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8-2018 Multiscale Behavior of Fused Deposition Additively Manufactured Thermoplastic Cellular Materials Kaitlynn Melissa Conway Clemson University, [email protected]

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Recommended Citation Conway, Kaitlynn Melissa, "Multiscale Behavior of Fused Deposition Additively Manufactured Thermoplastic Cellular Materials" (2018). All Theses. 2954. https://tigerprints.clemson.edu/all_theses/2954

This Thesis is brought to you for free and open access by the Theses at TigerPrints. It has been accepted for inclusion in All Theses by an authorized administrator of TigerPrints. For more information, please contact [email protected]. MULTISCALE BEHAVIOR OF FUSED DEPOSITION ADDITIVELY MANUFACTURED THERMOPLASTIC CELLULAR MATERIALS

A Thesis Presented to the Graduate School of Clemson University

In Partial Fulfillment of the Requirements for the Degree Master of Science Mechanical Engineering

by Kaitlynn Melissa Conway August 2018

Accepted by: Dr. Garrett J. Pataky: Thesis Advisor, Committee Chair Dr. Joshua D. Summers Dr. Huijuan Zhao Abstract

Cellular materials are known for being lightweight as well as deforming in unique ways. Cellular materials have become more viable due to additive manufacturing (AM). AM cellular materials are easier to fabricate compared to traditional cellular materials and AM cellular materials are not as limited in geometry as traditional fabrication methods were. AM materials were studied in this paper in a two-phase approach. Phase 1 focused on the global mechanical properties of AM cellular materials. Phase 2 focused on the crazing of AM thermoplastic glassy polymers and how additive manufacturing affects the behavior or cellular materials.

Because cellular materials do not have a consistent cross sectional area throughout the material, there is not a standard cross sectional area to use for property calculations. The author introduced an effective area for in-plane loading that normalized cellular materials by the amount of area present to allow accurate, direct comparisons between cellular materials of different unit cell geometries, unit cell dimensions, cellular materials of different stock material and comparisons between cellular material and solid materials. Strains calculated from DIC displacement measurements were used to validate the behavior observed using the effective area compared to how the cellular material was actually deforming.

It was observed that the AM honeycomb material crazed at the plastic hinges that formed.

Crazing was studied in AM acrylonitrile butadiene styrene (ABS) and extruded ABS to compare how crazing behavior differed in AM materials versus extruded materials. Extruded ABS crazes were thin with an average width of 10 m and appeared simultaneously throughout the cross section of a dog bone specimen when theµ macro crazing threshold stress was reached. AM ABS

ii crazes were an order of magnitude wider with an average width of 100 m and appeared at one or two locations when the macro crazing threshold stress was reached.µ Further crazing spread from the original craze locations as the material was further strained. Using DIC to detect macro crazing in AM ABS dog bone specimens and MicroCT scans to locate voids in the specimens, crazing was discovered to initiate in the large voids inherent in the AM process. Understanding how AM thermoplastics deform is critical for the development of using AM thermoplastic cellular materials.

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Acknowledgements

I would like to first thank my advisor Dr. Garrett J. Pataky for pushing me to become a better researcher. His high standards have taught me the importance of quality work, as well as the importance of quality when presenting my work. I also would like to acknowledge his endless patience when I ruined specimens, broke equipment and made the same mistakes countless times in a row.

I would like to thank Dr. Joshua D. Summers and Dr. Huijuan Jane Zhao for agreeing to be on my committee and meeting with me throughout my time here to discuss my research. Your assistance and patience is incredibly appreciated.

I would like to thank my family for their continuous love and support, as well as for introducing me to my love affair with science. My parents have always encouraged me to be curious and ask questions. They are always interested to hear about my research and classes and have encouraged me throughout my education. I would like to thank my sister for being someone I can laugh with and never farther than one text away.

I would like to thank Clemson University, the Clemson Mechanical Engineering Department, all of my professors, all of the welcoming people and all of the friends I have made during my time here.

I would especially like to thank my office mates of Office 125, who have made my time here so much more enjoyable: Vivic Harrinanan, Lauren Carter, Jody Bartanus, Jacob Biddlecom, Matt

Williams, Mitra Shabani, Cameron Abarotin and Diana Burden.

iv I would like to especially thank my undergraduate alma mater, LeTourneau University, not only for providing me with such a solid foundation in mechanical engineering, but also for showing me what it means to use your vocation for the glory of God.

I would like to thank the Sonoco Institute of Packaging Design and Graphics and the Department of Food, Nutrition and Packaging Science for use of their 3D printers and CNC table. I would like to thank W. Aaron Snyder for his continuous patience and willingness to help me while printing hundreds of specimens, as well as assisting with the varied assortment of tasks I recruited him for. When I first introduced myself and asked to use his 3D printer, I never dreamed he would become one of my closest friends.

I would also like to thank Travis Pruitt and the Godley-Snell building for use of their MicroCT scanner.

v Table of Contents

Abstract ...... ii Acknowledgements ...... iv List of Figures ...... viii List of Tables ...... x Chapter 1. Motivation of Additively Manufactured Cellular Materials ...... 1 Chapter 2. Literature Review ...... 5 2.1 Fused Deposition Additive Manufacturing ...... 5 2.2 Thermoplastics used in Fused Deposition Additive Manufacturing ...... 6 2.2.1 Poly (Lactic Acid) ...... 6 2.2.2 Acrylonitrile Butadiene Styrene ...... 6 2.3 Crazing ...... 7 2.3.1 Prediction of Micro Craze Initiation ...... 10 2.4 Cellular Materials...... 11 Chapter 3. Phase 1: Global Properties and Local Mechanisms of Additively Manufactured Cellular Materials ...... 15 3.1. Methods and Materials ...... 15 3.2 Calculation of Effective Area ...... 17 3.2.1 Footprint Area ...... 18 3.2.2 Column Area ...... 18 3.2.3 Effective Area ...... 18 3.3. Results ...... 19 3.3.1 Honeycomb Cell Behavior ...... 20 3.3.2 Brick Cell Behavior ...... 23 3.4. Discussion ...... 25 3.4.1 Comparison of Area Methods ...... 25 3.4.2 Mechanical Behavior using the Effective Area Method ...... 27 3.5 Conclusions ...... 32

vi Chapter 4. Phase two: Deformation of Additively Manufactured Acrylonitrile Butadiene Styrene ...... 33 4.1 Methods and Materials ...... 33 4.2 Results and Discussion ...... 36 4.2.1 Macro Craze Initiation Identified by DIC ...... 36 4.2.2 The Effects of Voids on Macro Craze Initiation ...... 42 4.3 Conclusions ...... 45 Chapter 5. Conclusions ...... 46 Chapter 6. Future Work ...... 48 Chapter 7. References ...... 50

vii List of Figures

Figure 1: Honeycomb cellular material sandwich panel with outer sandwich boards to support cellular core [24] ...... 2 Figure 2: Material crazing, craze fibrils extending in direction of force, craze walls forming perpendicular to direction of force [58] ...... 7 Figure 3: Honeycomb cellular solid in the X-Y and Y-Z planes. = 30°, wall thickness t varied .. 16

Figure 4: Brick cellular solid in the X-Y and Y-Z planes. Wall thicknessθ t varied...... 16 Figure 5: Load Frame with Honeycomb Specimen and Camera for DIC ...... 17 Figure 6: Honeycomb engineering stress-strain response using the (a) column area method (b) effective area method and (c) footprint area method. The effective area method resulted in consistent similar elastic behavior regardless of the specimen type or wall thickness ...... 20 Figure 7: Brick engineering stress-strain response using the (a) column area method (b) effective area method and (c) the footprint area method. The effective area method resulted in similar elastic behavior regardless of the wall thickness of the specimens...... 20 Figure 8: Axial strain values of honeycomb specimen with a wall thickness of 1.70 mm at global strains of (a) yy = 0.005 (b) yy = 0.0075 (c) yy = 0.010 and (d) the location of each DIC image on theε global stress-strainε response of theε material first in pure stretching (a) and then cell walls bend and plastic hinges form (circled) as the material begins to yield (b,c)...... 23 Figure 9: (a) Axial strain(b) Shear strain values from DIC of brick specimen with a wall thickness of 1.7mm at a global strain of (c) = 0.0059. Axial cell walls of brick specimen in tension, shear stress concentrations develop at intersection𝜺𝜺 of axial and transverse cell walls, which likely led to brittle failure of brick specimen...... 25 Figure 10: Honeycomb cellular material (a) y = 0.0033, no plastic hinges. (b) y = 0.017, crazing initiates as plastic hinges form, circled...... σ σ 29 Figure 11: Local axial strains of honeycomb specimen showing plastic hinging. (a) t = 0.95 mm, clear double plastic hinging. (b) t = 1.70 mm, single plastic hinge ...... 30 Figure 12: Dimensions of dog bone specimen in mm. Gradually narrowing cross sectional area caused crazing to begin in a predictable location...... 34

viii Figure 13: Experimental setup of the dual camera system with an ABS dog bone in the load frame and all lighting concentrated on the front of the specimen. Crazing seen as dark lines due to change in density as light refracted through the specimen...... 35 Figure 14: Stress-strain response of AM and Extruded (E) ABS dog bones. Bucknall micro-crazing prediction at 0.25 y. Macro crazing is observed at 0.8 y for AM ABS and 1.05 y for E ABS. .... 37

Figure 15: Extrudedσ ABS dog bone (a) virgin and (b) macroσ crazing. Crazes appearσ simultaneously across the cross section at the macro crazing threshold 1. y. Crazes uniform and thin with a width of approximately 10 m...... 05σ 38 Figure 16: Extruded ABS DIC grey level uncertaintyµ measurements. Green and red areas signify macro crazing...... 40 Figure 17: Craze propagation in AM ABS at global strains of (a) yy= 0.020 (b) yy = 0.023 and

(c) yy = 0.025. Macro crazes approximatly 100 μm wide. AMε macro crazes εinitiate in single locationε (circled) and propagate from that location across the width ...... 41 Figure 18: DIC yy values of AM ABS specimen loaded to a global yy = 0.023. Red areas signify crazing...... ε ε ...... 42 Figure 19: (a) DIC yy values of AM ABS specimen at a global strain of yy = 0.024. (b) MicroCT scans mapped to largeε (>100 m) internal voids to the location of macroε craze initiation in the specimen...... µ ...... 43 Figure 20: MicroCT scans of AM ABS specimen showing growth of internal voids. (a) Virgin specimen with internal void of 100 μm circled; (b) Specimen after macro crazing observed, same internal void grew to 240μm, circled. Internal voids drive macro crazing in AM ABS...... 44

ix List of Tables

Table 1: Young’s Modulus and area comparisons between honeycomb cellular materials of different wall thicknesses. Effective area moduli collapse to a similar modulus as solid dog bone for all wall thicknesses...... 22 Table 2: Young’s Modulus and area comparisons between brick cellular materials of different wall thicknesses. Effective area moduli collapse to a similar modulus as solid dog bone for all wall thicknesses...... 24

x Chapter 1. Motivation of Additively Manufactured Cellular

Materials

In the automotive and aerospace industries, there is an increasing demand for lightweight yet strong materials [1]. Due to this, there has been a large interest in two-dimensional periodic cellular materials [2–6], three-dimensional truss materials [7–11], their material properties and their mechanical behavior as they deform. Periodic two-dimensional cellular materials have a surface topography of a repeating cellular shape in the X-Y plane and are extruded in the Z plane

[12]. Truss materials have different repeating cellular shapes in the X-Y plane, X-Z plane and Y-Z plane [13]. Through an extensive literature review no standard method was found for determining cross sectional area of these periodic cellular and truss materials in order to calculate global properties such as stress or Young’s modulus. Different researchers use different areas, which do not allow for strength comparisons between findings [1, 2, 4–7, 9, 10, 14]. Additionally, most researchers use an area that does not consider the amount of material used [5–7, 9, 15].

This does not allow normalized comparisons between different unit cell geometries and dimensions as well as between cellular materials and their bulk properties. In this thesis, an effective area is proposed for property calculations that normalizes cellular materials by the volume of material present to allow for comparisons between cellular materials with any unit cell geometry or size. An effective area is needed for both cellular materials and truss materials; however, the focus of this paper is on 2D periodic cellular materials.

Additive Manufacturing (AM) has made cellular materials more viable [1]. AM allows for more geometry variation than traditional cellular material paper folding fabrication techniques [16]. By

1 building parts layer-by-layer instead of by traditional manufacturing techniques, cellular material geometries that would have been difficult and costly, if not impossible, can be fabricated with AM technologies [17–19]. The absence of tooling within AM eliminates the need to manufacture large numbers of parts from expensive molds for the parts to become cost effective [20]. Additionally, improvements in AM technologies such as increased precision and a smoother surface finish have allowed AM technologies to produce end-use parts [21]. AM cellular materials do not depend on sandwich boards for support as historically fabricated cellular materials did [1, 4, 22, 23]. Figure

1 shows a sandwich panel made with a honeycomb cellular material core. The core is made from folding paper or sheets of aluminum and gluing them to the outer boards.

Figure 1: Honeycomb cellular material sandwich panel with outer sandwich boards to support cellular core [24]

Additively manufacturing cellular materials allows the materials to be loaded in-plane in ways that were not practical when cellular materials had to be supported by sandwich boards such as in- plane tension [1, 3], compression [1, 2, 4–6, 25] and shear [12, 26–29]. Cellular materials are used much more frequently for in-plane loading situations than they were in the past. Additionally,

2 honeycombs and brick geometric shapes loaded in-plane present an ideal geometry for studying plastic hinging that develops in bending and flexing geometries compared to cellular materials that only deform by stretching [30].

AM has been proven to be a useful prototyping tool because it does not depend on expensive molds or complex tooling [17]. AM materials however were frequently weaker than their bulk counterparts due to internal voids, printing flaws and loss of molecular orientation [31, 32]. New

AM parts are stronger than they were historically due to new stock materials, [33, 34] better fabrication [18, 35] and improved post processing methods [36]. Because of these advances, engineers are designing AM parts to support structural loads [34, 37].

An impressive use of AM technology has been fabricating unmanned aerial vehicles (UAVs) using fused deposition (FD) AM. The advanced additive research center of University of Sheffield printed a fixed UAV completely from acrylonitrile butadiene styrene (ABS) [38]. Researchers at the Istanbul Technical University created a vertical take-off and landing UAV made from FD AM poly lactic acid (PLA) [39, 40]. Aurora Flight Sciences and Stratasys teamed up to print the first jet engine UAV using FD AM polyetherimide (PEI) and acrylonitrile styrene acrylate (ASA) [34]. The use of AM polymers as structural components, expounds on the need to fully understand the behavior and deformation mechanisms of AM polymers.

In AM ABS cellular materials, crazing has been observed when the material is loaded. Crazing has mostly been observed when plastic hinges form in the AM cellular material. Crazing is a failure mechanism seen in ABS when a specimen is under a tensile load [41]. Crazing was heavily studied in glassy polymers and ABS in particular in the 1970-1980’s [41–45]. Crazing has been observed in AM ABS [31, 32, 36, 46], however there are not thorough studies of how crazing behaves in AM

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ABS compared to extruded ABS. It has been hypothesized that internal voids that appear AM ABS act as a mechanism that causes crazing to initiate and propagate in different ways than extruded

ABS [31].

In this paper, a two-phase approach investigates the global properties of cellular materials as well as the local mechanisms driving the global behavior. Phase 1 considers the global properties of cellular materials with the proposed effective area and the local mechanisms of AM thermoplastic cellular materials and how macro crazing initiated in ABS AM cellular materials as plastic hinges formed. Phase 2 compares the behavior of macro crazing in AM materials and extruded materials and what mechanisms drive crazing in each material.

Chapter 2. is a literature review of the state of the field of additive manufacturing, with emphasis on FD AM of ABS and PLA; crazing, particularly to AM and extruded ABS; and cellular materials, particularly calculating their global properties. Chapter 3. discusses a proposed approach of how global properties of cellular materials should be calculated using the effective area and the local mechanisms in brick and honeycomb cellular materials. Chapter 4. compares crazing in AM and extruded ABS. Chapter 5. concludes the study and Chapter 6. considers future work within the fields.

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Chapter 2. Literature Review

2.1 Fused Deposition Additive Manufacturing

AM is a fabrication method where a part is built by adding material layer by layer [17, 18, 35]. Due to this building technique, additive manufacturing can build geometries that would be difficult or impossible with subtractive fabrication methods [20]. Additionally, there is little wasted material in the AM processes because the ratio of the amount of material used verse the amount of material in the printed part is very low [17].

FD is the most commonly used polymer AM process [34]. In FD AM, the stock material is a thermoplastic polymer in the form of a flexible monofilament, that is fed into the extruder on the cross head of the printer, heated above its glass transition temperature to a semi-liquid form and then extruded onto the build surface layer by layer [17, 18, 31, 32, 35, 36, 46]. The most common materials used for FD are acrylonitrile butadiene styrene (ABS) and poly-lactic acid (PLA) [37, 41,

47, 48].

AM materials are weaker than their stock materials due to internal voids and loss of molecular orientation that are inherent to the extrusion process [31, 36, 46]. Work has been done to improve the strength of AM materials by varying build orientation [21, 37], print speeds [18], infill directions [18, 31], infill densities [18, 49], infill geometries [49], layer thickness [18], perimeter thicknesses [18] and nozzle temperatures [35]. While improvements have been made with optimizing these settings, AM materials are still significantly weaker than extruded parts [31, 46].

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2.2 Thermoplastics used in Fused Deposition Additive Manufacturing

ABS and PLA are two of the most common materials for FD AM [17]. Both are thermoplastic glassy polymers.

2.2.1 Poly (Lactic Acid)

PLA is formed from the condensation of lactic acid, a chiral molecule [50, 51], to a low molecular weight prepolymer state. The prepolymer is then converted to PLA by increasing the molecular weight either through ring opening polymerization or from the addition of chain coupling agents

[52]. PLA is a biodegradable material with a two phase degradation process and is derived 100% from renewable resources including corn and sugar beets [53]. Extruded PLA has a reported tensile modulus of 3.5GPa [53] and a glass transition temperature of 50-60°C. PLA is a linear polymer and therefore has a low ability to plastically deform and will often fail in a more brittle manner than other thermoplastics such as ABS [50, 51].

2.2.2 Acrylonitrile Butadiene Styrene

ABS is a rubber-toughened thermoplastic made of a polystyrene (PS) matrix with small butadiene rubber particles within the matrix [54, 55]. The addition of the butadiene particles increases the fracture resistance of ABS between 5-20% compared to pure PS [54]. Variation in the improvement of toughness between PS and ABS is due to the size and amount of added butadiene particles [54]. ABS has a glass transition temperature of 110°C making it an ideal thermoplastic for FD AM [37]. ABS is amorphous which means that it has no true melting temperature [37].

Extruded ABS has a reported tensile modulus between 2.0 and 2.6GPa [56].

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2.3 Crazing

Crazing is a tensile deformation phenomenon of high molecular weight glassy polymers [57] where amorphous polymer chains realign in the direction of force. Craze walls form perpendicular to the direction of maximum (tensile) principal stress. When crazing begins, amorphous polymer chains realign in the axial direction and become load bearing, connecting the craze walls which form in the transverse direction shown in Figure 2 [58].

Figure 2: Material crazing, craze fibrils extending in direction of force, craze walls forming perpendicular to direction of force [58]

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As the chains realign the density of that area decreases, causing light to be refracted differently, which, when a craze is large enough, will allow the craze to be observed with the human eye [41–

43, 45, 54, 59–63]. A visualization of the mechanics of crazing is found in [44]. When the craze fibers realign they act as a toughening mechanism for the polymer. Some fibers break during crazing, however stresses are distributed between many realigning fibers and the craze continues to support larger loads until localized stresses increase elsewhere in the specimen and another area begins to craze. Eventually, in a heavily crazed area of the specimen, too many load- supporting fibers reach maximum extension and fail causing a crack to develop [55]. Crazes are capable of supporting a load, and the density of a craze is less than the uncrazed material. This distinguishes it from a crack, which has a density of zero [42].

Crazing begins at stress concentrations in the material [59]. In homogenous materials, those stress concentrations are often minor scratches or flaws on the surface. Crazing has also been reported to initiate at small inclusions or voids in the material [59, 64, 65]. In ABS, small rubber particles are added to the polymers to increase their toughness in impact loading. In extruded

ABS, micro crazing initiates around and between these small rubber ball inclusions [41, 45, 64].

Micro-crazes are small crazes that initiate in the stress fields around small inclusions in the material and provide toughening behavior. When the global stresses are large enough, the micro crazes around the small inclusions or micro crazes that initiate from locations of stress concentrations like a surface flaw, can initiate macro crazing. Macro crazes are the large crazed regions perpendicular to loading that are visible to the human eye. Evidence from a transmission electron microscope shows the thickness of a micro craze to be between 12 and 20 nm when crazing initiates [59]. Crazing cannot be seen under a light microscope until they are more than

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200 nm thick, half the wavelength of violet light [59]. This study defines macro crazing as detectable on the mesoscale through optical images. Macro crazing is a population of many micro crazes with populations consisting of 10,000 or greater. Macro crazes are considered to −2 initiate once visible to the human eye which is𝑐𝑐 𝑚𝑚when the area of the concentrated micro crazing exceeds m. There is some debate about how these macro crazes initiate. Bucknall postulated100µ that crazes initiate in locations where voids already exist. Argon proposed that micro crazes initiate first and then propagate when the small rubber inclusions deform, introducing a void between the inclusion and the matrix, and then growth of micro crazes initiates macro crazing [59, 60, 64]. Both agreed that voids are considered to ease craze formation. In extruded materials macro crazing is primarily a surface phenomenon initiating from small scratches and flaws on the surface of the specimen [42]. Micro crazes are known to initiate at surface flaws as well as at internal inclusions [42].

In AM components, internal voids often appear from printing errors and between the printed rasters [31, 37]. AM parts often also have an undesirable surface finish that could initiate crazing if the component is not polished after printing [21]. While crazing has been identified in AM components, in this extensive literature review there have not been studies found showing where and when the crazing initiates. Studies also lack an understanding of how crazing drives the behavior and mechanics of AM components. Researchers have hypothesized that voids in AM materials act as a mechanism to drive crazing in AM structures, but have not compared the locations of internal voids to where macro crazes initiate in AM components [31]. The aim of phase two of this study is to address where and when macro crazing initiates in AM ABS

9 components, to show that voids drive the behavior of crazing in AM components, and how crazing affects the integrity of said components.

2.3.1 Prediction of Micro Craze Initiation

Bucknall introduced in 2006 a new criterion for craze initiation and an equation that could be used to predict when surface crazing initiated in a specimen [59]. Bucknall’s criterion considered crazing to begin due to surface flaws. Bucknall’s criterion followed linear elastic fracture mechanics and the Griffith equation for the energy required to propagate crack growth. Bucknall adapted Griffith’s equation and treated a craze as a similar mechanism as a crack. Instead of considering the fracture energy to find for the craze to propagate, Bucknall considered

𝐼𝐼𝐼𝐼 1𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 the amount of energy, , and𝐺𝐺 global stresses,𝜎𝜎 , needed for a craze to open, shown in

𝐼𝐼𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 1𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 Equation 1. 𝐺𝐺 𝜎𝜎

( ) 1 (1) (1 ) 2 𝐸𝐸𝐺𝐺𝐼𝐼 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝜎𝜎1𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 ≥ � 2 2 � 𝑌𝑌 − 𝑣𝑣 𝜋𝜋𝑎𝑎0 where E is the Young’s Modulus of the material, Y is a geometric factor, ν is the Poisson’s ratio and is the flaw size. is estimated as the craze tip opening displacement. Craze tip

0 𝐼𝐼𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 opening𝑎𝑎 displacement 𝐺𝐺 is found in literature to be between 6 and 15nm [59]. The energy

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 needed for a craze to initiate𝛿𝛿 can be predicted using the equation below:

( ) = (2) 𝐺𝐺𝐼𝐼 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝜎𝜎𝑦𝑦𝛿𝛿𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 where is the yield strength of the material. Bucknall’s criterion was used in this paper as

𝑦𝑦 benchmark𝜎𝜎 to predict micro crazing initiation.

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2.4 Cellular Materials

Traditionally, cellular materials had been used as the core in sandwich materials and therefore were studied in out-of-plane bending and crushing [22, 23]; less work had been performed studying in-plane loading [66, 67]. With the improvement of additive manufacturing (AM), industries and researchers have begun additively manufacturing cellular materials at a lower cost and fabrication time than traditional methods. AM can make cellular materials with different geometric shapes that would have been extremely costly or impossible with traditional fabrication methods [17]. Additionally, AM cellular materials can support themselves without the dependence of the outer sandwich boards that the older methods needed. This advance in additive manufacturing led to AM cellular materials with new unit cell designs and completely new loading profiles than what has generally been studied and well understood [68–71].

Researchers are now studying cellular materials with new unit cells and loading profiles including in-plane loading of AM cellular materials not supported by sandwich boards [8]. Cellular materials are used much more frequently in in-plane loading situations than they have in the past.

Additionally honeycombs and other geometric shapes loaded in-plane present an ideal geometry for studying plastic hinging that develops in bending and flexing geometries [30].

Cellular materials need to be studied two different ways: the behavior of the unit cell under various loading conditions, and the behavior of the cellular material as a large material comprised of a repeating cellular pattern. A single unit cell is analyzed as a structure or mechanism and how that mechanism behaves when loading is applied. Consideration is given to whether the beams and joints in the mechanism will flex, stretch or hinge. How the mechanism deforms changes the way the mechanism behavior is evaluated. Gibson and Ashby described the behavior of unit cells

11 of various geometries under different loading conditions [30]. They used Timoshenko’s beam theories to describe the loads, stresses and strains seen by each beam of the unit cell when the cell is loaded [72, 73]. A significant distinction Gibson and Ashby make between different unit cell shapes are those shapes that are bending dominated and those that are stretching dominated

[30]. In stretching dominated unit cells, the collapse strength is controlled by the axial strength of the cell walls; in bending dominated cells the collapse strength is controlled by the flexural strength of the cell walls [74]. Masters and Evans expanded on their work to show that a cellular solid, and hexagonal honeycomb in particular, can deform three ways: hinging, flexing and stretching [75]. While a unit cell may dominantly deform one way, it can experience all three types of deformation simultaneously [75]. Many researchers expanded Gibson and Ashby’s and

Masters and Evans’ works to different unit cell geometries [2, 4, 13, 68]. Topological optimization research found new unit cell geometries and dimensions to improve the targeted material properties and behavior of a unit cell [76–78]. The mechanics Gibson and Ashby found to describe the behavior of a unit cell depended on the dominate deformation mode a unit cell experienced as well as which members of the unit cell carried axial and transverse loads. Gibson and Ashby’s work has led to an understanding of the behavior of different unit cell shapes and being able to compare different unit cell geometries as well as understand the local stresses that different cell walls and joints of various unit cell geometries would experience in different loading conditions.

To fully understand the behavior of a cellular material, the global properties of a cellular material must also be understood.

Gibson and Ashby described the mechanics of a single unit cell; others have expanded their work to consider an entire cellular material as a mechanism [2, 4, 10, 14]. By considering the cellular

12 material a mechanism, the entire cellular material is defined by the primary deformation mechanisms of the unit cell. When evaluating a cellular material’s uniaxial global properties, the overall deformation performance is not linked to the individual cell deformation mode. Using a methodology that changes depending on the main deformation mechanism the unit cell of the material experienced is not descriptive of the full behaviors the material may experience.

Additionally, this does not allow for accurate comparisons between two unit cells that are dominantly driven by different deformation mechanisms. Also, considering only the dominate deformation method when a material may be deforming by multiple mechanisms at once would suppress the true behavior of the material [75]. The cross sectional area used for global property calculations of cellular materials should just consider the amount of bulk material the cellular material consists of. By only considering the amount of bulk material the cellular material consists of, the global properties of cellular materials with unit cells that deform by different mechanisms can accurately be compared to each other.

The footprint area is a common way researchers currently calculate the cross-sectional area for the engineering stress of a cellular material by expanding the Gibson and Ashby equations. The footprint area is found by multiplying the entire cross section of the specimen by the thickness of the specimen [2, 4–6, 15, 71]. Other researchers only considered the cross sectional area of all the beams that support the axial force to calculate the global properties of the material [4, 9], referred to as the column area. Calculating engineering stress using the column or footprint method does not take into consideration the relative volume of the material. It does not allow for accurate comparisons of cellular materials with different unit cell geometries and dimensions, nor how the cellular material differs from the bulk material. Other studies have tried to calculate

13 the stress of cellular materials and truss materials in a way that better represents the amount of stock material used in the material design [1]. Researchers do not all use the same method for calculating stress because there is not an established method for calculating the global mechanical properties of cellular materials [79]. Some only reported their materials force-displacement behavior [11, 25] and others reported a stress but were vague about how they calculated the global stress of their cellular material [3, 8, 19]. Understanding both the single unit cell mechanism behavior as well as the cellular material global behavior is important in defining the full behavior of different cellular materials.

A cellular material is a material that is made of repeating unit cells. To be considered a material, the author of this paper borrowed from the homogenization theory and recommend considering a cellular material a new material, and not repeating unit cells, when the threshold of 10 by 10- repeated unit cells is met [80]. To fully characterize the global behavior of cellular materials, the cellular material should be treated as a new material and its global properties should be independently investigated from the beam theory used to analyze a single unit cell.

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Chapter 3. Phase 1: Global Properties and Local

Mechanisms of Additively Manufactured Cellular Materials

3.1. Methods and Materials

To experimentally compare the engineering stress results using the footprint area, column area and the effective area, specimens with unit cells of honeycombs and brick, Figure 3 and Figure 4, of varying cell wall thickness were subjected to in-plane tension. The cell shapes were chosen to isolate each deformation mode: honeycomb cells are bending dominated and brick cells are stretching dominated [30]. The honeycomb specimens were composed of 11 by 11 cells with measured uniform wall thicknesses of 0.95, 1.70 and 2.25mm and brick specimens were composed of 11 by 11 cells with measured uniform wall thicknesses of 1.03 and 1.70mm.

Honeycomb specimens were additively manufactured from poly-lactic acid (PLA) filament using a

Makerbot Replicator 2 and brick specimens were additively manufactured from acrylonitrile butadiene styrene (ABS) filament using a Makerbot Replicator 2X. All specimens were printed in the X-Y plane and extruded in the Z direction, indicated in Figure 3 and Figure 4. AM solid dog bones of ABS and PLA were also tested to compare the behavior of the honeycomb and brick specimens with ABS and PLA solid AM properties. Both ABS and PLA specimens were used to show results were not a material phenomenon but were due to geometry.

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Figure 3: Honeycomb cellular solid in the X-Y and Y-Z planes. = 30°, wall thickness t varied

𝜃𝜃

Figure 4: Brick cellular solid in the X-Y and Y-Z planes. Wall thickness t varied

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The specimens were loading in tension using a screwdriven load frame at a constant strain rate of

10 . For a digital image correlation (DIC) analysis a Point Grey GS3 camera with a 0.5x −4 −1 Navitar𝑠𝑠 lenses and adapter captured pictures at a frame rate of 1 Hz. The experimental setup is shown in Figure 5. Before testing, specimens were polished with increasingly fine sandpaper up to P4000 grit and speckled using an Iwata airbrush and black Aztek paint. Images were used to calculate global and local strains experienced by the specimens using commercial DIC software

Vic 2D.

Figure 5: Load Frame with Honeycomb Specimen and Camera for DIC 3.2 Calculation of Effective Area

Two methods often used by researchers to calculate the cross sectional area of cellular materials are the footprint area and the column area. Neither area normalizes the cellular materials by the amount of stock material present nor by the geometry or dimensions of the unit cell. The author of this paper proposes an effective area to normalize cellular materials by the amount of stock

17 material present in the cellular material, which will allow for accurate comparisons between cellular materials of different unit cell geometries, dimensions, number of unit cells and comparisons between cellular materials and their stock material.

3.2.1 Footprint Area

Consider two cellular materials that have the same unit cell shape, size and number of cells, but different cell wall thickness, as seen in Figure 3. The footprint cross sectional area is the entire width of the cellular material divided by its depth, = . Using the footprint

𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 method [5, 6], cellular materials with similar unit cell geometries𝐴𝐴 and𝑊𝑊 cell∗ 𝑑𝑑 numbers but different cell wall thicknesses would have the same cross sectional area with no consideration given to the amount of material composing each specimen.

3.2.2 Column Area

The column area only considers the cross sectional area of cell walls that would carry axial load if the cellular material was considered a mechanism [9]. The column area better accounts for the amount of material used than the footprint area, however transverse cell walls are still not accounted for in the area calculations. The cellular area is most often used for geometries where cell walls are only parallel to the axial direction and the transverse direction, such as the brick cellular material in Figure 4.

3.2.3 Effective Area

The effective area proposed by the authors for calculating the engineering stress of cellular materials considers the amount of stock material composing the cellular material. The effective area is calculated by multiplying the depth of the material by the surface area (SA) of the cellular

18 material in the X-Y plane, just where material is present, and normalizing that over the length of the material.

= (3) 𝑆𝑆𝑆𝑆 ∗ 𝑑𝑑 𝐴𝐴𝐸𝐸𝐸𝐸𝐸𝐸 𝐿𝐿

= (4)

𝐹𝐹 𝜎𝜎𝐸𝐸𝐸𝐸𝐸𝐸 𝐴𝐴𝐸𝐸𝐸𝐸𝐸𝐸 The method of calculating the engineering stress using the effective area considers the amount of stock material in the cellular material. It allows for comparisons between the cellular materials of different geometries and dimensions as well as between the cellular material and the stock material. It also accounts for cell geometries that have varying cell dimensions such as cell wall thickness [71].

The effective area proposed is a closed form solution. As the cellular material walls increase in thickness, the effective area increases. As the wall thickness approaches the width of the cell, the cellular material approaches a solid material. It is obvious that the effective area of a solid dog bone would be the cross sectional area.

3.3. Results

Global strain results were calculated using Vic 2D by using the mean average of all local axial strains. The stress of each specimen was calculated by dividing the force experienced during the test by the footprint area, column area and the effective area to calculate the footprint engineering stress, column engineering stress and the effective engineering stress of each specimen and can be seen for the honeycomb in Figure 6 and the brick in Figure 7.

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Figure 6: Honeycomb engineering stress-strain response using the (a) column area method (b) effective area method and (c) footprint area method. The effective area method resulted in consistent similar elastic behavior regardless of the specimen type or wall thickness

Figure 7: Brick engineering stress-strain response using the (a) column area method (b) effective area method and (c) the footprint area method. The effective area method resulted in similar elastic behavior regardless of the wall thickness of the specimens.

3.3.1 Honeycomb Cell Behavior

Shown in Figure 6a, the footprint stress-strain response of the honeycomb specimens with different wall thicknesses were plotted against the stress-strain response of the solid PLA dog bone. The specimens all had different elastic moduli and yield strengths. The solid dog bone had the largest modulus and yield strength and the thinnest walled honeycomb specimens had the smallest.

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The column stress-strain response of the honeycomb specimens also all had different moduli and yield strengths. However, all the honeycomb specimens’ moduli were larger than the solid dog bone, and the specimen with the thinnest cell walls had the largest modulus.

Using the effective stress-strain curves, shown in Figure 6b, collapsed the curves down to the same elastic moduli and initial elastic behavior. The yield strengths of the specimens were still proportional to the wall thickness. The solid dog bone had the highest yield strength and the thinnest walled honeycomb specimens had the lowest.

The elastic modulus and cross sectional area of each honeycomb wall thickness are in Table 1. All honeycomb specimens had similar Young’s Moduli of approximately 3.2GPa when using the effective area method, which was comparable to the Young’s Modulus of the solid dog bone of

3.1GPa. When using the footprint or column area method, the Young’s Modulus varied depending on wall thickness of the material. The honeycomb specimens all had similar cross sectional areas of approximately 200mm when using the footprint area method. The column and effective 2 areas were dependent on the amount of material used and therefore changed with the cell wall thickness of the material.

Honeycomb Cellular Material Wall Thickness (mm) Area Method t = 0.95 t = 1.70 t = 2.25 Dog Bone Column Area E (GPa) 4.9 4.0 3.7 3.1 Area ( ) 41 67 97 𝟐𝟐 𝐦𝐦𝐦𝐦 Effective Area E (GPa) 3.4 2.9 3.2 3.1 Area ( ) 60 94 111 𝟐𝟐 𝐦𝐦𝐦𝐦 Footprint Area E (GPa) 1.0 1.3 1.8 3.1 Area ( ) 194 202 197 𝟐𝟐 𝐦𝐦𝐦𝐦

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Table 1: Young’s Modulus and area comparisons between honeycomb cellular materials of different wall thicknesses. Effective area moduli collapse to a similar modulus as solid dog bone for all wall thicknesses.

DIC measured the local strains of the honeycomb cellular material as it was loaded in tension.

Axial strains of the honeycomb are shown at different global strain levels, = 0.005, =

0.0075 , = 0.010 are shown in Figure 8a, b and c respectively. The locations of each𝜀𝜀 DIC image𝜀𝜀 compared𝜀𝜀 to the entire loading profile are shown in Figure 8d. Concentrations of comparatively larger strains appear where the bending moments are the greatest, as circled in Figure 8b. As the specimen was strained further the global strains, shown in Figure 8d, and the large localized strains where the specimen was hinging increased, shown in Figure 8c.

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Figure 8: Axial strain values of honeycomb specimen with a wall thickness of 1.70 mm at global strains of (a) = 0.005 (b) = 0.0075 (c) = 0.010 and (d) the location of each DIC image on the global

stress𝑦𝑦𝑦𝑦-strain response𝑦𝑦𝑦𝑦 of the material𝑦𝑦𝑦𝑦 first in pure stretching (a) and then cell walls bend and plastic 𝜀𝜀 𝜀𝜀 hinges form (circled)𝜀𝜀 as the material begins to yield (b,c).

3.3.2 Brick Cell Behavior

When the column stress-strain curves of the brick specimens were plotted against the solid ABS dog bone, shown in Figure 7a, the elastic modulus of the brick specimens were greater than the solid dog bone specimens. However, when the footprint area method of the brick specimens were plotted against the solid ABS dog bone, shown in Figure 7c, the elastic modulus of the brick specimens were less than the solid dog bone. When the effective stress-strain curves were

23 plotted, Figure 7b, the elastic modulus was the same for all the specimens. Following the trend of the honeycomb specimens, the dog bone specimens had the largest yield strength and the thicker walled brick specimen had a larger yield strength than the thinner walled brick specimens.

The Young’s Modulus and cross sectional area of the brick specimens of each wall thickness are shown in Table 2. When using the effective area method, all brick specimens had a similar Young’s

Modulus to the solid dog of approximately 1.5GPa. The footprint and brick moduli were not consistent among wall thicknesses nor were they similar to the Young’s modulus of the solid dog bone.

Brick Cellular Material Wall Thickness (mm) Area Method t = 1.03 t = 1.70 Dog Bone Column Area E (GPa) 4.8 3.6 1.5 Area ( ) 39 64 𝟐𝟐 𝐦𝐦𝐦𝐦 Effective Area E (GPa) 1.7 1.5 1.5 Area ( ) 107 151 𝟐𝟐 𝐦𝐦 𝐦𝐦 Footprint Area E (GPa) 0.8 1.0 1.5 Area ( ) 233 235 𝟐𝟐 𝐦𝐦𝐦𝐦 Table 2: Young’s Modulus and area comparisons between brick cellular materials of different wall thicknesses. Effective area moduli collapse to a similar modulus as solid dog bone for all wall thicknesses.

The brick specimen all failed at a lower global strain than the bulk material and all failed in a brittle manner. DIC measured the local strains of the brick cellular material as it was loaded in tension.

Figure 9 shows the local axial strains and local shear strains at a global strain of = 0.0059 in

Figure 9a and b respectively. Figure 9a shows that the largest axial strains were concentrated𝜀𝜀 in the vertical walls not connected to horizontal walls. Figure 9b shows that there were large

24 concentrations of shear strains at the intersection of the vertical and horizontal walls, which were most likely responsible for the specimen failing at those intersections in a sudden brittle manner.

Figure 9c shows the location of the DIC images compared to the global behavior of the specimen.

Figure 9: (a) Axial strain(b) Shear strain values from DIC of brick specimen with a wall thickness of 1.7 mm at a global strain of (c) = 0.0059. Axial cell walls of brick specimen in tension, shear stress concentrations develop at intersection of axial and transverse cell walls, which likely led to brittle failure 𝜺𝜺 of brick specimen. 3.4. Discussion

3.4.1 Comparison of Area Methods

The footprint area method suggested that the stiffness of cellular and truss materials increased as the cell wall thickness increased. However, the volume of material in the specimen was not considered in the area calculations. Using the footprint area for each specimen, the elastic modulus appeared to be dependent on the cell wall thickness. However, the stress calculations using the effective area determined that the elastic moduli of the specimens were completely independent from the cell wall thickness. This follows the classical mechanics understanding of stress, that the thickness of a material does not affect the axial strength of that material. The footprint area suggested a relationship of the strength of the specimen to the thickness of the cell walls that simply does not exist. The footprint area would make accurate comparisons between

25 different cellular and truss materials difficult because the area does not reflect changes in the geometry or dimensions of the unit cell.

Using the column area presented a similar issue to the footprint method, but instead of computing a strength that was less than the effective area strength, the strength computed with the column area strength was greater. The stresses computed with the column area suggested that the thinner the cell walls are for the brick specimen, the stronger the material became. In addition to this again showing a relationship between the elastic modulus and the thickness of the cell walls that does not actually exist, the column area predicts that as a cell wall thickness goes to zero, the stiffness of the cellular material would approach infinity. Another shortcoming of the column area is if the thickness of the horizontal arms or the spacing between the vertical arms was changed, that change would not be reflected in the area calculation.

Two problems arose with using the relative density instead of the effective area [2, 4, 10, 14]. The first problem has already been discussed; researchers used the relative density of the cellular and truss materials to account for the amount of stock material making up the cellular or truss materials. However, the strength of those specimens were often still reported as a function that would change based on the deformation mechanism expected to drive the unit cell behavior [4].

The other issue with using the relative density is the relative volume of the cellular or truss material is normalized by the material used for creating the cellular or truss specimens.

Normalizing a cellular or truss material based on the density of the stock material would be useful for comparing purely the geometric influence a cellular or truss design would have on specimens that was comprised of different unit cells and different stock materials. However, that would unnecessarily complicate a comparison that would be more direct if two geometries made from

26 the same stock material were compared instead. It would also make comparing the strengths of cellular materials made with different unit cell geometries and different stock materials, such as the PLA honeycomb cellular material in Figure 6 and the ABS brick cellular material in Figure 7 difficult.

The effective area introduced in this paper calculates the stress of a cellular material by considering the amount of stock material present in the cellular material. Numerical modeling is heavily used in the study of cellular materials, so calculating the effective area, even for complex geometries, would be simple [16, 69, 81]. The effective area method does not change depending on the deformation mechanisms driving the unit cell of the material. Additionally, the effective area accurately represents the strength of the cellular material compared to its solid material counterparts. It allows for direct comparisons between different unit cell geometries and unit cells of different thicknesses and dimensions.

There is clearly also a need for a uniform area to use for truss materials. The effective area can be expanded to truss materials, however the focus of this paper is on an effective area for cellular materials.

3.4.2 Mechanical Behavior using the Effective Area Method

The work of Gibson and Ashby show that hexagonal honeycombs are a bending dominated geometry [30]. In bending dominated geometries, there is an initial linear elastic region followed by a plateau region defined by the formation of plastic hinges at the areas of highest bending moment, controlling the global behavior [30]. It has been previously reported that the linear elastic region is uniform, elastic cell wall bending [30]. Having different wall thicknesses, it would be logical to conclude that the different specimens should have different initial elastic moduli

27 because the flexural modulus has a cubic relationship to the thickness of the beam that is bending

[30]. Therefore the stress-strain curve of Figure 6a agrees with the findings of literature [30].

The honeycomb specimens with different wall thicknesses’ effective stress-strain response had the same elastic moduli as the solid dog bone, indicating that the honeycomb specimens were stretching initially, not bending, as thought by Gibson and Ashby [30]. Additionally, it was pointed out by Lee, Choi and Choi that Gibson and Ashby’s modulus of elasticity calculations became singular as θ, shown in Figure 3, approaches 0° if only bending deformation is assumed [79].

During the plastic region of the stress-strain curve, bending in the walls of the honeycomb specimens became the dominant deformation mode. Plastic hinges developed at the points of greatest bending moment as seen in the DIC concentrations of strains in Figure 8. This was reflected in the global response of the cellular material as the material begins to yield, as seen in

Figure 8d. The thinner the cell walls, the lower the global strains were when the plastic region began. Gibson and Ashby report that the plastic (plateau) region began at the same strain regardless of the thickness of the wall; however, that was not what was observed in the footprint engineering stress or the effective engineering stress of the AM honeycomb cellular material.

Instead, the plastic region began at a greater strain for thicker cell walls. At the beginning of the plastic region, localized plastic hinging appeared and was recorded using DIC shown in Figure 8.

In the elastic region (Figure 8a) there was no concentration of strains that would indicate bending.

The vertical arms of the honeycomb were in tension in the axial direction and the horizontal arms were in tension in the transverse direction. The cell walls did not bend and localized plastic hinging did not appear until the after the material yields. When the localized plastic hinges formed, whitening of the material appeared in the plastic hinges as seen in Figure 10. The

28 whitening of the material, circled in Figure 10b, was identified as crazing. A further investigation into crazing in AM materials is explored in Chapter 4

Figure 10: Honeycomb cellular material (a) = 0.0033, no plastic hinges. (b) = 0.017, crazing initiates as plastic hinges form, circled. 𝜎𝜎𝑦𝑦 𝜎𝜎𝑦𝑦 The footprint method suppresses that the honeycomb cellular material was initially stretching dominated, not bending dominated. However, because the effective area graph showed all of the honeycomb specimens having the same elastic modulus as the solid AM dog bone, the effective area revealed that the honeycombs initially were in pure stretching. Changing the wall thicknesses did not change the stiffness of the honeycomb specimens, it only effected the yield strength.

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Figure 11: Local axial strains of honeycomb specimen showing plastic hinging. (a) t = 0.95 mm, clear double plastic hinging. (b) t = 1.70 mm, single plastic hinge

DIC strains of the honeycomb specimen with a wall thickness of 0.95 mm in Figure 11a show clearly double plastic hinges developing at the cell wall intersection. Gibson and Ashby discuss that double plastic hinges form as both axial cell walls bend and each cell wall plastically deforms at the section of its maximum moment [30]. In the honeycomb specimens with thicker cell walls of 1.7mm a single plastic hinge develops, as shown in Figure 11b. The single plastic hinge suggests that in the thicker cell walls the walls themselves are not bending, but instead the intersection is plastically deforming. The changing mechanism as the cell walls become thicker explains why the honeycombs with thicker cells walls are deforming later.

The brick specimen was a stretching dominated geometry, meaning that the cell walls extended under a tensile load and did not rotate or bend as seen in the honeycomb specimen. The effective

30 engineering stress-strain curve of the brick specimen had the same modulus as the solid AM dog bone. It was the stock material of the cellular material, rather than the geometry of the unit cell, that drove the elastic stress-strain behavior of the brick cellular material. Similar to the honeycomb, the yield strengths of the brick specimens were lower than the solid AM dog bone.

As the cell walls of the brick specimens are increased, the yield strength also increased, and approached the behavior of the solid dog bone.

In Figure 9, it was found that the horizontal walls braced the vertical cell walls of the brick specimens during loading. If the material was just long, slender, vertical columns, the axial strains would have been consistent throughout each column. When the horizontal bracing cell walls were added, the axial strains were no longer consistent throughout the vertical column. Instead, the local strains were largest on the side of the vertical beam not intersecting the horizontal beam and smallest on the side of the horizontal beam intersecting the vertical beam, as shown in Figure

9a. Shear strains also developed where the bracing material connected to the vertical cell walls, shown in Figure 9b below. Increased shear strains in these locations led to strain concentrations that caused the material to fail at those points. These horizontal cell walls changed the material behavior of the brick specimen compared to slender columns or the solid AM dog bone. The columns stretched elastically, similarly to the solid dog bone, however as the specimens stretched, strain concentrations developed at the joints of the horizontal and vertical cell walls.

Instead of yielding, as the solid AM dog bone did, one joint failed and a crack rapidly propagated through the brick specimen due to increased load on other legs, causing the brittle behavior observed. The effective area showed that the brick specimens are stretching dominated in the elastic region. The brick failed at a significantly lower global strain than the solid dog bone. The

31 horizontal walls created additional strain concentrations that caused the brick specimens to all fail brittlely regardless of the wall thickness, whereas instead the solid AM dog bone failed in a ductile manner. This matches what has been seen in literature about the brittle facture behavior of periodic cellular materials [3].

3.5 Conclusions

• The effective area allowed for accurate, direct comparisons of cellular materials with

different unit cell geometries, different unit cell dimensions, different numbers of unit

cells, comparisons between cellular materials and solid materials and between cellular

materials of different stock materials.

• The DIC local strains showed that added material, such as horizontal walls of the brick

specimens effect how the cellular material deforms.

• Honeycomb specimens are initially stretching dominated and then plastic hinges form as

the honeycomb yields and becomes bending dominated.

• The thickness of the cell walls affects the yield stress of the honeycomb specimens.

• Brick specimens are stretching dominated until large shear strain concentrations cause a

joint to crack and the entire specimen fails catastrophically.

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Chapter 4. Phase two: Deformation of Additively

Manufactured Acrylonitrile Butadiene Styrene

4.1 Methods and Materials

To investigate crazing behavior in AM ABS, dog bone specimens were additively manufactured and cut from a sheet of extruded ABS. The AM dog bone specimens were additively manufactured by FD 3D printing using ABS filament acquired from Makerbot in a Makerbot

Replicator 2X. For comparison, dog bone specimens made from a sheet of extruded ABS were milled using an Esko Kongsberg C cutting table with 3mm diameter router bit. All materials used for the specimens were white. The specimens had a gauge length of 3mm, width of 15mm and thickness of 2mm. The specimens were designed with a gradually narrowing cross section with a constant cross section for the 3mm gage length in the middle of the specimen so that the global stresses would be highest at the middle of the specimen. Crazing consistently initiated at the middle of the specimens. An illustration of the specimen is shown in Figure 12.

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Figure 12: Dimensions of dog bone specimen in mm. Gradually narrowing cross sectional area caused crazing to begin in a predictable location.

The specimens were loaded in tension using an MTS Landmark 370 hydraulic load frame at a constant displacement rate of 3μm/s. A dual camera setup was used to identify crazing on the macroscale. Two Point Grey cameras with Navitar lenses were positioned with one facing the front of the specimen, the other facing the back of the specimen. All lighting was concentrated on one side, defined as the front of the specimen for this study. The back of each sample was illuminated from light refracting through the specimen. This method made it possible to detect macro crazing with digital image correlation (DIC). DIC was used to calculate the local and global strains of the specimen and the onset of crazing. The setup provided a double measurement method: one camera focused directly on the DIC speckle pattern for analyzing the correlations and global strains of the specimen and a second camera on the backside of the specimen for first identification of macro crazing. The experimental setup is shown in Figure 13.

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Figure 13: Experimental setup of the dual camera system with an ABS dog bone in the load frame and all lighting concentrated on the front of the specimen. Crazing seen as dark lines due to change in density as light refracted through the specimen.

As crazing traditionally initiates at surface flaws, a consistent surface finish was desired. The specimens were mechanically polished with increasing sandpaper grits beginning with P120 grit sandpaper and progressing until P4000. The specimens were then re-polished with P1500 grit sandpaper to introduce a known flaw size of m. The specimens were speckled using an Iwata airbrush and black Aztek airbrush paint. 5µ

For identification of printing errors resulting in small voids and areas of differing densities, a

MicroCT scanner with a minimum resolution of m was used to locate and map out the internal voids in the specimen before loading. The specimens9µ were then loaded in tension until a global stress of 1.25 ( ) was reached and then rescanned. A stress of 1.25 ( ) ensured that the

𝐼𝐼 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝐼𝐼 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 micro-crazing𝜎𝜎 predicted stress was reached but macro crazing had not yet𝜎𝜎 occurred. The process was repeated until macro crazing was identified during subsequent loading. Scans of each

35 specimen as a virgin, after it had been loaded to the Bucknall micro-crazing stress and after it had been loaded until macro crazing was observed, were compared to identify how internal voids changed during crazing in each specimen.

4.2 Results and Discussion

4.2.1 Macro Craze Initiation Identified by DIC

In extruded ABS, micro-crazing begins at the interface between the polystyrene (PS) matrix material and the small rubber inclusions added to the PS to increase toughness. Crazing has long been considered a surface phenomenon, initiating at either surface flaws or interfaces in the material, such as the interface between PS and the rubber inclusions [42, 59]. Micro-crazes are known to start at considerably lower stresses than the material’s yield stress, often between one third and one half of the yield strength [55, 59, 82]. The micro-crazes grew in size and number as the material was strained until a “threshold” stress [83] was reached [42, 59, 84]. Once that threshold stress was reached macro crazing occurs [64, 83, 85]. During macro crazing, single crazes grow, linking together several inclusions [59, 83].

The stress-strain behaviors are shown in Figure 14. The Bucknall prediction of the micro-crazing stress and the stress where macro crazing was observed were marked on the stress-strain curve of each material in Figure 14. Micro-crazing has been reported to initiate as early as one third of the yield strength [59]. However, the Bucknall craze initiation predicted micro-crazing to begin at

0.22 for the bulk dog bone and 0.23 for the AM dog bone. The Bucknall criterion gave an

𝑦𝑦 𝑦𝑦 earlier𝜎𝜎 crazing initiation prediction than 𝜎𝜎micro-crazing is reported in literature [55, 59, 82]. At the predicted micro-crazing stress, no identifiable change in material behavior was found. Macro crazing appeared in the AM ABS specimen at 0.80 and by the time the specimen began to yield

𝜎𝜎𝑦𝑦

36 the center of the specimen was heavily crazed. Macro crazing was not observed in the extruded material until after the specimen had reached its yield strength.

Figure 14: Stress-strain response of AM and Extruded (E) ABS dog bones. Bucknall micro-crazing prediction at 0.25 . Macro crazing is observed at 0.8 for AM ABS and 1.05 for E ABS.

𝑦𝑦 𝑦𝑦 𝑦𝑦 There were observable𝜎𝜎 differences in the appearance of𝜎𝜎 the macro crazes in AM𝜎𝜎 ABS compared to extruded ABS. When the extruded specimens crazed, the crazes were uniform and thin, less than m in width. They did not originate from one point, but simultaneously appeared across the entire10µ cross section of the specimen at the thinnest part of the dog bone. As the dog bone

37 was loaded further in tension the crazing became denser at the middle, the thinnest part of the dog bone, as existing macro crazes grew in size and new macro crazes initiated. Crazing also began to initiate further from the middle of the specimen as the heavily crazed locations toughened and stress concentrations further away from the middle of the specimen grew [42, 45]. In Figure 15a the virgin specimen was untested and craze free while in Figure 15b macro crazes have developed spanning across the entire cross section. The crazes were densest in the middle of the dog bone where the cross sectional area was smallest and decreased in density farther from the middle of the dog bone, as the cross sectional area increased. This crazing behavior closely matched what was described in literature for extruded ABS [45, 54, 60, 85].

Figure 15: Extruded ABS dog bone (a) virgin and (b) macro crazing. Crazes appear simultaneously across the cross section at the macro crazing threshold 1.05 . Crazes uniform and thin with a width of approximately 10 m. 𝜎𝜎𝑦𝑦 µ

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The initiation of macro crazing in the extruded specimens was not detectable with the human eye.

DIC sigma, a measurement of uncertainty in the DIC analysis, was found to be the earliest indicator of macro crazing. Sigma is proportional to the grey level noise squared and inversely proportional to the gradient control of the image [86]. Sigma values increase when there is a transition in the image from light to dark or dark to light. When the specimen crazed, the material density inside the craze decreased which changed how the light refracted through the material, thus causing the craze to appear darker. The DIC sigma analysis of the extruded ABS dog bone is shown in

Figure 16. The areas of high sigma values were macro crazes in the specimens, the sigma values were proportional to the density of crazing. The sigma values were greatest in the middle of the specimen and decreased above and below the middle, as the crazing density decreased.

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Figure 16: Extruded ABS DIC grey level uncertainty measurements. Green and red areas signify macro crazing.

In the AM ABS specimens macro crazes appeared at 0.80 . Unlike extruded ABS, the crazing

𝑦𝑦 appeared in one or two locations at 0.80 . After yielding,𝜎𝜎 further crazing propagated from the

𝑦𝑦 initial craze, branching across the cross section.𝜎𝜎 Macro crazing in AM ABS was not as uniform as crazing in extruded ABS, but was instead thicker, approximately 100 m wide. Figure 17 shows the crazing propagation for the AM ABS dog bone specimen. In Figureµ 17a the location where crazing originated on the left side of the specimen was circled. In Figure 17b crazing continued to branch out from the original craze location, and in Figure 17c as the specimen continued to heavily craze, a crack developed at the craze initiation site. For the AM ABS, the DIC sigma and

𝑦𝑦𝑦𝑦 calculations identified macro crazing at the same time, however it was easier to identify macro𝜀𝜀 crazing progression using the DIC values because it better differentiated crazing from

𝜀𝜀𝑦𝑦𝑦𝑦 40 measurement noise. The DIC analysis of an AM ABS specimen is shown in Figure 18. The

𝑦𝑦𝑦𝑦 initial craze to appear is identified𝜀𝜀 on the left side in red, by the high values as the craze began

𝑦𝑦𝑦𝑦 to form. A second macro craze initiation site was identified by the𝜀𝜀 high values on the right

𝑦𝑦𝑦𝑦 side of the image. 𝜀𝜀

Figure 17: Craze propagation in AM ABS at global strains of (a) = 0.020 (b) = 0.023 and (c) = 0.025 . Macro crazes approximately 100 μm wide. AM macro crazes𝑦𝑦𝑦𝑦 initiate in𝑦𝑦𝑦𝑦 single location (circled)𝑦𝑦𝑦𝑦 and propagate from that location across𝜀𝜀 the width 𝜀𝜀 𝜀𝜀

41

Figure 18: DIC values of AM ABS specimen loaded to a global = 0.023. Red areas signify crazing.

𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦 4.2.2 The Effects𝜀𝜀 of Voids on Macro Craze Initiation 𝜀𝜀

After MicroCT scanning the extruded ABS macro crazed specimens, no internal voids were identified. Several voids were found in the AM dog bones using the CT scanner. Interestingly, voids were often found several in a line, showing these voids were formed from systematic printing error.

42

Figure 19: (a) DIC values of AM ABS specimen at a global strain of = 0.024. (b) MicroCT scans mapped to large (>100 m) internal voids to the location of macro craze initiation in the specimen. 𝜀𝜀𝑦𝑦𝑦𝑦 𝜀𝜀𝑦𝑦𝑦𝑦 Internal voids identified byµ the MicroCT scanner were mapped to their locations in the dog bone specimens and compared to the results from DIC, shown in Figure 19. Figure 19a shows the DIC

measurements of an AM ABS dog bone. The circled red spots in Figure 19a were areas of

𝑦𝑦𝑦𝑦 𝜀𝜀large localized strain. Macro crazing initiated at both circled locations of large strain concentrations. Further macro crazing propagated from those original macro crazes as the specimen was loaded further, eventually spanning the entire cross section. Figure 19b shows the

MicroCT scans of the specimen before loading. Comparing the slices of the MicroCT scan corresponding with the locations of the two areas circled in Figure 19a, internal voids were identified at the locations where crazing originated in the specimen. The dark internal voids in

Figure 19b that correspond to the high strain concentrations in Figure 19a are circled in white.

Internal voids in the AM ABS specimens were identified in the virgin scans, and the two post loading scans. The sizes of the voids in all three scans for each specimen were similar to each

43 other. Voids that were m in width did not change in size or appearance between the virgin specimen and the Bucknall100µ prediction scans, when the specimens were loaded to 7.4MPa. In

Figure 20, scans of the same location are shown of a virgin specimen and after that specimen was loaded to 30MPa and macro crazing had been observed. The internal voids circled in Figure 20 grew from m to m as the specimen macro crazed.

100µ 240µ

Figure 20: MicroCT scans of AM ABS specimen showing growth of internal voids. (a) Virgin specimen with internal void of 100 μm circled; (b) Specimen after macro crazing observed, same internal void grew to 240 μm, circled. Internal voids drive macro crazing in AM ABS.

As the crazes increased in size and density, the voids the crazes originated from, also grew. In AM

ABS components, crazes were not thin and uniform like the macro crazes that appeared evenly in

44 extruded ABS, but instead were thick, non-uniform crazes that began in one location. Micro- crazing in AM ABS may still appear at the interface between the matrix material and the small rubber inclusions as occurs in the extruded ABS. However, the voids in AM ABS, not micro-crazing around the rubber inclusions, were the mechanism that initiated macro crazing in AM ABS.

There was no evidence of micro-crazing having any effects on the mechanical behavior of the specimens once they reached the stress initiation levels predicted by Bucknall. The Bucknall criterion assumed that micro-crazing initiates at surface flaws, which is true for most extruded materials. While AM parts have significantly more surface flaws than extruded parts [31], crazing in AM specimens were driven by the internal voids and had a fundamentally different behavior than the extruded ABS specimens. In this study, there were different macro crazing behaviors between AM and extruded ABS. No evidence of micro-crazing was identified, but may be identifiable on a smaller scale leading to further understand of craze initiation in ABS materials.

4.3 Conclusions

• Extruded and AM ABS crazed in fundamentally different manners.

o Extruded ABS macro crazes were thin and uniform, about 10 μm wide and

appeared simultaneously across the specimen when the macro crazing

threshold was reached.

o AM ABS macro crazes were thick, about 100 μm wide. When the macro crazing

threshold was reached macro crazes initiated at internal voids within the

specimen.

• As the AM ABS specimens were strained past the macro crazing threshold, Internal voids

within the specimen grew in size.

45

Chapter 5. Conclusions

This study experimentally showed that added material, such as the horizontal bracing walls in the brick cellular material, changed how the material deforms. The effective area utilized in this study was the only area method that accurately considered the full amount of material present regardless of the geometry of the unit cell, the dimensions of the unit cell and the thickness of the cell walls. The effective engineering stress normalized the global force applied to the cellular material by the total amount of material present, allowing accurate direct global strength comparisons between different cellular materials as well as cellular materials and their stock materials. As AM honeycomb cellular materials were strained, crazing initiated at the plastic hinges.

Macro crazing in AM ABS appeared fundamentally different from extruded ABS. In extruded ABS macro crazes were thin, about 10 m in width, and appeared uniformly and simultaneously across the entire cross section of the specimensµ when the macro crazing threshold [83] was reached, at about 1.05 . Crazes increased in density as the specimens continued to yield, and further

𝑦𝑦 crazing initiated𝜎𝜎 farther from the middle of the specimen. AM ABS macro crazes were an order of magnitude wider than the extruded crazes, measuring about 100 m in width. AM macro crazing initiated in one location, where large internal voids of about 100µ m in thickness were identified within the material using a MicroCT scanner. Further macro crazingµ in the AM ABS propagated from the locations of the original macro crazes. MicroCT scans of a virgin AM ABS specimen and of the specimen loaded until the initiation of macro crazing showed internal voids

46 grew from 100 m to 240 m. Internal voids inherent with additive manufacturing were shown to be the mechanismµ that drovµ es macro craze initiation in AM ABS.

47

Chapter 6. Future Work

The initiation of micro-crazing is not understood in AM ABS. Micro-crazing may initiate at the interface between the PS and the rubber inclusions in ABS, or like macro crazing, could be driven by the internal voids inherent in additive manufacturing. While internal voids were identified as driving macro crazing, would increasing printing quality and decreasing the size of internal voids delay or completely suppress crazing in AM parts? Another factor to consider is the effect of the extrusion path used while fabricating AM parts. Would different extrusion paths change the voids sizes and shapes, thereby effecting when crazing initiates in AM materials? The effect of surface finish in AM parts should also be investigated. If a part was not polished after fabrication, would a rough surface finish cause macro crazing to propagate from a surface flaw as predicted by

Bucknall?

Testing should be continued to obtain more statistically significant material properties of cellular materials using the effective area. The effective area should be expanded to truss materials.

Material properties and the mechanical behaviors of AM cellular materials should be compared to cellular materials made by other fabrication methods such as extrusion.

Further testing is needed to test if the effective area method shows consistent results in other loading conditions such as compression, bending or shear.

Further investigation into crazing is needed in AM cellular materials. Crazing appeared as plastic hinges formed in honeycomb cellular materials. However, it is unknown whether crazing drives hinging or hinging drives crazing. How would a bending dominate cellular material such as

48 honeycombs behave in cyclic loading? Would crazing propagate in the plastic hinges during cyclic loading or would it reach a steady state?

49

Chapter 7. References

1. Brenne F, Niendorf T, Maier HJ (2013) Additively manufactured cellular structures-

Impact of microstructure and local strains on the monotonic cyclic behavior under

uniaxial and bending load.pdf. J Matierals Process Technol 213:1558–1564

2. Ren XJ, Silberschmidt V V. (2008) Numerical modeling of low density cellular materials.

Comput Mater Sci 43:65–74

3. Lipperman F, Ryvkin M, Fuchs MB (2007) Fracture toughness of two-dimensional cellular

material with periodic microstructure. Int J Fract 146:279–290 . doi: 10.1007/s10704-

007-9171-5

4. Wang A-J, McDowell DL (2004) In-Plane Stiffness and Yield Strength of Periodic Metal

Honeycombs. J Eng Mater Technol 126:137 . doi: 10.1115/1.1646165

5. Papka SD, Kyriakides S (1998) Experiments and full-scale numerical simulations of in-

plane crushing of a honeycomb. Acta Mater. 46:2765–2776

6. Restrepo D, Mankame ND, Zavattieri PD (2016) Programmable materials based on

periodic cellular solids. Part I: Experiments. Int J Solids Struct 100:485–504 . doi:

10.1016/j.ijsolstr.2016.09.021

7. Lee S, Barthelat F, Hutchinson JW, Espinosa HD (2006) Dynamic failure of metallic

pyramidal truss core materials - Experiments and modeling. Int J Plast 72:2118–2145

8. Joshi S, Ju J, Berglind L, et al (2010) Experimental Damage Characterization of Hexagonal

Honeycombs Subjected to In-Plane Shear Loading. In: ASME 2010 International Design

50

Engineering Technical Conference and Computers and Information in Engineering

Conference. Quebec, Canada, pp 1–7

9. Choi S, Sankar B V A micromechanical method to predict the fracture toughness of

cellular materials. Aerosp. Eng.

10. Dong L, Deshpande V, Wadley H (2015) Mechanical response of Ti-6Al-4V octet-truss

lattice structure. Int J Solids Struct 60:107–124

11. O’Masta MR, Dong L, St-Pierre L, et al (2017) the Fracture Toughness of octet-truss

lattices. J mechancis Phys solids 6:271–289

12. Ju J, Summers JD, Ziegert J, Fadel G (2012) Design of Honeycombs for Modulus and Yield

Strain in Shear. J Eng Mater Technol 134:011002 . doi: 10.1115/1.4004488

13. Deshpande VS, Fleck N, Ashby MF (2017) Effective Properties of the Octet- Truss Lattice

Material. doi: 10.1016/S0022-5096(01)00010-2

14. Wallach JC, Gibson LJ (2001) Mechanical behavior of a three-dimensional truss material.

Int J Solids Struct 38:7181–7196

15. Torquato S, Gibiansky L V, Silva MJ (1998) Effective mechanical and transport properties

of cellular solids. 40:71–82

16. Vigliotti A, Pasini D (2012) Linear multiscale analysis and finite element validation of

stretching and bending dominated lattice materials. Mech Mater 46:57–68 . doi:

10.1016/j.mechmat.2011.11.009

17. Gao W, Zhang Y, Ramanujan D, et al (2015) The status, challenges and future of additive

51

manufacturing in engineering. Comput Des 69:65–89

18. Torres J, Cole M, Owji A, et al (2016) An approach for mechanical property optimization

of fused depostion modeling with polylactic acid via design of experiments. Rapid

Prototyp J 22:387–404

19. Alsalla H, Hao L, Smith C (2016) Fracture toughness and tensile strength of 316L stainless

steel cellular lattice structures manufactured using the selective laser melting technique.

Mater. Sci. Eng. A 669:1–6

20. Weller C, Kleer R, Piller FT (2015) Economic implicatins of 3D printing: Market structure

models in light of additive manufacturing revisited. Int J Prod Econ 43–56

21. Hague* R, Mansour S, Saleh N Material and design considerations for rapid

manufacturing. Int. J. … 37–41

22. Chang CC, Ebcioglu IK (1961) Effect of Cell Geometry on the Shear Modulus and on

Density of Sandwich Panel Cores. J Basic Eng December:513–517

23. Burton WS, Noor AK (1997) Assessment of continuum models for sandwich panel

honeycomb cores. Comput. Methods Appl. Mech. Eng. 145:341–360

24. Davalos JF, Qiao P, Frank Xu X, et al (2001) Modeling and characterization of fiber-

reinforced plastic honeycomb sandwich panels for highway bridge applications. Compos.

Struct. 52:441–452

25. Liu Q, Ma J, Xu X, et al (2017) Load bearing and failure characteristics of perforated

square CFRP tubes under axial crushing. Compos Struct 160:23–35 . doi:

52

10.1016/j.compstruct.2016.10.032

26. Ju J, Ananthasayanam B, Summers JD, Joseph P (2010) Design of Cellular Shear Bands of

Non-Pneumatic Tire - Investigation of Contact Pressure. SAE Int 3:598–606

27. Ju J, Summers JD, Ziegert J, Fadel G (2009) Design of Honeycomb Meta-Materials for High

Shear Flexure. Vol 5 35th Des Autom Conf Parts A B 805–813 . doi: 10.1115/DETC2009-

87730

28. Ju J, Summers JD, Ziegert J, Fadel G (2009) Cyclic energy loss of honeycombs under in-

plane shear loading. ASME 2009 Int Mech Eng Congr Expo 283–289 . doi:

10.1115/IMECE2009-12658

29. Kolla A, Ju J, Summers JD, et al (2010) Design of chiral honeycomb meso-structures for

high shear flexure. ASME 2010 Int Des Eng Tech Conf Comput Inf Eng Conf 43–49 . doi:

10.1115/DETC2010-28557

30. Gibson LJ, Ashby MF (1997) Cellular Solids, structures and properties, 2nd ed. Cambridge

University Press, Cambridge

31. Rodríguez JF, Thomas JP, Renaud JE (2003) Mechanical behavior of acrylonitrile

butadiene styrene fused deposition materials modeling. Rapid Prototyp. J. 9:219–230

32. Ziemian CW, Cipoletti DE, Ziemian SN, et al (2014) Monotonic and Cyclic Tensile

Properties of ABS Components Fabricated by Additive Manufacturing. In: Proceedings of

25th International Solid Freeform Fabrication Symposium. Austin, TX, pp 525–541

33. Niendorf T, Brenne F (2013) Steel showing twinning-induced plasticity processed by

53

selective laser melting - An additively manufactured high performance material. Mater.

Charact. 85:57–63

34. Klippstein H, Diaz De Cerio Sanchez A, Hassanin H, et al (2018) Fused Deposition

Modeling for Unmanned Aerial Vehicles (UAVs): A Review. Adv Eng Mater 20:1–17 . doi:

10.1002/adem.201700552

35. Aliheidari N, Tripuraneni R, Ameli A, Nadimpalli S (2017) Fracture resistance

measurement of fused deposition modeling 3D printed polymers. Polym Test 60:94–101 .

doi: 10.1016/j.polymertesting.2017.03.016

36. Hart KR, Dunn RM, Sietins JM, et al (2018) Increased fracture toughness of additively

manufactured amorphous thermoplastics via thermal annealing. Polym (United Kingdom)

144:192–204 . doi: 10.1016/j.polymer.2018.04.024

37. Torrado Perez AR, Roberson DA, Wicker RB (2014) Fracture surface analysis of 3d pritned

tensile specimens of novel ABS-based materials. J Fail Anal Prev 343–353

38. Roberts C, Nicholson G (2014) FDM printed fixed wing UAV. In:

www.amrc.co.uk/news/printed-uav

39. Aktas YO, Ozdemir U, Dereli Y, et al (2016) Design of a commercial hybrid VTOL UAV

system. J Intell Robot Syst 84:639–664

40. Aktas YO, Ozdemir U, Dereli Y, et al (2013) Rapid prototyping of a fixed-wing VTOL UAV

for design testing. J Intell Robot Syst 371–393

41. Matsuo M, Wang T, Kwei T (1971) Crazing behavior of polystyrene containing two rubber

54

balls - model for ABS plastics. Abstr Pap - Am Chem Soc 10:104

42. Kambour RP (1973) A Review of Crazing and Fracture in Thermoplastics. J Polym Sci

Macromol Rev 7:1–154 . doi: 10.1002/pol.1973.230070101

43. Wang TT, Matsuo M, Kwei T (1971) Criteria of Craze Initiation in Glassy Polymers. J. Appl.

Phys. 42:4188

44. Matsuo M (1969) Fine Structures and Fracture Processes in Plastic-Rubber Two-Phase

Polymer Systems. II. Observation of Crazing Behaviors Under the Electron Microscope.

Polym Eng Sci 9:206–212

45. Argon AS, Hannoosh JG, Salama MM Initiation and Growth of Crazes in Glassy

Polymers.pdf

46. Hart KR, Wetzel ED (2017) Fracture behavior of additively manufactured acrylonitrile

butadiene styrene (ABS) materials. Eng. Fract. Mech. 177:1–13

47. Herzog D, Seyda V, Wycisk E, Emmelmann C (2016) Addtive manufacturing of metals.pdf.

Acta Mater 117:371–392

48. Lim S, Buswell RA, Le TT, et al (2012) Developments in Construction Scale Additive

Manufacturing Processes Loughborough.Pdf. Autom Constr 21:262–268

49. Fernandez-Vicente M, Calle W, Ferrandiz S, Conejero A (2016) Effect of Infill Parameters

on Tensile Mechanical Behavior in Desktop 3D Printing. 3D Print. Addit. Manuf. 3:183–

192

50. Kulinski Z, Piorkowska E (2005) Crystallization, structure and properties of plasticized poly

55

(L-lactide). Polymer (Guildf). 46:10290–10300

51. Lunt J (1998) Large-scale production, properties and commercial applications of

polylactic acid polymers. Polym Degration Stab 59:146–152

52. Garlotta D (2001) A Literature Review of Poly(Lactic Acid). J. Polym. Environ. 9:63–84

53. Drumright BRE, Gruber PR, Henton DE (2000) Polylactic Acid Technology. Adv Mater

48674:1841–1846

54. Bucknall CB (2001) Applications of microscopy to the deformation and fracture of rubber-

toughened polymers. J. Microsc. 201:221–229

55. Tijssens MGA, Van Der Giessen E, Sluys LJ (2000) Modeling of crazing using a cohesive

surface methodology. Mech. Mater. 32:19–35

56. (2018) MakeItFrom.com. www.makeitfrom.com/materials-properties/Acrylonitirle-

Butadiene-Styrene-ABS

57. Aegon AS, Hannoosh JG (1977) Initiation of crazes in polystyrene. Philos. Mag. 36:1195–

1216

58. Matsuo M (1966) Observation of crazes in ABS-polymer and high-impact polystyrene

under the electron microscope. Polymer (Guildf). 7:421–425

59. Bucknall CB (2007) New criterion for craze initiation. Polymer (Guildf). 48:1030–1041

60. Argon AS Craze initiation in glassy polymers - Revisited

61. Bucknall CB (2012) Role of surface chain mobility in crazing. Polym. (United Kingdom)

53:4778–4786

56

62. De Focatiis DSA, Buckley CP (2011) Craze initiation in glassy polymers: Quantifying the

influence of molecular orientation. Polymer (Guildf). 52:4045–4053

63. Arzhakova O V., Dolgova AA, Yarysheva LM, et al (2015) Specific features of the

environmental crazing of poly(ethylene terephthalate) fibers. Polym. (United Kingdom)

56:256–262

64. Ramsteiner F, McKee GE, Breulmann M (2002) Influence of void formation on impact

toughness in rubber modified styrenic-polymers. Polymer (Guildf). 43:5995–6003

65. Li H, Jiang G, Fang Q, Wang T Experimental investigation on the essential work of mixed-

mode fracture of PC-ABS alloy.pdf

66. Kee Paik J, Thayamballi AK, Sung Kim G (1999) The strength characteristics of aluminum

honeycomb sandwich panels. Thin-Walled Struct. 35:205–231

67. A. Petras MPFS (1999) Failure mode maps for honeycomb sandwich panels. Compos

Struct 237–252

68. Sun Y, Pugno NM (2013) In plane stiffness of multifunctional hierarchical honeycombs

with negative Poisson ’ s ratio sub-structures. Compos Struct 106:681–689 . doi:

10.1016/j.compstruct.2013.05.008

69. Chen Q, Pugno N, Zhao K, Li Z (2014) Mechanical properties of a hollow-cylindrical-joint

honeycomb. Compos Struct 109:68–74 . doi: 10.1016/j.compstruct.2013.10.025

70. Sun Y, Wang B, Pugno N, et al (2015) In-plane stiffness of the anisotropic multifunctional

hierarchical honeycombs. Compos Struct 131:616–624 . doi:

57

10.1016/j.compstruct.2015.06.020

71. Chuang CH, Huang JS (2002) Elastic moduli and plastic collapse strength of hexagonal

honeycombs with plateau borders. Int. J. Mech. Sci. 44:1827–1844

72. Timoshenko SP, Goodier JN (1970) Theory of Elastic Stability, 3rd ed. McGraw-Hill, New

York

73. Timoshenko SP, Young DH (1965) Theory of Structures. McGraw-Hill, New York

74. Deshpande VS, Ashby MF, Fleck NA (2001) Foam Topology Bending Versus Stretching

Dominated Architectures. Acta Mater 49:1035–1040

75. Masters IG, Evans KE Models for the Elastic Deformation of Honeycombs.pdf

76. Bendsoe MP, Sigmund O (2004) Topology Optimization. Springer-Verlag Berlin

Heidelberg, New York

77. Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: A survey

on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct.

Optim. 16:68–75

78. Huang X, Radman A, Xie YM (2010) Topological design of microstructures of cellular

materials for maximum bulk or shear modulus. Comput Mater Sci 193:1 . doi:

10.1002/nme

79. Lee J, Choi JB, Choi K (1996) Application of homogenization FEM analysis to regular and

re-entrant honeycomb structures. J. Mater. Sci. 31:4105–4110

80. Saiki I, Terada K, Ikeda K, Hori M (2002) Appropriate number of unit cells in a

58

representative volume element for micro-structural bifurcation encountered in a multi-

scale modeling. Comput. Methods Appl. Mech. Eng. 191:2561–2585

81. Brezny R, Green DJ (1990) The effect of cell size on the mechanical behavior of cellular

materials. Acta Metall Mater 38:2517–2526 . doi: 10.1016/0956-7151(90)90263-G

82. Tijssens MGA, Giessen E Van Der (2002) A possible mechanism for cross-tie fibril

generation in crazing of amorphous polymers. Polymer (Guildf). 43:831–838

83. Sternstein S, Myers F (1973) Yielding of glassy polymers in the second quadrant of

principal stress space. J. Macromol. Sci. Phys. B8:539–571

84. Kawaqoe M, Fujita H (2017) Macroscopic criterion for craze initiation in polystyrene.

Mech. Eng. J. 4:17-00347-17-00347

85. Ramsteiner F, McKee GE, Heckmann W, et al (1997) Rubber toughening of polystyrene-

acrylonitrile copolymers. Acta Polym 48:553–561 . doi: 10.1002/actp.1997.010481205

86. Sutton MA, Orteu JJ, Schreier HW (2009) Image correlation for shape, motion and

deformation measurements. Springer

59