.4.3). 
 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Displacement (mm)
Lo
ad
 (N
)
Measured
Material: SFSb30
Temperature: 70?F
Specimen: FLEX-59
Cast: 25Jan2011
Test: 02Feb2011
Rate: 0.025 in/min
 
Figure 5.5    Typical SFS-b Load-Deflection Curve: Point A ? Transition Point,  
Point B ? Failure 
 
A 
B 
78 
 
Figure 5.6    Undeformed, P=0 N 
 
 
Figure 5.7    Point A: Transition Point, P=5127 N 
 
79 
  
Figure 5.8    Point B: Failure 
 
The failure load is the highest for SFSb20, with the ones for SFSb30 and SFSb40 
being successively lower.  This is a similar trend to that of the SFS material, which had 
decreasing peak load averages with increasing volume fraction.  The average load at 
failure for SFSb20 is 8,119 N, for SFSb30 is 7,531 N, and for IPC40 is 6,615 N.  To 
compare with the behavior of the aluminum foam core sandwich, the average load at 
failure for the SFS-b sandwich is normalized by the plateau load experienced by the 
unfilled aluminum foam core sandwich.  The average normalized load at failure for 
SFSb20 is 20.76, for SFSb30 is 19.26, and for SFSb40 is 16.92.  In Figure 5.9 these 
values are shown as a histogram.  The plateau load for the aluminum foam core sandwich 
is the load at which the stress remains nearly constant while able to withstand a large 
increase in strain.  It is this load that is typically used as the desired design load.  Refer to 
Figure 3.5 for a typical stress-strain response of this type.  The SFS-b sandwiches do not 
experience a similar near constant load, but rather a steady increase (hardening behavior) 
80 
until failure.  This load at failure, when compared to the plateau load, is seventeen to 
twenty-one times higher than the design load for unfilled aluminum foam core 
sandwiches.  The SFS-b sandwiches show superior load bearing capacity compared to 
their unfilled aluminum foam counterpart.  SFS-b sandwiches also outperform both SFS 
and IPC sandwiches, which will be further discussed in Chapter 7. 
 
0
5
10
15
20
25
20% 30% 40%
Volume Fraction
Pe
ak
 Lo
ad
/A
LS
 P
lat
ea
u L
oa
d
SFSb
 
Figure 5.9    Normalized Measured Peak Load for Sandwich Structures with Syntactic 
Foam Core and Graded Face Sheets 
 
The average value for the mid-span deflection at failure for SFSb20 is 2.18 mm, 
for SFSb30 is 2.37 mm, and for SFSb40 is 2.35 mm.  To compare with the behavior of 
the aluminum foam core sandwich, the average deflection at failure for the SFS-b 
sandwich is normalized by the deflection at which the aluminum foam core sandwich 
behavior deviates from linearity.  The average normalized deflection at failure for 
81 
SFSb20 is 11.23, for SFSb30 is 12.26, and for SFSb40 is 12.13.  In Figure 5.10 these 
values are shown as a histogram.  Note that within the experimental scatter, there is no 
improvement between the 30% and 40% volume fractions although the latter is lighter 
overall. 
 
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
20% 30% 40%
Volume Fraction
?F
ail
ur
e/
?A
LS
, n
on
lin
ea
r 
SFSb
 
Figure 5.10    Normalized Measured Mid-Span (Load-Point) Deflection at Failure for 
Sandwich Structures with Syntactic Foam Core and Graded Face Sheets 
 
The average value for the transition load for SFSb20 is 5,796 N, for SFSb30 is 
5,725 N, and for SFSb40 is 5,090 N.  As with the peak load, to compare to the behavior 
of the aluminum foam core sandwich, the average transition load for the SFS-b sandwich 
is normalized by the plateau load experienced by the aluminum foam core sandwich.  The 
average normalized transition load for SFSb20 is 14.82, for SFSb30 is 14.64, and for 
SFSb40 is 13.02.  In Figure 5.11 these values are shown as a histogram.  This is the best 
82 
comparison that can be made between syntactic foam and unfilled aluminum foam core 
sandwiches, as both have a transition point.  With the SFS-b sandwich having a transition 
load of around thirteen to fifteen times greater than unfilled aluminum foam sandwiches 
and a similar transition deflection, the point at which plasticity begins to set in for the 
SFS-b sandwiches is greatly improved.  Evidently, there is no distinguishable difference 
in the transition load values within the experimental scatter between SFSb20 and 
SFSb30, with SFSb40 specimens showing a slightly lower value relative to the two 
others.  This suggests that face sheet yielding is likely responsible for the transition point 
in SFS-b sandwiches as the metallic ligaments of the graded face sheet help prevent shear 
failure of the face-core interface.   
 
0
2
4
6
8
10
12
14
16
18
20% 30% 40%
Volume Fraction
Tr
an
sit
ion
 Lo
ad
/A
LS
 P
lat
ea
u L
oa
d
SFSb
 
Figure 5.11    Normalized Measured Load at Transition Point for Sandwich Structures 
with Syntactic Foam Core and Graded Face Sheets 
 
83 
The average value for the transition deflection for SFSb20 is 0.93 mm, for 
SFSb30 is 0.99 mm, and for SFSb40 is 0.91 mm.  For a comparison, the average 
transition deflection for the SFS-b sandwich is normalized by the deflection at which the 
aluminum foam core sandwich behavior deviates from linearity.  The average normalized 
transition deflection for SFSb20 is 4.79, for SFSb30 is 5.11, and for SFSb40 is 4.69.  In 
Figure 5.12 these values are shown as a histogram.  With a four and a half to five times 
improvement over unfilled aluminum foam core sandwiches, SFS-b sandwiches are able 
to remain in the linear elastic regime much longer before the onset of plasticity. 
 
0.0
1.0
2.0
3.0
4.0
5.0
6.0
20% 30% 40%
Volume Fraction
?T
ra
ns
iti
on
/?A
LS
, n
on
lin
ea
r
SFSb
 
Figure 5.12    Normalized Measured Mid-Span (Load-Point) Deflection at Transition 
Point for Sandwich Structures with Syntactic Foam Core and Graded Face Sheets 
 
As before, the strain energy (U) absorbed by a specimen was calculated using the 
area under the load-deflection curve from the measured data.  That is, 
84 
 
0
( )U P d
?
? ?= ? . 
 
The average values for the strain energy absorbed are plotted in Figure 5.13 as a 
histogram.  The average for SFSb20 is 11.54 J, for SFSb30 is 12.01 J, and for SFSb40 is 
10.90 J. 
 
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
20% 30% 40%
Volume Fraction
En
er
gy
 A
bs
or
be
d (
J)
SFSb
  
Figure 5.13    Energy Absorbed for Sandwich Structures with Syntactic Foam Core and 
Graded Face Sheets 
 
In order to compare among varying volume fractions of microballoons in the SF, 
specific energy (J/kg) was calculated for each specimen.  The strain energy absorbed was 
divided by the mass of the particular specimen.  The mass was determined by, 
85 
 
tot core core faces facesm V V? ?= + . 
  
The details of material densities used are in Table 4.5.  The results for specific 
strain energy are shown in Figure 5.14.  The average for SFSb20 is 144.4 J/kg, for 
SFSb30 is 164.0 J/kg, and for SFSb40 is 163.8 J/kg.  Comparing the specific strain 
energies of SFS-b and IPC sandwiches (which accounts for the weight difference in 
removing the aluminum foam in the core), SFSb20 had a 71% improvement over its IPC 
counterpart, SFSb30 had a 76% improvement, and SFSb40 had a 118% improvement.  
With syntactic foam core outperforming IPC foam core for all volume fractions as well as 
being lighter with the removal of the aluminum foam matrix, it can be concluded that 
SFS-b sandwiches are far superior to a similar configuration with IPC foam core in their 
energy absorbing capabilities.  It is now apparent that the best core type is syntactic foam 
rather than IPC.  However, the face sheets simply need to be tailored to penetrate the SF 
core in the face-core region to reap the full benefits of the face and of the core by 
preventing premature face-core shear failure yet allowing effective load transfer between 
the face and the core. 
 
 
86 
0
20
40
60
80
100
120
140
160
180
200
20% 30% 40%
Volume Fraction
Sp
ec
ific
 E
ne
rg
y A
bs
or
be
d (
J/k
g)
SFSb
 
Figure 5.14    Specific Energy Absorbed for Sandwich Structures with Syntactic Foam 
Core and Graded Face Sheets 
 
Failure observed in SFS-b sandwiches typically manifested as tensile failure of 
the lower face sheet, likely due to a rupture in the SF core, with a crack propagating from 
the tensile zone upwards towards the compression zone.  Due to the dynamic nature of 
failure initiation, it could not be confirmed if lower face sheet yielding preceded and 
contributed to the core crack initiation or vice versa.  Images of a failed SFS-b sandwich 
are shown in Figure 5.15.  Also, some magnified images of a failed SFS-b sandwich are 
shown in Figure 5.16.  In Figure 5.16 notice in (a) and (b) that the face sheets have 
appeared to again fail in tension after yielding.  Also notice the abrupt breaks in the 
metallic ligaments in (c), as well as the SF still adhered to the metallic ligaments, 
indicating good adhesion due to silane treatment.  Though no images captured the actual 
failure event, the abrupt face sheet separation seen in Figure 5.16 (a) and (b) indicates 
87 
that the failure initiated in the core, expanding downward to the face sheet and upward to 
the compression zone. 
 
 
(a) 
 
(b) 
 
(c) 
Figure 5.15    Failed SFS-b Specimen with (a) Side, (b) Top Face, and (c) Bottom Face 
Views 
 
88 
   
(a)        (b)           (c) 
Figure 5.16    Magnified Images (a), (b) of Failure Surfaces and (c) From Below 
 
The behavior of SFS-b sandwiches resembles a bilinear response.  At the 
transition point, the behavior deviates from the initial linear elastic regime to the 
nonlinear regime.  The response of a typical specimen at each volume fraction is 
compared to the theoretical mid-span deflection calculation from Section 1.5.1 [16].  The 
load histories are used to calculate the theoretical deflections, along with geometric and 
elastic parameters.  To calculate predicted deflections based on linear elastic material 
behavior, the quasi-static elastic properties used for the syntactic foam found by Jhaver 
[17] were used once again.  (Refer back to Figure 3.7 for the stress-strain responses from 
which they were derived and Table 3.2 for the properties.)  There is good agreement 
between the theoretical and experimental values in the initial linear elastic regime for all 
volume fractions.  The predictions exhibit similar stiffness compared to those seen in the 
measured data.  Note that since the theoretical response is only for the linear elastic case, 
the response after the transition point cannot be compared.  The deviations after the 
elastic region are possibly due to the fact that the elastic modulus for syntactic foam core 
89 
is assumed to be the same in tension as in compression.  These comparisons between the 
predicted and experimental behavior are shown below in Figure 5.17 to 5.19. 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5
Displacement (mm)
Lo
ad
 (N
)
Measured
Elastic
Prediction
Material: SFSb20
Temperature: 70?F
Specimen: FLEX-57
Cast: 23Jan2011
Test: 10Feb2011
Rate: 0.025 in/min
 
Figure 5.17    Predicted vs. Experimental Mid-Span Deflection, SFSb20 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Displacement (mm)
Lo
ad
 (N
)
Measured
Elastic
Prediction
Material: SFSb30
Temperature: 70?F
Specimen: FLEX-59
Cast: 25Jan2011
Test: 02Feb2011
Rate: 0.025 in/min
 
Figure 5.18    Predicted vs. Experimental Mid-Span Deflection, SFSb30 
 
90 
0
1000
2000
3000
4000
5000
6000
7000
8000
0.0 0.5 1.0 1.5 2.0 2.5
Displacement (mm)
Lo
ad
 (N
)
Measured
Elastic
Prediction
Material: SFSb40
Temperature: 70?F
Specimen: FLEX-65
Cast: 01Feb2011
Test: 10Feb2011
Rate: 0.025 in/min
 
Figure 5.19    Predicted vs. Experimental Mid-Span Deflection, SFSb40 
 
 Figure 5.20 shows a load-displacement overlay of the three specimens used as 
examples, with each containing a different volume fraction of microballoons in the SF 
core. 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Crosshead Displacement (mm)
Lo
ad
 (N
)
20%
FLEX-57 (SFS20)
30%
FLEX-59 (SFS30)
40%
FLEX-65 (SFS40)
Material: SFS-b
Temperature: 70?F
Overlay
 
Figure 5.20    Overlay of Measured Load-Displacement of SF Core Sandwich Structures 
with Graded Face Sheets and Different Vf of Microballoons in the SF 
SFSb20 
SFSb30 
SFSb40 
91 
 
 The transition deflection is virtually the same for all the three cases.  After the 
transition, nonlinear behavior is similar across the different cases with decreasing 
stiffness as volume fraction increases.  While SFSb30 has the greatest energy absorbing 
capacity, the 30% and 40% Vf cases have the same specific energy absorbing capacity.  
So if energy absorption is the driving factor, perhaps the 30% Vf case might be the best 
core material.  However, if both weight saving and energy absorbing capacity are both 
important attributes, then the 30% and 40% Vf  would both warrant consideration. 
 
5.3 Summary 
 
 With the addition of the graded face sheets, the syntactic foam core sandwiches 
(SFS-b) outperformed IPC foam core sandwiches in all metrics (comparisons are 
discussed in Chapter 7).  Not only did it outperform the IPC core sandwiches, but without 
the metallic matrix in the core, the syntactic foam core sandwiches are lighter.  It is easy 
to see now that the IPC core sandwiches, though substantially better than conventional SF 
core sandwiches, was an inferior material for flexural loading conditions due to its 
weakness under the tensile conditions.  As a single continuous phase the syntactic foam 
does not experience the interphase separation that IPC foam does that essentially acts as 
micro-defects, ultimately leading to tensile failure.  The core integrity is better with the 
syntactic foam.  These results were not seen with the first type of SFS sandwiches.  The 
poor bond between the sanded face sheets and the core was not able to effectively 
transfer load between the face and the core.  Failure would occur prematurely when the 
92 
face sheet and core would debond, leaving the core to bear the entire load.  The graded 
face sheets in the SFS-b sandwiches remedied this problem, allowing for effective load 
transfer throughout the specimen while minimizing face-core shear jump. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
93 
 
 
 
CHAPTER 6 
FULL-FIELD DEFORMATION MEASUREMENTS USING DIGITAL IMAGE 
CORRELATION METHOD 
 
6.1 Digital Image Correlation (DIC) Principle  
 
Digital image correlation (DIC) is a relatively new optical method and is based on 
the principle of locating a point (or region of interest) in the deformed image of an object 
relative to its location in the undeformed state [20,21,22,23].  The object surface is 
decorated with a random pattern (in this case a random black/white speckle).  The 
decoration is illuminated using white light sources to produce diffusely reflected light 
from the specimen surface.  The light intensity (grayscales) of the surface is used for the 
pattern matching process.  The recording of the surface patterns is done using a digital 
camera with a relatively high pixel count (typically on the order of one to ten megapixels) 
to achieve good spatial resolution.   
During a typical digital imaging process, an analog intensity field I(x,y) is 
converted into a discrete field D(x,y).  The output from an image is typically a two 
dimensional array of intensity levels (D(i,j) consisting of i rows and j columns).  If 
discrete intensity fields D and D? are available for two load levels (or, reference and 
deformed states), then a subset d from D (say, a 15 x 15 pixel subimage from a 1000 x 
94 
1000 pixel image) is chosen and its location in D? (also a 1000 x 1000 pixel image) is 
searched. 
A typical random speckle pattern in undeformed and deformed states is shown in 
Figure 6.1.  The highlighted box on the undeformed image indicates the area to track 
during correlation.  The box on the deformed image indicates the same area after 
undergoing deformation.  A schematic of the planar deformation is depicted in Figure 
6.2.   
 
 
(a)       (b)
Figure 6.1    (a) Undeformed and (b) Deformed Speckle Images 
 
95 
 
Figure 6.2    Tracked Subimage for Image Correlation   
 
 A subimage with O as the center is displaced to O? after deformation.  If u and v 
denote displacement components in the x- and y- directions, the process of deformation 
can be expressed using affine coordinate transformations to relate O?(x?,y?) with O(x,y).  
This requires an accurate interpolation method to express intensity variation within the 
subimage. 
 For a subimage centered at point O in the undeformed state, the discretely 
sampled intensity and continuously interpolated intensity at O and a neighboring point P 
at positions (x,y) and (x+dx,y+dy) can be written as 
 
( ) ( , )
( ) ( , )
D O D x y
D P D x dx y dy
=
= + +  
 
The differential distances between neighboring points O and P are represented by 
dx and dy.  After deformation the intensity patterns recorded are expressed using 
 
' ( , ); ' ( , )x x u x y y y v x y= + = + . 
? O? 
? O 
? P 
? P? 
?x 
?y 
u 
v 
UNDEFORMED SUBIMAGE 
DEFORMED SUBIMAGE 
96 
So, 
'( ', ') ( ( , ), ( , ))
'( ' ', ' ') [ ( , ), ( , )]
'( ' ', ' ') [ ( , ) (1 ) , ( , ) (1 ) ]
D x y D x u x y y v x y
D x dx y dy D x dx u x dx y dy y dy v x dx y dy
u u v vD x dx y dy D x u x y dx dy y v x y dx dy
x y x y
= + +
+ + = + + + + + + + +
? ? ? ?+ + = + + + + + + + +
? ? ? ?
 
 
If the subimage is sufficiently small and displacement gradients are therefore 
nearly constant within the subimage, one can obtain u, v, ux?? , uy?? , vx?? , vy??  for each 
subimage.  This is generally done using one of the following measures: (1) magnitude of 
intensity difference, (2) sum of the squares of intensity value difference, (3) normalized 
cross-correlation, or (4) cross-correlation.  The most commonly used is normalized cross-
correlation where the following quantity,  
 
2 2
'( ') ( )
'( ') ( )
i
NCC
i i
D O D O
C
D O D O
=
?
? ?  , 
  
is maximized to provide the optimal estimation of all the six displacements and 
displacement gradients.  A number of optimization methods can be used for this purpose 
and include the so-called Newton-Raphson, coarse-fine, and Levenburgh-Marquardt 
methods.  Levenburgh-Marquardt method has been demonstrated to have superior 
convergence characteristics and is as fast as the Newton-Raphson method.  
 
 
97 
6.2 ARAMIS? Image Analysis Software 
 
 Full field deformation and strain analysis was performed using the 2D image 
correlation technique utilizing a spray-on speckle pattern.  The software used for the 
image post-processing was ARAMIS? (GOM mbH, Germany).  It is able to provide full 
field measurements using a photogrammetric method [24] as the specimen undergoes 
deformation during a test.  A Nikon D100 digital camera was used during experiments to 
record the grayscales (at 10-bit resolution) corresponding to the specimen deformation.  
Although the camera had a 6 megapixel resolution, during time-lapse photography only 
1500 x 1000 pixels were used for easy throughput of grayscale information into a laptop 
using Nikon Capture software (Version 4.0).  The entire image is regularly divided into a 
number of smaller sub-images (facets).  The photogrammetric principles used to evaluate 
the images track facets in each successive image.  From each facet, a single measurement 
results after computation.  The facet size used (15 x 15 pixels) was a good compromise 
between accuracy and computational time.  The goal is to have a good representation of 
the speckle pattern within the facet.  This digital image processing provides full field 
displacement and strain contours throughout the test.  Furthermore, not only can this be 
implemented in quasi-static situations, but also in dynamic situations [25].   
The deformation gradient tensor F (comprised of ux?? , uy?? , vx?? , vy?? ) creates a 
functional connection of the coordinates of the deformed points Pv,i with the coordinates 
of the undeformed points Pu,i [26].  They are connected through the relation 
 
, ,v i j u i= +P u F Pg  , 
98 
where, 
 ,v i =P  Deformed point coordinates 
 ,u i =P  Undeformed point coordinates 
 j =u  Rigid body translation 
 
 The different coordinate systems defined through the calculation process are 
shown in Figure 6.3.  The coordinates of the points (e.g. pu and pv in the figure) are 
calculated in the global x-y coordinate system.  For 2D analysis, the local undeformed 
coordinate system x?-y? is parallel to x-y, but moved to coincide with the point pu.  The 
x?-y? coordinate system for the strain calculation is independent of rigid body movement 
and rotation.   
 
 
Figure 6.3    Coordinate System Definition 
 
 To calculate the deformation gradient tensor F, the coordinates of each point must 
be known both in the undeformed and deformed state.  This tensor can be interpreted as 
99 
an affine transformation which transforms a unit square into a generic quadrilateral.  In 
order to calculate F for a point, a number of neighboring points are needed.  For this 
calculation, a homogeneous state of strain is assumed for the set of adjacent points.  The 
width of the field is the reference length for evaluating strain. (For example in Figure 6.4, 
the width of the field is three points or pixels.  The reference length is then three pixels.)  
The number of surrounding points can be changed, but a 3x3 neighborhood is shown in 
Figure 6.4 below.   
 
 
Figure 6.4    3x3 Point Neighborhood for 2D Strain Calculation 
 
6.3 Experimental Setup 
 
 Section 3.1 details the TPB test setup used in conjunction with DIC method and 
time-lapse photography.  The impact test counterparts were carried out using the speckle 
pattern and camera and are detailed in Section 6.5. 
 
100 
6.4 Optical Measurement Results 
 
 Using built-in algorithms in ARAMIS?, displacement and strain fields were 
computed and illustrated.  With this capability, it is relatively simple to obtain local 
displacement and strain information, rather that relying on the global load and 
displacement measurements made using the testing machine.  To ensure the ARAMIS? 
results are reliable, local and global displacement measurements were compared for each 
specimen just below the load roller (the machine displacement data given is for the 
crosshead).  An example of this is shown in Figure 6.5.  This is one example, with every 
specimen compared and shown in Appendix A.  Since the camera recorded images in ~2 
second intervals, there is understandably a small lag in the ARAMIS? displacements.   
 
0
1000
2000
3000
4000
5000
6000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Displacement (mm)
Lo
ad
 (N
)
Measured
ARAMIS
Material: IPC30
Temperature: 70?F
Specimen: FLEX-16
Cast: 15Apr2010
Test: 09Jun2010
Rate: 0.025 in/min
 
Figure 6.5    Global/Local Displacement Comparison, FLEX-16 
 
101 
Also, to check the strain calculations, a sample (129mm length x 5.7mm width x 
21mm height) of PMMA (E = 3 GPa) was tested in three-point bending and the strains 
calculated using ARAMIS?.  These dimensions were chosen to match the planar 
dimensions of the sandwich specimens under investigation.  The comparison is shown in 
Figure 6.6.  The measured load was used to calculate the maximum tensile stress using 
0;
x
x y c
My
I? = ==  and theoretical elastic strain was calculated using 
x
x E
?? = .  The optical 
measurement of strain and the theoretical prediction are plotted in Figure 6.6, with good 
agreement between the two being evident.  The error bars are determined from the plot in 
Figure 6.7.  Also plotted are strain (?x) and shear strain (?xy) variations, in Figures 6.7 and 
6.8, respectively, along the beam height (y) at x=25mm (x=0 is the mid-span of the 
beam).  Theoretical shear strain is calculated using VQIb? =  and 2xy G?? = .  A rather good 
agreement is seen in the ?x plot.  Note the strange nonlinear behavior at the top and 
bottom of the sample.  Considering the known behavior of PMMA, it can be concluded 
that any optical measurements around the top and bottom of the specimen have an 
increased amount of error.  This plot shows a maximum error of approximately 600 
?strains, which was determined to be the error associated with optical strain 
measurements.  The ?xy plot trend was the same as the elastic prediction with an error of 
approximately 1000 ?strains. 
 
102 
0
10
20
30
40
50
60
70
0.0 0.5 1.0 1.5 2.0 2.5
Strain (%)
St
re
ss
 (M
Pa
)
Measured
ARAMIS
Material: PMMA
Temperature: 70?F
Specimen: PMMA-1
Test: 04Mar2011
Rate: 0.025 in/min
 
Figure 6.6    Strain Calibration Using PMMA 
 
-10.8
-8.3
-5.8
-3.3
-0.8
1.7
4.2
6.7
9.2
-1.50 -1.00 -0.50 0.00 0.50 1.00 1.50
?x (%)
y 
(m
m) Elastic
Predicition
ARAMIS
Material: PMMA
Temperature: 70?F
Rate: 0.025 in/min
Load: 1,650 N
 
Figure 6.7    PMMA Strain (?x) Along the Height of the Beam 
 
103 
-10.8
-8.3
-5.8
-3.3
-0.8
1.7
4.2
6.7
9.2
0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007
?xy (rad)
y 
(m
m) Elastic
Prediction
ARAMIS
Material: PMMA
Temperature: 70?F
Rate: 0.025 in/min
Load: 1,650 N
 
Figure 6.8    PMMA Shear Strain (?xy) Along the Height of the Beam 
 
6.4.1 Syntactic Foam (SFS) Results 
 
The series of images shown in Figures 6.9 to 6.17 are typical ARAMIS? results 
for tests conducted on SFS sandwiches.  Each of these experiments are summarized in 
sets of three images: the first image corresponding to a point in the linear response 
regime, the second image corresponding to just before failure, and the third image 
corresponding to just after failure.  Note the presence of strain concentration due to the 
loading roller in particular.  Though it is hard to conclusively determine given the low 
amount of deflection in the beam, the u-displacement fields are similar to what is 
expected from the beam theory.  Note the units: u-displacement is measured in 
millimeters, ?x is measured in percent, and ?xy is measured in strains.  Also note that the 
correlated images contain twenty contours.  The u-displacement increment is 50?m, ?x 
increment is 0.25%, and ?xy increment is 4,000 ?strains. 
104 
 
 
 
Figure 6.9    ARAMIS? Results for SFS20 (FLEX-38, u) 
 
 
 
 
x 
y 
P=2346N 
P=2869N 
P=4946N 
105 
 
 
 
Figure 6.10    ARAMIS? Results for SFS20 (FLEX-38, ?x)  
 
 
 
x 
y 
P=2346N 
P=2869N 
P=4946N 
106 
  
  
  
Figure 6.11    ARAMIS? Results for SFS20 (FLEX-38, ?xy) 
 
 
 
 
 
x 
y 
P=2346N 
P=2869N 
P=4946N 
107 
 
 
 
Figure 6.12    ARAMIS? Results for SFS30 (FLEX-39, u) 
 
 
 
 
x 
y 
P=2236N 
P=5468N 
P=3618N 
108 
 
 
 
Figure 6.13    ARAMIS? Results for SFS30 (FLEX-39, ?x) 
 
 
 
 
x 
y 
P=2236N 
P=5468N 
P=3618N 
109 
 
 
 
Figure 6.14    ARAMIS? Results for SFS30 (FLEX-39, ?xy) 
 
 
 
 
 
x 
y 
P=2236N 
P=5468N 
P=3618N 
110 
 
 
 
Figure 6.15    ARAMIS? Results for SFS40 (FLEX-24, u) 
 
 
 
 
x 
y 
P=2069N 
P=4080N 
P=2459N 
111 
 
 
 
Figure 6.16    ARAMIS? Results for SFS40 (FLEX-24, ?x) 
 
 
 
 
x 
y 
P=2069N 
P=4080N 
P=2459N 
112 
  
 
 
Figure 6.17    ARAMIS? Results for SFS40 (FLEX-24, ?xy)  
 
 
 
 
 
 
 
x 
y 
P=2069N 
P=4080N 
P=2459N 
113 
6.4.2 IPC Results 
 
The series of images shown in Figures 6.18 to 6.26 are typical optical results for 
tests conducted on IPC sandwiches.  In each of these sets of four images, the first image 
corresponds to a point in the linear portion of the loading regime, the second image 
corresponds to a point in the nonlinear regime, the third image corresponds to the point 
just before failure, and the fourth image corresponds to the point just after failure.  Notice 
that with the IPC, the strain concentration effects due to the rollers are relatively muted, 
as the interpenetrating core does a good job of evenly distributing the load.  Again, u-
displacement fields qualitatively resemble the ones expected from the beam theory. 
 
 
 
 
 
 
 
 
 
 
 
 
 
114 
 
 
 
 
Figure 6.18    ARAMIS? Results for IPC20 (FLEX-10, u) 
 
 
 
 
x 
y 
P=824N 
P=3536N 
P=4922N 
P=3905N 
115 
 
 
 
 
Figure 6.19    ARAMIS? Results for IPC20 (FLEX-10, ?x) 
 
 
 
 
x 
y 
P=824N 
P=3536N 
P=4922N 
P=3905N 
116 
 
 
 
 
Figure 6.20    ARAMIS? Results for IPC20 (FLEX-10, ?xy) 
 
 
 
 
 
x 
y 
P=824N 
P=3563N 
P=4922N 
P=3905N 
117 
 
 
 
 
Figure 6.21    ARAMIS? Results for IPC30 (FLEX-16, u) 
 
 
 
 
x 
y 
P=1097N 
P=3997N 
P=5680N 
P=3741N 
118 
 
 
 
 
Figure 6.22    ARAMIS? Results for IPC30 (FLEX-16, ?x) 
 
 
 
 
x 
y 
P=1097N 
P=3997N 
P=5680N 
P=3741N 
119 
 
 
 
 
Figure 6.23    ARAMIS? Results for IPC30 (FLEX-16, ?xy) 
 
 
 
 
x 
y 
P=1097N 
P=3997N 
P=5680N 
P=3741N 
120 
 
 
 
 
Figure 6.24    ARAMIS? Results for IPC40 (FLEX-14, u) 
 
 
 
 
x 
y 
P=950N 
P=2845N 
P=4442N 
P=3159N 
121 
 
 
 
 
Figure 6.25    ARAMIS? Results for IPC40 (FLEX-14, ?x) 
 
 
 
 
x 
y 
P=950N 
P=2845N 
P=4442N 
P=3159N 
122 
 
 
 
 
Figure 6.26    ARAMIS? Results for IPC40 (FLEX-14, ?xy) 
 
 
 
 
 
 
x 
y 
P=950N 
P=2845N 
P=4442N 
P=3159N 
123 
6.4.3 Syntactic Foam (SFS-b) Results 
 
The series of images shown in Figures 6.27 to 6.35 are typical ARAMIS? results 
for tests conducted on syntactic foam core sandwiches with graded face sheets (SFS-b).  
In each of these sets of three images, the first image corresponds to a point in the linear 
regime, the second image corresponds to a point in the nonlinear regime, and the third 
image corresponds to the point just before failure.  In the SFS-b sandwiches, the 
concentration effects due to the rollers once again dominate.  Also of note is that the 
shear strains are higher compared to that of the SFS sandwiches due to the more efficient 
load transfer throughout the structure enabled by the graded face sheets.  Once again, the 
u-displacement fields are what you would expect from the beam theory. 
 
 
 
 
 
 
 
 
 
 
124 
 
 
 
Figure 6.27    ARAMIS? Results for SFSb20 (FLEX-57, u)  
 
 
 
x 
y 
P=3491N 
P=7187N 
P=8155N 
125 
 
 
 
Figure 6.28    ARAMIS? Results for SFSb20 (FLEX-57, ?x)  
 
 
 
x 
y 
P=3491N 
P=7187N 
P=8155N 
126 
 
 
 
Figure 6.29    ARAMIS? Results for SFSb20 (FLEX-57, ?xy)  
 
 
 
 
x 
y 
P=3491N 
P=7187N 
P=8155N 
127 
 
 
 
Figure 6.30    ARAMIS? Results for SFSb30 (FLEX-59, u) 
 
 
 
 
x 
y 
P=2990N 
P=6717N 
P=7559N 
128 
 
 
 
Figure 6.31    ARAMIS? Results for SFSb30 (FLEX-59, ?x) 
 
 
 
 
x 
y 
P=2990N 
P=6717N 
P=7559N 
129 
 
 
 
Figure 6.32    ARAMIS? Results for SFSb30 (FLEX-59, ?xy) 
 
 
 
 
 
x 
y 
P=2990N 
P=6717N 
P=7559N 
130 
 
 
 
Figure 6.33    ARAMIS? Results for SFSb40 (FLEX-65, u) 
 
 
 
 
x 
y 
P=2207N 
P=6054N 
P=6735N 
131 
 
 
 
Figure 6.34    ARAMIS? Results for SFSb40 (FLEX-65, ?x) 
 
 
 
 
x 
y 
P=2207N 
P=6054N 
P=6735N 
132 
 
 
 
Figure 6.35    ARAMIS? Results for SFSb40 (FLEX-65, ?xy)  
 
 
 
 
 
 
 
x 
y 
P=2207N 
P=6054N 
P=6735N 
133 
6.5 Impact Tests 
 
 The impact tests conducted in this work were only conducted on IPC and SFS-b 
types using a single volume fraction (30%) of microballoons in the SF.  The purpose of 
these tests was to further elaborate on the failure mechanisms in the quasi-static case, as 
well as begin to understand dynamic characteristics of these sandwich architectures.  
Also, the feasibility of using DIC method in conjunction with a high-speed digital camera 
to study impact response of sandwich structures is illustrated.  
 Impact tests were conducted using an Instron Dynatup 9250-HV drop tower to 
deliver low velocity impact to IPC foam core and SFS-b sandwich structures with 30% 
volume fraction of microballoons in the SF.  The nominal specimen size used for 
dynamic testing was 127mm x 25mm x 18.5mm (5? length x 1? width x 0.73? height).  
Each face sheet had a nominal thickness of 0.813mm, giving a core thickness of 
~16.9mm.  The specimen was supported over a 4.5 inch span and was impacted by a 
hemispherical impactor of radius 0.5 inch. 
Two different cameras were used to capture the dynamic event.  The first was a 
Phantom v710 digital high-speed camera with a single 1280 x 800 CMOS sensor.  This 
camera recorded a video of the event and was used to determine the overall impact 
response on a large time scale.  (Using a resolution of 800 x 600 pixels and a framing rate 
of 13,000 frames per second, the total recording duration was ~0.75 seconds.)  Images 
from the Phantom camera were used to determine the time at which crack initiation was 
likely to occur.  (To view a video of the impact event created using the Phantom camera, 
refer to the disk in the back cover of this thesis.)  Using this estimated time, parameters 
134 
were selected for the second camera, a Cordin Model 550 high-speed digital camera, 
which captured the speckle patterns during the dynamic event over a time period of ~600 
microseconds.  (The Cordin camera is capable of simultaneously recording at much 
higher spatial resolutions (1000 x 1000 pixels) and speeds and hence was preferred to the 
Phantom camera.)  The drop tower has an instrumented tup and a pair of anvils for 
recording impact force and reaction force histories, respectively.  Two high intensity 
flash lamps, triggered by the camera, were used to illuminate the specimen surface.  Two 
separate computers were also used in the setup.  One was used to record the force 
histories, and the other was used to control the camera and store the digital images.  A 
schematic of the test setup with the Cordin camera is shown in Figure 6.36.  The setup 
consists of (1) high-speed digital camera, (2) drop tower impactor tup, (3) delay 
generator, (4) specimen, (5) light sources, (6) DAQ ? drop tower, (7) DAQ ? camera, (8) 
lamp control unit, and (9) drop tower controller. 
 
Region of Interest
(25mm x 25mm)
 
Figure 6.36    Schematic of Impact Test Setup: (1) high-speed digital camera, (2) drop 
tower impactor tup, (3) delay generator, (4) specimen, (5) light sources, (6) DAQ ? drop 
tower, (7) DAQ ? camera, (8) lamp control unit, and (9) drop tower controller 
135 
 A picture of the impact test setup is shown in Figure 6.37 which shows (1) high-
speed camera, (2) drop tower impact tup, (3) specimen, and (4) light source. 
 
  
Figure 6.37    Impact Test Setup: (1) high-speed camera, (2) drop tower impactor tup,   
(3) specimen, and (4) light source 
 
The high-speed camera employs CCD technology with a high-speed rotating 
mirror optical system.  The camera is capable of capturing images at a rate of 2,000,000 
frames per second at a resolution of 1000 x 1000 pixels for each image.  Thirty-two (32) 
independent image sensors are positioned circumferentially around a five-facet high-
speed rotating mirror that reflects and sweeps light over the sensors.  The 32 sensors 
function as individual cameras that operate sequentially by means of internal electronic 
triggering.  Minor misalignments occur, such as differences in focus and rotational 
discrepancies between successive images.  This is resolved by grouping the images into 
pairs that consist of an undeformed and a deformed image recorded by the same sensor.  
1 
2 
3 
4 
136 
Before impact a set of 32 images was recorded in the area of interest with the desired 
frame rate (50,000 frames per second for this work).  After aligning the optics, the 
rotating mirror was brought to the desired speed.  The camera and lamps were triggered 
by the operator.  This set of 32 images (one per sensor) of the specimen surface was then 
stored for use as undeformed, or reference, images.  Maintaining all the same camera 
settings, a second set of 32 images was recorded as the specimen experienced the impact 
event.  During the test, the camera and flash lamps were triggered by the tup as it 
contacted a copper strip adhered to the top of the specimen.  The first image was 
identified, and then sequential pairs were made in the undeformed and deformed sets 
(i.e., in the first set of 32 undeformed images, each image has a corresponding deformed 
image in the second set).  Each of the 32 pairs was analyzed separately.  (To view a video 
of the impact event created using the Cordin camera, refer to the disk in the back cover of 
this thesis.)  The impactor velocity used in this work was 5 m/s.  The camera viewing 
area is shown in Figure 6.38 and was approximately 25mm x 25mm. 
 
 
  
Figure 6.38    Camera Viewing Area 
 
 IPC foam core sandwiches with a 30% volume fraction of microballoons in the 
SF core were impact tested.  Figures 6.39 and 6.40 show a sample of correlated images 
137 
from the Cordin camera on an IPC30 specimen.  Shown here are the u-displacement and 
normal strain (?x) fields.  Note that the correlated images contain twenty contours.  The u-
displacement increment is 25?m and ?x increments are 0.2%. 
 
 
 
 
Figure 6.39    ARAMIS? Results for IPC30 (DYN-29, u) 
 
 
 
 
 
 
t=530?s 
t=550?s 
t=510?s 
Crack 
initiation 
138 
 
 
 
Figure 6.40    ARAMIS? Results for IPC30 (DYN-29, ?x) 
 
 
 
 The normal (dominant) strain, ?x, image preceding visible crack initiation (t=530 
?s) contains an anomaly not seen in the previous images in the area where the crack 
forms.  Also, no significant strain concentration at the impact edge is seen since the 
impactor head is hemispherical and the front face of the specimen is far removed from 
the specimen mid-plane.  Since the crack first forms in the core, then propagates to the 
lower face and upper compression zone, it can be concluded that the mechanism likely 
t=530?s 
t=550?s 
t=510?s 
Crack 
initiation 
139 
responsible for both quasi-static and dynamic failure in the IPC foam core sandwiches is 
tensile failure of the core.   
 SFS-b sandwiches with a 30% volume fraction of microballoons in the SF were 
also impact tested.  Figures 6.41 and 6.42 show a sample of correlated images from the 
Cordin camera on an SFSb30 specimen.  Shown here are the u-displacement and normal 
strain (?x) fields. 
 
 
 
 
Figure 6.41    ARAMIS? Results for SFSb30 (DYN-35, u) 
 
t=530?s 
t=550?s 
Crack 
initiation 
t=510?s 
140 
 
 
 
Figure 6.42    ARAMIS? Results for SFSb30 (DYN-35, ?x) 
 
 
Similar to the IPC foam core sandwiches, the crack first forms in the tensile 
region of the SFS-b sandwich core, only then propagating to the lower face and upper 
compression zone.  It can be concluded that the initial mechanism likely responsible for 
both quasi-static and dynamic failure in the SFS-b foam core sandwiches is also tensile 
failure of the core.   
Figures 6.43 and 6.44 show plots of the strain energy absorbed by the specimen as 
a function of time for the IPC30 and SFSb30 sandwiches, respectively.  The results are 
t=530?s 
t=550?s 
Crack 
initiation 
t=510?s 
141 
summarized in Tables 6.1 and 6.2.  The Impulse software (for the drop tower) 
automatically performs energy calculations using the following relationship, 
 
( ) ( ) ( ) ( )E t K t V t Ea t Const= + + =  
 
where E(t) is the total energy in the system (which remains constant), K(t) is the kinetic 
energy of the drop weight, V(t) is the potential energy of the drop weight, and Ea(t) is the 
strain energy absorbed by the specimen up to time t.  Graphically, Ea(t) is simply the area 
under the load-deflection curve.  It is calculated mathematically using the mass (m), 
velocity (v(t)), and position (x(t)) of the drop weight (trapezoid integration used to find 
v(t) and x(t)) in the equation, 
2 21( ) ( ) ( )
2 impactEa t m v v t mgx t? ?= ? +? ? . 
 
 
0
2
4
6
8
10
12
14
16
0.0 0.5 1.0 1.5 2.0
Time (ms)
En
er
gy
 A
bs
or
be
d (
J)
DYN-18
(IPC30)
DYN-20
(IPC30)
DYN-29
(IPC30)
Material: IPC30
Temperature: 70?F
Overlay
 
Figure 6.43    Strain Energy History, IPC30 
Core crack 
initiation 
Core is 
cracked; 
specimen 
continues 
to absorb 
energy 
Core is 
intact 
142 
 
 
0
2
4
6
8
10
12
14
16
0.0 0.5 1.0 1.5 2.0
Time (ms)
En
er
gy
 A
bs
or
be
d (
J)
DYN-34
(SFSb30)
DYN-35
(SFSb30)
DYN-36
(SFSb30)
Material: SFSb30
Temperature: 70?F
Overlay
 
Figure 6.44    Strain Energy History, SFSb30 
 
Table 6.1    IPC30 Impact Test Results 
Specimen Impact Energy Specific Energy Energy Absorption
Number Type VF(%) Speed (m/s) Absorbed (J) Absorbed (J/kg) Rate (J/ms)
18 IPC 30 5.0 10.8 157.8 12
20 IPC 30 5.0 12.1 178.0 12
29 IPC 30 5.0 11.0 161.1 12
NUM OF SAMPLES          3 3 3
AVERAGE          11.3 165.6 12
STANDARD DEVIATION          0.7 10.8 0  
 
Table 6.2    SFSb30 Impact Test Results 
Specimen Impact Energy Specific Energy Energy Absorption
Number Type VF(%) Speed (m/s) Absorbed (J) Absorbed (J/kg) Rate (J/ms)
34 SFSb 30 5.0 8.4 136.5 20
35 SFSb 30 5.0 8.8 143.1 20
36 SFSb 30 5.0 9.2 146.7 20
NUM OF SAMPLES          3 3 3
AVERAGE          8.8 142.1 20
STANDARD DEVIATION          0.4 5.2 0  
 
Core crack 
initiation 
143 
 Two major aspects of note are the rate of energy absorption and the total strain 
energy absorbed by the specimen.  While the SFSb30 sandwiches had a higher rate of 
energy absorption, the IPC30 sandwiches actually had greater energy absorption capacity 
under impact conditions.  When compared to IPC30 sandwiches, the SFSb30 sandwiches 
had 22.1% less strain energy absorption and a 14.2% drop in specific energy absorption.  
Both architectures experienced visible core crack initiation at ~550 ?s.  Note the 
difference in Figures 6.43 and 6.44 after that time.  SFS-b sandwich energy absorption 
only occurs from time zero up to the time of crack initiation.  The IPC foam core 
sandwiches continue to absorb energy even after the onset of a crack.   
The impact tests in this work were only conducted using 30% volume fraction of 
microballoons in the SF.  The purpose of these tests was to further expound on the failure 
mechanisms in the quasi-static case, as well as begin to understand the failure 
mechanisms in the dynamic case.  Also, the feasibility of using DIC method in 
conjunction with a high speed digital camera to study impact behavior of sandwich 
structures is illustrated.  Contrary to the quasi-static case, IPC foam core sandwiches 
appear to outperform the syntactic foam core sandwiches with graded face sheets.  The 
presence of the interpenetrating phases seems to have a positive effect under dynamic 
conditions, though the crack still initiates in the tensile region of the core. 
  
 
 
 
 
144 
 
 
 
CHAPTER 7 
CONCLUSIONS 
 
7.1 Comparison of Results and Conclusions 
 
 In this thesis, flexural responses of sandwich structures with syntactic foam (20%-
40% volume fractions) core were studied.  Three types of sandwich structures were 
studied.  The first type had a regular syntactic foam core (identified as SFS) with simply 
adhered aluminum face sheets.  The second one employed an aluminum-syntactic foam 
interpenetrating core (identified as IPC) in an attempt to prevent the face-core debond 
seen in the SFS sandwiches.  The third type consisted of a syntactic foam core with 
graded face sheet (identified as SFS-b).  Static three-point bend tests were carried out on 
all three types of sandwich structures and global load-deflection responses were 
measured.  The three different architectures were comparatively examined in terms of 
peak load, mid-span deflection at failure, nonlinearity of the response, and strain energy 
absorbed. The global measurements were supplemented by digital image correlation 
measurements on the core to map 2D deformations and strains.  The global 
measurements, measured normal and shear strain fields, and optical microscopy were 
used to discern failure responses of the three architectures. 
145 
In the case of the syntactic foam core sandwiches (SFS), the load-deflection 
behavior was essentially linear elastic in nature.  However, for the IPC foam core 
sandwiches and syntactic foam core sandwiches with graded face sheets (SFS-b), there is 
a noticeable kink or a ?knee?, giving the appearance of a bilinear flexural response.   
 The SFS sandwiches failed predominantly due to face-core debonding with a 
large scatter in measured peak load and crosshead deflection at failure.  They also 
showed very limited nonlinearity in load-deflection response.  The IPC core sandwiches 
showed a substantial improvement in terms of deflection at failure and a significant 
nonlinearity in load-deflection responses.  The peak load, however, showed a slight 
reduction.  The nonlinearity in this architecture is primarily due to face sheet yielding as 
well as debonding between the phases of the interpenetrating composite foam core.  The 
SFS-b sandwiches, on the other hand, showed substantial improvement in both the peak 
load and mid-span deflection at failure and exhibited nonlinearity in the response similar 
to IPC foam core sandwiches.  This is attributed to a gradual shear strain variation at the 
graded face-core interface (unlike the SFS sandwiches) resulting in face sheet yielding 
before final failure. 
Considering that the SFS material possibly did not reach its full potential and 
comparing the specific strain energies (which accounts for the weight difference in 
adding the aluminum foam into the core), IPC20 had a 25% improvement, IPC30 had a 
59% improvement, and IPC40 had an 88% improvement.  While the peak load decreased 
slightly, for the small penalty of added weight the IPC foam core significantly improved 
the value of deflection-to-failure experienced and thus the strain energy absorbed. 
146 
With the IPC30 having the highest average values for all metrics in the IPC foam 
core test group (most pronounced specific energy absorbed), an optimum IPC foam 
volume fraction of SF likely exists somewhere around 30%. 
Though IPC foam core sandwiches outperformed the SFS counterparts, the 
syntactic foam core sandwiches with graded face sheets (SFS-b) outperformed the IPC 
foam core sandwiches.  This architecture was able to maintain linear load-deflection 
behavior much longer than the IPC foam core architecture with an improvement in load 
at the (linear to nonlinear) transition point of 244%, 230%, and 211% for SFSb20, 
SFSb30, and SFSb40, respectively.  The improvements in mid-span deflection at the 
transition point were 222%, 234%, and 225% for SFSb20, SFSb30, and SFSb40, 
respectively.  Comparing the specific strain energies to those of IPC foam core 
sandwiches (which accounts for the weight difference in the core), SFSb20 had a 71% 
improvement, SFSb30 had a 76% improvement, and SFSb40 had a 118% improvement.  
Remember that ideally the data needs to be normalized by a sandwich consisting of 
aluminum face sheets separated by an empty core.  However, this being impractical, the 
unfilled 20ppi aluminum foam core sandwich response was used to normalize the data.  
Comparisons of all three architectures are shown in Figures 7.1 to 7.6. 
 
147 
0
5
10
15
20
25
20% 30% 40%
Volume Fraction
Pe
ak
 Lo
ad
/A
LS
 P
lat
ea
u L
oa
d
SFS
IPC
SFSb
 
Figure 7.1    Normalized Measured Peak Load for Sandwich Structures with SF and IPC 
Foam Cores 
0
2
4
6
8
10
12
14
20% 30% 40%
Volume Fraction
?F
ail
ur
e/
?A
LS
, n
on
lin
ea
r 
SFS
IPC
SFSb
 
Figure 7.2    Normalized Measured Mid-Point (Load-Point) Deflection at Failure for 
Sandwich Structures with SF and IPC Foam Cores 
148 
0
2
4
6
8
10
12
14
16
18
20% 30% 40%
Volume Fraction
Tr
an
sit
ion
 Lo
ad
/A
LS
 P
lat
ea
u L
oa
d
IPC
SFSb
 
Figure 7.3    Normalized Measured Load at Transition Point for Sandwich Structures with 
SF and IPC Foam Cores 
0
1
2
3
4
5
6
20% 30% 40%
Volume Fraction
?T
ra
ns
itio
n/
?A
LS
, n
on
lin
ea
r
IPC
SFSb
 
Figure 7.4    Normalized Measured Mid-Point (Load-Point) Deflection at Transition Point 
for Sandwich Structures with SF and IPC Foam Cores 
149 
0
2
4
6
8
10
12
14
20% 30% 40%
Volume Fraction
En
er
gy
 A
bs
or
be
d 
(J)
SFS
IPC
SFSb
 
Figure 7.5    Energy Absorbed for Sandwich Structures with SF and IPC Foam Cores 
 
0
20
40
60
80
100
120
140
160
180
200
20% 30% 40%
Volume Fraction
Sp
ec
ific
 E
ne
rg
y A
bs
or
be
d (
J/k
g)
SFS
IPC
SFSb
 
Figure 7.6    Specific Energy Absorbed for Sandwich Structures with SF and IPC Foam 
Cores 
 
150 
The superior material based on all these metrics is the syntactic foam core 
sandwiches with graded face sheets (SFS-b).  The only instance it might not be 
considered the optimal choice might be when considering the IPC foam core sandwiches 
for their ability to use the metallic foam network to hold it together longer.  Depending 
on the combination of desired properties, the volume fraction of microballoons could be 
tailored to fit the needs of different applications. 
Using the calculated strains from the image correlation process, plots of dominant 
strain (?x) and shear strain (?xy) as a function of thickness were obtained.  The strains 
extracted were at x=25 millimeters (from the center of the beam).  This distance from the 
center was approximately half way between the loading and support rollers, minimizing 
the stress concentration effects created by the rollers.  The syntactic foam (SFS), IPC 
foam, and syntactic foam (SFS-b) core material of the same volume fraction were 
compared for a similar applied load.  Figure 7.7 shows an example of the dominant 
flexural normal strain ?x results at a load of ~4,000 N for the 20% volume fraction of 
microballoons in the SF.   
 
151 
-10.65
-8.15
-5.65
-3.15
-0.65
1.85
4.35
6.85
9.35
-0.45 -0.35 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.35 0.45
?x (%)
y 
(m
m) FLEX-38(SFS20)
FLEX-10
(IPC20)
FLEX-57
(SFSb20)
Material: IPC/SFS 
Temperature: 70?F
Rate: 0.025 in/min
Load: 4,000 N
 
Figure 7.7    20% Vf: Strain (?x) Variation Along the Height of the Sandwich Core 
 
At 4,000N load, the SFS sandwich was still in the linear region, while the IPC 
foam core and SFS-b sandwiches had entered the nonlinear regime.  Notice that the SFS 
and SFS-b sandwiches are generally exhibiting similar trends.  This makes intuitive sense 
considering the core material in each is the same syntactic foam.  When comparing the 
results with linear beam theory (where a linear strain variation through the thickness is 
expected), one can observe that near the top and bottom of the beam, the behavior 
deviates from linearity.  This can be explained by the effects of face sheets restricting the 
motion of the neighboring material points in the core, and by the increased amount of 
image processing errors near the face sheets.  Also, there is a shift in the neutral axis from 
the center of the beam in the SF core cases.  This can be explained by the severity of the 
stress concentration effects of the loading point in the SF core cases.  The expected 
general trend of greater strain experienced in the IPC foam core compared to syntactic 
foam of the same volume fraction is confirmed.  Remember that the SFS sandwiches 
152 
failed because of the intense shear stresses seen at the faces, causing face-core 
debonding.  The main idea to take away from the shear strain plots is that both IPC core 
and SFS-b sandwiches have done a better job of mitigating the intensity of the shear 
strains (and thus stresses) at the faces.   Figure 7.8 shows an example of the ?xy results at 
a load of ~4,000N for the 20% volume fraction of microballoons in the SF.   
 
-10.65
-8.15
-5.65
-3.15
-0.65
1.85
4.35
6.85
9.35
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040
?xy (rad)
y 
(m
m
) FLEX-38
(SFS20)
FLEX-10
(IPC20)
FLEX-57
(SFSb20)
Material: IPC/SFS 
Temperature: 70?F
Rate: 0.025 in/min
Load: 4,000 N
 
 Figure 7.8    20% Vf: Shear Strain (?xy) Variation Along the Height of the Sandwich Core 
 
 In the impact tests, two major aspects of note are the rate of energy absorption and 
the total strain energy absorbed by the specimen.  While the SFSb30 sandwiches had a 
higher rate of energy absorption, the IPC30 sandwiches actually had greater energy 
absorption capacity under impact conditions.  When compared to IPC30 sandwiches, the 
SFSb30 sandwiches had 22% less strain energy absorption and a 14% drop in specific 
energy absorption.  The SFSb30 absorbed energy at a rate of ~20 J/ms, while the IPC30 
153 
absorbed at a rate of ~12 J/ms.  Both architectures experienced visible core crack 
initiation around the same time.  SFS-b sandwich energy absorption only occurs from 
time zero (impact) up to the time of crack initiation.  The IPC foam core sandwiches, 
however, continue to absorb energy even after the onset of a crack resulting in greater net 
energy absorbed until complete failure.   
 
7.2 Future Work 
 
 The primary focus of this work was to understand flexural failure behavior of IPC 
and syntactic foam core sandwiches under quasi-static loading conditions.  An attempt 
was made to illustrate the feasibility of studying the same under impact loading 
conditions.  Experiments indicate an improved response of the IPC foam core sandwich 
over the SFS sandwich, including energy absorption.  However, in light of the failure 
mechanism typically observed in the IPC foam core, an effort was made to create a 
syntactic foam core sandwich with a graded face sheet to promote better load transfer 
throughout the sandwich.  The superior material that emerged and is recommended is the 
SFS-b sandwich architecture.   
Since most structures undergo combined loading it would be of interest to fully 
characterize the core material in tension and bending.  This study has not tested any of 
the core material without face sheets, and therefore cannot speculate on the properties of 
the core alone.   One particular future objective of interest would be to obtain mechanical 
properties (elastic modulus, Poisson?s ratio) of the core materials in bending and tension.  
Jhaver [17] was able to obtain mechanical properties of the materials in question, but in 
154 
compression only.  While the experimentally derived properties from compression should 
be close to those seen in bending, it would be advantageous to confirm this 
experimentally.  
The failures seen in the SFS sandwiches stemmed from debonding of the face-
core interface.  The face sheet would typically separate from the core, leaving the core as 
the only load bearing component.  Very shortly after this debond, the core would 
catastrophically fail.  This is unlike the IPC sandwich where a more synergistic 
relationship between the core and face was observed.  However, with the IPC core 
sandwich, interphase separation (between aluminum ligaments and SF) in the tensile 
region was the source of failure.  To better harness the face-core relationship for the 
syntactic foam core, smoother transition from face sheet to core needs to exist.  One 
possible solution is to have face sheets with a thin layer of brazed aluminum foam similar 
to that of the IPC.  A better response was achieved by better linking the face and core 
(SFS-b sandwiches), preventing the debond typically seen in the SFS sandwiches.  The 
useful extent of this thin layer of foam was not explored here.  In this work all of the 
graded face sheets had a layer of ~2 mm of aluminum foam brazed to the aluminum face 
sheet.  It would be beneficial to test varying thicknesses of this brazed layer of foam to 
determine at what depth the best overall response occurs while still maintaining the 
integrity of the syntactic foam core.  Another closely related idea that could be explored 
would be to change the method by which the core and face are fused.  With such stiff 
materials currently being used, it might be advantageous to attempt to use a more 
compliant layer as a transition layer from the core to the faces. 
155 
The impact tests in this work were only conducted using 30% volume fraction of 
microballoons in the SF.  The purpose of these tests was to further elaborate on the 
failure mechanisms in the quasi-static case, as well as begin to understand the failure 
mechanisms in the dynamic case.  Future work should involve varying the microballoon 
volume fraction.  Also, the feasibility of using DIC method in conjunction with a high 
speed digital camera to study impact behavior of sandwich structures is illustrated.  
Contrary to the quasi-static case, IPC foam core sandwiches appear to outperform the 
syntactic foam core sandwiches with graded face sheets.  The presence of the 
interpenetrating phases seems to have a positive effect under dynamic conditions.  These 
tests serve as a first step on the path to dynamic characterization of sandwich structures 
with syntactic foam and IPC foam core architectures. 
 
 
 
 
 
 
 
 
 
 
 
 
156 
 
 
 
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Plastics, Rubber, and Composites Processing and Applications 24 (1995) 271-275. 
 
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158 
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Digital Image Correlation.  Optics and Lasers in Engineering 27 (1997) 409-428. 
 
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Deformation and Strain Measurement.  Proceedings of SEM 2002 Annual 
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159 
 
 
 
 
APPENDIX A 
GLOBAL/LOCAL DISPLACEMENT COMPARISONS 
 
 The following are comparisons between the global load-displacement data from 
the machine and the local displacement data from the image correlation for each of the 
specimens used as examples throughout the thesis. 
 
0
1000
2000
3000
4000
5000
6000
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Displacement (mm)
Lo
ad
 (N
)
Crosshead
ARAMIS
Material: SFS20
Temperature: 70?F
Specimen: FLEX-38
Cast: 12Jul2010
Test: 14Sept2010
Rate: 0.025 in/min
 
Figure A.1    Global/Local Displacement Comparison, FLEX-38 (SFS20) 
 
160 
0
1000
2000
3000
4000
5000
6000
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Displacement (mm)
Lo
ad
 (N
)
Crosshead
ARAMIS
Material: SFS30
Temperature: 70?F
Specimen: FLEX-39
Cast: 04Oct2010
Test: 26Oct2010
Rate: 0.025 in/min
 
Figure A.2    Global/Local Displacement Comparison, FLEX-39 (SFS30) 
 
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Displacement (mm)
Lo
ad
 (N
)
Crosshead
ARAMIS
Material: SFS40
Temperature: 70?F
Specimen: FLEX-24
Cast: 18May2010
Test: 15Jul2010
Rate: 0.025 in/min
 
Figure A.3    Global/Local Displacement Comparison, FLEX-24 (SFS40) 
 
161 
0
1000
2000
3000
4000
5000
6000
0.0 0.5 1.0 1.5 2.0 2.5
Displacement (mm)
Lo
ad
 (N
)
Crosshead
ARAMIS
Material: IPC20
Temperature: 70?F
Specimen: FLEX-10
Cast: 30Sept2009
Test: 21Apr2010
Rate: 0.025 in/min
 
Figure A.4    Global/Local Displacement Comparison, FLEX-10 (IPC20) 
 
0
1000
2000
3000
4000
5000
6000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Displacement (mm)
Lo
ad
 (N
)
Crosshead
ARAMIS
Material: IPC30
Temperature: 70?F
Specimen: FLEX-16
Cast: 15Apr2010
Test: 09Jun2010
Rate: 0.025 in/min
 
Figure A.5    Global/Local Displacement Comparison, FLEX-16 (IPC30) 
 
162 
0
1000
2000
3000
4000
5000
0.0 0.5 1.0 1.5 2.0 2.5
Displacement (mm)
Lo
ad
 (N
)
Crosshead
ARAMIS
Material: IPC40
Temperature: 70?F
Specimen: FLEX-14
Cast: 07Oct2009
Test: 21Apr2010
Rate: 0.025 in/min
 
Figure A.6    Global/Local Displacement Comparison, FLEX-14 (IPC40) 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5
Displacement (mm)
Lo
ad
 (N
)
Crosshead
ARAMIS
Figure 1.1-1    Flexural Response of SF Sandwich (20%) at Room Temperature
Material: SFSb20
Temperature: 70?F
Specimen: FLEX-57
Cast: 23Jan2011
Test: 10Feb2011
Rate: 0.025 in/min
 
Figure A.7    Global/Local Displacement Comparison, FLEX-57 (SFSb20) 
 
163 
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Displacement (mm)
Lo
ad
 (N
)
Crosshead
ARAMIS
Figure 1.1-1    Flexural Response of SF Sandwich (30%) at Room Temperature
Material: SFSb30
Temperature: 70?F
Specimen: FLEX-59
Cast: 25Jan2011
Test: 02Feb2011
Rate: 0.025 in/min
 
Figure A.8    Global/Local Displacement Comparison, FLEX-59 (SFSb30) 
 
0
1000
2000
3000
4000
5000
6000
7000
8000
0.0 0.5 1.0 1.5 2.0 2.5
Displacement (mm)
Lo
ad
 (N
)
Crosshead
ARAMIS
Figure 1.1-1    Flexural Response of SF Sandwich (40%) at Room Temperature
Material: SFSb40
Temperature: 70?F
Specimen: FLEX-65
Cast: 01Feb2011
Test: 10Feb2011
Rate: 0.025 in/min
 
Figure A.9    Global/Local Displacement Comparison, FLEX-65 (SFSb40) 
 
 
 
164 
 
 
 
APPENDIX B 
SELECT ARAMIS? IMAGES 
 
The series of images shown in Figure B.1 are typical ARAMIS? ?y results for 
tests conducted on IPC sandwiches.  This case (IPC30) is simply used as an example to 
illustrate the ?y trends.  In the set of four images, the first image corresponds to a point in 
the linear regime, the second image corresponds to a point in the nonlinear regime, the 
third image corresponds to the point just before failure, and the fourth image corresponds 
to the point just after failure.  Note the units are measured in percent.  Also note that the 
correlated images for IPC30 contain twenty contours with an increment of 0.15%.  The 
strains are evenly distributed, with muted concentration effects. 
The series of images shown in Figure B.2 are typical ARAMIS? ?y results for 
tests conducted on SFS-b sandwiches.  Again, this case (SFSb30) is used as an example.  
In the set of three images, the first image corresponds to a point in the linear regime, the 
second image corresponds to a point in the nonlinear regime, and the third image 
corresponds to the point just before failure.  As before, the units are in percent.  The 
correlated images for SFSb30 also contain twenty contours, but this time with an 
increment of 0.5%.  Notice the concentration effects seen in this case. 
 
 
 
165 
  
  
  
  
Figure B.1    ARAMIS? Results for IPC30 (FLEX-16, ?y) 
 
 
 
 
 
x 
y 
P=1097N 
P=3997N 
P=5680N 
P=3741N 
166 
 
 
 
Figure B.2    ARAMIS? Results for SFSb30 (FLEX-59, ?y) 
 
 
 
 
 
 
 
x 
y 
P=2990N 
P=6717N 
P=7559N