Metal and Polymer Foam Hybrid Materials: Design, Fabrication and Analysis

METAL AND POLYMER FOAM HYBRID MATERIALS: DESIGN, FABRICATION AND ANALYSIS

Julianna E. Campbell

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Materials Science and Engineering University of Toronto

METAL AND POLYMER FOAM HYBRID MATERIALS: DESIGN, FABRICATION AND ANALYSIS

Julianna E. Campbell Master of Applied Science Graduate Department of Materials Science and Engineering University of Toronto 2009

Two novel hybrid materials for use in sandwich cores of structural materials are designed, manufactured and mechanically tested. Each material is a hybrid of metal and polymer foam. One set of hybrids is fabricated using an aluminium micro-truss filled with varying densities of polyurethane foam. Increases up to 120% in stiffness, 372% in strength, 740% in resilience and 106% in impact energy over the aluminium micro-truss are obtained from compression and impact testing. Furthermore, the stiffness of these hybrids can be tailored according to the density of the polyurethane foam. Another set of hybrids is fabricated using a rapid prototyped ABS polymer truss that is foamed and electroplated with nanocrystalline nickel. Increases up to 1525% in stiffness, 1165% in strength and 650% in energy absorption over the foamed ABS truss are obtained. Furthermore, the gain in strength, stiffness and energy absorption outweigh the gain in density in these hybrid materials.

ii Acknowledgements

This work could not have been completed without the help and support of many col- leagues and friends. First and foremost I would like to thank my supervisors, Dr. Hani Naguib and Dr. Glenn Hibbard. Their guidance and support was invaluable throughout the course of this research. Further thanks goes to the Hybrid Materials group, especially to Marc Suralvo for helping with the electroplating of the ABS trusses, to Ian Stewart for helping to fabricate the aluminium PCMs and to Brandon Bouwhuis and Eral Bele for their help with the inelastic buckling models. A special thanks also to those in the SAPL group: Linus Leung, Christine Chan, Aaron Price, Reza Rizvi, Eunji In, Choonghee Jo, Joe McRae, Jack Chang, Dina Badawy and all of the summer students for their support, help and advice, and most importantly for making this experience enjoyable. To my parents, Ian and Linda, sisters, Katie and Laura, brothers-in-law, Roland and Bryan and many friends who have been waiting for me to ﬁnish school for many years now - I think this is it - thanks for your support through all of the years! Most of all I would like to thank my husband, Scott. I am forever grateful for his endless patience and support throughout this process and for all of his help with my research and latex. Without him, this thesis would never have been completed.

iii Contents

1 Materials to Fill the High-Strength, Low-Density Void 1 1.1 Materials Selection Charts: Looking at Materials Space ...... 2 1.2 Hybrid Materials that Fill the Empty Space in Materials Selection Charts 4 1.3 Objective of Thesis ...... 7 1.4 Overview of Thesis ...... 9 1.5 Conclusion: Developing Hybrid Materials to Fill Materials Space . . . . . 10

2 Structural Materials: Sandwich Structures 11 2.1 Sandwich Structures ...... 11 2.2 Lattice Sandwich Core Materials ...... 13 2.2.1 Polymer Foams: Bending-dominated cellular materials ...... 14 2.2.2 Periodic Cellular Metal Micro-Trusses: Stretch-dominated lattice materials ...... 16 2.3 Hybrid Materials ...... 19 2.3.1 Polymer Foam Matrix Hybrid Materials ...... 19 2.3.2 Plated Hybrid Materials ...... 20 2.4 Conclusion: Current Hybrid Materials Missing the Low-Density Advan- tage of Foam ...... 22

3 Pyramidal PCM and Polyurethane Hybrid Materials 23 3.1 Materials and Sample Manufacture ...... 23

iv Contents

3.2 Experimental Method and Mechanical Testing ...... 26 3.2.1 Compression Testing of PCM, PU Foam and Hybrid Materials . . 27 3.2.2 Impact Testing of PCM, PU Foam and Hybrid Materials . . . . . 27 3.3 Results of Mechanical Testing ...... 29 3.3.1 Stiﬀness of PCM, PU Foam and Hybrid Materials ...... 31 3.3.2 Strength of PCM, PU Foam and Hybrid Materials ...... 36 3.3.3 Resilience of PCM, PU Foam and Hybrid Materials ...... 40 3.3.4 Impact Resistance of PCM, PU Foam and Hybrid Materials . . . 41 3.4 Conclusion: PCM/PU Foam Hybrid Materials Oﬀer Advantages Over Constituent Parts ...... 49

4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 50 4.1 Sample Development and Manufacture ...... 50 4.1.1 Rapid Prototyping the ABS trusses ...... 51 4.1.2 Batch Foaming of the ABS Trusses ...... 51 4.1.3 Electroplating of ABS Trusses ...... 59 4.1.4 Summary ...... 60 4.2 Experimental Method and Mechanical Testing ...... 60 4.3 Results of Mechanical Testing ...... 62 4.3.1 Mechanical Properties of Foamed and Plated ABS Trusses . . . . 67 4.3.2 Eﬀects of Foaming and Plating ...... 71 4.3.3 Buckling Analysis of Plated ABS Trusses ...... 80 4.4 Summary ...... 84

5 Conclusions and Future Work 85

References 89

v List of Figures

1.1 Typical material selection chart ...... 3 1.2 Hybrid materials are a combination of two or more existing materials . . 4 1.3 Four main types of hybrid materials ...... 6 1.4 Materials selection chart of Young’s modulus versus density ...... 8

2.1 Examples of sandwich structures ...... 12 2.2 Example of honeycomb ...... 13 2.3 Examples of periodic cellular metal (PCM) micro-trusses ...... 17

3.1 Manufacturing the pyramidal PCMs ...... 24 3.2 Schematic of the mold used to create the hybrid materials ...... 25 3.3 Pyramidal PCM, PU foam and hybrid samples ...... 27 3.4 Gardner impact tester ...... 28 3.5 Representative stress-strain curves - high density ...... 30 3.6 Representative stress-strain curves - low density ...... 30 3.7 Comparison of stiffness for pyramidal PCM, polyurethane foam and hybrids 32 3.8 Comparison of stiffness and density for the PCM, foams and hybrids . . . 34 3.9 Comparison of hybrid stiffness and foam stiffness ...... 35 3.10 Comparison of strength for pyramidal PCM, polyurethane foam and hybrids 36 3.11 Comparison of strength and density for the PCM, foams and hybrids . . 37 3.12 Comparison of the strength of the polyurethane foam samples found experimentally and using Menges model ...... 39

vi List of Figures

3.13 Comparison of the strength of the hybrid samples found experimentally and using Menges model ...... 39 3.14 Comparison of resilience for pyramidal PCM, polyurethane foam and hybrids 40 3.15 Comparison of resilience and density for the PCM, foams and hybrids . . 41 3.16 Damage profile for the pyramidal PCM ...... 42 3.17 Damage profile for the PU foams ...... 43 3.18 Damage profile for the PCM/PU foam hybrids ...... 43 3.19 Comparison of impact failure modes for the PCM, foams and hybrids . . 45 3.20 Comparison of impact energy for crack formation in the PU foam samples 46 3.21 Comparison of impact energy for pyramidal PCM and hybrids ...... 47 3.22 Comparison of impact energy of the hybrid versus the sum of its parts (the PCM and PU foam) ...... 47 3.23 Comparison of impact energy and density ...... 48

4.1 Schematic diagram of fused deposition modeling (FDM) process . . . . . 52 4.2 CAD drawing of polymer truss ...... 53 4.3 Rapid prototyped polymer truss sample ...... 54 4.4 SEM micrograph of the cross-section of the ABS truss ...... 54 4.5 Photo of rapid prototyped ABS trusses ...... 56 4.6 Percentage of volume expansion of rapid prototyped ABS trusses versus foaming temperature ...... 56 4.7 Micrographs of the foamed structure of the rapid prototyped ABS trusses 57 4.8 Nanocrystalline nickel plated ABS truss ...... 59 4.9 Failure of ABS trusses due to edge eﬀects ...... 61 4.10 Restriction plate used during compression testing to eliminate edge eﬀects 61 4.11 Representative stress-strain curves where strain is calculated using both the total truss height and the core height ...... 62 4.12 Representative stress-strain curves for the unplated ABS trusses . . . . . 63 4.13 Representative stress-strain curves for the plated ABS trusses ...... 63

vii List of Figures

4.14 Comparison of representative stress/strain plot and derivative/strain plot for plated samples foamed at 85 ◦C ...... 65 4.15 Comparison of representative stress/strain plot and derivative/strain plot for unplated samples foamed at 85 ◦C...... 66 4.16 Fracture at the node joint of the plated ABS truss at peak strength . . . 67 4.17 Representative stress-strain curves of the plated and unplated rapid prototyped ABS trusses ...... 68 4.18 Mechanical properties of the nano-Ni plated and unplated ABS trusses . 70 4.19 Material selection charts for mechanical properties of the nano-Ni plated and unplated ABS trusses ...... 72 4.20 Decreasing trends in specific stiffness, specific strength and specific energy absorption of the foamed ABS trusses ...... 73 4.21 Comparison of the strength of the ABS foam trusses found experimentally and using the Gibson/Ashby model ...... 75 4.22 Relative ratios for mechanical properties of the foamed ABS trusses . . . 77 4.23 Relative ratios for mechanical properties of the nano-Ni plated and unplated ABS trusses ...... 79 4.24 Comparison of the theoretical and experimental force per strut versus the cross-sectional area of the core for pinned (k=1) end conditions . . . . . 82 4.25 Comparison of the theoretical and experimental strength versus the cross- sectional area of the core for pinned (k=1) end conditions ...... 82 4.26 Comparison of hybrid strength with previous studies ...... 83

5.1 Materials selection chart with PCM/PU foam and ABS/nanoNi hybrid materials ...... 88

viii List of Tables

3.1 Nine different sample types ...... 26 3.2 Average results of strength, stiffness and resilience from compression tests 31 3.3 Percentage increase of density, strength, stiffness and resilience in the hybrid samples compared to the PCM ...... 32 3.4 Average results for the impact energy for given failure modes of the PCM 44 3.5 Average results for the impact energy for given failure modes of the PU foams ...... 44 3.6 Average results for the impact energy for given failure modes of the PCM/PU foam hybrids ...... 44

4.1 ABS truss dimensions ...... 52 4.2 Foaming parameters ...... 55 4.3 Summary of truss dimensions after foaming ...... 58 4.4 Thickness of nano-Ni coating on ABS trusses ...... 60 4.5 Average results of strength, stiﬀness and energy absorption ...... 69 4.6 Percentage increase of strength, stiﬀness and energy absorption of the nanocrystalline nickel plated trusses over the ABS foamed trusses . . . . 71

ix Chapter 1

Materials to Fill the High-Strength, Low-Density Void

There is a large demand for lightweight structural materials in the aerospace, automotive and consumer goods industries. In the aerospace industry, a reduction in the overall mass of an aircraft directly relates to an increase in the amount of payload or reduction in fuel consumption. The structural weight of an aircraft contributes 23 - 29% of its total take- off weight [1]. In an industry that relies on the transportation of goods and passengers for its profits, a decrease in the structural weight, and thus an increase in payload, would be highly beneficial. By reducing the number of total flights in order to move a specific total payload, aerospace companies would have lowered fuel costs, fewer crew hours and fewer flight hours. The aerospace industry requires materials that are high in strength and stiffness, but low in density for the fuselage and wings of aircraft. A reduction in density of the aircraft’s structural materials could greatly reduce the overall mass of the aircraft. In the automotive sector, a reduction in the overall mass of the body of an automobile would improve fuel economy. Similar to the aerospace industry, the automotive industry requires high strength materials, but here, an emphasis on impact resistance and energy absorption is also paramount for safety reasons.

1 Chapter 1 Materials to Fill the High-Strength, Low-Density Void 2

Moving away from vehicular applications, there are many consumer goods that also make use of similar high-strength, low-density structural materials such as skis and snowboards. For these applications high strength is important, as well as the ability to tailor the stiffness of the final product in order to create a superior piece of equipment for a given user. These three industries are just a sampling of those that require high-strength materials with low density that also have some additional requirement such as the ability to tailor the stiffness of the material, or increased impact resistance. The materials used for these applications have changed over time as new materials are developed with improvements over their predecessors. Ultimately, engineers and materials scientists are continually trying to improve upon or develop new materials that offer better mechanical properties for a given application, or are cheaper or faster to manufacture. A recent trend to develop multi-functional materials, materials that have desirable properties beyond strength, has also pushed the industry to develop new materials. Currently, there are many deficiencies in materials selection; to understand this we look to materials selection charts.

1.1 Materials Selection Charts: Looking at Materials

Space

Materials selection charts are used to aid engineers in choosing the optimal material for a speciﬁc task. Based on a certain set of design criteria, these charts help to narrow down the choices of available materials for a given application. Modulus, strength, density and cost are some of the primary properties that materials selection charts map out, however, many other properties are charted where a given application requires them, such as impact resistance. An example of a materials selection chart for strength versus density is given in Figure 1.1 [2]. In this ﬁgure, it is easy to pick out the high strength, high density metals in the upper right-hand corner of the chart, and the lower density, lower strength polymer foams in the lower left-hand corner of the chart. However, there are many areas Chapter 1 Materials to Fill the High-Strength, Low-Density Void 3

Figure 1.1: Typical material selection chart [2]. Chapter 1 Materials to Fill the High-Strength, Low-Density Void 4

Figure 1.2: Hybrid materials are a combination of two or more existing materials chosen to provide the ﬁnal hybrid material with properties that are not inherent to any of its constituent materials [3]. in the chart which are void of any materials including the high strength, low density region. Although some of these areas can never be accessed due to restraints on atomic size and forces, other areas could be ﬁlled with new materials that are developed either by new alloys, polymers or the like, or by combinations of two or more existing materials. The former option can be prohibitively costly and uncertain, so the latter option is the method chosen by many researchers [3].

1.2 Hybrid Materials that Fill the Empty Space in

Materials Selection Charts

Hybrid materials are a combination of two or more existing materials as shown in Fig- ure 1.2. The materials are chosen in such a way as to design a ﬁnal hybrid material that has properties that are not inherent to any of its constituent parts. There are four Chapter 1 Materials to Fill the High-Strength, Low-Density Void 5 main types of hybrid materials outlined in Figure 1.3 including composites, sandwich structures, lattices and segmented structures [3].

This study examines hybrid materials made of lattices from the third group to be used as cores for the sandwich structures of the second group. The third group of materials, lattices, is considered to be a hybrid of solid (typically a metal or polymer) and gas, wherein the properties of the gas become a relevant consideration in terms of thermal conductivity, compressibility and other properties. The two main types of lattice materials are bending-dominated and stretch-dominated lattices. Bending-dominated lattices are typically foams that fail due to the yielding, buckling or fracturing of their cell walls, whereas stretch-dominated lattices are typically triangulated lattice structures that are designed to ensure the struts of the lattice stretch rather than bend. By stretching, the stretch-dominated latices have a higher structural eﬃciency over the bending-dominated lattices [3].

The hybrids that will be developed in this study make use of both types of lattice structures in order to make use of the lower density properties of polymer foams (bending-dominated lattices) and the higher strength properties of metal trusses (stretch- dominated lattices). By using these two types of materials, the newly developed hybrids become multi-functional by offering additional advantages over their individual counterparts, such as greater impact resistance, along with improved mechanical properties such as strength and the ability to tailor the stiffness of the final material.

An emerging trend in materials science focuses on multi-functional materials, or rather materials that offer something in addition to load carrying ability such as enhanced vibrational or acoustical damping, or heat transfer capabilities [4–9]. Periodic cellular metals (PCMs) are a stretch dominated lattice structure that have been identified as being potential core materials for sandwich structures since they offer this multi-functionality. PCMs have superior load carrying capabilities and offer additional properties such as heat transfer and energy absorption [4, 5]. The hybrids developed in this study make use of the PCM architecture in order to take advantage of the stretch-dominated lattice Chapter 1 Materials to Fill the High-Strength, Low-Density Void 6

Figure 1.3: Four main types of hybrid materials: composites, sandwich structures, lattices and segmented structures [3]. Chapter 1 Materials to Fill the High-Strength, Low-Density Void 7

system and the potential for multi-functionality in terms of impact resistance and the ability to tailor the stiﬀness of the hybrid material.

1.3 Objective of Thesis

The overall objective of this thesis is to develop low density, high strength materials to be used as structural materials in the aerospace, automotive and consumer goods industries. These hybrid materials are also multi-functional in terms of greater impact resistance and the ability to tailor their stiffness. In so doing, an empty area of materials space will be filled with new hybrid materials as suggested by Ashby [3]. In particular an attempt will be made to fill the area found between existing bending lattice polymer foams and stretch lattice PCMs as shown in Figure 1.4, giving engineers a new material option for structural applications. In addition, a multi-functional hybrid material is developed that offers improved impact resistance as well as increased strength, stiffness and resilience.

Two types of novel hybrid materials are designed, fabricated and tested. Each of the hybrid materials makes use of both metal and polymer foam using a stretch-dominated lattice structure in hopes of capitalizing on the strength of the metal truss while reducing the overall density of the ﬁnal material by including polymer foam. The overall objective is considered in two ways: ﬁrst, a hybrid material is created using a periodic cellular metal (PCM) with metal struts which are surrounded by polymer foam, and second, a hybrid material is created using a PCM where a foam truss core is coated in metal. By examining these two distinct cases, this work expands materials space and provides new options for structural materials for use in the aerospace, automotive and consumer goods industries. Chapter 1 Materials to Fill the High-Strength, Low-Density Void 8

Figure 1.4: Materials selection chart of Young’s modulus versus density. Stretch dominated lattices have been found to ﬁll an existing hole in this chart [3]. Chapter 1 Materials to Fill the High-Strength, Low-Density Void 9

1.4 Overview of Thesis

The hybrid materials in this work are specifically designed using a periodic cellular architecture with both polymer foam and metallic components. Chapter 2 gives an overview of these periodic structures and how they have been have been used in hybrid materials in the past. Further insight is given into the use of these structures as cores in sandwich structures, and how sandwich structures have evolved and become invaluable in structural applications. The main work of this thesis follows in Chapters 3 and 4, split over two chapters in order to discuss the two distinct hybrid materials that are developed and tested. Chapter 3 discusses the first set of hybrid materials which make use of an aluminium metal truss system surrounded by polyurethane foam. An overview of the design, manufacture and testing of these hybrid materials is given followed by a discussion of the results of the mechanical testing. Overall, these hybrids exhibit up to 372% higher strength, 740% higher resilience and 106% greater impact energy than their PCM truss counterparts. It is also found that the stiffness can be tailored based on the density of the foam. Chapter 4 examines the second set of hybrid materials. These hybrids make use of a foamed ABS polymer truss system which is then electroplated with nanocrystalline nickel. Similarly, an overview of their design, manufacture and testing is given, followed by a discussion of the results and the effects of foaming and plating. Overall, the plating of the trusses greatly increases their mechanical properties including up to 1165% greater strength, 1525% greater stiffness, 650% greater energy absorption compared to thier foamed ABS truss counterparts. It is also found that plating, and foaming the ABS trusses is advantageous in terms of strength, stiffness and energy absorption, despite the gain in density due to the addition of the nanocrystalline nickel. Chapter 5 summarizes the key contributions of this work and how they relate back to the objectives of creating new structural materials for use in the aerospace, automotive and consumer goods industries, thus filling some of the holes in materials space. Recommendations are made for future work on this topic. Chapter 1 Materials to Fill the High-Strength, Low-Density Void 10

1.5 Conclusion: Developing Hybrid Materials to Fill

Materials Space

The need for high strength, low density materials is apparent for structural applications in the aerospace, automotive and consumer goods industries. A trend towards ﬁnding multi- functional materials has pushed the need for new material development. Hybrid materials created using two or more existing materials in various designs are a relatively inexpensive approach to this problem. This work explores two such materials and determines their feasibility as materials options for the given applications. Chapter 2

Structural Materials: Sandwich Structures

Sandwich structures are a commonly used structural material used for aircraft, auto- motives and consumer goods such as skis and snowboards. There are many different materials used for the core of sandwich structures, including foams and micro-trusses. Much research has been performed on improving sandwich structures including developing new core materials by examining different truss architectures, filling trusses with various materials, and plating trusses and metallic foams. This chapter will elucidate the background and literature summary of sandwich structures and their core materials including various truss architectures and hybrid materials.

2.1 Sandwich Structures

There is an ongoing need for lightweight structural materials in the aerospace and automotive industries. Past trends led to the use of sandwich structures in which two high-strength skin layers are separated by a central core which provides stiﬀness against bending and buckling [3,10]. Examples of sandwich structures with various core materials are given in Figure 2.1. The face sheet materials are selected based on their strength

11 Chapter 2 Structural Materials: Sandwich Structures 12

Homogeneous core materials:

Wood Cores Foam Cores

Structured core materials:

Honeycomb Cores Corrugated Cores Textile Cores

Figure 2.1: Examples of sandwich structures [11]. and stiffness as they carry most of the load [3]. Lightweight, stiff materials are chosen for the core as they must have the shear strength, shear modulus and compressive strength needed to withstand the shear stresses that the core undergoes [3, 12]. Less material is used in a sandwich structure than in its monolithic counterpart, which can allow for significant savings due to reduced material costs [13].

Sandwich structures are commonly manufactured with a lattice core made of honeycomb, metallic foam or polymer foam, and composite or metal face sheets [10, 14]. Honeycomb cores can be made in varying shapes and with various materials such as aluminium, glass reinforced plastics, aramid, carbon ﬁbre and kevlar [16]. Hexagonal honeycomb cores, as shown in Figure 2.2, made with aluminium 5052 alloy have compressive strengths of up to 15 MPa depending on their wall and cell thickness [16]. Common polymer foams used for sandwich cores include ABS, epoxies, phenolics, polypropylene, polyurethane and polyvinyl chloride. The hybrid materials developed in this study will use ABS and polyurethane (PU) foam. In sandwich core structures, ABS foam typically has a density in the range of 641 - 897 kg/m3 and a compressive strength ranging from 15.8 to 25.5 MPa, while rigid polyurethane foam has densities varying from 21 to 400 kg/m3 and compressive strengths varying from 0.10 to 13.8 MPa [16,17]. Chapter 2 Structural Materials: Sandwich Structures 13

Figure 2.2: Example of honeycomb [15].

Much research has been focused on sandwich structures and how to optimize their design based on a given set of loading conditions [13, 18–20]; however there have since been advances in the materials available for sandwich construction. Periodic cellular metals (PCMs) make use of a truss-like geometry which can be used as a core material since they oﬀer superior load carrying capacity and can provide multi-functionality such as heat transfer capabilities and energy absorption [4,5].

2.2 Lattice Sandwich Core Materials

Most sandwich structures make use of lattice materials as their core material. Lattice materials are lightweight due to their inherent cellular structure. As mentioned in Chap- ter 1, they are considered to be hybrids of a solid material, such as a polymer or metal, and gas. The gas is an important component of these structures as it contributes to various material properties such as thermal conductivity and compressibility [3].

There are two types of lattice materials; bending-dominated foams and stretch- dominated micro-trusses [21]. Both have been used as sandwich core materials in the past, and this study uses both bending- and stretch-dominated lattices to create novel hybrid materials which capitalize on the best properties of both types of materials. Chapter 2 Structural Materials: Sandwich Structures 14

2.2.1 Polymer Foams: Bending-dominated cellular materials

Polymer foams are bending-dominated cellular materials that fail along their cell edges due to either plastic bending, elastic buckling, or fracture for plastic, elastomeric, or brittle foams, respectively [3]. Sandwich cores are commonly made using rigid polymer foams [22]. Among the most frequently used polymers for this application is polyurethane.

Polyurethane (PU) foam is available commercially as a spray-foam product for insulation, or for other applications in a two-phase system in which the two components are mixed thoroughly before curing. For sandwich structures, the foam is injection molded into a cold-cavity die [16]. PU oﬀers superior thermal insulation and the ability to bond well with the sandwich face sheets [10]. It is also dimensionally stable and maintains high mechanical properties at high and low temperatures [23]. Studies into the eﬀect of the density of polyurethane foam show that at lower densities, the damping capacity increases [24,25]. The failure modes of rigid polyurethane foam change depending on the porosity of the foam [26, 27]. Theocaris tested various porosities of rigid polyurethane foams in compression and tension and found that with an increase in porosity, the failure mode would change from being stronger in compression to being stronger in tension [26].

Various models have been developed to predict the mechanical properties of polymer foams based on their relative density and the properties of the parent polymer [28, 29]. Menges et al. developed the following model to predict the compressive strength [29],

2 βD = αEpja0.0425χ (2.1)

where α is a clamping factor, Ep is the elastic modulus of the polymer, j is a determination factor (0.53 for PU), a is a reduction factor (a = βD−measured/βD−calculated) and χ is the relative density. In particular, for rigid polyurethane foam, this reduces to [29]:

2 2 βD = 1250χ [kp/cm ] (2.2) Chapter 2 Structural Materials: Sandwich Structures 15 in units of kilopond per centimeter squared (1 kp=9.80665 N). This model was derived by theoretically determining the buckling behaviour of the cell bars during compression, as the cell walls contribute little to the structural strength of the foam, and comparing the model with experimental data [29]. Rigid polyurethane foam is used in the design and manufacture of the ﬁrst set of hybrid materials in the present work.

Another model that is commonly used to predict the strength of polymer foams is the Gibson/Ashby model [28]. For elastic-plastic foams in compression, the model states [28]:

σ ρ 3/2 ρ = C1 φ CDCF + C2(1 − φ) (2.3) σYS ρs ρs

where σYS is the yield strength of the parent polymer, φ is a constant between 0 and 1 based on the number of open and closed cells in the foam (φ = 0 for closed cells, φ = 1 for open cells), ρ is the density of the foam, ρs is the density of the solid polymer, C1 and C2 are constants (for φ = 1,C1 = 0.3 , φ = 0,C1 = 0.44 for relative density < 0.2)

1/2 and CDCF is a density correction factor (1 + (ρ/ρs) ) which can be included, but has small inﬂuence.

The second set of hybrid materials in this study will be manufactured using acrylonitrile- butadiene-styrene (ABS). Although ABS is not as commonly used in a foamed structure compared to polyurethane, it is often used in rapid prototyping manufacturing, and has been selected based on its ability to form a porous (foam) structure [30–35]. The second group of hybrid materials in this study will use a rapid prototyped structure using ABS.

Due to the current methods of rapid prototyping available, the polymer making up the sample can not be foamed as it is being manufactured. Therefore a batch foaming method will be used to generate the porous structure [31] after the trusses have been manufactured. In this method, a sample is placed in a pressurized chamber which is

ﬁlled with a gas (commonly CO2 or N2) at a given pressure. The sample becomes saturated with the gas over a period of time after which the pressure is rapidly released. The sample is then placed in a hot water bath wherein the thermodynamic instability Chapter 2 Structural Materials: Sandwich Structures 16 of the rapid pressure drop and increase in temperature causes the cells to nucleate and grow. Finally, the sample is then quenched in a cool water bath in order to control the cell growth and left to air dry to allow the remaining gas to escape [36]. Although rapid prototyped ABS parts which has been foamed has not been considered in past studies, solid ABS rapid prototyped parts have been researched. For example, methods have been developed to optimize the design criteria for rapid prototyped ABS parts [37]. Much of the research surrounding the use of ABS as a core material is related to its use in hybrid materials which will be discussed in Section 2.3.2.

2.2.2 Periodic Cellular Metal Micro-Trusses: Stretch-dominated lat-

tice materials

Stretch-dominated lattices are open-cell systems that make use of a truss-like geometry in order to reduce the overall amount of material used and thus reduce the structure’s mass [6,15,38]. The term ’periodic cellular metals (PCMs)’ refers to tubes, beams or wires arranged in a three-dimensional repeating architecture that are used to make up their lattice structure [3]. Figure 2.3 shows some examples of periodic cellular metal micro- trusses developed using various geometries including pyramidal, tetrahedral, kagome and others [7]. Previous studies show that PCMs offer the same lightweight advantages as honeycomb cores, but with additional multi-functionality such as cooling and vibration control [5]. Compared to metallic foams, PCMs have higher specific strength and stiffness [6, 7, 39]. Additional properties such as thermal management, dynamic load protection, acoustic damping and better crush strength make PCMs an attractive alternative to honeycomb or metallic foam cores [7–9]. Much research has centered around the processing of these micro-trusses [40–43]. Some studies examined the effects of heat treatments on these structures, especially when adding faceplates [40, 41]. Other studies looked at the effects of using different manufacturing techniques [42,43]. Chapter 2 Structural Materials: Sandwich Structures 17

(a) tetrahedral (b) pyramidal (c) 3-D Kagomé

(d) Diamond weave (e) hollow truss (f) egg-box

Figure 2.3: Examples of periodic cellular metal (PCM) micro-trusses [7].

Mostly, PCM research has focused on the mechanical testing, failure analysis and modeling of these structures [41, 44–49]. Mechanical properties of PCMs vary greatly depending on geometry of the truss, geometry of the strut and the material used. Pyra- midal PCMs manufactured using aluminium alloy 3003 that have been resistance brazed to face plates of the same material have a compressive strength of up to 0.95 MPa [41]. In terms of failure, it has been found that PCMs typically fail by Euler buckling, shear buckling or face wrinkling and that this failure depends on the properties of the bulk material and the geometry of the PCM [6, 45]. PCMs that are not restricted with face sheets fail by plastic hinging collapse [47]. McShane et al. examined the energy absorption and shock resistance of these lattices [50]. They found that the sandwich plates have a higher shock resistance than similar monolithic plates which was veriﬁed with ﬁnite element method (FEM) simulations [50].

A model for the strength of an ideal PCM in compression was developed by Deshpande et al. [51]:

2 σPCM = σF ρRsin ω (2.4)

where σF is the failure strength of the strut, ρR is the relative density and ω is the strut angle. The failure strength of the strut, σF , is dependent on the slenderness ratio L/r Chapter 2 Structural Materials: Sandwich Structures 18

(where L is the length of the strut and r is the radius of gyration). For small slenderness

ratios, corresponding to short, stocky struts which fail by yielding, σF ≡ σYS, the yield strength. However, for larger slenderness ratios, the struts of the PCM fail by buckling

and σF ≡ σCR, the critical buckling stress.

The critical buckling stress was developed by Shanley and is given by [52]:

k2π2E I k2π2E σ = t = t (2.5) CR AL2 (L/r)2

where k accounts for the rotational stiﬀness of the strut (k=1 corresponds to pinned ends,

k=2 corresponds to ﬁxed ends), Et is the tangent modulus, I is the moment of inertia, A is the cross-sectional area and L is the length of the strut. For very high slenderness ratios, elastic buckling will occur and Et ≡ E, Young’s modulus. However, in the elastic to plastic region of the stress strain curve, various models have been developed to model the strain behaviour [53,54]. The Ramberg-Osgood model is one such constitutive relationship [53]: σ σ N = + 0 (2.6) E σYS

where is the strain, σ is the stress, E is the Young’s modulus, 0 is the plastic strain

corresponding to the yield strength, σYS (0.002) and N is a strain hardening exponent. By ﬁnding the derivative to equation 2.6,

−1 N−1−1 ∂ 1 0 σ Et = = + N (2.7) ∂σ E σYS σYS

the critical stress can be calculated. By solving equations 2.5 and 2.7 together, the

slenderness ratio required for σ = σCR is:

r L E = π t . (2.8) r σ

In the Deshpande model described above, the PCM is assumed to have perfectly aligned struts with perfectly uniform cross-sections, which is rarely the case. Therefore it often Chapter 2 Structural Materials: Sandwich Structures 19 over-predicts the actual strength of the PCM [40,42,55–57]. A knockdown factor has been included in many studies to account for the slight abnormalities in strut cross-section and alignment [58–60]. Overall the research trends for PCMs found that they offer greater strength-to-weight and stiffness-to-weight ratios over metallic foams. PCMs have been manufactured using various techniques, materials and geometries. They outperformed metallic foams in terms of strength and stiffness and are comparable to honeycombs, yet at reduced cost and increased multi-functionality [61]. The multi-functional benefits include properties such as heat transfer and impact resistance. Although considered to be a hybrid material with gas themselves, these structures were also used with other materials to create further hybrids. Their open porosity allows ample opportunity to fill them with various materials in order to further enhance their mechanical properties, or add additional multi-functionality [62].

2.3 Hybrid Materials

Hybrid materials can be developed by combining existing materials in order to access new regions of materials property space [63]. This section will explore the development of previous hybrid materials used for sandwich cores including polymer foam matrix hybrids and plated trusses.

2.3.1 Polymer Foam Matrix Hybrid Materials

Many studies have examined using polymer foams as a matrix material for various hybrid structures. For example, by adding fibers or fabrics to polyurethane (PU) foam it has been found that there is an optimum fiber content that increases tensile strength, hardness and impact strength of the PU foam [64–67]. Other groups had success improving the impact resistance of honeycomb cores by fully or partially filling the cells of the honeycomb with polymer foam [68–71]. Similarly, the cells of PCMs have been filled with polymers and hard ceramics in order to increase impact resistance [56,62,72]. Chapter 2 Structural Materials: Sandwich Structures 20

Very little research has considered the addition of polymer foams to PCMs, however similar studies of filling other lattice structures with polymer foams exist [73, 74]. One such study examined the effects of adding a phenolic polymer foam to the empty spaces in a corrugated lattice made from fiber reinforced plastic [73]. Other similar studies found that energy absorption could be improved by adding polyurethane foam to egg-box type lattices manufactured using fabric composites [74]. The first set of hybrid materials in this study extends this previous work by examining PCMs filled with polyurethane foam. In these hybrids, the foamed polymer further decreases the density of the overall hybrid material compared to using a solid polymer, and improvements are made in strength, stiffness and impact resistance over the PCM alone.

2.3.2 Plated Hybrid Materials

Some of the hybrid materials examined in this study are electrolytically plated with nanocrystalline nickel. Nanomaterials are named such due to their small grain size. They received recent acclaim due to their desirable properties such as increased strength, hardness and toughness [75–77]. Electrodeposition has become a common method to produce nanostructured materials as it is simple, inexpensive and versatile [78, 79]. The second set of hybrid materials in this study use electrolytically deposited nanocrystalline nickel plating due to its high yield strength [79]. Although this is a fairly recent branch of research, there have been some studies that follow similar trends. Some of this research has focused on plating PCMs, while other research has explored plating polymer lattices. Bouwhuis et al. examined the effects of plating nanocrystalline nickel on plain carbon steel PCMs and found that a thin coating of approximately 50 µm would double the inelastic buckling resistance of the struts of the micro-truss [60]. This same group examined the effects of plating nanocrystalline nickel on metal foams and found that their samples had a non-uniform coating thickness. Though they observed an increase in the overall strength, there was not a significant increase in the specific strength of the Chapter 2 Structural Materials: Sandwich Structures 21 coated foams [59]. They concluded that a uniform coating thickness would have increased the specific strength. In a similar study, Boonyongmaneerat et al. examined the effects of electrodepositing Ni-W on reticulated aluminium foams and found that the plated foams had greater absolute and specific strength and absolute energy absorption [80]. They were able to obtain uniform coating thicknesses on their samples by adjusting the deposition time, the bath chemistry and the applied current.

Looking at polymer lattices, Gordon et al. explored the idea of plating nanocrystalline nickel on pyramidal periodic cellular structures made of a rapid prototyped acrylic based polymer [58]. They found that at a coating thickness of approximately 15 µm (on a polymer strut cross-section of 0.18 mm by 0.39 mm), a 350% increase in elastic modulus and a 500% increase in peak strength could be obtained over that of the polymer core. Further increases were found by increasing the thickness of nanocrystalline nickel. Markkula et al. used rapid-prototyped ABS and plated pyramidal, tetrahedreal and strut-reinforced tetrahedral lattices with copper and nickel [81]. They found that their plated ABS hybrids had increased stiﬀness, yield strength, ultimate strength, and strain-to-failure over the pure ABS lattices.

Electroplating of other rapid prototyping materials has also been examined. Saleh et al. looked at the mechanical properties of electroplated sterolithographed parts [82]. They used rapid prototyped parts made from an epoxy based resin which were then coated with varying thicknesses of copper/nickel. Testing of tensile coupons resulted in higher Young’s modulus, tensile strength and impact strength. Liu et al. studied the bending properties of nickel coated photo-polymers used in stereolithography [83]. They found that a thin layer of nickel could improve the strength and stiﬀness of the rapid prototyped parts.

The second set of the hybrid materials in this study follow a similar trend to Gordon and Markkula [58,81]. Rapid prototyped ABS pyramidal lattice structures are foamed to obtain different densities. These lattices are then electrodeposited with nanocrystalline nickel. Although Markkula has looked at the effects of plating rapid prototyped ABS Chapter 2 Structural Materials: Sandwich Structures 22 lattice structures with nickel, the effect of foaming these trusses, and thus further reducing their density will add value to the current research trends.

2.4 Conclusion: Current Hybrid Materials Missing the

Low-Density Advantage of Foam

Much research has gone into the area of hybrid materials in hopes to fill in the empty areas of materials space with the goal of developing materials with superior mechanical properties. In terms of structural materials, there is a great need for low density, high strength materials in the aerospace, automotive and consumer goods industries. Many of those exploring hybrid materials to date had success increasing strength, stiffness and impact resistance, while maintaining a low density; however, the materials studied to date lack the additional low density advantage of the cellular structure of foam. PCMs have been filled with many materials including polymers and ceramics, but foam offers the opportunity to further reduce the density. The first set of hybrid materials in this study extends the range of PCMs by filling them with polyurethane foam. This set of hybrids constitutes a metal PCM strut surrounded by a polymer foam. Conversely, the second set of hybrid materials in this study examines materials made of a polymer foam strut which is plated with metal. These hybrid materials extend the work done by Markkula et al. by foaming the ABS lattices and plating them with nanocrystalline nickel rather than a copper/nickel combination. The present work will demonstrate that the small grain size in the nanocrystalline nickel provides increased strength to the ABS trusses. These novel hybrid materials will help to expand materials space and give engineers further options when looking for structural materials which are low in density and high in strength, stiffness and impact resistance. Chapter 3

Pyramidal PCM and Polyurethane Hybrid Materials

This chapter will focus on hybrid materials developed using aluminium periodic cellular metals (PCMs) with a pyramidal architecture that are ﬁlled with polyurethane foam. In this case, the hybrid materials have a metal strut which is reinforced by the surrounding polymer foam. Various densities of polyurethane (PU) foam were combined with pyramidal PCMs to create the hybrid materials. These materials were then mechanically tested in compression and impact in order to compare their stiﬀness, strength, resilience and impact energy with that of the PU foam and PCM.

3.1 Materials and Sample Manufacture

To manufacture the hybrid samples, two separate materials: the PCM and the polymer foam, were required. The pyramidal PCMs were manufactured using a perforation stretching method [15]. A sheet of aluminium 3003 with square perforated holes was trimmed to ﬁt the PCM press as shown in Figure 3.1(a). The trimmed sheet was annealed at 600 ◦C for one hour in order to increase its formability while being shaped into the pyramidal truss form of

23 Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 24

(a) (b)

Figure 3.1: Manufacturing the pyramidal PCMs requires (a) a sheet of Al 3003 with square perforations which is placed in (b) a press with pins on alternating nodes both above and below the Al sheet. The press is compressed and the (c) resultant PCM is removed. Faceplates are adhered to the top and bottom of the PCM (d). the PCM. It was then quenched in water and placed in the press. The PCM press had pins on alternating nodes both below and above the sheet as shown in Figure 3.1(b). The press was then compressed at a constant displacement of 5 mm/min. The pins applied a force to the nodes to stretch them to an overall displacement of 6.5 mm which resulted in the desired pyramidal geometry as shown in Figure 3.1(c).

In the ﬁnal step, faceplates of the same perforated aluminium 3003 were adhesively bonded to the PCM by surface roughing the nodes and faceplates before applying a small amount of acrylic adhesive. The ﬁnal pyramidal PCM which was used to create the hybrid materials is shown in Figure 3.1(d). These samples were approximately 56 mm by 56 mm with a thickness of 10 mm and a density of 337 ± 1 kg/m3.

Two types of commercially available polyurethane foam were used to create the hybrid materials for this study. The ﬁrst was a single-phase rigid polyurethane insulating foam by Dow Chemical, while the second was a two-phase rigid polyurethane foam produced Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 25

Wooden Frame Polypropylene

PCM Foam

Figure 3.2: Schematic of the mold used to create the hybrid materials. Two wooden frames coated with either a sheet of polypropylene or cotton fabric, sandwiched the PCM and uncured PU foam. The clamped wooden frames restricted the direction of foam expansion and provided a level surface on the ﬁnal hybrid materials. by Smooth-On. This two-phase foam consisted of two liquid subcomponents that were mixed in equal amounts by volume before being applied. The hybrid PCMs were fabricated using an upper and lower wood and plexiglass frame. Layers of either cotton fabric or polypropylene, for the one-phase and two-phase PU foams respectively, were used between the PCM and the frame to allow for easy release after the foam was fully cured. To produce the hybrids using the one-phase foam, some of the foam was layered onto the bottom plate, then the PCM was placed on top of the uncured foam, and more foam was layered on top of the PCM. To produce the hybrids using the two-phase foam, the PCM was placed directly on the lower plate and the uncured foam mixture was poured over top of the PCM. Finally, the top plate was placed over the PCM and uncured foam mixture. A schematic of this setup is given in Figure 3.2. The two plates were then clamped together to ensure that the pressure of the foam expansion during the curing process did not cause the plates to separate. This restricted the direction of foaming and allowed for the sample to have a level and uniform top and bottom face. The hybrids were then left for at least 2 or 24 hours for the two- and one-phase foams, respectively, to cure. Once the curing process was complete, the clamps were released and the hybrid was removed from the mold. Excess foam was trimmed from the hybrids to create the ﬁnal samples. Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 26

Table 3.1: Nine diﬀerent sample types.

PCM Polyurethane Foam Hybrid Materials (density, kg/m3) (PU foam density, kg/m3) Pyramidal One-phase (83 ± 3) Pyramidal PCM/(83 ± 3) Two-phase (113 ± 2) Pyramidal PCM/(113 ± 2) Two-phase (232 ± 2) Pyramidal PCM/(232 ± 2) Two-phase (290 ± 2) Pyramidal PCM/(290 ± 2)

Reference foam samples were made in a similar manner as the hybrid materials as described above, however, for the foam samples, the PCM was excluded from the mold. These samples had dimensions that were comparable to the PCMs and hybrid materials and along with mechanical testing, these samples were used to calculate the density, ρ, of the PU foams using m ρ = (3.1) V

where m is the mass of the sample and V is the volume of the sample. The one- phase Dow Chemical foam had a density of 83 ± 3 kg/m3, while three densities of the two-phase Smooth-On foam were used to create the hybrid materials: 113 ± 2 kg/m3, 232 ± 12 kg/m3 and 290 ± 6 kg/m3 (supplier reported nominal densities of 80 kg/m3, 160 kg/m3 and 240 kg/m3, respectively).

Overall, nine different sample types were manufactured including the pyramidal PCMs, four different polyurethane foams and four different hybrid materials. The different samples are shown in Figure 3.3 and outlined in Table 3.1.

3.2 Experimental Method and Mechanical Testing

The nine diﬀerent samples underwent two types of mechanical testing: compression testing to obtain the stress-strain curves of the materials; and impact testing to obtain the impact resistance of the materials. Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 27

(a) (b)

(c)

Figure 3.3: Samples tested include: (a) pyramidal PCM with faceplates, (b) polyurethane foam and (c) hybrid.

3.2.1 Compression Testing of PCM, PU Foam and Hybrid Materials

All compression testing was performed using a Shimadzu AG-1 load frame at a constant displacement of 1 mm/min due to the strain rate sensitivity of the PU foams. The PCM and hybrid samples were loaded in uniaxial compression until truss core collapse occurred by inelastic buckling failure [6]. Foam samples were loaded in uniaxial compression until failure due to bending and crumpling of the cell walls [84]. Nominal strains were measured from the cross-head displacement [85–89].

3.2.2 Impact Testing of PCM, PU Foam and Hybrid Materials

Impact testing of the PCM, PU foams and PCM/2-phase PU foam hybrid materials was performed using a Gardner Impact tester (Qualitest IG-1142) as shown in Figure 3.4a. This impact tester comprises an aluminium tube with graduated markings that is used to guide a cylindrical mass to the point of impact with a specimen as shown in Figure 3.4b. Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 28

Tube with graduated markings

Mass

Sample

(a) (b)

Figure 3.4: Photo (a) and schematic diagram (b) of Gardner impact tester. A 0.227 kg mass was initially dropped from a height of 25.4 mm. The sample was inspected for damage, then replaced. The test continued with the mass being released from increasing increments of 25.4 mm in height to obtain the entire damage proﬁle of the samples.

An ASTM standard was not followed due to the strict dimensions of the samples, instead, the impact energy was measured as by placing the mass over the central node of the PCM and hybrid samples and releasing it from increasing heights. First, the 0.227 kg (0.5 lb) mass was released from a height of 25.4 mm (1 in.) above the sample as shown in the schematic in Figure 3.4b. The sample was then removed and inspected for damage after which the test was repeated with the mass being released from an increasing height in increments of 25.4 mm until surface damage was observed. This method provided the impact energy at which the sample was damaged. In this case the impact energy was equivalent to the potential energy (PE) where

PE = mgh (3.2) and m is the mass, g is the gravitational constant and h is the height at which the mass was dropped from. Frictional eﬀects in the tube were considered to be negligible. Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 29

3.3 Results of Mechanical Testing

Stress-strain curves for each sample were used to determine the strength, stiﬀness and resilience. For these curves, the apparent stress, σ, was calculated as

F σ = (3.3) Ap

where F is the force measured under the compression test and Ap is the projected area of the PCM truss or hybrid sample. Representative curves for each of the various densities of polyurethane foam, the PCM and the hybrids are given in Figures 3.5 and 3.6. For each of the stress-strain curves there is an initial linear elastic region, a collapse plateau and for some curves, the final densification section. The shape of the hybrid curves changes between Figure 3.5 and Figure 3.6. For the hybrids made with the lower density foams shown in Figure 3.6, the shape of the stress-strain curve tends to follow that of the PCM, while for the hybrids made with the higher density foams, the shape of the stress-strain curve tends to follow that of the foam. This suggests that either the PU foam or the PCM may dominate in the hybrid material depending on the density of the PU foam. This becomes more evident when examining the stiffness of these materials in section 3.3.1.

The stiffness, strength and resilience were calculated using the stress-strain curves. The stiffness was calculated from the maximum slope of the curve before the initial peak. The strength was calculated using the peak stress value. However, in the cases where there was no definitive peak, an intersection between the maximum slope before the first inflection point, and the minimum slope after the first inflection point was used to determine the strength. Finally, the resilience, which is the maximum energy per volume that can be stored elastically, was calculated by integrating up to the peak (as defined by the strength).

The results from at least three samples were used to obtain an average result for each sample type. The error was calculated based on the standard deviation of the Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 30

H: ρ=290 kg/m³ 6

PU: ρ=290 kg/m³ 5

H: ρ=232 kg/m³ 4

Stress (MPa) PU: ρ=232 kg/m³

1 PCM

0 0 0.1 0.2 0.3 0.4 0.5 Strain (mm/mm)

Figure 3.5: Representative stress-strain curves for the PCM, the two higher density polyurethane foams and their hybrid counterparts.

H: ρ=113 kg/m³

1.5

1 H: ρ=83 kg/m³ PCM Stress (MPa)

PU: ρ=113 kg/m³ 0.5

PU: ρ=83 kg/m³

0 0 0.05 0.1 0.15 0.2 Strain (mm/mm)

Figure 3.6: Representative stress-strain curves for the PCM, the two lower density polyurethane foams and their hybrid counterparts. Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 31

Table 3.2: Average results of strength, stiﬀness and resilience from compression tests over at least three samples. Labels 83, 113, 232, 290 indicate density of foam in kg/m3, PU refers to the polyurethane foam samples and H refers to the hybrid samples.

Sample Density (kg/m3) Stiﬀness (MPa) Strength (MPa) Resilience (kJ/m3) PCM 337 ± 1 34.4 ± 4.2 1.13 ± 0.02 37 ± 3 83PU 83 ± 3 1.5 ± 0.5 0.17 ± 0.04 14 ± 8 83H 357 ± 10 21.3 ± 1.2 1.23 ± 0.03 47 ± 2 113PU 113 ± 0 7.7 ± 0.8 0.51 ± 0.05 21 ± 4 113H 395 ± 3 34.6 ± 6.2 1.80 ± 0.03 86 ± 9 232PU 232 ± 12 12.9 ± 1.1 2.56 ± 0.07 243 ± 33 232H 537 ± 17 24.9 ± 3.2 3.86 ± 0.53 309 ± 42 290PU 290 ± 6 80.9 ± 6.1 4.46 ± 0.02 117 ± 8 290H 650 ± 44 75.8 ± 6.9 5.33 ± 0.20 186 ± 32

three diﬀerent sample results. The percentage diﬀerence for each of the properties was calculated using

Phybrid − PPCM %difference = ∗ 100 (3.4) PPCM

where P refers to a specific property, either density (ρ), stiffness (E), strength (σ) or resilience (J). The average results for the apparent density and absolute strength, stiffness and resilience for each sample type are listed in Table 3.2, while the percentage difference for density, strength, stiffness and resilience of the hybrid samples compared to the PCM are given in Table 3.3. The apparent density was calculated by

m ρ = (3.5) V

where m is the mass of the sample and V is the volume of the sample.

3.3.1 Stiﬀness of PCM, PU Foam and Hybrid Materials

The results for the average stiffness of the materials are represented by Figure 3.7. The foam samples, represented by the columns labeled with a ’PU’ show a trend of increasing stiffness with increasing foam density. However, the stiffness of the hybrids shows a Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 32

Table 3.3: Percentage increase of density, strength, stiﬀness and resilience in the hybrid samples compared to the PCM. Labels 83, 113, 232, 290 indicate density of foam in kg/m3.

Sample Density Stiﬀness Strength Energy Absorption (kg/m3) (MPa) (MPa) (MJ/m3) 83H 6% -38% 9% 26% 113H 17% 1% 59% 132% 232H 59% -27% 241% 740% 290H 93% 120% 372% 405%

100

40 Stiffness (MPa)

0 PCM 83PU 83H 113PU 113H 232PU 232H 290PU 290H

Figure 3.7: Comparison of stiffness for pyramidal PCM, polyurethane foam (PU) and hybrids (H). Labels 83, 113, 232, 290 indicate density of foam in kg/m3. Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 33 different trend. For the hybrids made with the 113 and 290 kg/m3 PU foams the stiffness of the overall sample is dominated by the component with the greatest stiffness. For example, in the case of the 113 kg/m3 PU foams, the stiffness of the PCM was much greater than that of the foam which resulted in the overall stiffness of the hybrid being similar to that of the PCM alone. Whereas for the 290 kg/m3 PU foam, the foam had a greater stiffness than the PCM and therefore the stiffness of the corresponding hybrid was similar to that of the foam alone. These results suggest that the stiffness of the hybrids can be tailored for a specific application to be greater than or equal to the stiffness of the PCM alone, depending on the density of the polyurethane foam used to create the hybrid.

For the hybrids made with the 83 and 232 kg/m3 PU foams, the results do not follow the same trend. Though the stiffness of these hybrids is greater than their PU foam counterparts, it is also below that of the PCM. This suggests that the stiffness of the PCM did not dominate in these cases, and in fact, was somehow reduced by the presence of the foam. In these cases it is suspected that the face plates of the PCM fully or partially separated during the manufacturing process, possibly due to the expansion forces of these particular foams. During the compression test, the face plates would be forced to make contact with the PCM, so it was difficult to determine if this was the case, however, by considering how the failure progressed, this theory is possible. If the face plates did separate during manufacturing, the struts of the PCM trusses in the hybrid may start to splay out slightly before buckling. The PU foam would inhibit the truss movement to a degree, however, as the cells of the PU foam begin to buckle, they would condense and would restrict the movement of the PCM nodes much in the same way that the face plate did. The failure of the inner PCM would then revert back to buckling, however, a greater overall strain would be seen for the sample as is the case for the hybrids made with the 232 kg/m3 foam.

Although the greater strain is not evident in the hybrid samples made with the 83 kg/m3 PU foam, it is suspected that a similar eﬀect occurred. If the face plates Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 34

100

PU Foams Hybrids 80

40 PCM

Stiffness (MPa) 83PU 83H 113PU 113H 20 232PU 232H 290PU 290H 0 0 200 400 600 800 1000 Density (kg/m3)

Figure 3.8: Comparison of stiffness and density for the PCM, foams (PU) and hybrids (H). Labels 83, 113, 232, 290 indicate density of foam in kg/m3. Error bars are omitted for standard deviations less than 2 MPa and 10 kg/m3. had partially separated for these samples, the density of the foam would not be high enough to restrict the movement of the struts to the same degree as in the case of the samples made with the 232 kg/m3 foam, and again the trusses would start to splay out instead of buckling. However, in the case of the 83 kg/m3 foam, the cell walls of the foam would also collapse and condense under a smaller force than for the samples made with the 232 kg/m3 foams. This would create the restriction around the nodes which is needed to cause buckling in the struts. Overall, this effect would take place under a lesser overall strain than for the samples made with the 232 kg/m3 foam due to the difference in foam density. Ultimately, further testing and examination of the hybrid materials made with these foams would be required in the future to determine if this were in fact the case, or if some other effect reduced the stiffness of these materials. The relative density and stiffness of the PCM, foams and hybrids are illustrated in Figure 3.8. In this plot, the low density foams form a group at the left-hand side (the outlined symbols), while the hybrids form a group towards the right-hand side (the solid Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 35

100

40 Hybrid Stiffness (MPa) 83H 20 113H 232H 290H 0 0 20406080100 Foam Stiffness (MPa)

Figure 3.9: Comparison of hybrid stiﬀness and foam stiﬀness. Labels 83, 113, 232, 290 indicate density of foam in kg/m3. Error bars are omitted for standard deviations less than 2 MPa.

symbols) due to their greater density caused by the addition of the PCM. When looking for a material with a stiffness in the range of 20 - 40 MPa, both the PCM, and lower density foam hybrids are viable options, whereas the higher stiffness options include the 290 kg/m3 foam and hybrid. The stiffness property can be examined along with other material properties in order to optimize the material selection process.

By comparing the stiffness of the hybrid samples and the stiffness of the polyurethane foam in Figure 3.9 the effect of the dominating PCM stiffness is more evident. The 83, 113 and 232 kg/m3 foam hybrids fall within the area bounded by the dashed lines which correspond to the stiffness of the PCM. Outside of the dashed lines, the stiffness of the foam will dominate, as is the case for the 290 kg/m3 foam hybrid. Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 36

3 Strength (MPa) 2

0 PCM 83PU 83H 113PU 113H 232PU 232H 290PU 290H

Figure 3.10: Comparison of strength for pyramidal PCM, polyurethane foam (PU) and hybrids (H). Labels 83, 113, 232, 290 indicate density of foam in kg/m3.

3.3.2 Strength of PCM, PU Foam and Hybrid Materials

The results for the average absolute strength of the materials are represented by Fig- ure 3.10. Both the foam samples (represented by columns labeled ’PU’) and the hybrid samples (represented by the columns labeled ’H’) show an increasing trend of strength with increasing foam density. Furthermore, the hybrid samples have a greater strength than either of the PCM or foam components. For example, by examining the columns for the 113 kg/m3 foam (113PU) and hybrid (113H), the increase in the 113 kg/m3 foam/PCM hybrid is evident next to the 113 kg/m3 foam.

For the most part, the strength of the hybrid is approximately equal to the sum of its constituent parts, the PCM and the PU foam. However, in the hybrid made with the 113 kg/m3 foam, the strength of the hybrid is greater than the sum of the PCM and the 113 kg/m3 foam strengths. In all cases, by adding the foam to the PCM, the struts of the PCM have been reinforced against buckling, their ﬁrst failure mode [6]. The foam supports the struts from every side and restricts their movement to provide greater Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 37

Hybrids 6

PU Foams 5

PCM 3 83H

Strength (MPa) Strength 113PU 2 113H 83PU 232PU 1 232H 290PU 290H 0 0 100 200 300 400 500 600 700 Density (kg/m3)

Figure 3.11: Comparison of strength and density for the PCM, foams (PU) and hybrids (H). Labels 83, 113, 232, 290 indicate density of foam in kg/m3. Error bars are omitted for standard deviations less than 0.1 MPa and 6 kg/m3.

overall strength. In developing a hybrid material, the strength of the new hybrid has become equal to or greater than the sum of its constituent parts.

A comparison of the strength and density of the PCM, foams and hybrids is given in Figure 3.11. From this plot, the trend of the lower density foams on the left-hand side, and higher density hybrids on the right-hand side is again apparent. The increasing trend of strength with density is also apparent for both the foams and the hybrids. Furthermore, it is evident that the hybrids have greater strength when compared to the foams.

The strength of the PU foams and the hybrids has been successfully modeled using the theory developed by Menges [29]. In order to model the behaviour of the strength in rigid polyurethane foams Menges developed the following equation [29]:

2 βD = αEpja0.0425χ (3.6) Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 38

where β is the strength, D refers to the compressive mode, α is a clamping factor, Ep is the elastic modulus of the polymer, j is a determination factor (0.53 for PU), a is a reduction factor (a = βD−measured/βD−calculated) and χ is the relative density. In particular, for rigid polyurethane foam, this reduces to [29]:

2 2 βD = 1250χ [kp/cm ] (3.7) in units of kilopond per centimeter squared (1 kp=9.80665 N). In Figures 3.12 and 3.13 the strength of the two-phase polyurethane foams and hybrids follow the trend of the Menges model. However, the one-phase, 83 kg/m3 foam and hybrid samples are slightly over-predicted in the Menges model. This is likely due to the fact that although the one- phase 83 kg/m3 foam was marketed as a rigid foam, which is what the Menges model considers, it actually had some characteristics inherent to ﬂexible polyurethane such as large strain response which the two-phase foams did not exhibit [90].

In terms of the expected strength of the PCM, the Deshpande model was used to predict the strength of the PCM [51]. The Deshpande model uses the equation [51]

2 σPCM = σF ρRsin ω (3.8)

where σPCM is the strength of the PCM, σF is the failure strength, ρR is the relative density and ω is the truss angle. The failure strength, σF , is dependent on the slenderness ratio of the struts. For small slenderness ratios, σF is equal to the yield strength (σYS).

However, for medium to high slenderness ratios, σF is equal to the critical buckling stress,

σCR, determined by [52] k2π2E I k2π2E σ = t = t (3.9) CR AL2 (L/r)2

where k accounts for the rotational stiﬀness, Et is the tangent modulus, I is the moment of inertia, A is the cross-sectional area and L is the length of the strut. Alternatively, the critical stress can be deﬁned in terms of the slenderness ratio (L/r) where r is the Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 39

3 Strength (MPa) Strength 2

0 0 50 100 150 200 250 300 350 400 Density (kg/m3)

Foams Menges

Figure 3.12: Comparison of the strength of the polyurethane foam samples found experimentally and using Menges model. Error bars are omitted for standard deviations less than 0.1 MPa and 3 kg/m3.

3 Strength (MPa) Strength 2

0 0 100 200 300 400 500 600 700 800 Density (kg/m3)

Menges Hybrids

Figure 3.13: Comparison of the strength of the hybrid samples found experimentally and using Menges model. Error bars are omitted for standard deviations less than 0.1 MPa and 3 kg/m3. Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 40

400

300 ) 3

200 Resilience (kJ/m

100

0 PCM 83PU 83H 113PU 113H 232PU 232H 290PU 290H

Figure 3.14: Comparison of resilience for pyramidal PCM, polyurethane foam (PU) and hybrids (H). Labels 83, 113, 232, 290 indicate density of foam in kg/m3.

√ radius of gyration (r = I/A, or t/ 12 for a rectangular cross-section). Experimentally, the PCM was found to have a strength of 1.13 ± 0.02 MPa, whereas the Deshpande model calculated the strength of the PCM to be 50.84 MPa. It is common for this model to over-predict the strength of the PCM as the model is taken as an ideal case for a perfectly uniform, perfectly straight strut [40,42,55–57,59].

3.3.3 Resilience of PCM, PU Foam and Hybrid Materials

The results for the average absolute resilience of the materials are represented in Fig- ure 3.14. The addition of the foam to the PCM increased the resilience of the hybrids regardless of the foam density. In general, there was an increasing trend in the resilience of the sample with foam density for both the PU foam and hybrid samples, with the exception of the 232 kg/m3 foam samples. The comparatively lower modulus for the 232 kg/m3 foam and hybrid, as discussed in section 3.3.1, resulted in larger elastic energy absorption. Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 41

400 PCM 83PU Hybrids 83H PU Foams 113PU 300 113H 232PU

) 232H 3 290PU 290H

200 Resilience (kJ/m

100

0 0 100 200 300 400 500 600 700 Density (kg/m3)

Figure 3.15: Comparison of resilience and density for the PCM, foams (PU) and hybrids (H). Labels 83, 113, 232, 290 indicate density of foam in kg/m3. Error bars are omitted for standard deviations less than 10 kJ/m3 and 7 kg/m3.

A comparison of the resilience and density of the PCM, foams and hybrids is given in Figure 3.15. This material selection chart can be used with those in Figures 3.8 and 3.11 to determine the ideal material for a given application in terms of its density, stiﬀness, strength and resilience.

3.3.4 Impact Resistance of PCM, PU Foam and Hybrid Materials

A Gardner impact test was performed on each of the PCM, two-phase PU foam and two- phase PU foam/PCM hybrid samples. The surface damage of each sample was observed throughout the test and it was found that the three distinct sample types (PCMs, PU foams and PCM/PU hybrids) each had diﬀerent damage proﬁles.

Initially, the PCMs were able to withstand any failure as shown in Figure 3.16a. Eventually they began to fail by the inelastic buckling of their struts at the point of impact as shown in Figure 3.16b. Next, a depression became visible on the top face sheet Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 42

(a) (b)

Figure 3.16: Damage proﬁle for the pyramidal PCM includes (a) no damage, (b) inelastic buckling of the local struts, (c) top face sheet depression, and (d) base sheet deformation. of the PCM as shown in Figure 3.16c. Finally, the base sheet began to deform due to the continuous buckling of the struts as shown in Figure 3.16d.

The damage proﬁle for each of the PU foam densities contained the same failure modes. An initial, undamaged foam sample is shown in Figure 3.17a. Upon ﬁrst impact, the foam displayed slight surface depression as shown in Figure 3.17b. As the impact energy increased, a crack formed in the depression as shown in Figure 3.17c. Finally, complete penetration of the foam would occur as shown in Figure 3.17d.

The hybrid samples had fewer visible failure modes. Initially they withstood the impact as shown in Figure 3.18a. Eventually, a depression would form on their surface as shown in Figure 3.18b. Finally, shearing would occur at the metal/foam interface. This ﬁnal mode could not be captured in a photo so a schematic is given in Figure 3.18c.

The impact energies required to reach the various failure modes for the PCM, PU foams and hybrid materials are summarized in Tables 3.4, 3.5 and 3.6, respectively. Figure 3.19 compares the failure modes of the various samples. The only common Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 43

(a) (b)

Figure 3.17: Damage proﬁle for the PU foams includes (a) no damage, (b) surface depression, (c) crack in surface depression, and (d) complete penetration.

(a) (b)

(c)

Figure 3.18: Damage proﬁle for the PCM/PU foam hybrids includes (a) no damage, (b) surface depression and (c) shearing at the metal/foam interface. Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 44

Table 3.4: Average results for the impact energy for given failure modes of the PCM.

Impact Energy (mJ) Inelastic Buckling Depression Base Sheet Deformation PCM 283 ± 0 339 ± 0 640 ± 33

Table 3.5: Average results for the impact energy for given failure modes of the PU foams. Labels 113, 232, 290 indicate density of foam in kg/m3.

Impact Energy (mJ) Depression Crack Penetration 113PU 57 ± 0 337 ± 0.033 697 ± 33 232PU 57 ± 0 640 ± 182 1187 ± 57 290PU 57 ± 0 867 ± 131 1488 ± 33

Table 3.6: Average results for the impact energy for given failure modes of the PCM/PU foam hybrids (H). Labels 113, 232, 290 indicate density of foam in kg/m3.

Impact Energy (mJ) Depression Shearing at Metal/Foam Interface 113H 414 ± 33 678 ± 0 232H 546 ± 33 867 ± 33 290H 697 ± 33 1130 ± 655 Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 45

2.00 Penetration Shearing 1.75 Base Deform. Crack Depression 1.50 Inelast. Buckl. No Failure 1.25

1.00

0.75 Impact Energy (J)

0.50

0.25

0.00 PCM 113PU 232PU 290PU 113H 232H 290H

Figure 3.19: Comparison of impact failure modes for the PCM, foams (PU) and hybrids (H).

failure mode was the depression of the surface face. As mentioned above, the PCMs underwent inelastic buckling of the struts, surface depression and deformation of the base sheet. The PU foams underwent surface depression, cracking in the depression and complete penetration. Finally, the hybrids underwent surface depression and shearing at the metal/foam interface.

Each of the foam samples exhibited surface damage in the form of an indentation from the first impact test at a height of 25.4 mm. The PCM and hybrid samples continued to resist the impact beyond the first test, and up to a greater impact energy. These samples did not begin to show a surface depression until a height of at least 152.4 mm. Since the PU foams all exhibited damage from the first impact, smaller increments of impact energy are required in order to compare their initial damage. However, upon continuing the testing, the sample would eventually crack as the impact energy was increased. Figure 3.20 compares the impact energies of the foam for samples that have a visible crack in the depression that formed on their surface. This figure shows that there Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 46

0.9

0.8

0.7

0.6

0.5

0.4

Impact Energy (J) 0.3

0.2

0.1

0.0 113PU 232PU 290PU

Figure 3.20: Comparison of impact energy for crack formation in the PU foam samples. is an increasing trend of crack resistance with increasing foam density.

In order to compare all of the diﬀerent types of samples, the surface depression failure mode was used. Figure 3.21 compares the impact energy for surface depression of the PCM, the PU foams and the hybrids. Since the PU foams all exhibited surface damage upon ﬁrst impact at an impact energy of 57 mJ, they are represented as one entry in Figure 3.21.

Figure 3.21 shows that the impact energies of the hybrid materials are greater than that of the PU foam or PCM alone. There is also an increasing trend in impact energy with the density of the foam used to create the hybrid. So by increasing the density of the foam a hybrid material with greater impact energy is created. In this case, the addition of the PU foam allows for energy to be transferred from the PCM to the PU, creating a material with a greater overall impact resistance. Furthermore, with each of the foam densities the impact energy of the hybrid is greater than the sum of the impact energy of the PU foam and PCM. This is shown more clearly in Figure 3.22. The diagonal line indicates the values where the impact energy of the hybrid would be equal to that of the Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 47

0.8

0.7

0.6

0.5

0.4

0.3 Impact Energy (J)

0.2

0.1

0.0 PU PCM 113H 232H 290H

Figure 3.21: Comparison of impact energy for pyramidal PCM and hybrids (H). Labels 113, 232, 290 indicate density of foam in kg/m3.

0.8

0.7

0.6

0.5

0.4

0.3

Impact Energy of Hybrid Impact Energy 0.2

0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Impact Energy of PCM + PU foam

Figure 3.22: Comparison of impact energy of the hybrid versus the sum of its parts (the PCM and PU foam). Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 48

0.8 PCM 113PU 0.7 Hybrids 113H 232PU 0.6 232H 290PU 290H 0.5

0.4

0.3 Impact Energy (J) PU Foams 0.2

0.1

0.0 0 100 200 300 400 500 600 700 800 Density (kg/m3)

Figure 3.23: Comparison of impact energy and density. Labels 113, 232, 290 indicate density of foam in kg/m3. Error bars are omitted for standard deviations less than 0.04 J and 2 kg/m3.

PU foam plus the PCM. Any point above this line would indicate that the impact energy is greater than the sum of the PCM and PU foam. The data points in Figure 3.22 line up above one another due to the fact that the impact energy of the PCM was constant and the impact energy of the PU foams was also constant, regardless of foam density. Therefore, the sum of the impact energy of the PCM and PU foam would be the same regardless of PU foam density.

A comparison of the impact energy and density of the PCM, foams and hybrids is given in Figure 3.23. The low density foams appear towards the left-hand side of the plot, however they oﬀer little in terms of impact resistance as can be seen by the low impact energy at which they fail. The PCM performs relatively well, with an average density and impact energy, however the hybrid samples oﬀer much more in terms of the impact energy which they can undergo before failure. Although there is a slight loss in terms of the density of the hybrids, the gain in impact resistance is substantial. Chapter 3 Pyramidal PCM and Polyurethane Hybrid Materials 49

3.4 Conclusion: PCM/PU Foam Hybrid Materials Oﬀer

Advantages Over Constituent Parts

A novel hybrid created from a pyramidal PCM architecture and rigid polyurethane foam has been designed, fabricated and tested in uniaxial compression and impact resistance. The hybrid materials exhibited a number of interesting properties including the ability to tailor the stiffness of the hybrid by using different densities of polyurethane foam. Also, the strength and resilience of the hybrid was greater than the strength and resilience of the PCM and the polyurethane foam components. In some instances the strength and/or resilience of the hybrid samples even exceeded the sum of the strength and/or resilience of the PU foam and PCM. Furthermore, the impact energy required for surface deformation of the hybrids was greater than both the PU foam and the PCM, and by increasing the foam density, the impact energy also increased. Finally, in general, the strength, resilience and impact energy had an increasing trend with foam density. In developing a new material of PU foam and pyramidal PCM architecture, a hybrid material that offers up to 372% greater strength, 740% greater resilience and 106% greater impact resistance over its PCM counterpart has been created. These properties increase the options of materials available for structural applications by increasing the property space as discussed previously. Chapter 4

Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel

This chapter will focus on hybrid materials developed with an ABS periodic cellular polymer structure, created by rapid prototyping, which has been foamed and plated with nanocrystalline nickel. Unlike the previous chapter, in which the hybrid materials consisted of a metal truss in which the struts were surrounded by polymer foam, the hybrids in this chapter have polymer foam struts surrounded by metal. The ABS trusses were foamed using a batch foaming method in order to obtain three diﬀerent densities for which the amount of polymer was kept constant, and thus three diﬀerent strut dimensions were obtained. After plating, the hybrids were mechanically tested in compression in order to compare their properties.

4.1 Sample Development and Manufacture

The samples for this study were created using three main steps. First, the initial samples were manufactured using ABS in a rapid prototyping method. Next, the as-received samples were foamed using a batch foaming method. Finally, a subset of the foamed and unfoamed samples were plated with nanocrystalline nickel to increase their strength.

50 Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 51

4.1.1 Rapid Prototyping the ABS trusses

Rapid prototyping is a method that uses a CAD drawing to create a three-dimensional model built up in layers, typically using a polymer. There are many diﬀerent types of rapid prototyping processes. Stereolithography is a method that uses liquid resin which is polymerized using photons (light) to create the ﬁnal model. Selective laser sintering (SLS) uses layers of powder which are sintered using a carbon dioxide laser. In fused deposition modeling (FDM) layers of extruded polymer are built up to create the model. Laminated object manufacturing (LOM) uses a laser to cut bonded layers of paper, plastic, metal or composite into the model shape. In ballistic particle manufacturing (BPM) layers are built up with droplets of melted materials which are shot at previous layers, much like an ink jet printer. Finally, three-dimensional printing uses a similar concept in which drops of binder are shot at a layer of powder to build up the layers of the model [91].

The method used in this chapter is a fused deposition modeling method (FDM). In this method, layers of the model are built up using a thermoplastic ﬁlament that is extruded through a heated nozzle as shown in Figure 4.1. The samples in this study used acrylonitrile butadiene styrene (ABS), a common thermoplastic used in FDM which is also known to be foamable [30–35].

The samples were manufactured according to the dimensions in Table 4.1, using the file shown in Figure 4.2. The final sample is shown in Figure 4.3, while Figure 4.4 shows an SEM micrograph of the inner structure of one of the individual struts. In this figure, you can see the individual layers of ABS that were used to create the sample.

4.1.2 Batch Foaming of the ABS Trusses

In order to create the cellular, foamed sample, a batch foaming process was used [31]. In this method, a sample is placed in a pressurized chamber which is ﬁlled with a gas

(commonly CO2 or N2) at a given pressure. The sample becomes saturated with the gas Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 52

Figure 4.1: Schematic of fused deposition modeling (FDM) process [91].

Table 4.1: ABS truss dimensions Lattice geometry Pyramidal Material ABSplus Number of unit cells 4 x 3/4 Strut length 7.3 mm Strut cross-section Square Strut thickness 3.10 mm Strut angle 45 ◦ Total truss length 22.8 mm Total truss width 22.8 mm Total truss thickness 10 mm Total surface area 2313 mm2 Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 53

TrussWidth

TrussLength

StrutWidth StrutWidth

5mm5mm

c4_rpCADc4_rpCAD (a)

StrutLength StrutLength

TrussHeight TrussHeight

StrutThickness 5mm StrutThickness 5mm (b) c4_rpCAD2 Figure 4.2: CAD drawing of polymer truss a) oblique and b) edge on. c4_rpCAD2

Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 54

5 mm

Figure 4.3: Rapid prototyped polymer truss sample.

500 μm

Figure 4.4: SEM micrograph of the cross-section of the ABS truss. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 55

Table 4.2: Foaming parameters.

Parameter Value

Gas CO2 Saturation pressure 4 MPa Saturation time 24 hrs Foaming water bath temperature 85, 90 or 95 ◦C Foaming time 240 s Quenching water bath temperature Room temp. Quenching time 60 s

(the rate of which depends on the material’s solubility and diﬀusion rate), over a period of time after which the pressure is rapidly released. The sample is then immediately placed in a hot water bath wherein the thermodynamic instability of the rapid pressure drop and increase in temperature causes the cells to nucleate and grow. The sample is then quenched in a cool water bath in order to control the cell growth and left to air dry to allow the remaining gas to escape [36].

The parameters used for foaming in this study are given in Table 4.2 and are based on some of the parameters found in a previous study [31]. CO2 gas was used to saturate the samples at a pressure of 4 MPa over a period of 24 hours. The samples were placed in a hot water bath at temperatures of either 85, 90 or 95 ◦C for 240 s after which they were quenched in a room temperature water bath to control the cell growth.

The resultant foamed trusses are shown in Figure 4.5. The three diﬀerent foaming temperatures resulted in three diﬀerent volume expansions. Overall, there is an increasing trend of percentage volume expansion with foaming temperature as shown in Figure 4.6. Volume expansion ratios of 80 ± 1 %, 137 ± 3 % and 281 ± 3 % were obtained at foaming temperatures of 85 ◦C, 90 ◦C and 95 ◦C, respectively.

The individual foamed structures were also analyzed by scanning electron microscopy (SEM). A strut of the foamed ABS trusses was fractured in order to reveal the inner cross-section. These samples were then coated with platinum using a sputter coater in order to make their surfaces conductive. The micrographs of the foamed struts shown in Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 56

Figure 4.5: Photo of rapid prototyped ABS trusses, from left: as received, 85 ◦C, 90 ◦C, 95 ◦C foaming temperature.

300

250

200

150

100 % Volume Expansion

0 84 86 88 90 92 94 96 Water Bath Temperature (°C)

Figure 4.6: Percentage of volume expansion of rapid prototyped ABS trusses versus foaming temperature. Errors ranging from 1.4 to 2.9 % are not shown. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 57

(a) (b)

Figure 4.7: Micrographs of the foamed structure of the rapid prototyped ABS trusses: (a) as received, (b) 85 ◦C, (c) 90 ◦C and (d) 95 ◦C foaming temperatures.

Figure 4.7 were taken using a JEOL JSM 6060 scanning electron microscope (SEM). A reference micrograph of the solid ABS truss is given in Figure 4.7a, while micrographs for the foamed structures at foaming temperatures of 85 ◦C, 90 ◦C and 95 ◦C are given in Figures 4.7b, c, and d, respectively. The average cell size was calculated using ImageJ, an image processing software package. The average cell size increased with foaming temperature from 8 ± 2 µm to 11 ± 4 µm based on an average of at least 12 cells. The cell density, N, is the number of cells per unit volume and was calculated using the following equation, 3 n 2 ρ N = ∗ p (4.1) A ρf where n is the number of cells in a viewing area, A, ρp is the density of the solid ABS Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 58

Table 4.3: Summary of truss dimensions after foaming. Labels 80, 135 and 280 correspond to the approximate percent volume expansion of the ABS foamed trusses.

Solid 80 135 280 Truss Properties Width (mm) 22.91 ± 0.03 26.80 ± 0.14 29.66 ± 0.09 35.20 ± 0.17 Length (mm) 22.94 ± 0.05 26.83 ± 0.12 29.62 ± 0.16 35.26 ± 0.12 Height (mm) 10.13 ± 0.03 13.30 ± 0.08 14.35 ± 0.11 16.35 ± 0.08 Strut Properties Width (mm) 3.07 ± 0.02 3.33 ± 0.12 3.74 ± 0.16 4.37 ± 0.14 Thickness (mm) 3.10 ± 0.03 3.82 ± 0.06 4.18 ± 0.05 4.70 ± 0.06 Length (mm) 7.28 ± 0.06 9.47 ± 0.07 10.27 ± 0.48 12.11 ± 0.69 Angle ( ◦) 44.67 ± 2.08 46.67 ± 2.25 47.67 ± 0.58 44.67 ± 1.53 Slenderness Ratio 8.13 ± 0.10 8.60 ± 0.14 8.51 ± 0.41 8.94 ± 0.52 Cross-sectional Area (mm2) 9.51 ± 0.10 12.71 ± 0.50 15.62 ± 0.69 20.54 ± 0.70 Second Moment of Inertia (mm4) 7.62 ± 0.13 15.42 ± 0.69 22.74 ± 1.07 37.72 ± 1.46

truss, and ρf is the density of the foamed ABS truss. The cell density ranged from 5.7 x 109 µm/cm3 to 8.1 x 109 µm/cm3 based on an average of three viewing. Both the average cell size and the cell density are in the range for microcellular foams which have a cell size in the range of 10 µm and a cell density in the range of 109 cells/cm3 [35].

A summary of the dimensions of the various samples is given in Table 4.3. Values for truss width, length and thickness and strut width, length and thickness were measured using calipers at various locations on the sample for each of the six samples. The values reported in Table 4.3 are the average of at least three measurements per sample. The standard deviation of these measurements is reported as the error. The slenderness ratio is calculated using L/r where L is the length of the strut and r is the radius of gyration √ which is equivalent to t/ 12 for rectangular cross-sections (t is the thickness of the strut). Finally, the second moment of inertia is calculated using

wt3 I = (4.2) 12 where t is the thickness of the strut and w is the width of the strut. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 59

5 mm

Figure 4.8: Nanocrystalline nickel plated ABS truss.

4.1.3 Electroplating of ABS Trusses

The electroplating of the ABS trusses was performed at Integran Technologies (Toronto, Ontario). In order to plate the ABS trusses using the method of electrodeposition, the samples were ﬁrst metallized using a proprietary process in order to create an electrically conductive surface. Once the samples were metallized, nanocrystalline nickel was electrolytically deposited on them using a procedure similar to Cheung et al. [92]. The ﬁnal nanocrystalline nickel plated ABS truss is shown in Figure 4.8.

During plating, a thickness of approximately 250 microns was desired. To determine the actual thickness of a given sample the mass of the sample before and after plating was compared in the following equation

m − m t = 2 1 (4.3) ρSA

where t is the thickness of the metal coating, m is the mass of the sample before (m1) and

3 after (m2) plating, ρ is the theoretical density of Ni (8.9 g/cm ) and SA is the predicted surface area of the sample, based on the original CAD model for the unfoamed sample, and a scaled CAD model for the foamed samples. The calculated coating thickness are Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 60

Table 4.4: Thickness of nano-Ni coating on ABS trusses.

Sample Thickness (% volume expansion) (µm) Solid 235 ± 17 80 233 ± 19 135 255 ± 13 280 242 ± 7 given in Table 4.4.

4.1.4 Summary

Eight different sample types have been manufactured: four ABS trusses at varying densities both plated and unplated. These samples will each undergo mechanical testing in order to obtain their stress-strain profile and calculate their stiffness, strength and energy absorption during strut failure.

4.2 Experimental Method and Mechanical Testing

The eight different sample types underwent uniaxial compression testing to obtain the stress-strain curves of the materials. Past studies have found that edge effects are relatively small in PCM samples with a 2 x 2 unit cell size when periodically rigid boundary conditions were applied to each node [93]. Preliminary studies on solid ABS trusses showed fracture of the face sheet struts before buckling of the core struts as shown in Figure 4.9. Therefore, the restriction plate shown in Figure 4.10, similar to that used in [93], was designed in order to eliminate the possibility of edge effects that would not be apparent in samples with a greater number of unit cells. As in Chapter 3, all compression testing was performed using a Shimadzu AG-1 load frame at a constant displacement of 1 mm/min. The ABS trusses, both plated and not-plated, were loaded in uniaxial compression until truss core collapse occurred by inelastic buckling failure. Nominal strains were measured from the cross-head displacement [85–89]. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 61

5 mm

Figure 4.9: Failure of ABS trusses due to edge eﬀects.

Figure 4.10: Restriction plate used during compression testing to eliminate edge eﬀects. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 62

30 Stress(MPa) 20

10 Truss Height Core Height 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Strain(mm/mm)

Figure 4.11:C4_ssstraincomp Representative stress-strain curves where strain is calculated using both the total truss height and the core height.

4.3 Results of Mechanical Testing

Stress-strain curves for each sample were used to determine the strength, stiffness and energy absorption during strut failure. Typically for periodic structures the faceplate is considered effectively rigid and is therefore not included in the overall height when calcu- lating strain. However, for these samples, the thickness of the faceplates is a significant fraction of the overall height of the truss. By comparing stress-strain curves where the strain has been calculated using both the total truss height and only the core height, as shown in Figure 4.11 it is apparent that the curve calculated with the core height returns strains greater than one. This indicates that the faceplates in these samples cannot be considered effectively rigid and are in fact contributing a small amount of strain to the overall sample. Therefore, the strains for subsequent samples were calculated using the total truss height rather than just the core height.

Representative curves for each of the various densities of ABS, unplated and plated are given in Figures 4.12 and 4.13, respectively. The curves in Figure 4.12 for the Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 63

10 Solid 9 80 135 8 280 7

Stress (MPa) 4

0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Strain (mm/mm)

Figure 4.12: Representative stress-strain curves for the unplated ABS trusses. Labels 80, 135 and 280 correspond to the approximate percent volume expansion of the ABS foamed trusses.

30 Solid 80 25 135 280

15 Stress (MPa) 10

0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Strain (mm/mm)

Figure 4.13: Representative stress-strain curves for the plated ABS trusses. Labels 80, 135 and 280 correspond to the approximate percent volume expansion of the ABS foamed trusses. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 64 unplated samples follow the typical curve trend for the compression of polymer foam. There are three distinct areas: the initial linear elastic region, the collapse plateau and the final densification section [94]. These figures show that with increasing density, the Young’s modulus increases and the plateau stress increases. Typically, the strain at the onset of densification would decrease with increasing density, however the trends in Figure 4.12 show the opposite. This is likely due to the design of the restriction plates used for the compression tests in order to control edge effects. Unfortunately, the top and bottom plate came into contact during testing in the plateau region, so the curves include the compression of the steel confinement plates as well as the compression of the ABS trusses. This would skew the location of the onset of densification and inhibits the ability to calculate energy absorption by published methods as discussed below in Section 4.3.1. Different sets of restriction plates were manufactured for each set of samples due to the differing faceplate thickness which was dependent on volume expansion. Therefore, the faceplates would meet at varying strain values as shown in Figure 4.12.

It is apparent from the stress-strain curves for the plated samples, given in Figure 4.13, that these samples have a much greater strength due to the nanocrystalline nickel coating. These curves follow similar trends to those in Figure 4.12, however with some distinct differences. In Figure 4.13, there is again an initial elastic region. However, before peak strength is obtained, there are a few instantaneous load drops. These drops can be more easily identified by plotting the slope of the tangent of the stress-strain curves versus strain as in the example for the plated samples foamed at 85 ◦C in Figure 4.14. However, in comparison, Figure 4.15 which compares the same data for unplated samples, has no discernible steep troughs. These load drops relate to small cracks at the joint of the nodes. These cracks grew until peak stress as shown in Figure 4.16. After each load drop, the slope of the curve remains constant until peak strength. Beyond peak stress, the load drops became greater as the nanocrystalline nickel coating began to fracture and delaminate from the ABS truss core. Beyond the collapse strength final densification occurred. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 65

16 14 12 10 8 6 Stress(MPa) Stress(MPa) 4 2 0 0 0.02 0.04 0.06 0.08 0.08 Strain(mm/mm)

c4_deriva (a) 600 600 400 400 200 200 0 0 0 0.02 0.04 0.06 0.08 0 0.02 0.04 0.06 0.08 dσ/dε -200

dσ/dε -200 -400 -400 -600 -600 -800 -800 Strain(mm/mm) Strain(mm/mm)

c4_derivb c4_derivb (b) 2 Figure 4.14: Comparison of2 (a) a representative stress/strain plot and (b) a deriva- ◦ tive/strain plot for plated1.6 samples foamed at 85 C. 1.6

1.2 1.2

0.8 0.8 Stress(MPa) Stress(MPa) 0.4 0.4

0 0 0 0.02 0.04 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1 Strain(mm/mm) Strain(mm/mm) c4_deriv2a c4_deriv2a 16 14 12 10 8 6 Stress(MPa) 4 2 0 0 0.02 0.04 0.06 0.08 Strain(mm/mm)

c4_deriva 600

400

200

0 Chapter 4 Rapid prototyped0 ABS Truss 0.02 Cores 0.04 Plated with0.06 Nanocrystalline 0.08 Nickel 66

dσ/dε -200

-400

-600

-800 Strain(mm/mm)

c4_derivb

1.6

1.2

0.8 Stress(MPa) 0.4

0 0 0.02 0.04 0.06 0.08 0.1 Strain(mm/mm)

c4_deriv2a (a)

20 dσ/dε

0 0 0.02 0.04 0.06 0.08 0.1 Strain(mm/mm)

c4_deriv2b (b)

Figure 4.15: Comparison of (a) a representative stress/strain plot and (b) a derivative/strain plot for unplated100 samples foamed at 85 ◦C. Experimental 90 Theoretical 80 Theoretical with knockdown

σ(MPa) 40

0 9 11 13 15 17 19 21 StrutCrossSectionArea(mm 2)

c4_buckling2

Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 67

5 mm (a) (b)

Figure 4.16: (a) SEM fracture at the (b) node joint of the plated ABS truss at peak strength.

By comparing pairs of plated and unplated curves at a given density, as in Figure 4.17, an increase in the plateau stress of the unplated samples and the collapse strength of the plated samples can be seen.

4.3.1 Mechanical Properties of Foamed and Plated ABS Trusses

Using the stress-strain curves, the stiffness, strength and energy absorption were obtained. The stiffness was calculated from the maximum slope of the curve before the initial peak. The strength was calculated using the peak stress value. In the cases where there was no definitive peak, an intersection between the maximum slope before the first inflection point, and the minimum slope after the first inflection point was used to determine the strength. Energy absorption during strut failure depends on the onset of densification strain, for which there are many definitions [8, 40, 85, 95–98]. For metallic foams, it has been defined as: the strain at twice the peak stress [95], the strain at 1.5 times the stress at 50% strain [96], the strain where the stress-strain curve starts to rise [97], or it can scale with relative density [85]. For PCMs the densification strain has multiple definitions as well: the strain at which the stress returns to peak stress [40], or a range of values between 0.5 and 0.6 [8, 98]. Due to the fact that the confinement plates made contact during compression testing of the uncoated samples, an arbitrary value of strain 4.5 4.5 NOT-PLATED 4.0 NOT-PLATED 4.0 PLATED PLATED

3.53.5

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2.02.0 Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 68 1.51.5

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c4_energyc4_energy 2525 20 2020 20 15 1515 10 1010 5 Stress(MPa)

Stress(MPa) 5 Stress(MPa) Stress(MPa) Stress(MPa) Stress(MPa) Stress(MPa) Stress(MPa) 55 0 00 0 0 0.1 0.2 0.3 0.4 00 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0 0.1 0.2 0.3 0.4 Strain(mm/mm)Strain(mm/mm) Strain(mm/mm)

c4_ss_subfig1c4_ss_subfig1 (a) c4_ss_subfig2(b) 1515 10

8 1010 6

4 55 Stress(MPa) Stress(MPa) Stress(MPa) Stress(MPa) Stress(MPa) Stress(MPa) Stress(MPa) Stress(MPa) 2

00 0 00 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0 0.1 0.2 0.3 0.4 0.4 Strain(mm/mm)Strain(mm/mm) Strain(mm/mm)

c4_ss_subfig3c4_ss_subfig3 (c) c4_ss_subfig4 (d)

Figure 4.17: Representative stress-strain curves of the plated and unplated rapid prototyped ABS trusses: (a) as received, (b) 85 ◦C, (c) 90 ◦C and (d) 95 ◦C foaming temperatures. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 69

Table 4.5: Average results of strength, stiﬀness and energy absorption from compression tests over three samples. Labels 80, 135, 280 indicate % volume expansion of the ABS core, S refers to the as-received unfoamed samples, ABS refers to the ABS unplated samples and H refers to the hybrid Ni plated samples.

Sample Density Stiﬀness Strength Energy Absorption (kg/m3) (MPa) (MPa) (MJ/m3) S-ABS 341 ± 1 97.3 ± 4.9 5.38 ± 0.10 1.14 ± 0.03 S-H 1031 ± 18 404 ± 9 22.30 ± 1.26 3.88 ± 0.12 80ABS 193 ± 2 37.9 ± 0.5 2.08 ± 0.07 0.43 ± 0.01 80H 946 ± 52 350 ± 115 14.28 ± 0.01 2.25 ± 0.04 135ABS 147 ± 2 23.1 ± 2.8 1.31 ± 0.05 0.27 ± 0.01 135H 875 ± 23 309 ± 53 14.04 ± 0.52 1.86 ± 0.24 280ABS 92 ± 1 10.7 ± 0.8 0.58 ± 0.02 0.12 ± 0.01 280H 653 ± 9 173 ± 7 7.3 ± 0.5 0.91 ± 0.08 corresponding to 25% of the original micro-truss height was chosen as an upper boundary.

The results from three samples were used to obtain an average result for each sample type. The error was calculated based on the standard deviation of the three diﬀerent sample results. The average results for density, strength, stiﬀness and energy absorption for each sample type are listed in Table 4.5.

The results of the average stiffness, strength and energy absorption of the materials are given in Figure 4.18. There are a couple of generalized trends in Figure 4.18. First of all, there is a general decreasing trend with decreasing density. Although not linear, this trend occurs for both strength and energy absorption. For stiffness, however, there is a slight increase from the stiffness of the solid plated sample, to the stiffness of the plated sample with the 80% volume expansion ABS truss. Although there is a slight increase, the solid sample falls within the error bounds of the foamed sample, and it is expected that with further testing that the trend would become strictly decreasing.

The second trend in Figure 4.18 is that the plated samples have a higher absolute stiﬀness, strength and energy absorption than the unplated, however, the percentage increase in the strength and stiﬀness of the plated samples over the unplated was greatest in the samples foamed at 280% volume expansion (1165% and 1525%, respectively). The Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 70

500 NOT-PLATED 500 450 PLATED NOT-PLATED 400450 PLATED

350400

300350

250300

200250 Stiffness(MPa) 150200 Stiffness(MPa) 100150 100 50 50 0 0 0 50 100 150 200 250 300 0 50 100%VolumeExpansion 150 200 250 300 %VolumeExpansion c4_stiffness (a) c4_stiffness 25 25 NOT-PLATED PLATED NOT-PLATED 20 PLATED 20

15 15

Strength(MPa) 10 Strength(MPa)

5 5

0 0 0 50 100 150 200 250 300 0 50 100%VolumeExpansion 150 200 250 300 %VolumeExpansion c4_strength c4_strength (b)

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c4_energy (c) 25 20

20 Figure 4.18: Mechanical properties of the nano-Ni15 plated and unplated ABS trusses: (a) 15 10 stiﬀness, (b) strength and10 (c) energy absorption. 5 Stress(MPa) Stress(MPa) 5

0 0 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 Strain(mm/mm) Strain(mm/mm)

c4_ss_subfig1 c4_ss_subfig2 15 10

8 10 6

4 5 Stress(MPa) Stress(MPa) 2

0 0 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 Strain(mm/mm) Strain(mm/mm)

c4_ss_subfig3 c4_ss_subfig4

Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 71

Table 4.6: Percentage increase of strength, stiﬀness and energy absorption of the nanocrystalline nickel plated trusses over the ABS foamed trusses. Labels 80, 135, 280 indicate % volume expansion of ABS, S refers to the as-received unfoamed samples.

Sample Density Stiﬀness Strength Energy Absorption S 203% 315% 315% 241% 80 391% 994% 588% 425% 135 495% 1239% 968% 593% 280 613% 1525% 1165% 650%

percentage diﬀerence for each of the properties was calculated using

Pplated − Pnot−plated %difference = ∗ 100 (4.4) Pnot−plated

where P refers to a specific property, either density (ρ), stiffness (E), strength (σ) or energy absorption (J). A summary of the percentage difference for density, stiffness, strength and energy absorption is given in Table 4.6.

The materials selection charts for these mechanical properties are given in Figure 4.19. As with the ﬁrst set of hybrid materials in Chapter 3, the low density ABS foam occupies the lower left area of each of the curves while the higher density hybrid occupies the upper right corner of each curve. So again, for a small gain in density a large gain in strength, stiﬀness and energy absorption is obtained.

4.3.2 Eﬀects of Foaming and Plating

In order to examine the effects of foaming on the ABS trusses, the specific strength, stiffness and energy absorption are plotted versus volume expansion in Figure 4.20. There is a decreasing trend in each of the specific strength, stiffness and energy absorption with increasing volume expansion. This is due to the overall cellular structure of the struts of the trusses. The increasing cell size produces a weaker overall structure with increasing volume expansion.

The strength of the ABS foam trusses has been modeled using the theory developed 1.4

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c4_energyratio

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400

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c4_stiffnessmsc (a)

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10 Strength(MPa) 10 Strength(MPa)

0 0 200 400 600 800 1000 1200 0 3 0 200 400Density(kg/m 600) 800 1000 1200 Density(kg/m 3) c4_strengthmsc (b) c4_strengthmsc 4.5

4.5 NOT-PLATED 4.0 PLATED NOT-PLATED 4.0 PLATED

) 3.5 3

) 3.5 3 3.0 3.0 2.5 2.5 2.0 2.0 1.5 1.5 EnergyAbsorption(MJ/m 1.0

EnergyAbsorption(MJ/m 1.0 0.5 0.5 0.0 0.0 0 200 400 600 800 1000 1200 0 200 400Density(kg/m 6003) 800 1000 1200 3 Density(kg/m ) c4_energymsc c4_energymsc (c)

Figure 4.19: Material selection charts for mechanical properties of the nano-Ni plated and unplated ABS trusses: (a) stiﬀness, (b) strength and (c) energy absorption. 60 Rapid Prototyped ABS Menges 50

Strength(MPa) 20

0 0 200 400 600 800 1000 1200 Chapter 4 Rapid prototyped ABS Truss CoresDensity(kg/m Plated3) with Nanocrystalline Nickel 73

strengthMengesABS

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6 4 SpecificStrength(MPa/g/cc) 4

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SpecificEnergy(MJ/m3/g/cc) 1.0 0.5 SpecificEnergy(MJ/m3/g/cc) 0.5 0.0 0 50 100 150 200 250 300 0.0 0 50 100%VolumeExpansion 150 200 250 300 %VolumeExpansion c4_specenergy

c4_specenergy (c)

Figure 4.20: Decreasing trends in (a) specific stiffness, (b) specific strength and (c) specific energy absorption of the foamed ABS trusses. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 74 by Gibson and Ashby [28]:

σ ρ 3/2 ρ = C1 φ CDCF + C2(1 − φ) (4.5) σYS ρs ρs

where σYS is the yield strength of the parent polymer, φ is a constant between 0 and 1 based on the number of open and closed cells in the foam (φ = 0 for closed cells, φ = 1 for open cells), ρ is the density of the foam, ρs is the density of the solid polymer, C1 and C2 are constants (for φ = 1, C1 = 0.3, for φ = 0, C1 = 0.44 for relative density <

1/2 0.2) and CDCF is a density correction factor (1 + (ρ/ρs) ) which can be included, but has small inﬂuence. To determine the strength of the ABS foam used in the trusses, the following relationship was used:

σABS−trussAtruss σABS−foam = (4.6) NsAcsin(ω)

where Atruss is the projected area of the ABS truss, Ns is the number of struts per truss sample, Ac is the cross-sectional area of the strut and ω is the strut angle. In Figure 4.21 the strength of the ABS foam trusses is plotted along with the Gibson and

Ashby model using values of 0.46, 0.67 and 0.94 for φ, C1 and C2, respectively. Although the experimental data does not match the model exactly, it does follow the overall trend. Variations from the projected model are due to the truss structure of the ABS foam, and the layering eﬀect of the rapid prototyping process which created a cellular structure of its own not accounted for in the Gibson/Ashby model.

In order to determine whether the foaming of the ABS trusses was advantageous, the ratio of the foamed samples and the solid samples is compared. By further normalizing these values with the ratio of the density of the foamed sample and the density of the solid sample it can be determined whether foaming of the ABS trusses was advantageous. An example of this calculation used to compare the strength of the samples is outlined in equation 4.7, which is equivalent to the ratio of speciﬁc strength (or strength-to-weight Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 75

40 RapidPrototypedABSTrusses 35 GibsonModel

15 Strength(MPa)

0 0 200 400 600 800 1000 1200 Density(kg/m 3)

strengthGAABS Figure 4.21: Comparison of the strength of the ABS foam trusses found experimentally and using Gibson/Ashby model.

Press Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 76 ratio) of the foamed and solid samples.

σfoamed σfoamed ρ r = σsolid = foamed (4.7) f ρfoamed σsolid ρsolid ρsolid

In this equation, if rf is greater than one, then foaming alone is beneficial. In other words, any decrease in strength is less than the decrease in density, so if one is restricted to a certain value for density when selecting a material, a greater strength material could be obtained by foaming a higher density material then by using a solid material. By comparing the values of r, the effect of foaming can be determined. For example, the greater the r value, the less the decrease in strength compared to the decrease in density. Figure 4.22 compares the r values (the normalized ratios) for the foamed ABS trusses for each of the mechanical properties investigated including stiffness, strength and energy absorption. For each of the properties, the r value is below one, indicating that there is no advantage in terms of strength, stiffness or energy absorption due to the foaming of the ABS truss. This is due to the change in the cellular structure as mentioned previously. However, the addition of nanocrystalline nickel shows the value of foaming the ABS trusses. In order to determine whether the addition of nanocrystalline nickel or the foaming of the ABS trusses was advantageous, the ratio of the plated samples and the unplated samples is compared similar to the method above. By normalizing these values with the ratio of the density of the plated sample and the density of the unplated sample the value of plating the ABS trusses with nanocrystalline nickel can be determined. An example of this calculation used to compare the strength of the samples is outlined in equation 4.8, which is equivalent to the ratio of specific strength (or strength-to-weight ratio) of the plated and not-plated samples.

σplated σplated σnot−plated ρplated r = ρplated = σnot−plated (4.8) ρnot−plated ρnot−plated

In this equation, if r is greater than one, then the addition of the nanocrystalline nickel 0.8

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0.0 -50 0 50 100 150 200 250 300 350 Chapter 4 Rapid prototyped ABS Truss%VolumeExpansion Cores Plated with Nanocrystalline Nickel 77

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0.0 0.0 -50 0 50 100 150 200 250 300 350 -50 0 50 100 150 200 250 300 350 %VolumeExpansion %VolumeExpansion

c4_stiffnessratiof c4_energyratiof (c)

Figure 4.22: Relative ratios for mechanical properties of the foamed ABS trusses: (a) stiffness, (b) strength and (c) energy absorption. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 78 is beneficial. In other words, the gain in strength is greater than the gain in density, so if one is restricted to a certain value for density when selecting a material, a greater strength material could be obtained by plating a lower density material (in this case, the ABS truss) then by using a solid material. Furthermore, by comparing the values of r, the effect of foaming can be determined. For example, the greater the r value, the greater the gain in strength compared to the increase in density.

Figure 4.23 compares the r values for the nanocrystalline nickel coated samples for each of the mechanical properties investigated including stiffness, strength and energy absorption. Starting with Figure 4.23a, the normalized ratio is always greater than one. Therefore, the gain in stiffness obtained by plating the samples with nanocrystalline nickel is greater than the gain in density. Furthermore, the normalized ratio increases and then plateaus with increasing foamed volume expansion. This tells us that foaming the ABS truss is also advantageous. A similar trend is observed in Figure 4.23b for strength wherein the addition of the nanocrystalline nickel and the foaming of the ABS truss core is also advantageous. The normalized ratio for energy absorption is given in Figure 4.23c. Again, the ratio is always greater than one, indicating that the gain in energy absorption is greater than the gain in density, however in this figure the trend does not continually increase with increasing volume expansion. There is a peak effect around those samples with a volume expansion of 135%. This indicates that there may be an ideal amount of foaming for these truss materials, or that there may be an ideal coating thickness-to-strut thickness ratio which is exemplified in the samples foamed with a volume expansion of 135% and a coating of approximately 250 µm. This theory is supported by the fact that the strength and stiffness plateau around the samples with a volume expansion of 135% as well. Further investigation by examining various volume expansions and various coating thicknesses would be needed to determine if there is in fact an ideal amount of foaming or coating thickness-to-strut thickness ratio.

Overall, the trends for stiﬀness, strength and energy absorption all show that it is advantageous to plate the ABS foamed trusses with nano-nickel. Furthermore, it is also 2.5

2.0

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0.0 Chapter 4 Rapid prototyped-50 ABS 0 Truss 50 100 Cores 150 Plated 200 with 250 Nanocrystalline 300 350 Nickel 79 %VolumeExpansion

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c4_stiffnessratio %VolumeExpansion

c4_energyratio (c)

500 NOT-PLATED Figure 4.23: Relative ratios450 forPLATED mechanical properties of the nano-Ni plated and unplated

ABS trusses: (a) stiﬀness,400 (b) strength and (c) energy absorption.

350

300

250

200 Stiffness(MPa) 150

100

0 0 200 400 600 800 1000 1200 Density(kg/m 3)

c4_stiffnessmsc Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 80 advantageous to foam the ABS trusses, but there is likely an ideal amount of foaming or coating thickness-to-strut thickness ratio.

4.3.3 Buckling Analysis of Plated ABS Trusses

In order to determine the theoretical strength of the nanocrystalline nickel coated ABS trusses, a model using hollow nanocrystalline tubes was considered. In this model, the critical strength (σCR) of nanocrystalline tubes with a rectangular cross-section was calculated using [52] k2π2E I k2π2E σ = t = t (4.9) CR AL2 (L/r)2 where k accounts for the rotational stiffness of the strut (k=1 corresponds to pinned ends, k=2 corresponds to fixed ends), Et is the tangent modulus, I is the moment of inertia, A is the cross-sectional area and L is the length of the strut [52]. Alternatively, the critical stress can be defined in terms of the slenderness ratio (L/r) where r is the radius of gyration. The tangent modulus in this case was calculated based on the Ramberg- Osgood model applied to nanocrystalline nickel [53],

σ σ N = + 0 (4.10) E σYS

where is the strain, σ is the stress, E is the Young’s modulus, 0 is the plastic strain

(0.002) corresponding to the yield strength, σYS and N is a strain hardening exponent. By ﬁnding the derivative to equation 4.10,

−1 N−1−1 ∂ 1 0 σ Et = = + N (4.11) ∂σ E σYS σYS the critical stress can be calculated. Using the critical stress of the nanocrystalline nickel sleeve, the force per strut can be calculated using

Fper−strut = σCRAc (4.12) Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 81

where Ac is the cross-sectional area of the nanocrystalline nickel sleeve. Using equation 4.12 the resolved critical force of the nanocrystalline nickel truss can be calculated using

FPCM = Ns(Fper−strut)sin(ω) (4.13)

where Ns is the number of struts per truss sample and ω is the strut angle. Finally, the overall strength of a truss made with nanocrystalline sleeves can be calculated by

FPCM σPCM = β (4.14) At

where At is the projected area of the truss sample and β is a knockdown factor used to account for the slight abnormalities in strut cross-section and alignment. A previous knockdown factor of 0.59 has been reported for a nanocrystalline nickel plated truss using an acrylic polymer with diﬀering truss dimensions to the present study [58].

Figure 4.24 shows the theoretical and experimental force per strut versus the cross- sectional area of the core for pinned (k=1) end conditions. The experimental force per strut was calculated similarly using equations 4.15 and 4.14,

σPCM At Fper−strut:experimental = . (4.15) Nssin(ω)

The pinned end conditions have been found to work for nanocrystalline nickel coated micro-trusses in previous studies [60]. Using a knockdown factor of β=0.18 a close match between the experimental and theoretical data can be obtained. This trend continues with the comparison of the strength of the truss as shown in Figure 4.25. Here, the experimental strength was calculated as

∆σ = σplated − σunplated. (4.16)

Again, a knockdown factor of β=0.18 is used to obtain a correlation between the theoretical and experimental data. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 82

9 Experimental 8 Theoretical Theoretical with knockdown 7 9 6 Experimental 8 Theoretical 5 Theoretical with knockdown 7 4 6 3 Forceperstrut(kN) 5 2 4 1 3 Forceperstrut(kN) 0 2 9 11 13 15 17 19 21 2 1 StrutCrossSectionArea(mm )

c4_buckling1 Figure 4.24: Comparison0 of the theoretical and experimental force per strut versus the 9 11 13 15 17 19 21 cross-sectional area100 of the core for pinned (k=1) end conditions. 2 StrutCrossSectionArea(mmExperimental) 90 c4_buckling1 Theoretical 80 Theoretical with knockdown 100 70 Experimental 90 60 Theoretical 80 Theoretical with knockdown 50 70 σ(MPa) 40 60 30 50 20

σ(MPa) 40 10 30 0 20 9 11 13 15 17 19 21 StrutCrossSectionArea(mm 2) 10

c4_buckling20 9 11 13 15 17 19 21 StrutCrossSectionArea(mm 2)

c4_buckling2 Figure 4.25: Comparison of the theoretical and experimental strength versus the cross- sectional area of the core for pinned (k=1) end conditions. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 83

20 Micro-Truss/Foam 18 Hybrids Micro-Truss 16 Hybrids

Strengthσ(MPa) Foam Hybrids 6

0 0.0 0.2 0.4 0.6 0.8 1.0 Densityρ(g/cc) Foamed ABS/Nano-Ni Trusses Bouwhuis et al. (2008) CellMet Bouwhuis et al. (2009) Acta Mater. Bouwhuis et al. (2008) Compos. Sci. Technol. Bele et al. (2009) upcoming Acta Mater. Gordon et al. (2009) Acta Mater.

c4_deltastrength Figure 4.26: Comparison of hybrid strength with previous studies.

To see how the results of these hybrid materials compare with other similar ones, the change in strength and the change in density is compared in Figure 4.26. In this figure, the plated ABS trusses fill an area between the hybrids from previous studies which fulfills the objective of designing a hybrid material to fill an empty area of materials space. Chapter 4 Rapid prototyped ABS Truss Cores Plated with Nanocrystalline Nickel 84

4.4 Summary

In this chapter novel hybrid materials were designed and manufactured using rapid prototyped ABS truss cores that were foamed to varying volume expansions and electroplated with nanocrystalline nickel. The hybrid materials had up to 1165% greater strength, 1525% stiffness and 650% energy absorption compared to their unplated counterparts. Also, there was a decreasing trend in the absolute value of these mechanical properties with decreasing core density, however in general, there was an increasing percentage difference in the plated trusses with decreasing density. Furthermore, by examining their normalized ratios, the plating of the trusses with nanocrystalline nickel was advantageous in terms of the mechanical properties of stiffness, strength and energy absorption, despite the gain in density. Similarly, by examining the normalized ratios, the foaming of the samples is advantageous as well, and there may be an ideal amount of volume expansion, or an ideal coating thickness-to-strut thickness ratio. Overall these hybrids give a new option for low density, high strength materials that can be used in the aerospace, automotive or consumer goods industries as cores for sandwich materials. Chapter 5

Conclusions and Future Work

Two sets of novel metal and polymer foam hybrid materials were designed, developed, manufactured and tested. In the first set the effect of surrounding a metal strut with a polymer foam was examined. Aluminium periodic cellular metals made of a pyramidal architecture were filled with varying densities of polyurethane foam. The PU foam acted to inhibit the struts of the PCM from buckling, thus increasing the strength of the hybrid material. Furthermore, the foam also contributed to energy transfer and absorption during impact testing, creating a hybrid material that can withstand greater impact energy. These hybrid materials offered a number of advantages over their micro-truss or foam counterparts:

the ability to tailor the stiﬀness depending on the density of the polyurethane foam;

an increase in stiﬀness of up to 120% over the aluminium PCM in the hybrid using the 290 kg/m3 density polyurethane foam;

an increase in strength between 9% and 372% over the aluminium PCM in the hybrids using the 83 kg/m3 density polyurethane foam and the 290 kg/m3 density polyurethane foam, respectively;

85 Chapter 5 Conclusions and Future Work 86

an increase in resilience between 26% and 740% over the aluminium PCM in the hybrids using the 83 kg/m3 density polyurethane foam and the 232 kg/m3 density polyurethane foam, respectively;

an increase in impact energy between 22% and 106% over the aluminium PCM in the hybrids using the 113 kg/m3 density polyurethane foam and the 290 kg/m3 density polyurethane foam, respectively;

a greater than sums eﬀect where the impact energy of the hybrids made with the 113, 232 and 290 kg/m3 PU foams is greater than the sum of the impact energy of the PCM and the PU foam combined; and

an increase in mechanical properties with an increase in foam density.

In the second set of hybrid materials the reverse effect was examined by looking at a foamed polymer strut surrounded by metal. The ABS cores for these hybrid materials were manufactured using a rapid prototyping technique. They were then foamed and electroplated with nanocrystalline nickel. The hybrid materials have greater overall strength, stiffness and energy absorption over the ABS trusses. More importantly, the slight increase in density gained by plating the ABS trusses was insignificant compared to the increase in stiffness, strength and energy absorption. Furthermore, the value of foaming the ABS truss cores could also be seen by examining the normalized ratios. These hybrid materials also offered a number of advantages over their ABS micro-truss counterparts:

an increase in stiﬀness between 315% to 1525%;

an increase in strength between 315% to 1165%;

an increase in energy absorption between 241% to 650%; and

the increases in mechanical properties was greater than the increase in density due to plating. Chapter 5 Conclusions and Future Work 87

This preliminary study of these novel hybrid materials has resulted in a new set of materials each with a unique set of properties. Both sets of hybrids saw an increase in strength and resilience. Furthermore, in the first set of hybrids, the stiffness of the final hybrid material can be tailored by adjusting the density of the polyurethane foam used in the manufacture of the hybrid. Increased impact resistance could be obtained with increasing foam density.

The value of adding nanocrystalline nickel, and foaming the ABS trusses could also be seen in terms of increased strength, stiﬀness and energy absorption. In this set of hybrid materials, although there was a gain in density due to the addition of the nanocrystalline nickel, it was outweighed by the gain in strength, stiﬀness and energy absorption.

These results provide a framework for further investigation into these hybrid materials. There is still some question about delamination of the face sheets of the PCM/PU foam hybrids. This could be controlled by spot welding the face sheets to the nodes. Further testing in terms of three-point bending would also be valuable. For the second group of hybrids, varying the thickness of the nanocrystalline nickel in the ABS/nanoNi trusses would help to identify if there is an ideal coating thickness to strut thickness ratio. Further investigation into various foamed densities would also help to identify if there is an ideal foam density for these hybrid materials. Due to geometrical con- straints of the foaming and testing equipment used, impact testing was not performed on the ABS/nanoNi trusses. By creating a larger sample, with more cells, an impact test could be performed and would provide valuable insight to the impact resistance of these materials.

In attempting to find new low density, high strength materials for the aerospace, automotive and consumer goods industries, hybrid materials have been developed that offer substantial gains in strength, stiffness, resilience, energy absorption and impact resistance. Furthermore, these new hybrid materials offer multi-functionality in terms of impact resistance and the ability to tailor the stiffness of the material. Figure 5.1 is a materials selection chart that shows the hybrid materials developed in this thesis. As 60 Rapid Prototyped ABS Menges 50

Strength(MPa) 20

0 0 200 400 600 800 1000 1200 Density (kg/m 3)

ChapterstrengthMengesABS 5 Conclusions and Future Work 88

25 ABS ABS/nano-Ni Hybrids PU 20 PCM/PU Hybrids PCM

10 Strength(MPa)

0 0 0.2 0.4 0.6 0.8 1 1.2 Density (Mg/m 3)

c5_strengthmsc Figure 5.1: Materials selection chart with PCM/PU foam and ABS/nanoNi hybrid ma- c4_deltastrength terials. demonstrated previously in Figure 4.26, these new hybrids ﬁll a hole in the materials selection charts of current research trends for micro-truss hybrid materials. With continued research into the properties of these novel hybrid materials, it is expected that these materials will quickly become valuable for use as the cores of sandwich structures in structural applications in the aerospace, automotive and consumer goods industries. References

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