Design and Optimization of Hybrid Ballistic Protection Systems with Novel Configurations and Materials

Design and Optimization of Hybrid Ballistic

Protection Systems

by Yu-Yun M. Shiue

Department of Mechanical Engineering

McGill University, Montreal

Aug 2014

Submitted in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

The optimization of armour systems for maximal protection against ballistic threats is an active area of research, currently explored by many research groups. While multilayered designs and fabric-based systems prevail, systematic explorations of other possible configurations for armour materials remain scarce. New metal-ceramic hybrids offer the potential for improving existing armour systems, as they combine various attractive mechanical properties, such as light weight, high toughness, and ductility, which cannot be offered by either material alone.

In this thesis, a systematic exploration of designs for ballistic materials is carried out using numerical simulations of ballistic impacts. The smoothed particle hydrodynamics (SPH) method is adopted as an accurate and stable numerical method.

The SPH method is first validated by simulating the classic Taylor impact test and comparing with theoretical results. The distribution and structure of combinations of hard and soft materials within the ballistic targets is systematically studied to maximize the ballistic performance. Overall, the addition of hard inclusions enhances the ballistic performance of the hybrid targets. The simulations confirm that a two-layer design with a hard ceramic front layer and a ductile metal backing layer is found to be the best armour configuration within the design space of multilayered materials. Sufficient backing material is critical for exceptional ballistic performance.

Actual ballistic impact tests were performed on chromium-chromium sulfide (Cr-

CrS) cermets, which have high toughness and excellent adhesion between the alumina

ii inclusions and the cermet matrix. The samples are synthesized with the self-propagating high-temperature synthesis (SHS) method, which allows production of net-shape samples, with a metal content that can be systematically varied. The results of the experimental tests demonstrate that the high density Cr-CrS cermets have higher resistance compared with an alumina-steel two-layer design with a similar areal density.

The performance of the Cr-CrS cermets demonstrates that it is an attractive material for the design of novel ballistic protection systems.

In summary, the computational and experimental studies in this research were integrated. The ballistic defeating structures and mechanisms explored in this research can be used as guidelines to optimize the design of high performance ballistic protection systems.

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Résumé

L’optimisation des systèmes de blindage pour une protection maximale contre les menaces balistiques est un domaine de recherche actuellement exploré par de nombreux groupes de recherche. Bien que la conception multicouches et des systèmes à base de tissu prévalent, les explorations systématiques d’autres configurations d’armure possibles restent rares. De nouveaux hybrides métal-céramique ouvrent des possibilités d’améliorer les systèmes d’armure existants. En effet, ils combinent plusieurs propriétés mécaniques attrayantes, telles que la légèreté, la ductilité et une haute dureté, qui ne peuvent être offertes par aucun de ces matériaux pris séparément.

Dans cette thèse, une exploration systématique de modèles pour matériaux balistiques est effectuée à l’aide de simulations numériques d’impacts balistiques. La méthode smoothed particle hydrodynamics (SPH) est adoptée en tant que méthode numérique exacte et stable. La méthode SPH est premièrement validée en simulant le test d’impact classique de Taylor et en comparant avec les résultats théoriques. La distribution et la structure des combinaisons de matériaux durs et mous dans les cibles balistiques sont systématiquement étudiées pour maximiser les performances balistiques. En général, l’ajout des matériaux durs améliore les performances balistiques des cibles hybrides. La simulation confirme qu’une conception à deux couches, composée d’une couche de parement en céramique dure et d’une couche de support en métal ductile se révèle être la meilleure configuration d’armure à l’intérieur de l’espace de conception de matériaux multicouches. Des matériaux de support suffisants sont essentiels pour atteindre une performance balistique exceptionnelle.

Les tests d’impact balistique ont été réalisés sur les cermets Cr-Crs, qui possèdent une dureté élevée et une excellente adhésion entre les inclusions d’alumine et la matrice de cermet. Les échantillons sont synthétisés avec la méthode self-propagating high- temperature synthesis (SHS), laquelle permet la production d’échantillon de forme finie, avec un contenu en métal pouvant être varié systématiquement. Le résultat des tests expérimentaux démontre que les cermets de haute densité en Cr-Crs offrent une résistance plus élevée qu’une conception à deux couches en acier aluminé avec une densité surfacique similaire. La performance des cermets en Cr-Crs démontre qu’il s’agit un matériau attrayant pour la conception de systèmes de blindage novateurs.

En résumé, les études computationnelles et expérimentales dans cette recherche sont intégrées. Les structures balistiques défoncées et les mécanismes découverts dans cette recherche peuvent être utilisés comme lignes directrices pour optimiser la conception de haute performance des systèmes de protection balistique.

Acknowledgements

The research in this thesis was co-funded by both The Natural Sciences and

Engineering Research Council of Canada (NSERC), and our industrial partner company,

Allen Vanguard Ltd.

I would like to specially thank my supervisor, Prof. François Barthelat, for all the guidance and advice on my PhD studies. From validation techniques, to optimization design and technical writing, Prof. Barthelat provided novel ideas and valuable opinions to inspire and motivate me accomplishing all the work. I would also like to thank my co- supervisor, Prof. David Frost. Prof. Frost provided the 2nd opinions and correct grammatical constructions when I needed extra information and supports. I would also like to thank Dr. Deju Zhu (postdoctoral fellow) for all the discussion and guidance in building simulation models and using different software.

For the experiments included in this thesis, I would like to thank Ms. Atefeh

Nabavi (PhD student) and Mr. Alexander Capozzi (MSc student) for manufacturing the target samples. The work was presented in the TMS 141st Annual Meeting & Exhibition at Orlando, FL (Nabavi et al., 2012). I would also like to thank Prof. Oren E. Petel and

Mr. Alexander Capozzi for measuring the mechanical properties of the Cr-CrS cermets.

The work was under preparation to be submitted (Petel et al.). I would also like to thank

Dr. Jean-Philippe Dionne (Research Director) and Mr. Clint Hedge (Specialist) for organizing and performing the impact tests at Allen Vanguard Ltd.

I would like to thank my colleagues, Ms. Atefeh Nabavi, Mr. Ahmad Khayer

Dastjerdi, Mr. Seyed Mohammad Mirkhalaf, Ms. Jihane Ajaja, Mr. Lawrence Szewciw,

Mr. Sacha Cavelier, Dr. Sacheen Bekah, and Dr. Reza Rabiei for all the professional discussion and supportive companion throughout my PhD studies. I would also like to thank my friends, Mr. Shih-Hao Lin and Mr. André Slupik, for helping me translating the abstract of this thesis into French résumé.

Last but not least, I would like to thank my family for supporting me all the way through my engineering studies, especially during those stuck and dark times with endless model failure and thesis revision. Thanks to all the faith from my mom, Ms. Yang

Jane, my dad, Prof. Angus Shiue, my sis, Prof. Ivy Shiue, and my brother, Lt. Roy Shiue, that I’ll finish my PhD degree someday.

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Table of contents

Abstract ...... ii

Résumé ...... iv

Acknowledgements ...... vi

Table of contents ...... viii

List of figures ...... xi

List of tables ...... xvi

Chapter 1: Introduction ...... 1

1.1 Armour materials and structures ...... 1

1.2 Addition of hard and millimeter-size inclusions ...... 4

1.3 Overview of the simulation methods ...... 6

1.4 Chromium–chromium sulfide (Cr-CrS) cermets ...... 8

1.5 The SHS combustion method ...... 10

1.6 Dissertation structure ...... 12

Chapter 2: The SPH method ...... 14

2.1 Theory and implementation ...... 14

2.2 The material models ...... 19

Chapter 3: Validation of the SPH method ...... 25

3.1 Theoretical equations ...... 26

3.2 SPH simulations ...... 30

3.3 Validation of symmetric planes ...... 31

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3.4 Comparison of SPH results with theoretical results ...... 33

3.5 Parametric studies ...... 43

Chapter 4: Ballistic impact simulations ...... 48

4.1 Overview of the model ...... 48

4.2 Effects of target geometries on ballistic performance...... 51

4.3 Ballistic performance of hard and soft materials ...... 59

Chapter 5: Multi-layered configuration simulations ...... 62

5.1 Five-layer target design with constant volume ...... 62

5.2 Confining the ceramic phase ...... 70

5.3 Effect of steel strength on optimum design with constant volume ...... 77

5.4 Five-layer target design with constant mass ...... 81

5.5 Effects of steel strength on optimum designs with constant mass ...... 84

Chapter 6: Ballistic simulations of steel targets containing finite inclusions ...... 87

6.1 Steel targets with SiC disks ...... 88

6.2 Steel targets with hexagonal SiC plates ...... 91

6.3 Steel targets with spherical SiC inclusions ...... 95

6.4 Steel targets with chains of spherical SiC inclusions ...... 101

6.5 Steel targets with chains of hollow of filled spherical SiC inclusions ...... 104

6.6 Steel targets with staggered spherical SiC inclusions ...... 114

6.7 Steel targets with tilted SiC plates ...... 116

Chapter 7: Cr-CrS cermets and ballistic penetration tests ...... 120

7.1 Fabrication of Cr-CrS targets ...... 120 ix

7.2 Mechanical properties ...... 123

7.3 Ballistic impact tests with the Cr-CrS targets ...... 124

Chapter 8: Conclusions ...... 141

8.1 Summary of accomplishments ...... 141

8.2 Original contributions ...... 146

8.3 Pathways towards ballistic protection design optimization ...... 147

References ...... 149

List of figures

Figure 1.1: The standard two-layer armour design ...... 2 Figure 1.2: A soldier installing a BAE Systems Small Arms Protective Insert (SAPI) plate (Hess, 2011) ...... 4 Figure 1.3: The micrograph of Cr-CrS cermets (Navabi et al., unpublished raw data) ...... 6 Figure 1.4: The propagation of combustion wave in the SHS method (Eugene and Oleg, 2010) ...... 9 Figure 1.5: Examples of hybrid armour designs ...... 11

Figure 2.1: Box sort and neighbour search (Lacome, 2001) ...... 16

Figure 2.2: Loop of a SPH cycle (Lacome, 2001) ...... 19 Figure 2.3: A material’s elastic-plastic behaviors with isotropic and kinematic hardening (Krieg and Key, 1976) ...... 21 Figure 3.1: Taylor impact model with a thin cylindrical impactor ...... 27

Figure 3.2: (a) Whole and (b) quarter-sized Taylor impact models ...... 32

Figure 3.3: 20 µs after the impact on (a) whole and (b) quarter-sized Taylor impact

models ...... 33

Figure 3.4: Cylindrical impactor indicating particles chosen for analysis ...... 34

Figure 3.5: Snapshots of the Taylor impact simulation ...... 35

Figure 3.6: Normal σxx stresses in the Taylor cylindrical impactor ...... 36

Figure 3.7: Normal σyy stresses in the Taylor cylindrical impactor ...... 37

Figure 3.8: Normal σzz stresses in the Taylor cylindrical impactor ...... 38

Figure 3.9: Effective stresses in the Taylor cylindrical impactor ...... 39

Figure 3.10: Lagrangian t-X diagram of the Taylor cylindrical impact ...... 40

Figure 3.11: Length ratios of the 4 Taylor cylindrical impactors ...... 42

Figure 3.12: An X-t diagram of the 4 Taylor cylindrical impacts ...... 43

Figure 3.13: Final cylinder lengths of 4 models with different smoothing length ...... 45

Figure 4.1: A simple ballistic impact model ...... 49 Figure 4.2: 20 μs after a 980 m/s impact on a steel cylinder target 150 mm in diameter and 50 mm thick ...... 52 Figure 4.3: Penetration depths for the ballistic models with a 980 m/s impact ...... 53

Figure 4.4: Penetration depths for the ballistic models with a 1500 m/s impact ...... 54 Figure 4.5: Effective stresses in a target 150 mm in diameter and (a) 40 and (b) 50 mm thick at 10 μs after a 1500 m/s impact ...... 56 Figure 4.6: Steel plate used in impact experiments (Martineau, Prime, and Duffey, 2004) ……………………………………………………………………………………………58 Figure 4.7: Penetration depths of the experiment and simulation models with different impact velocities ...... 59 Figure 4.8: 60 μs after a 2000 m/s impact on (a) steel and (b) SiC targets ...... 61

Figure 5.1: Quarter of a five-layer ballistic impact model ...... 64

Figure 5.2: Five-layer targets performance with constant volume ...... 66

Figure 5.3: Kinetic energy of the projectiles over time after a 2500 m/s impact for the

configurations with the best performance ...... 68 Figure 5.4: Sequential contour of a WC sphere projectile with a 2000 m/s impact on a (a) [CCMMM] and (b) [MMMMM] target ...... 69 Figure 5.5: Sequential effective stresses in the [CCMMM] model with a 2500 m/s impact ……………………………………………………………………………………………71 Figure 5.6: Sequential effective stresses in the [MCCMM] model with a 2500 m/s impact ……………………………………………………………………………………………72

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Figure 5.7: 100 μs after a 2500 m/s impact on the (a) [MCCMMM] and (b)

[MCCMMM] targets ...... 73

Figure 5.8: Sequential effective stresses in the [MCCMMM] model with a 2500 m/s impact ...... 74

Figure 5.9: Sequential effective stresses in the [MCCMMM] model with a 2500 m/s impact ...... 75

Figure 5.10: 100 μs after a 2500 m/s impact on the (a) [ M CCMMM] and (b)

[MCCMMM] targets ...... 76

Figure 5.11: Kinetic energy of the projectiles over time after a 2500 m/s impact ...... 77 Figure 5.12: Five-layer targets performance with half strength of steel and constant volume ...... 79 Figure 5.13: Kinetic energy of the projectiles over time after a 2000 m/s impact ...... 80

Figure 5.14: Five-layer targets performance with constant mass ...... 82

Figure 5.15: Kinetic energy of the projectiles over time after a 1200 m/s impact ...... 83

Figure 5.16: Five-layer targets performance with half strength of steel and constant mass ……………………………………………………………………………………………85 Figure 6.1: Kinetic energy of the projectiles over time after a 1200 m/s impact ...... 90 Figure 6.2: 30 μs after a 1200 m/s impact on a quarter (a) [CMMMM] (b) [MMMMM] (c) 64 mm in diameter SiC disk and (d) 42 mm in diameter SiC disk targets ...... 91 Figure 6.3: Quarter models with SiC hexagonal plates (a) 16 mm and 1 mm (b) 16 mm and 0.5 mm (c) 8 mm and 1 mm and (d) 8 mm and 0.5 mm in the diameter and plates distance ...... 93 Figure 6.4: Kinetic energy of the projectiles over time after a 1500 m/s impact ...... 95

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Figure 6.5: Quarter-models with SiC spherical inclusions. The impact occurred at the center of the target (lower left corner of the quarter model) (a) 6 mm wide and impact on a sphere (b) 6 mm wide and impact between spheres (c) 3 mm wide and impact on a sphere (d) 3 mm wide and impact between spheres ...... 97 Figure 6.6: Kinetic energy of the projectiles over time after a 1200 m/s impact ...... 99 Figure 6.7: Sequential effective stresses in the steel target with a 1200 m/s impact on a 3 mm in diameter SiC sphere ...... 100 Figure 6.8: Sequential effective stresses in the steel target with a 1200 m/s impact on a 6 mm in diameter SiC sphere ...... 100 Figure 6.9: Quarter models with cubic packing spherical SiC inclusions with an impact (a) right on a sphere and (b) between four spheres ...... 101 Figure 6.10: A quarter model with chains of SiC sphere inclusions ...... 102

Figure 6.11: Kinetic energy of the projectiles over time after a 1200 m/s impact ...... 103

Figure 6.12: A quarter model with chains of hollow SiC sphere inclusions ...... 105

Figure 6.13: Kinetic energy of the projectiles over time after a 1200 m/s impact ...... 108 Figure 6.14: Sequential effective stresses on the steel matrix in the model with hollow SiC sphere inclusions with a 1200 m/s impact ...... 109 Figure 6.15: Sequential effective stresses on the steel matrix in the model with steel-filled spherical SiC inclusions with a 1200 m/s impact ...... 110 Figure 6.16: Sequential effective stresses on the SiC spheres in the model with hollow SiC sphere inclusions with a 1200 m/s impact ...... 111 Figure 6.17: Sequential effective stresses on the SiC spheres in the model with steel filled spherical SiC inclusions with a 1200 m/s impact ...... 112

Figure 6.18: Sequential effective stresses on the (a) B4C and (b) steel fillings in the model with spherical filled SiC inclusions with a 1200 m/s impact ...... 113 Figure 6.19: The staggered configuration of SiC sphere inclusions ...... 115

Figure 6.20: Kinetic energy of the projectiles over time after a 1200 m/s impact ...... 116 Figure 6.21: Quarter models with SiC plates tilted (a) 15 (b) 30 (c) 45 and (d) 60 degrees from the impact surface ...... 117 xiv

Figure 6.22: Kinetic energy of the projectiles over time after a 1200 m/s impact ...... 118 Figure 7.1: The (a) macro- and (b) micrograph of Cr-CrS cermet products (Navabi et al., 2012) ...... 122 Figure 7.2: A (a) schema of the flyer plate impact test and (b) photograph of a Cr-CrS cermet with the two Manganin gauges (Petal et al., 2014) ...... 124 Figure 7.3: An inlaid (a) cermet with alumina inclusion and (b) pure alumina targets ... 126

Figure 7.4: Geometries and dimensions of the PC backing plates ...... 127

Figure 7.5: The arrangement of the ballistic impact tests ...... 128

Figure 7.6: Fragment-Simulating Projectiles (FSP) with different geometries and sizes …………………………………………………………………………………………..129 Figure 7.7: The geometries and dimensions of the caliber .30 Fragment-Simulating Projectile (MIL-DTL-46593B (MR), 2008) ...... 129 Figure 7.8: The settings of the (a) gas gun and (b) aligning partition in the ballistic impact tests ...... 130 Figure 7.9: A target (a) before and (b) after a ballistic impact ...... 131

Figure 7.10: The PC backing plates after a ballistic impact ...... 131

Figure 7.11: Penetration depths of the first round of ballistic impact tests...... 133 Figure 7.12: Photographs of a (a) Cr-CrS cermet target with a PE backing rod and (b) clamped target...... 136 Figure 7.13: Photographs of a (a) two-layer target with a PE backing rod and (b) the clamping settings for the target ...... 136 Figure 7.14: (a) front and (b) side views of a fixed target ...... 137 Figure 7.15: The (a) front and (b) back views of a deformed steel disc after a ballistic impact ...... 138 Figure 7.16: (a) A PE rod before the test and (b) the PE rod cut into two sections after the

ballistic impact ...... 138

Figure 7.17: Penetration depths of the second round of ballistic impact tests ...... 139

List of tables

Table 3.1: Properties variables of the cylindrical impactor ...... 31

Table 3.2: Geometries of the 4 Taylor cylindrical impactors ...... 41

Table 4.1: Properties variables of the projectile and target materials ...... 50

Table 4.2: The diameters and thicknesses of the ten cylinder targets ...... 51

Table 6.1: Geometries and masses of four models ...... 89

Table 6.2: Properties variables of the ceramic inclusions ...... 106

Table 7.1: The dimensions of the cermet and alumina targets ...... 125

Table 7.2: The dimensions of the cermet and two-layer targets ...... 135

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Chapter 1: Introduction

1.1 Armour materials and structures

Developing lightweight armour materials is a key requirement for improving the personal protective equipment used by military and security personnel. Since the middle ages, metals have been used as personal armour materials for their high stiffness and toughness. This kind of armour was, however, extremely heavy and mostly reserved for mounted knights. Lighter and harder ceramic materials have been in development for armour systems since the early 1960’s, with the drawback that ceramics are relatively brittle with a low toughness in comparison with metals. Based on the above, the combination of metal and ceramic in a composite material, which is denoted a cermet (or ceramic-metal) composite, is needed to achieve high hardness combined with ductility while keeping the weight low for the armour design (Yadav and Ravichandran, 2003).

Accordingly, research into the manufacturing and testing of cermets has become important and popular for armour design, especially focusing on cermets with homogeneous and highly dispersed microstructures (Brekhovskikh et al., 1972). Cermets that exhibit optimum mechanical properties are achieved by uniformly distributing hard ceramic phases consisting of fine particles within a ductile binder metal phase (Gurland and Norton, 1952). In this case, the mechanism of reinforcement is associated with the increasing difficulty of moving dislocations within the matrix phase (Reed-Hill and

Abbaschian, 1994). Dislocations are the lattice defects accumulating along slip planes and lead to the discrepancy between computed and actual yield stresses of crystal materials. 1

A two-layer design, on the other hand, has become a standard configuration for modern armour systems (Lee and Yoo, 2001; Arias et al., 2003; Gonçalves et al., 2004;

Übeyli, Yıldırım, and Ögel, 2008). In this type of armour system, the outer material is made of a hard and high-purity ceramic, while the backing plate is made of a softer and more ductile material such as metal or polymer. As shown in Figure 1.1, the function of the outer ceramic layer is to erode and fragment the projectile, while resisting the penetration. The hard ceramic layer with high compressive strength forms conoid structures during the impact and reduces the local pressure on the backing layer

(Hetherington, 1992). The function of the backing layer is to absorb the remaining kinetic energy of the projectile, to contain the comminuted ceramic particles, and to prevent the projectile from completely penetrating the armour (Wilkins, 1978). In the two-layer configuration, the ceramic provides hardness for the armour system, but needs the confinement by the ductile backing layer to operate properly.

Vo Deformed projectile

Ceramic outer layer

Ductile backing layer

Figure 1.1: The standard two-layer armour design.

Some protective vests used by military personnel are comprised of multiple layers of a ballistic fabric (e.g., Kevlar) reinforced with a ceramic plate composed of, for example, boron carbide (Shokrieh and Javadpour, 2008). These vests are expensive, heavy, and rigid, and provide protection against ballistic threats over a limited area. Rigid and flat armour plates can only cover the torso, as shown in Figure 1.2, leaving other parts of the body, such as limbs, head and neck, poorly protected against threats in modern war theatres (Rustemeyer, Kranz, and Bremerich, 2007). In addition, the materials and arrangement used in the two-layer design has been optimized, and there are few opportunities for further improvement (Wilkins and Landingham, 2004). Therefore, new materials and configurations with enhanced mechanical properties as well as the potential to be manufactured into complex shapes, are needed for the design of the next generation of personal defense systems. This thesis focuses on studying the optimization of different ballistic target configurations by using numerical simulations. The optimal results were cooperated in manufacturing and testing actual experimental specimens.

Figure 1.2: A soldier installing a BAE Systems Small Arms Protective Insert (SAPI) plate (Hess, 2011).

1.2 Addition of hard and millimeter-size inclusions

Studies of hybrid materials are meant to fill gaps in material property space, and have attributes not offered by either material alone (Ashby, 2005). For example, a Ti-6Al-

4V matrix incorporating Al2O3 rods filled with B4C powders demonstrated projectile deflection, impact crater self-sealing, and forced shear localization (Gu and Nesterenko,

2007), which could not be achieved by any single alloy.

Ceramic inclusions have been found to enhance ballistic performance through several specific mechanisms. Projectiles are blunted, eroded, or even shattered by ceramic inclusions, since the inclusions are hard and can efficiently reduce the kinetic

4 energy of the projectile (Roeder and Sun, 2001; Karandikar et al., 2009). Ceramic inclusions can also distribute an impact load over larger volumes within armour materials, and over wider areas onto the backing materials (Arias et al., 2003). Thereby, ceramic inclusions can increase the stiffness and yield stress of composite materials

(Qiao, Yang, and Bobaru, 2008). Ceramic inclusions can also deflect a projectile, and force shear localization alongside specific directions (Gu and Nesterenko, 2007). Finally, compressive stress waves, which reflect off boundaries between inclusions and target matrices, can relieve tensile stresses and reduce damage inside the hybrid composites

(Sotiropoulos, 1993). Based on the above, adding ceramic inclusions into ballistic impact targets is a promising approach to enhance armour designs.

Design guidelines for armour systems with different inclusion configurations and arrangements are however currently not available. Numerical simulation provides an invaluable tool for the exploration of different configurations of matrix and inclusions, and can greatly accelerate the design process (United States Department of Energy,

2010). Some design examples of ballistic impact targets with ceramic inclusions are shown in Figure 1.3. The examples shown consist of hard ceramic inclusions of various shapes embedded within a matrix consisting, for example, of a cermet containing a mixture of chromium particles in a chromium-sulfide continuous phase. The ability to synthesize such an arrangement will be discussed within the thesis.

Vo Vo Vo

CCeramic inclusions Cr-CrS cermet

Figure 1.3: Examples of hybrid armour designs.

1.3 Overview of the simulation methods

Ballistic impact simulations are usually performed by using either an Eulerian or

Lagrangian approach (Schwer, 2004). Since non-deformable meshes are used in the

Eulerian method, the shape of the impactor becomes illegible as the penetration proceeds, due to material tangling in the fixed Eulerian cells. As for the Lagrangian method, there are two main techniques, which both require ddiminishing or eliminating large mesh distortions, and need a large experience base. One of the Lagrangian approaches is the so called pilot-hole technique (Chen, 2004). Even though it works well for common impact simulations, the pilot-hole technique requires a priori knowledge of the impact trajectory to remove the elements from the target mesh. The other Lagrangian method, known as mesh erosion, ssimply removes distorted elements based upon a user supplied criterion

(Swegle et al., 1994). It is hard to interpret the ballistic modeling results with the Eulerian approach, and thhe experience-based traditional Lagrangian approaches are not suitable for the optimization process. Accordingly, another simulation method, the smoothed particle

6 hydrodynamics (SPH) method, provides an alternate numerical approach, which alleviates many of the above limitations.

The SPH method was developed by Lucy, Gingold, and Monaghan first in 1977, for astrophysics simulations (Gingold and Monaghan, 1977; Lucy, 1977). Later, the SPH method was introduced to investigate dynamic fluid flows with large deformations (Liu and Liu, 2003). In 1991, the SPH method was introduced to solve solid mechanics problems by Libersky and Petschek (1991). Later in 2000, the SPH method was extended to study ballistics by Parshikov et al. (2000). The SPH method overcomes some fundamental limitations of conventional mesh-based numerical methods used in engineering computational mechanics. The SPH method is meshfree by replacing the elements, used in conventional numerical methods, by particles discretizing the physical domain (Lacome, 2001). These particles interact according to the governing conservation equations, and to material properties specified by the user (Jones and Belton, 2006).

Since there is no grid and connectivity between particles, the SPH method avoids convergence problems associated with element distortion or tangling from extreme deformations.

In this thesis, the SPH method was chosen for analyzing the ballistic impact simulation models, and used as a guideline for the novel armour design. The primary objective is using numerical analyses to study hybrid material systems with various geometries and material properties, and to provide a methodology for optimizing the ballistic performance of the hybrid systems. Further theories and details of the SPH method will be discussed in the next chapter.

1.4 Chromium-chromium sulfide (Cr-CrS) cermets

As for novel ballistic materials that may be produced with a flexible geometrical arrangement of inclusion, the chromium-chromium sulfide (Cr-CrS) system was chosen to be manufactured and studied in this thesis. Among ceramic materials, sulfides have excellent wettability to form hybrid materials with metal and other ceramics, leaving a large space for composites design (Kaun, 1993). Metal sulfides have many valuable characteristics including hardness, semi-conductivity, catalytic properties, etc., and they are in high demand in the chemical, metallurgical, and electrical industries (Vaughan and

Craig, 1978). The main limitation of metal sulfides is that when synthesized from their constituent powders in a combustion process, they typically generate large amount of gaseous products. Consequently, the final metal sulfide products typically have high porosity and low strength (Chianelli, Daage, and Ledoux, 1994). One exception to this general rule is chromium sulfide, in which the synthesis produces little or no gaseous products based on equilibrium calculations (Goroshin et al., 1996). During the synthesis of chromium sulfide, neither toxic materials nor by-products are produced. In addition, chromium sulfide is chemically stable at normal conditions, and insensitive to moisture

(Vaqueiro et al., 2001). Finally, chromium sulfide has low density and superior hardness compared with other metal sulfides (Hibble, Walton, and Pickup, 1996). Based on the above, chromium sulfide was chosen as the base material for new armour material studied in this thesis.

To reach high toughness, a Cr-CrS composite system is proposed to combine the high strength of ceramics and high ductility of metals. The mechanical properties of Cr-

CrS cermets can be manipulated by changing the proportion of chromium in the 8 precursor, which will lead to different chemical compositions in the products. The microstructure of Cr-CrS cermets photographed by a scanning electron microscope

(SEM) is shown in Figure 1.4. The lighter areas are chromium regions whereas the darker regions correspond to CrS. In Cr-CrS cermets, the CrS phase acts as a hard component while the Cr phase serves as the ductile component of the cermet. The desired scenario in the case of high-speed impact on this material is for the CrS phase to provide high hardness to pulverize the projectile, and the Cr phase to provide high ductility to dissipate the kinetic energy from the projectile. Overall, the combination of Cr-CrS phases provides a flexible system to successfully defeat ballistic projectiles.

CrS

Figure 1.4: The micrograph of Cr-CrS cermets (Navabi et al., 2012).

In this thesis, alumina (Al2O3) plates were further inserted into the Cr-CrS cermets as ceramic inclusions. Impact tests were conducted to compare the ballistic performance of cermet specimens with and without ceramic inclusions.

1.5 The SHS combustion method

In this thesis, the self-propagating high-temperature synthesis (SHS) method was adopted for synthesizing the inclusion-matrix system. The SHS method is a combustion technique that has been extensively used for synthesizing hundreds of different types of materials in the past thirty years (Sohn and Wang, 1996). The SHS method was first discovered by Merzhanov, Borovinskaya, and Shkiro, while they studied the combustion of titanium-boron mixture in 1971, and later introduced the name SHS in 1984 in the

USSR (Merzhanov, 2007). The SHS method is based on highly exothermic chemical reactions, and uses the heat generated by the reactions to sustain synthesis process in a combustion wave (Makino, 2001). Thereby, the combustion wave propagating in the SHS method spontaneously transforms raw materials into synthesized products, as shown in

Figure 1.5. After initiating a gasless flame in the reactants, the heat released by the hot reaction zone supports a propagating wave, which leads to the synthesis of the products

(Fu et al., 2003). Based on the thermodynamics calculations, the following conditions are required to support a self-sustained SHS reaction:

1800 (1-1),

and 2000 (1-2), 10

0 where Τad is the adiabatic combustion temperature, ΔH f298 is the enthalpy of the product formation, and Cp298 is the molar heat capacity of the product at the temperature of 298K

(Munir and Anselmi-Tamburini, 1989).

Product of reaction

Combustion front

Synthesis direction Mixture of initial reactant

t=0 s t=0.1 s t=2.7 s t=4.0 s

Figure 1.5: The propagation of combustion wave in the SHS method (Eugene and Oleg, 2010).

Since the SHS process is self-sustained and the heat is provided by the combustion reaction, it does not require an external energy source and consumes a relatively low energy as a “green” manufacturing technique (Goroshin, Lee, and Herring,

2000). The SHS method is highly time efficient due to the extremely fast chemical reactions and wave propagations (Gennari et al., 2003). The high reaction and cooling rates in the SHS method also prevent undesirable grain growth, which may weaken mechanical properties in the products, and usually occurs in conventional sintering methods (Fu et al., 2003). The SHS method produces high purity products, considering that the high temperature reaction volatilizes impurities during the synthesis (Mizera,

1997). The SHS method does not require complex equipment for the synthesis process, 11 and is a low-cost technique (Merzhanov, 2004). With direct synthesis, net-shape articles can easily be produced by the SHS method, which is one of the objectives for manufacturing personal armour with better body coverage (Sohn and Wang, 1996). The

SHS method is suitable for metal and ceramic adhesion by virtue of the fact that ceramic phases can grow inside the liquid metal during the synthesis process, which is crucial for manufacturing composite materials with different configurations (Varma et al., 1998).

1.6 Dissertation Structure

This dissertation aims to investigate the design and optimization of hybrid ballistic protection systems with novel configurations and materials. The SPH simulation method was used to streamline the design process, and to provide an efficient approach to determine the optimum armour configuration. The SHS combustion method was adopted for manufacturing Cr-CrS cermet targets, some of them with alumina inclusions.

In chapter 2, the theory and implementation of the SPH method is discussed. The theory and application of material models, which is adopted in the further SPH models, is also covered. To have more confidence in the results of the simulation models, in chapter

3, the SPH method is validated by comparing the theoretical calculation and simulation results of simple Taylor impacts. The use of symmetric planes and default parameters in the SPH models is also validated. In chapter 4, simple ballistic simulation models are constructed. The modeling focuses on analyzing the effects of target geometries on the projectile resistance performance. The results are compared to actual impact tests previously done by other scholars. Afterwards, different material models in the SPH 12 simulations for interpreting different materials characteristics are studied. As a guideline for complex hybrid systems, chapter 5 and 6 focus on simulation designs with different target configurations and materials arrangements. Chapter 5 focuses on the ballistic optimization of multilayered targets. Different material arrangements, with constraints of constant target volume or mass are studied. In chapter 6, the ballistic performance of targets with embedded ceramic inclusions and different configurations is explored. All the results are compared with the best design in chapter 5. In chapter 7, experimental methods of manufacturing hybrid targets and measuring the mechanical properties of Cr-

CrS cermets are discussed. Discussions of the results of impact tests are also included.

Finally, chapter 8 highlights the key findings of this research and the novel contributions to the materials and designs of hybrid ballistic protection systems.

Chapter 2: The SPH method

The conventional grid-based Lagrangian methods assume a fixed connectivity between nodes to construct the spatial structure (Hayhurst and Clegg, 1997). However, problems with large deformations make the calculation break down due to severe distortions in the Lagrangian grids (Swegle et al., 1994). In contrast, the SPH method is a meshfree numerical method. It has the advantage of being able to model systems with free surfaces or large deformations, while avoiding the mesh tangling issues that occur in traditional Lagrangian methods (Lacome, 2001). The SPH method is a useful tool for analyzing high-velocity impact and penetration behaviors in solid materials (Schwer,

2004). Since the SPH method is completely meshless, it is relatively easy to build up simulation models even with very complicated geometry, which consequently leads the

SPH method to broad applications (Johnson, Stryk, and Beissel, 1996).

There are two main sections in this chapter. The first section focuses on the theory that forms the basis of the SPH method, and the other section discusses the material models used within the SPH simulation models, which will be adopted in the further chapters.

2.1 Theory and implementation

In the SPH method, the physical domain is divided into discrete elements, which are referred to as particles (Lacome, 2001). The SPH method has the advantage of combining traditional Lagrangian formulations with the particle approximation (Vesenjak

14 and Ren, 2009). The Kernel approximation function in three dimensions used in the SPH method is based on randomly distributed particles (Jones and Belton, 2006).

, (2-1), where x is the position of particles, and h is the smoothing length. The Kernel function is defined by the following function θ, which is the most commonly used by the SPH community (Swegle et al., 1994).

1 0 1 θ(u) = 2 1 2 (2-2), 0

where , and d is the interparticle distance |x-x’|.

Particles in the SPH method are computed with a regular interpolation function to solve the entire problem (Lacome, Espinosa, and Garonne, 2003). The interpolation function in the SPH method is known as the dimensionless smoothing length, which varies from particle to particle in time and space (Swegle et al., 1994).

∝ (2-3), where ρ is the density of particles occupying the neighbourhood, and m is the portion of mass carried by each particle. The smoothing length increases when particles separate from each other, to keep the same number of particles in the neighbourhood (Lacome,

2001). As shown in Figure 2.1, a smoothing length is used corresponding to half of the radius of the so-called “influence neighbour sphere” to search for neighbouring particles 15 within the influence neighbour sphere. In other words, at each time step, the distance between each pair of particles is computed to determine if both of the particles are inside the influence neighbour sphere. The neighbouring particles are the ones being considered for interparticle forces to calculate the stresses and strains in the SPH simulations. By determining the smoothing length to build the influence neighbour sphere, sufficient particles are certain to be kept within the neighbour sphere to validate continuum variables, and avoid problems in extreme material compression and expansion (Goyal,

Huertas, and Vasko, 2013).

Figure 2.1: Box sort and neighbour search (Lacome, 2001).

In the SPH simulations, the physical domain is split into cellular boxes of a given size, and the neighbour search accounts only for particles within the same and neighbouring boxes regarding the influence domain, as shown in Figure 2.1. By reducing the quantity of distance calculations, the computational time is largely reduced, and the modeling efficiency is significantly increased (Lacome, 2000).

Particles in the SPH method possess individual material properties, and behave

16 according to the fluid dynamics (Swegle et al., 1994). The SPH method is governed by the mass, momentum, and energy conservation laws, which are expressed as interparticle forces (Zhou, Liu, and Han, 2006). The equations governing the evolution of mechanical variables are expressed as summation interpolants as follows (Jones and Belton, 2006):

∙ ∑ (2-4),

∑ (2-5),

and ∑ (2-6),

where xi is the spatial coordinate of particle i, and (Michel et al.,

2005).

There are 8 essential steps in the SPH method integration cycle, as shown in

Figure 2.2 (Lacome, 2001). The commercial code LS-DYNA is used for solving the mechanics in the simulation models. By calculating the explicit Lagrangian mechanics, the SPH method implemented within LS-DYNA is very efficient at solving high strain rate and large deformation problems. In the first step in the SPH integration cycle, the velocity and displacement of each particle are given in LS-DYNA. Next, the parameters of velocity and displacement are injected into the approximation function, and the smoothing length is automatically computed by LS-DYNA by using the divergence function, as shown in equation (2-7), to interpret flow behaviors in a three dimensional vector field.

(2-7).

In the third step, the smoothing length is used as half of the radius to build the influence neighbour sphere, and to search for neighbour particles within the sphere. Afterwards, the density and strain rate of the influence sphere are calculated by using the continuity equation and Kernel approximation in the fourth step. Further in the fifth step, the pressure, energy, and stress of the influence sphere are calculated by using the energy conservation law and equation of state, based on the results in the fourth step. In the sixth step, the particle force is collected by inputting the results in the fifth step into the momentum conservation law and Kernel approximation. Afterwards in the seventh step, the contact and boundary conditions are determined, based on the results in the sixth step.

Last in the eighth step in the SPH calculation cycle, the acceleration of each particle can be obtained and further used to integrate and update the particle velocity and position in the first step. In the end, the calculation of the SPH integration cycle is continued and repeated.

There is no need for special contact algorithms in the SPH method since it is meshfree (Lacome, 2001). The contact will automatically occur when the particles of one part are located within the influence neighbour sphere of the particles of other parts

(Vesenjak and Ren, 2009).

Velocity, position LS-DYNA

Acceleration Smoothing length LS-DYNA SPH

Contact, boundary condition Neighbour search LS-DYNA SPH

Particles force Density, strain rate SPH SPH

Pressure, energy, stress LS-DYNA

Figure 2.2: Loop of a SPH cycle (Lacome, 2001).

2.2 The material models

There are two material models adopted in this research within the SPH simulation models: the plastic kinematic (PK) and Johnson-Holmquist (JH) material models. The PK model was adopted for interpreting metallic materials while the JH model was adopted for interpreting ceramic materials with damage and failure effects. The details of the two material models are given below. 19

2.2.1 The plastic kinematic material model

The plastic kinematic (PK) material model is a very cost effective model, and can be applied to metal, composite, and plastic materials (LS-DYNA Keyword User’s

Manual, 2007). Strain-rate effects and failure criteria can be provided within the PK model.

The PK material model uses a bilinear stress strain curve to calculate stress values with the loading below and beyond the yield strength. The plastic deformation in materials will occur when the loading is above the yield strength. Within the elastic region, the Young’s modulus, given as an initial material property, is used as the slope of the stress strain curve. In the plastic region, the strain hardening modulus is used as the slope instead. The strain hardening modulus is defined by the ultimate strength in the specimen (Riley, Sturges, and Morris, 2002).

(2-8),

where σU is the ultimate strength with 0.2% permanent elongation of the original dimension, σY is the yield strength, and εY is the yield strain.

The combination of isotropic and kinematic hardening can be specified by varying the parameter in the PK model. The elastic-plastic behavior of a material with isotropic and kinematic hardenings is shown in Figure 2.3, where l and lo are deformed and undeformed lengths of the specimen under uniaxial tension and compression, and Eh is the slope of the strain hardening modulus.

σU

σY Eh

E 2σY

ln Kinematic hardening

Isotropic hardening

Figure 2.3: A material’s elastic-plastic behaviors with isotropic and kinematic hardening (Krieg and Key, 1976).

Materials with isotropic hardening only yield once the compression loading reaches the yield strength of the materials. The yield stress increases when the specimen is reloaded with previous plastic deformation, and the compression yield stress grows the same amount in the materials with the isotropic hardening. Kinematic hardening considers the Bauschinger effect, as the yield stress decreases when the direction of strain is changed, and is useful for specimens under cyclic loadings (Håkansson, Wallin, and

Ristinmaa, 2005). In general, isotropic hardening requires less storage, and is more efficient (LS-DYNA Keyword User’s Manual, 2007). Materials adopting the PK model in this thesis are specified with isotropic hardening.

2.2.2 The Johnson-Holmquist material model

The Johnson-Holmquist (JH) material model is one of the most widely used models in ballistic impact simulations, and is useful for modeling ceramics, glass, and other brittle materials (LS-DYNA Keyword User’s Manual, 2007). It is important to embody the effects of microscopic defects on the initiation and propagation of failure in ceramic materials (Meyers, 1994), and simulate the compressive failure and damage effects on the strength of residual materials after the high-energy ballistic impacts (Cronin et al., 2003). The strain-rate effects can also be provided in the JH model.

In the JH material model, two sets of stress-strain curves are used to interpret the intact and failed materials over hydrostatic pressure. The phenomena of strength increase in ceramics subjected to hydrostatic pressure, and the strength reduction in damaged ceramics are interpreted by plotting the yield stress against the pressure during the impact

(Johnson and Holmquist, 1994). Right after the impact, the elastic material properties are used for the initial stress state, and the pressure P is calculated by the equation of state based on the present material deformation ξ.

1 (2-9),

and (2-10),

where ρ is the current mass density, ρo is the initial mass density, S1, S2, S3 are material constants, and P is the pressure increment. The increment in pressure is caused by the accumulation of damage within the compressed material.

(2-11), where G is the shear modulus of the material. In the JH model, strengths of intact and fractured materials are divided by the Hugoniot Elastic Limit (HEL), which is also the transition point from elastic to plastic material strains prior to failure (Rosenberg, 1993).

(2-12),

where υ is the Poisson’s ration of the material, and Yc is the equivalent dynamic compressive strength.

For the two sets of stress-strain curves, the intact material stress is defined as

(Johnson and Holmquist, 1994)

∗ ∗ ∗1 (2-13),

* * * where A, N, C are material constants, εp is the inelastic strain, t is the time, and σ , P , T are normalized stress, pressure, and tensile strength.

∗ ∗ ∗ ; ; (2-14).

The post-yield response and gradual softening of ceramic materials are described by the fractured material stress. . ∗ ∗ 1 (2-15), where B, M, C are material constants.

Based on equations (2-13) and (2-15), the present material stress is defined as

∗ ∗ ∗ ∗ (2-16),

where D is the indicator of the accumulation of damage.

∆ ∑ (2-17),

where εf is the fracture plastic strain, and under a constant pressure defined as

∗ ∗ (2-18),

where D1 and D2 are material constants.

In the JH material model, strain rate effects are secondary compared to pressure effects (Anderson, Johnson, and Holmquist, 1995). In this thesis, strain rate effects were not used for materials adopting the JH model.

Chapter 3: Validation of the SPH method

The SPH method was developed almost four decades ago (Gingold and

Monaghan, 1977; Lucy, 1977), but it has been applied to solve problems of continuum solid and fluid mechanics for only about a decade (Liu and Liu, 2003). So far, little research has been carried out assessing the accuracy and validity of the SPH method for the applications of solid mechanics (Fourey et al., 2013). Therefore, one of the first tasks in this thesis was to validate the SPH method, and the Taylor impact test was chosen for the validation. The Taylor impact test is one of the simplest and most popular tests for studying high strain rate behavior in ductile materials (Taylor, 1948), and there are abundant data and information about the Taylor impact test to support the validation. The

Taylor test consists of a cylindrical impactor with a specified diameter and length impacting a rigid wall at a pre-defined velocity. Upon impact, elastic and plastic stress waves travel along the axis of the cylinder which deforms elastically and plastically.

Because the system is essentially one-dimensional, the amplitude and velocity of the stress waves traveling in the cylinder can be calculated using closed form solutions. The length of the rod after impact is often used to determine the yield strength of the material at high rates of deformations (Wilkins and Guinan, 1973).

To validate the SPH method, results from theoretical calculations and the SPH simulation analysis of stress waves in Taylor cylindrical impactors were compared. To save computational time, quarter models were used with appropriate boundary conditions. The quarter models were also validated by comparing with full models.

Finally, a detailed study of the SPH simulation parameters was performed.

3.1 Theoretical equations

This section introduces the theoretical calculations of the amplitude and propagating velocity of stress waves in a Taylor cylindrical impactor. The calculations are based on existing theoretical analysis available in the literature (Boresi and Schmidt,

2003; Meyers, 1994). The amplitude of the stress waves was calculated by using the relations between stresses and strains while the velocity of stress waves was calculated by considering one dimensional equilibrium.

3.1.1 Stress-strain relations

Based on Hooke’s law, stresses and strains are proportional in a linear elastic material (Boresi and Schmidt, 2003). For an isotropic linear elastic material, we have

(3-1),

(3-2),

and (3-3), where E is the Young’s modulus and ν is the Poisson’s ratio of the material. The material of the cylinder in the Taylor impact test is homogeneous and the geometry and boundary conditions are axisymmetric about z-axis, as shown in Figure 3.1. Accordingly, σxx = σyy in the cylinder (note that Cartesian coordinates are preferred over cylindrical coordinates to be constant with the SPH model). Equations (3-1) to (3-3) can then be reduced to

1 (3-4),

(3-5),

and 2 (3-6).

8 mm zLo

80 mm

X Y

Figure 3.1: Taylor impact model with a thin cylindrical impactor.

The propagation speed of plastic stress waves is slower than the elastic stress waves, and the excessively mushroom-shaped deformation in the cylindrical impactor occurs in an impact posteriorly (Meyers, 1994). In the early stage of an impact, particles at the center of a cylindrical impactor close to the impact end only experiences vertical compressive displacements along the z-axis without other horizontal displacements, i.e.,

εxx is equal to zero at z = 0. Accordingly, equation (3-4) can be solved:

(3-7).

The horizontal stresses σxx and σyy are caused by the interference of reflecting stresses from the surrounding surface inside the cylindrical impactor. By substituting σxx in equation (3-6), we obtain

1 (3-8).

Inverting equation (3-8), we obtain

(3-9).

Based on the von Mises yielding criterion, the effective stress can be written as

6 (3-

10).

Since σxx = σyy and all three shear stresses, τxy, τyz, and τzx, are relatively small and can be ignored, in a Taylor cylindrical impactor under one-dimensional loading in the z direction, equation (3-10) can be reduced to

| | (3-11).

By substituting σxx from equation (3-7) into equation (3-11), we obtain

(3-12).

Under the yielding criterion, the effective stress σe is equal to the yielding stress σY.

Therefore, σzz can be further calculated by inverting equation (3-12).

| | (3-13).

This equation provides the amplitude of the stress wave traveling through a ductile cylinder of yield strength σY.

3.1.2 1D equilibrium equations

Stress equilibrium in dynamic condition can be reduced, in the one dimensional wave propagation case, to the equation (Meyers, 1994):

(3-14).

After the cancellation of Aσ, equation (3-14) can be divided by Aδz, and reduced to

(3-15).

Recalling Hooke’s law for elastic deformation, σ = Eε. By substituting σ in equation (3-

15), we obtain

(3-16).

By transposing we obtain the velocity of an elastic wave longitudinally propagating in a thin bar in a bounded medium as the square root of equation (3-16).

(3-17).

This equation provides the velocity of the 1D elastic stress wave which is governed by the Young’s modulus and mass density of the material.

3.2 SPH simulations

This section focuses on the construction of the SPH models. The software package LS-DYNA was used to build and analyze the SPH models. The pre-processor

LS-PrePost was used to generate particle coordinates for the cylindrical impactor and assign a partial mass to each particle in the models. A rigid wall was built by creating a solid box and putting a rigid plane on the top surface of the box as the impact plane.

Variables in the Taylor impact models were given as followings. The axis of the cylindrical impactor was parallel to the z direction. The diameter of the cylindrical impactor was 8 mm and the length was 80 mm, as indicated in Figure 3.1 in the previous section. The initial impact velocity was 300 m/s along the negative z-axis. The distance between particles was 0.5 mm, and a Von Mises plastic kinematic (PK) material model without hardening was used. The property variables of the cylindrical impactor used in the PK material model are shown in Table 3.1. The mass density, Young’s modulus, and

Poisson’s ratio were obtained from actual data for chromium sulfide samples, which will be further discussed in Chapter 7. In addition, isotropic hardening was used as perfect plasticity without hardening in the cylindrical impactor since the validation is to compare the results with the basic calculations in the previous section 3.1.

Table 3.1: Properties variables of the cylindrical impactor.

Mass density 3850 (kg/m3)

Young’s modulus 5.084 (GPa)

Poisson’s ratio 0.24

Yield stress 500 (MPa)

Given the material properties, the relation between the transverse and longitudinal stresses in a cylindrical impactor can be calculated by substituting the Poisson’s ratio into equation (3-7) mentioned in section 3.1.

. 0.316 (3-18). .

In the same manner, the relation between the effective and longitudinal stresses can be calculated by substituting the Poisson’s ratio into equation (3-12).

. |0.684 | (3-19). .

Finally, the theoretical velocity of elastic stress waves can be calculated by substituting both the Young’s modulus and mass density into equation (3-17).

. 1149 / (3-20).

3.3 Validation of symmetric planes

To save computing time and data storage space, two symmetry planes (x-z and y- 31 z) were introduced. Accordingly, only quarter-sized models were built, as shown in

Figure 3.2 (b). To achieve this, Matlab was used to exclude particles with either negative x or y coordinates, and reassign particle numbers. As a result, 33,280 particles were used for generating an intact cylinder, and 8,320 particles were used for generating a quarter model.

(a) (b)

Rigid wall

Figure 3.2: (a) Whole and (b) quarter-sized Taylor impact models.

To validate the use of symmetry planes, the final lengths of the cylinders after impact were used as indicators. At 10 µs after impact, the lengths of both the whole and quarter impactors were 74.69 mm, as shown in Figure 3.3. At 100 µs after impact, the length of the whole impactor was 36.05 mm while the length of the quarter impactor was

36.04 mm. The discrepancy between the results was within 0.03% and deemed acceptable. Based on the above, quarter models with symmetry planes were validated as accurate and equivalent to whole models.

(a) (b)

Figure 3.3: 20 µs after the impact on (a) whole and (b) quarter-sized Taylor impact

models.

3.4 Comparison of SPH results with theoretical results

This section is aimed at obtaining modeling results from the SPH simulations for the comparison with the theoretical calculations listed in the previous sections 3.1 and

3.2. The study began with extracting the amplitude and velocity of stress waves in a single SPH Taylor impact model. Afterwards, wave velocities and final cylinder lengths in multiple models with different geometries were compared and discussed.

3.4.1 Single Taylor impact model analysis

In order to analyze the stress wave propagation within the cylindrical impactor,

33 we monitored the stress history of 10 particles selected along the axis of the impactor as shown in Figure 3.4. The distance between the selected particles was 8.5 mm.

Particles number: 1

Figure 3.4: Cylindrical impactor indicating particles chosen for analysis.

Sequential results of the cylindrical impactor from t = 0 to t = 200 (μs) after impact are shown in Figure 3.5, where t is the time after the cylindrical impactor impacted the rigid wall.

t=0 μs t=40 μs t=80 μs

V o L o

t=120 μs Rigid wall t=160 μs t= 200 μs

Figure 3.5: Snapshots of the Taylor impact simulation.

As for the assumptions in section 3.1.1, εxx = εyy = 0 at z = 0. The shear τxy, τyz, and τzx stresses were, as expected, relatively small and less than 1.70% of the magnitude of the normal σxx, σyy, are σzz stresses.

As mentioned in section 3.1.1, σxx = σyy in the cylinder upon impact since the material was homogeneous and the geometry and boundary conditions were axisymmetric about the z-axis. The related normal σxx and σyy stresses of the 10 selected particles in the cylindrical impactor are shown in Figures 3.6 and 3.7, respectively. Again, the SPH simulation results confirm the theoretical assumption that σxx and σyy are equal within the impactor. The discrepancy between the results was within 0.74% and deemed acceptable.

1.0 1 2 0.5 3 4 5 0.0 6 7 8 -0.5 9

(GPa) 10 xx  -1.0

-1.5

-2.0 0 20406080 time (s)

Figure 3.6: Normal σxx stresses in the Taylor cylindrical impactor.

As presented in the work by Lensky (1949), extremely high compressive stresses were induced immediately upon impact near the impact end. The nominal stresses rose to values higher than the yield strength of the materials. These transient events were also identified in the work by Jones et al. (1992), and occurred in our model, as shown in

Figure 3.6, 3.7, and 3.8.

1.0 1 2 0.5 3 4 5 0.0 6 7 8 -0.5 9

(GPa) 10 yy  -1.0

-1.5

-2.0 0 20406080 time (s)

Figure 3.7: Normal σyy stresses in the Taylor cylindrical impactor.

Figure 3.8 shows the normal σzz stresses of the 10 selected particles over time. The figure indicates the sequential increase of compressive σzz stresses from the impact to free end of the cylindrical impactor, and reveal the arrival of the front wave along the impactor axis. The stress history is only shown until 80 µs after impact, since the stresses afterwards became difficult to interpret due to multiple reflections of the waves inside the cylinder. The theoretical σxx calculated by equation (3-18), recalling that 0.316 , agreed with the simulation results which overlapped the σzz curve of particle number 10 in the early stage of impact in Figure 3.9. The discrepancy between the results was within

1.61% and deemed acceptable at 2.8 µs after the impact, right before the yielding of the cylindrical impactor.

1.0 1 2 0.5 3 4 5 0.0 6 7 8 -0.5 9

(GPa) 10 zz

 theoretical -1.0

-1.5

-2.0 0 20406080 time (s)

Figure 3.8: Normal σzz stresses in the Taylor cylindrical impactor.

As expected, the effective stresses in the cylindrical impactor reached a maximum of 500 MPa, the yield strength of the material, as shown in Figure 3.9. In addition, the theoretical σe calculated by equation (3-19), recalling |0.684 |, agreed with the simulation results which overlapped the σe curve of particle number 10 in Figure 3.9. The discrepancy between the results was within 0.74% and deemed acceptable.

0.6 1 Yield strength σY = 500 MPa 2 0.5 3 4 5 0.4 6 7 8 0.3 9

(GPa) 10 e

 theoretical 0.2

0.1

0.0 0 20406080100 time (s)

Figure 3.9: Effective stresses in the Taylor cylindrical impactor.

The Lagrangian t-X diagram of σzz stresses propagation in the cylindrical impactor is shown in Figure 3.10. The Lagrangian diagram is an approach to display the propagation of one dimensional stress wave by plotting the time history of longitudinal stresses at various positions along the impactor. It is popular for interpreting high strain rate impact tests, especially proper to predict the time and position of stress wave fronts as visualize the wave propagation (Bell, 1961). As shown in Figure 3.10, the linear relation of compressive stresses increasing from the impact end to the free end of the cylindrical impactor revealed the traveling of stress wave front along the axis of impactor.

The slope of the compressive stress arrival time over the distance from the impact end corresponded to the velocity of wave propagation in the cylindrical impactor. Further

39 discussion about stress wave velocities in modeling results compared with the theoretical calculation will be given in the next sub-section.

100 1 2 3 80 4 5 6 60 7 8 s)  9 10

time( 40 SPH wave velocity = 1203 m/s

0 0 20 40 60 80 distance (mm)

impact end free end 10 9 8 7 6 5 4 3 2 1

Figure 3.10: Lagrangian t-X diagram of the Taylor cylindrical impact.

3.4.2 Validation over different geometries

Based on the experimental results in the work of Wilkins and Guinan (1973), the ratio of final length of the cylinder over its initial length should be independent of the ratio of original cylinder length over diameter. Accordingly, four Taylor impact models

40 were built with different cylinder ratio of length over diameter for comparison. The detailed sizes of the cylinders are provided in Table 3.2.

Table 3.2: Geometries of the 4 Taylor cylindrical impactors.

Cylinder length Cylinder diameter Cylinder ratio

80 mm 4 mm 20

80 mm 8 mm 10

80 mm 16 mm 5

80 mm 32 mm 2.5

The simulation results of the four Taylor impact models agreed with the conclusion by Wilkins and Guinan’s (1973). As shown in Figure 3.11, the ratio of the final over the original cylinder length only increased slightly with a reduction of the ratio of the original cylinder length over the diameter. The discrepancy between the results was within 5.5% and deemed acceptable.

0.40

0.35 length ratio length

0.30 0 5 10 15 20 cylinder ratio

Figure 3.11: Length ratios of the 4 Taylor cylindrical impactors.

To validate the propagation velocities for the elastic stress waves in the computational results, the slopes of the linear relations between the distance from the impact surface to the time that the σzz stresses reached 100 MPa at each selected position were calculated. The modeling wave velocities for all 4 simulation models with different cylinder geometry are shown in Figure 3.12.

top end ratio slope (m/s) deviation 80 20 1105 -3.83% 10 1203 4.70% 70 5 1289 12.18% 2.5 1317 14.62% 60

50 20 10 40 5 2.5 30 distance(mm)

10 impact end 0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 time (ms)

Figure 3.12: An X-t diagram of the 4 Taylor cylindrical impacts.

Compared with the theoretical value in equation (3-20), i.e., CL = 1149 (m/s), the elastic stress wave propagation velocities from the model calculations with thin bar impactors and high geometry ratios of 20 and 10 fit the theoretical value well, condidering that the theoretical predictions were based on one-dimensaional calculations.

3.5 Parametric studies

In this section, the effects of key parameters used in the SPH simulations are examined, including the smoothing length, number of neighbour particles, and distance between particles. Only one variable was changed at a time, and three or four Taylor 43 impact models were built for each variable. The diameter was 8 mm for all the cylindrical impactors. Again, the final lengths of the cylindrical impactors were used as the indicator for comparison.

3.5.1 Smoothing length

The default value of the constant applied to the smoothing length (CSLH) for SPH models is 1.2. It is specified in the LS-DYNA Keyword User’s Manual (2007) that the default value of CSLH applies for most problems and is recommended. In addition, a

CSLH value of less than 1 is not admissible and CSLH larger than 1.3 will increase the computation time without further improvements in the accuracy. In this sub-section, four other Taylor impact models were built with values of CSLH of 1.0, 1.1, 1.3 and 1.4.

For all 4 models with different CSLH values, the impactor length was 74.69 mm at 10 µs after impact, exactly the same value with the model with a CSLH value of 1.2.

The effect of the CSLH value on the impactor length at 100 µs after impact is shown in

Figure 3.13. Overall, increasing the CSLH value slightly reduced the apparent hardness of the material, and reduced the final impactor length by 1.86%, 0.67%, and 0.11%, for values of CSLH of 1.1, 1.3, and 1.4, respectively. The effect was deemed negligible, and a value of CSLH of 1.2 (as recommended by the LS-DYNA user Manual) was chosen for all future simulations.

37.0

36.8

36.6

36.4 final length (mm) length final

36.2

36.0 1.0 1.1 1.2 1.3 1.4 CSLH

Figure 3.13: Final cylinder lengths of 4 models with different smoothing length.

3.5.2 Number of neighbours per particle

The variable of neighbours per particle (NNP) is the number for memory allocation of arrays during the initialization phase specified in the calculation. The default value of NNP is 300 and should apply for most applications as indicated in the LS-DYNA

Keyword User’s Manual (2007). In special cases, modifying the value of NNP may avoid memory allocation problems in the case of very high strain rates. In this sub-section, four other Taylor impact models were built with values of NNP of 100, 200, 400, and 500.

For all 4 models with different NNP values, the impactor lengths were all 74.69 mm at 10 µs after impact and 36.04 mm at 100 µs after impact, exactly the same values with the model with a NNP value of 300. Even though there was no change in the results, the value of NNP is only adjusted the density of neighbour particles inside the allocation sphere is very high, which can make the calculation unstable leading to premature termination of the calculation. In addition, the value NNP can be specified either positive or negative. As indicated in the LS-DYNA Keyword User’s Manual (2007), if the NNP value is positive, the memory allocation is dynamic; if the NNP value is negative, the memory allocation is static and only the closest SPH particles will be considered in the calculation. Based on the above, a value of NNP of 300 as recommended in the Manual is chosen for all future simulations.

3.5.3 Distance between particles

The distance between particles (PD) in the SPH method functions effectively as the size of the mesh used in the traditional finite element method. However, a smaller distance between particles not only leads to a larger computing time and storage, but also may lead to a high density of neighbour particles within the allocation sphere causing the solver to terminate. Sakakibara, Tsuda, and Ohtagaki (2008) investigated the effect of changing the distance between particles, and found that 0.5 mm was the convergence point for constant loading of a cylindrical specimen. In addition, in high-velocity impact studies, a distance of 0.5 mm is mostly used to avoid excessively dense particles within small volumes (Fountzoulas, Cheeseman, and LaSalvia, 2009).

In this sub-section, three other models were built with 0.125, 0.25, and 1 mm PD, i.e., 516480, 64960, and 1040 particles were used for composing the quarter models. At

10 µs after the impact, the impactor lengths were 74.93, 74.81, and 74.44mm, respectively. The model with 0.125 mm PD terminated automatically 37.5 µs after impact with too many particles in the influence neighbour sphere. The impactor lengths of the models with 0.25, and 1 mm PD were 36.62, and 35.04 mm, respectively, at 100 µs after impact. Overall, smaller values of PD led to higher particle densities, slightly increasing the apparent hardness of the material, and made the final impactor lengths slightly longer.

However these effects were minimal. Following previous studies (Fountzoulas,

Cheeseman, and LaSalvia, 2009), a value of 0.5 mm for PD was chosen for all future simulations.

To summarize the studies in this chapter, quarter SPH models with symmetry planes were validated as replacement for complete models to save computational resources. The SPH simulations of the Taylor experiments produced results which were consistent with theory in terms of stress amplitudes, material strength and stress wave velocities. Key parameters for the SPH simulations were found to have little effect on the overall results, when they were varied over a small range around the suggested default values. The results presented in this chapter contribute to building our confidence in the

SPH method. Further validations using ballistic impact configurations are presented in the next chapter.

Chapter 4: Ballistic impact simulations

Chapter 3 presented results from SPH simulations of the Taylor impact experiment, together with comparisons with theoretical models and experiments. The next step, presented in this chapter, is to model a simple ballistic impact, where a spherical projectile impacts a target of finite thickness with a pre-defined initial velocity.

There are two main sections in this chapter. The first section focuses on studying the effects of target diameter and thickness on the ballistic resistance performance. The results are compared to experimental results from Martineau, Prime, and Duffey (2004).

The second section aims at the validation of material models used in the SPH simulations.

The impact target was modeled using either the plastic kinematic material model for steel or the Johnson-Holmquist model for SiC. The modeling results were then compared with the objective of interpreting the effect of the different material characteristics of metal and ceramics.

4.1 Overview of the model

The ballistic models used in this chapter were built based on the experimental work of Martineau, Prime, and Duffey (2004). The geometry of the system is shown in

Figure 4.1. The projectile was modeled as a tungsten carbide (WC) sphere, and the target was either a high-strength low-alloy (HSLA) steel or SiC ceramic cylinder. The plastic kinematic (PK) material model was used for both the WC projectile and steel target, while the Johnson-Holmquist (JH) material model was used for the SiC target including

48 failure and damage effects. The property variables for all three materials used in the material models are tabulated in Table 4.1. The material properties of the WC projectile and steel target were taken from the work of Martineau, Prime, and Duffey (2004), while the material properties of the SiC target were taken from the work of Cronin et al. (2004).

The distance between particles was 0.5 mm, and further details of the simulation setup, including dimensions, boundary conditions, and impact velocities, are provided in each individual section.

Z WC projectile

X Y

Steel/SiC target

Figure 4.1: A simple ballistic impact model.

Table 4.1: Properties variables of the projectile and target materials. WC projectile (Martineau, Steel target (Martineau, SiC target (Cronin et al., 2004) Prime, and Duffey, 2004) Prime, and Duffey, 2004) Mass density: 14900 (kg/m3) Mass density: 7840 (kg/m3) Mass density: 3163 (kg/m3) Young’s modulus: 683 (GPa) Young’s modulus: 197 (GPa) Shear modulus: 183 (GPa) Poisson’s ratio: 0.24 Poisson’s ratio: 0.29 Intact normalized strength Yield stress: 3.63 (GPa) Yield stress: 730 (MPa) parameter A: 0.96 Fractured normalized strength parameter B: 0.35 Strength parameter for strain rate dependence C: 0.00 Pressure exponent parameter for fractured strength M: 1.00 Pressure exponent parameter for intact strength N: 0.65 HEL: 14.57 (GPa) PHEL: 5.9 (GPa) Parameter for plastic strain to fracture D1: 0.48 Exponent parameter for plastic strain to fracture D2: 0.48 First pressure coefficient S1: 204.79 (GPa) Second pressure coefficient S2: 0 Third pressure coefficient S3: 0

4.2 Effects of target geometries on ballistic performance

In order to explore the effects of target geometry and to provide guidelines for the choice of target size in the experiments, ten models were built with different diameter and thickness in this section. The diameters and the thicknesses of each target were tabulated in Table 4.2. The cylindrical targets were constructed with a larger radius than thickness to ensure the impact point will be affected by the stress waves reflected from the bottom surface prior to those from the lateral surface of the target, which is the case for real armour. Accordingly, the target with a diameter of 90 mm had a thickness of 40 mm. The projectile was a WC sphere 6 mm in diameter. For the boundary conditions in the simulation models, particles at the lower surface of the target were constrained in both translational and rotational movements in all three dimensions, while the top and side surfaces were free surfaces. Ten ballistic models were tested with 980 and 1500 m/s initial impact velocities along the negative z-axis. The velocities were chosen from the work of Martineau, Prime, and Duffey (2004) to compare with the previous experimental results.

Table 4.2: The diameters and thicknesses of the ten cylinder targets (in mm).

Diameter Thickness Thickness Thickness

90 40

110 40 45 50

130 40 45 50

150 40 45 50

The penetration depth was measured by taking the lowest z coordinate attained by the impacting projectile, as denoted shown in Figure 4.2 by the dashed line.

5.61 mm

WC Steel Plane of symmetry

Figure 4.2: 20 μs after a 980 m/s impact on a steel cylinder target 150 mm in diameter and 50 mm thick.

The penetration depths of the ten ballistic models with a 980 m/s impact are shown in Figure 4.3. The smallest target, 90 mm in diameter and 40 mm thick, had the deepest penetration by the WC projectile. The penetration depth decreased with increasing target diameter and thickness. The largest model, 150 mm in diameter and 50 mm thick, exhibited a penetration depth that was within 3% of the impact results from

Martineau, Prime, and Duffey (2004).

6.25 90 mm in diameter 110 mm in diameter 130 mm in diameter 150 mm in diameter

6.00

5.75 penetration depth (mm) depth penetration

5.50 40 45 50 target thickness (mm)

Figure 4.3: Penetration depths for the ballistic models with a 980 m/s impact.

The penetration depths of the ten ballistic models with a 1500 m/s impact are shown in Figure 4.4. The differences between the results were relatively insignificant, with the penetration depths within 0.22% for the various cases. In other words, the target size had little influence on the ballistic performance for the higher speed impacts. The discrepancy between the simulation and the impact results by Martineau, Prime, and

Duffey (2004) was about 11%.

9.6 90 mm in diameter 110 mm in diameter 130 mm in diameter 150 mm in diameter

9.5 penetration depth (mm) depth penetration

9.4 40 45 50 target thickness (mm)

Figure 4.4: Penetration depths for the ballistic models with a 1500 m/s impact.

In summary, larger targets had less influence from the reflection of stress waves since obviously it takes longer for the stress waves to travel through the target and reflect back from the free surface. The result suggest that using smaller pieces of armour materials will be more influenced from the reflected stress waves, leading to a weaker ballistic performance. As specified in the work of Meyers (1994), the velocity of the longitudinal elastic stress wave propagating in an isotropic material is given by Lamé’s equation with several parameters given by

(4-1).

The equation can be solved by specifying Young’s modulus (E) and Poisson’s ratio (ν), since the properties of homogeneous isotropic elastic materials can be determined by any two elastic moduli (Budiansky, 1976).

(4-2),

and (4-3).

Based on the above, the theoretical velocity of the longitudinal elastic stress wave propagating in the steel target should be

V 5738 m/s (4-4).

For the thickest target in our model (50 mm), the time for the longitudinal elastic stress wave to reflect from the bottom surface of the target and reach the impact surface is

17 (4-5), where L is the target thickness. It took approximately 20 μs for the projectile reaching the deepest penetration to be stopped by the steel targets for a 1500 m/s impact velocity.

Therefore the reflected wave interacted with the penetrating projectile before the projectile was arrested within the target. For a thin target, the time for the longitudinal elastic stress wave to be reflected and interact with the penetrating projectile is shorter than for a thicker target, as shown in Figure 4.5. Hence, in general reflected stress waves had a greater influence on targets with a small thickness.

Effective Stress (a) (Pa) (v-m)

reflecting wave

(b)

reflecting wave

Figure 4.5: Effective stresses in a target 150 mm in diameter and (a) 40 and (b) 50 mm thick at 10 μs after a 1500 m/s impact.

Since the lower end of the target were modeled as a rigid boundary, the reflected stress waves were also compressive waves as for the initial waves from the impact end.

When the two waves meet, the reflected stress waves amplify, increasing the potential for damage to the target. As a result, smaller targets result in high compressive stresses generated internally to the target which ultimately leads to deeper projectile penetration.

Target size effects were less significant with higher velocity impacts. Under higher velocity impacts, the target response is dominated by the compressive stresses from the impact, with rapid projectile penetration into the target. Accordingly, the time available for stress waves to reflect back into the impact zone is less, and therefore the reflected wave has less overall influence on the penetration dynamics.

The largest target, 150 mm in diameter and 50 mm thick, was further tested with a

2550 m/s impact, since it was the closest to the actual experimental plate tested in the 56 work of Martineau, Prime, and Duffey (2004). The steel plate used in these impact experiments is shown in Figure 4.6. As shown in Figure 4.7, the penetration depths of our simulation results are compared with the work of Martineau, Prime, and Duffey (2004).

The higher the impact velocity, the more kinetic energy the projectile carries, and hence the deeper the penetration depth into the target. The numerical simulations represent the experimental results well up to an impact velocity of 1500 m/s, but deviate from the actual impact test results at higher speed impacts. Several reasons might explain the discrepancies between the model and experimental results. Firstly, the strain rate dependence was not applied in our simulation models. Steel exhibits a higher yield strength with higher strain rate (Zener and Hollomon, 1944), and this is not included in the plastic kinematic (PK) material model we used. Note that in the work of Martineau,

Prime, and Duffey (2004), the experimental penetration depth did not increase monotonically with impact velocity, e.g., the penetration depth with a 1810 m/s impact was 8.79 mm while the penetration depth with a 2150 m/s impact was 8.41 mm, and hence disagree with the reasoning above. Although the computational results differ from the experimental penetration depths for high impact velocities, the general experimental trend is reproduced and the simulations are deemed to be a useful tool to explore the effect of different target geometries of composite targets on the overall penetration depth.

Figure 4.6: Steel plate used in impact experiments (Martineau, Prime, and Duffey, 2004).

20 experiment simulation

5 penetration depth (mm) depth penetration

0 1000 1500 2000 2500 impact velocity (m/s)

Figure 4.7: Penetration depths of the experiment and simulation models with different impact velocities.

4.3 Ballistic performance of hard and soft materials

For studying hybrid materials in ballistic protection designs, a different material model from the simple plastic kinematic (PK) model is needed for modeling brittle ceramics, to also include failure and damage effects. In this section, the Johnson-

Holmquist (JH) material model was introduced to represent SiC targets. The modeling results were then compared with steel targets to interpret the effect of different material characteristics.

The geometry of the ballistic impact models used in this section is given below.

The projectile was a WC sphere 6 mm in diameter, by taking the integral only from the simulation projectile used in the previous section. The target was a cylinder 80 mm in diameter and 15 mm thick. The target diameter was determined by taking the average value between the simulation and experiment targets diameters in the previous section.

For the boundary conditions, changes were made to meet the modeling requirements as described in the next chapters. Human tissue beneath a personal armour system represents a relatively soft material as compared with the tough armour material, and therefore it is more appropriate to model the interface between armour and body as a free surface rather than a rigid boundary. In this section, the particles at the outermost side of the cylinder target were constrained in both translational and rotational movements in all three dimensions, leaving the top and bottom surfaces of the target as free surfaces. The clamping boundary condition on the target sides was made to prevent the target drifting with the projectile after the impact. A drifting target with different velocities carried different amount of kinetic energy from the projectile, and made the analysis of the ballistic performance by comparing with the initial impact velocity inaccurate. For other simulation settings, the initial impact velocity of the projectile was 2000 m/s along the negative z-axis. The distance between particles was 0.5 mm, i.e., the projectile was comprised of 228 particles whereas the target contained 150,810 particles in the quarter model.

Lateral views of the ballistic impact results for the two different materials are shown in Figure 4.8. The red particles represented WC projectile, impacting from the top to the bottom surface of the targets along the negative z-axis. The grey particles in Figure

4.8 (a) represent the steel target, and pink particles in Figure 4.8 (b) represent the SiC target. The model with the steel target exhibited ductile fracture in which the fracture generated lumps of steel material. On the other hand, the model with the SiC target showed brittle fracture in which the target was pulverized and a larger area was deformed by the impact. Therefore, the plastic kinematic and Johnson-Holmquist material models are appropriate to capture the behavior of ductile and brittle targets subjected to ballistic impacts, respectively.

(a) Z (b) Z

Steel Y SiC Y

WC Plane of symmetry WC Plane of symmetry

Figure 4.8: 60 μs after a 2000 m/s impact on (a) steel and (b) SiC targets.

Chapter 5: Multilayered configuration simulations

A large number of experimental and computational studies have suggested that combining hard materials (e.g., ceramics) with softer, energy-dissipative materials (e.g., metals) is the most efficient approach for designing high performance armour (Demır et al., 2008; Gonçalves et al., 2004; Lee and Yoo, 2001; Wilkins, 1978). The two layer design, where the hard material is on the outside and the softer material serves as a backing plate, has now become the standard configuration for modern armour systems

(Lee and Yoo, 2001; Arias et al., 2003; Gonçalves et al., 2004; Übeyli, Yıldırım, and

Ögel, 2008). However, other studies have suggested alternative possible configurations for hard and soft materials, such as laminates and adhesive layer structures (Roeder and

Sun, 2001; Zaera et al, 2000). There are, in theory, an infinite number of possible ways to arrange hard and soft materials to design new armour systems. The exploration and optimization of possible new designs must therefore be carefully directed and focused. In this chapter, we constrain this search to configurations made of continuous layers of hard and soft materials.

5.1 Five-layer target design with constant volume

In order to investigate multilayered configurations, the target was divided into five layers, and each layer was modeled as either steel or silicon carbide (SiC) as a metallic or ceramic material, respectively. The total number of combinations of arrangements for hard and soft layers was therefore 2 32, and all possible

62 distributions of hard and soft layers were considered for the optimization study. Since the multilayered targets were not homogeneous, the penetration depth could no longer represent the ballistic performance of the whole target in this analysis. For example, a smaller penetration depth with a low velocity impact will not guarantee a better resistance of the unpenetrated bottom portion of the target with a higher velocity impact. In this section, the performance of each of the 32 models was evaluated by determining the critical impact velocity, defined as the impact velocity for which the projectile broke through the target completely. The ballistic limit velocity (BLV, also referred to as V50) is widely used in ballistic performance evaluation for which the projectile has a 50% chance of perforating the target at normal incidence (Hetherington, 1992).

For the first part of this study the volume of each target was kept constant. Each of the five layers had an identical thickness, and hard and soft layers were assigned regardless of their density. As a result, the target had different weights ranging from the weight of a pure ceramic target (the lightest target) to the weight of a pure metallic target

(the heaviest target). All the other simulation settings, such as the geometry and boundary conditions, were the same as those in section 4.2 for validating the material models. The ballistic impact model and the dimensions are shown in Figure 5.1. The projectile was a

WC sphere 6 mm in diameter, and the target was a cylinder 80 mm in diameter and 15 mm thick. Since the target was 15 mm thick, the thickness of each of the individual five layers was 3 mm. The thickness of each target layer was determined by rounding an integral number from the alumina disks used in the second round of impact experiments

(described in chapter 7). For the boundary conditions, the particles at the outermost side of the cylindrical target were constrained in both translational and rotational movements

63 in all three dimensions, leaving the top and bottom surfaces of the target as free surfaces.

For each target, the ballistic performance was assessed by determining which impact velocity would result in thorough penetration of the target. Since the impact velocity was an initial condition, the calculations were carried out by impacting each target with six different initial impact velocities (500, 1000, 1500, 2000, 2500, and 3000 m/s). The lowest impact velocity (500 m/s) was chosen since the weakest target (whole SiC layers) could only survive a 500 m/s impact and failed with a 1000 m/s impact. The highest impact velocity (3000 m/s) was chosen since even the best target failed with a 3000 m/s impact.

projectile

Vo target

X Y

Figure 5.1: Quarter of a five-layer ballistic impact model.

In the following discussions, the [C] represents a SiC ceramic layer and [M] represents a steel metallic layer. A sequence of these letters is then used to describe the

64 arrangement of the layers, from the top surface to the bottom surface. For example, a target with one ceramic layer on the impact side (top side) and with 4 metallic layers behind it denoted [CMMMM].

The results of this study are shown in Figure 5.2. The velocities indicate the impact velocity for which the target survived without being penetrated completely. The grey layers in Figure 5.2 represent a steel target and pink layers represent a SiC target. All designs survived the 500 m/s. impact, except the first configuration consisting of only

SiC layers. As the initial velocity was increased by increments of 500 m/s, fewer and fewer designs survived. Eventually, the best design was identified and consisted of two hard SiC layers on the top and three ductile steel layers at the bottom of the target, which survived a 2500 m/s impact. All 32 models failed when subjected to a 3000 m/s impact.

The results were consistent with previous studies by many researchers (Lee and Yoo,

2001; Arias et al., 2003; Gonçalves et al., 2004; Übeyli, Yıldırım, and Ögel, 2008), in that an outer ceramic layer with ductile backing layer would be the best configuration for ballistic armour made of continuous layers.

Figure 5.2: Five-layer targets performance with constant volume.

There were seven models which survived a 2000 m/s impact, but failed with a

2500 m/s impact. They were the [CCCMM], [CCMCC], [CCMMC], [CMCMM],

[CMMMM], [MCCMM], and [MCMMM] configurations. To differentiate the performance of the seven remaining models, an initial impact velocity of 2150 m/s was applied to the seven models. As a result, the projectile fragments were stopped by the target in three out of the seven models. The three surviving models were [CCMMM],

[CCCMM], and [MCMMM], all which had SiC ceramic layers near the impact surface,

66 and at least two steel layers at the bottom.

To further differentiate the best three models in terms of ballistic performance, the residual kinetic energy of the projectile was used as an additional indicator of ballistic performance. The residual kinetic energy is widely used in evaluating ballistic performance with diverse target structures, especially for thin plate perforation (Krishnan et al., 2010; Schwer, 2006; Straßburger et al., 2001). The total kinetic energy of the projectile over time was simply obtained by summing the kinetic energy of each particle associated with the projectile. Less kinetic energy remaining in the projectile indicated more energy was absorbed by the target, and hence represented a better ballistic performance. As shown in Figure 5.3, which compares the decay of the projectile kinetic energy with time, the best design corresponded to the [CCMMM] model, the 2nd best design was [CCCMM], and the 3rd best design was [CMMMM]. The [MCMMM] model could not be completed because of numerical instabilities, which caused some particles to reach infinite velocity. Therefore, only the projectile kinetic energy until 20 µs after the impact is shown in Figure 5.3. With a 2500 m/s impact, even though the projectile did not reach the bottom of the [MCMMM] target, the stress waves already fractured the bottom layer at 20 μs after impact. Therefore, the [MCMMM] model was deemed to have failed with a 2500 m/s impact.

3 CMMMM CCMMM CCCMM MCMMM

1 log (kinetic energy (J)) (kinetic log

0 01020304050 time (s)

Figure 5.3: Kinetic energy of the projectiles over time after a 2500 m/s impact for the

configurations with the best performance.

In summary, hard ceramic materials lead to good ballistic performance when they are placed on the impact side of the model. As shown in Figure 5.4, hard ceramic front layers deform and decelerate the projectile more effectively compared to targets with soft metallic layers at the impact surface. Ductile backing materials however are good for absorbing the remaining kinetic energy from the deformed projectile, and stopping it before it penetrates through the target completely. The consecutive ceramic-metal combination is therefore the best design within the layered structures explored in this

68 section.

(a) t=5 μs t=10 μs t=15 μs t=20 μs Z impact surface Y Plane of symmetry

(b) t=5 μs t=10 μs t=15 μs t=20 μs

Figure 5.4: Sequential contour of a WC sphere projectile with a 2000 m/s impact on a (a) [CCMMM] and (b) [MMMMM] target.

5.2 Confining the ceramic phase

Confinement of the ceramic at the impact surface has been found to be beneficial for armour performance (Ghiorse et al., 2003), and confinement is one of the main considerations for design optimization. However, the performances of our [CCMMM] and [MCCMM] models suggested that confining the front face of the ceramic does not improve performance. Further investigation on this issue will now be presented.

Figure 5.5 contains a sequence of images showing effective stresses in the

[CCMMM] target with a 2500 m/s impact indicating that the projectile impact induced a lateral stress distribution in the outer layers, leading to effective energy dissipation in the early stage of impact. The top ceramic layer fragmented the projectile, and the backing metallic layer absorbed the residual kinetic energy from the projectile.

t=5 μs t=10 μs Effective Stress (Pa) (v-m)

t=20 μs t=60 μs

Figure 5.5: Sequential effective stresses in the [CCMMM] model with a 2500 m/s impact.

We also re-examined the [MCCMM] target, where the ceramic layers were buried under a front metallic layer, potentially confining fragments upon pulverization. Figure

5.6 shows that the front layer proved to be very effective at confining the ceramic fragments. However, the top metallic layer in the [MCCMM] target could not effectively decelerate the projectile, and the ceramic lower layers could not efficiently absorb the kinetic energy of the projectile. In the latter stage of the impact, the bottom backing layer already deformed significantly, and could not stop the projectile. Eventually, the projectile penetrated the [MCCMM] target completely with a 2500 m/s impact. While the top steel layer prevented the pulverized ceramic layers from being dispersed, the insufficient backing layers led to an overall worse performance.

t=5 μs t=10 μs Effective Stress (Pa) (v-m)

t=20 μs t=60 μs

Figure 5.6: Sequential effective stresses in the [MCCMM] model with a 2500 m/s impact.

To further refine our study of the effect of confinement in our ballistic system, half of the top SiC layer in the [CCMMM] target was replaced by steel and specified as

[MCCMMM]. As shown in Figure 5.7 (a), even though the top half layer of steel confined the pulverized ceramic fragments, the thinner SiC layers could not provide enough resistance to the projectile with 2500 m/s impact and eventually led to complete penetration. After adding back the half layer of SiC in the middle of the target, i.e., moving a half layer of steel from the bottom to the top of the [CCMMM] target, the

performance of the [ MCC MMM] target was still worse than the [CCMMM] one with a

2500 m/s impact. As shown in Figure 5.7 (b), thinner steel layers at the bottom could not absorb all the remaining kinetic energy of the projectile and led to complete penetration.

(a) Z (b)

Y SiC

Steel Plane of symmetry Plane of symmetry WC

Figure 5.7: 100 μs after a 2500 m/s impact on the (a) [MCCMMM] and (b)

[MCCMMM] targets.

The sequential results of effective stresses in the [ M CCMMM] and

[MCCMMM] models are shown in Figure 5.8 and 5.9. The energy dissipation was distributed over a wider area at all stages in the [MCCMMM] model. However, since the thicker ceramic layer could more efficiently absorb the kinetic energy from the projectile before it reached to the ductile backing layer, the ballistic performance in the

[MCCMMM] model was superior to that of the [MCCMMM] model.

t=5 μs t=10 μs Effective Stress (Pa) (v-m)

t=20 μs t=60 μs

Figure 5.8: Sequential effective stresses in the [MCCMMM] model with a 2500 m/s impact.

t=5 μs t=10 μs Effective Stress (Pa) (v-m)

t=20 μs t=60 μs

Figure 5.9: Sequential effective stresses in the [MCCMMM] model with a 2500 m/s impact.

There were limitations on the thinnest replacement of the top ceramic layer by a steel layer due to the finite particle distance. Since the distance between particles was fixed at 0.5 mm and each layer of the target was 3 mm thick, the thinnest replacement

. was one sixth of a layer: . As a result shown in Figure 5.10 (a), one thin row of steel particles provided little confinement to the pulverized ceramic fragments and led to

overall less impact resistance in the [ M CCMMM] target. As shown in Figure 5.10 (b), adding back one row of SiC particles in the middle of the target still could not provide competitive performance with the [CCMMM] target.

(a) Z (b)

Y SiC

Steel Plane of symmetry WC Plane of symmetry

Figure 5.10: 100 μs after a 2500 m/s impact on the (a) [MCCMMM] and (b)

[MCCMMM] targets.

The decay histories of the projectile kinetic energies in all six models are shown in Figure 5.11. Both the [MCCMMM] and [MCCMMM] targets had apparently less kinetic energy absorption and worse performances. Accordingly, it was crucial to have a sufficient thickness of hard ceramic, two layers in total, close to the impact surface. Since

there were better confinement effects with the [ MCC MMM] target compared with the

[MCCMMM] one, the projectile kinetic energy absorption was slightly higher and led to better resistant performance of the [MCCMMM] target. However, overall, the best design was still the [CCMMM] target without confinement from the front.

3 CCMMM MCCMM 1 1 2 M 2 CCMMM 1 1 2 MCC 2 MMM 1 5 6 M 6 CCMMM 1 5 2 6 MCC 6 MMM

1 log (kinetic energy (J)) energy (kinetic log

0 0 20 40 60 80 100 time (s)

Figure 5.11: Kinetic energy of the projectiles over time after a 2500 m/s impact.

5.3 Effect of steel strength on optimum design with constant volume

The two-layer hard-soft target was found to be the best design in the previous sections, based on a specific combination of material properties. There are in reality numerous combinations of different ceramic and backing materials to construct armour systems. In this section, the effect of the properties of the metal layers will be investigated by arbitrarily reducing the values of the mass density, Young’s modulus, and yield stress by a factor of 2, while keeping all the other modeling parameters identical to the previous simulations. For the metallic target layers, the mass density was then 77 assigned a value of 3920 kg/m3, the Young’s modulus was 98.5 GPa, and the yield stress was 365 MPa. By doing so, effects of material properties were studied on changing the armour performance rankings of layers arrangements.

Six different initial impact velocities (500, 1000, 1500, 1750, 2000, and 2500 m/s) were applied to the 32 models. Since all models failed with an impact velocity of 2500 m/s, the higher impact velocity of 3000 m/s tested previously was not evaluated. In addition, since many models survived a 1500 m/s impact but failed at 2000 m/s, a 1750 m/s impact was introduced to further differentiate the performance.

The modeling results are shown in Figure 5.12, where the yellow layers represented metallic layers and pink layers represented SiC layers. In general, the performances were inferior with reduced (by a factor of 2) steel properties compared to the original designs in section 5.1. The [CCMMM] model was, however, still the design with the best performance among all the 32 arrangements. Three other targets survived a

1750 m/s impact but failed at 2000 m/s, in particular the [CCCMM], [CMCMM], and

[MCCMM] models. Except for the consecutive two material layouts such as the

[CCMMM] and [CCCMM] models, sandwich structures such as [CMCMM] and

[MCCMM] models also performed well with weaker metallic layers.

Figure 5.12: Five-layer targets performance with half strength of steel and constant volume.

The time histories of the projectile kinetic energies for the three models that survived a 1750 m/s impact other than the highest performing [CCMMM] model, i.e., the

[CCCMM], [CMCMM], and [MCCMM] models, are shown in Figure 5.13. By comparing the residual kinetic energy in the projectile, we note that after the top performing [CCMMM] model, the 2nd best design was the [CCCMM] target, and the 3rd

79 best design was the [MCCMM] target among the 32 volume constant models with reduced steel material properties.

3.0 CCCMM CMCMM 2.5 MCCMM

2.0

1.5

1.0

0.5 log (kinetic energy (J)) energy (kinetic log

0.0

-0.5 0 20 40 60 80 100 time (s)

Figure 5.13: Kinetic energy of the projectiles over time after a 2000 m/s impact.

In summary, changing the material properties of the target may lead to a change in the ranking of the best layered arrangements for the target design. Both consecutive two material configurations, i.e., outer ceramic layers with ductile backing layers, and sandwich structures, with another soft layer on the impact surface to confine the hard ceramic layers, are both good options when considering the design of ballistic protection systems. 80

5.4 Five-layer target design with constant mass

As low weight has always been one of the main concerns in armour design

(United States National Research Council, 2011), the objective of the work described in this section is to find the optimum distribution of hard and soft layers while maintaining a constant overall mass. All 32 possible sequences of the five layers were again considered, but the thickness of each layer was adjusted to keep the total mass constant. Since the density of steel is approximately two and half times the density of SiC, the thickness of a

steel layer was 0.4 times that of a SiC layer. Accordingly, a single SiC target layer . was 2.5 mm thick with 25,135 particles and a single steel layer was 1 mm thick with

10,054 particles in a quarter model. The other simulation parameters were kept the same for all the 32 five-layer models.

The results are shown in Figure 5.14, where the grey layers represent steel and the pink layers represent SiC. Since steel layers were much thinner in the constant weight designs, the best design among all the 32 targets was with only one layer of hard SiC on the top of the target close to the impact surface and four layers of ductile steel at the bottom. The [CMMMM] target was the only design to survive a 1200 m/s impact. All models failed with a 1500 m/s impact.

Figure 5.14: Five-layer targets performance with constant mass.

There were four models that survived a 1000 m/s impact, but failed with a 1200 m/s impact. They were the [CCMMC], [CCMMM], [CMCCC], and [CMMMC] models.

To differentiate the performance between the models that survived, the kinetic energy absorption efficiency was once again used as the indicator for evaluating the relative performance of the four targets with a 1200 m/s impact failure. By comparing the

82 projectile kinetic energy decay histories shown in Figure 5.15, it is apparent that the 2nd best design was the [CCMMM] model, and the 3rd best design was [CMCCC] model.

3 CCMMC CCMMM CMCCC CMMMC

1 log (kinetic energy (J)) energy (kinetic log

0 0 20 40 60 80 100 time (s)

Figure 5.15: Kinetic energy of the projectiles over time after a 1200 m/s impact.

The results were consistent with the concept of a two-layer design for optimum armour performance (Lee and Yoo, 2001; Arias et al., 2003; Gonçalves et al., 2004;

Übeyli, Yıldırım, and Ögel, 2008). Since the steel layers in this section were much thinner, the best design was the [CMMMM] target instead of the [CCMMM] target which provided sufficient backing material to absorb the remaining projectile kinetic energy.

The [CCMMM] target was still a good design, and had the 2nd best performance among all the 32 constant-mass five-layer designs. In the constant-mass designs, placing steel

83 layers between the SiC ceramic layers to generate a sandwich structure, such as in the case of the [CMCCC], [CCMMC], and [CMMMC] targets, also resulted in good ballistic performance.

5.5 Effects of steel strength on optimum designs with constant mass

Similar to the calculations in section 5.3, the effect of reducing the density,

Young’s modulus, and yield stress of the steel by a factor of 2 was considered, but this time with the constraint of a constant total mass. To maintain the total mass constant, the thicknesses of the metallic layers were adjusted. Since the assumed density was half that of steel, the thickness of the steel layers was adjusted to be twice that considered in the previous section. Accordingly, a single metallic layer was 2 mm thick with 20,108 particles in a quarter model. The other simulation parameters were kept the same for all the 32 five-layer models.

The results are shown in Figure 5.16, where the yellow layers represented the metallic material and the pink layers represented SiC. The best design was the

[CCMMM] model, which survived a 1400 m/s impact. The 2nd best design was

[CCMMC] which survived a 1300 m/s impact. All models failed with a 1500 m/s impact.

The two-layer and sandwich-structure targets in general were the best performers, and could be used as baseline configurations for further optimization in future armour designs.

Figure 5.16: Five-layer targets performance with half strength of steel and constant mass.

In general, models with reduced metallic strength had better performances than the designs with standard steel with constant mass. The impact velocities for which the projectile penetrated completely through the targets, were commonly higher in the models with reduced metallic strength than for the models with standard steel properties as discussed in the previous section. As the steel layers with half metallic strength were

85 thicker due to the reduced density, the impact results indicated that the thickness was more important than the material strength for backing layers with constant mass. The only two exceptions, which had a worse performance, were the [CMCCC] and

[CMMMM] models.

To conclude the studies in this chapter, the best design of the constant-volume five-layer arrangements was the [CCMMM] model while the best design of the constant- mass five-layer arrangements was the [CMMMM] model. Both results confirmed the work conclusions of many researchers (Lee and Yoo, 2001; Arias et al., 2003; Gonçalves et al., 2004; Übeyli, Yıldırım, and Ögel, 2008) that a hard-soft consecutive two material design is one of the best armour configurations. The benefits of confining the ceramic material by adding a layer of ductile material at the impact surface (Ghiorse et al., 2003) were not apparent in the SPH models while keeping the target mass constant and reducing the thickness of the backing layer. For reducing selected steel material properties, including the mass density, Young’s modulus, and yield stress by a factor of 2, the optimum design was still the [CCMMM] model. However, other five-layer arrangements were ranked in a different order for the ballistic performance. For the target design, materials arrangements and mechanical properties have to be considered together as a combination to achieve high performance in ballistic protection systems.

Chapter 6: Ballis tic simulations of steel targets containing finite inclusions

Hybrid material design is based on combining different materials in a predetermined configuration and scale to serve a specific engineering purpose (Kromm et al., 2002). The previous chapter focused on configurations consisting of layers of hard

(SiC) and softer (steel) materials. In this chapter other configurations are considered, focusing on SiC inclusions in a steel matrix while maintaining the overall mass constant.

In hybrid design, there are effectively an infinite number of different configurations, and of course it is not possible to study them all. Rather, we focus on using the SPH method to investigate the performance of seven types of hybrid ballistic impact models inspired from previous studies and patents.

Following the same framework as in the previous chapters, the projectile was a tungsten carbide (WC) sphere 6 mm in diameter, and the targets were cylinders 80 mm in diameter for all models. Since the density of the steel matrix is 2.5 times of the density of

SiC inclusions, the thicknesses of targets were adjusted to keep the total mass (or areal density) of the targets the same for all models. The WC projectile and steel matrices were modeled with the plastic kinematic material model, and the SiC inclusions were modeled with the Johnson-Holmquist model. For the boundary conditions, particles at the outermost side of the cylinder target were constrained in both translational and rotational movements in all three dimensions, leaving the top and bottom surfaces of the target as free surfaces. The distance between particles was 0.5 mm and two symmetry planes (x-z and y-z) were used for building quarter models. Since the differences of ballistic

87 performance between most of the models in this chapter were small, it would take enormous time and computation resources to obtain the critical impact velocity for each model. Consequently, the residual kinetic energy of the projectile was used as the indicator to evaluate ballistic performance for different target designs.

6.1 Steel targets with SiC disks

In the first method of incorporating ceramic inclusions in a metallic matrix, SiC cylinder disks were embedded at the top surface of the steel target. The design was chosen to replace continuous layers with the idea of confining the damage of the ceramic material to a single inclusion, to possibly improve the overall performance and impart the armour with multi-hit capabilities. Two new models were built based on the best design in section 5.3, i.e., the [CMMMM] model among the constant-mass five-layer targets.

The thickness of the SiC disks in the two new models was as 2.5 mm, the same as in the original [CMMMM] target. Different diameters for the SiC phase were chosen, from 80 mm in the original continuous layer down to 64 and 32 mm. The mass density of steel is about 2.5 times that of SiC, and hence to maintain the total target mass, the overall thickness of the target was decreased as the diameter of the SiC disk was decreased, from

6.5 mm to 6 and 5.5 mm for the 3 SiC disk diameters considered. The geometries and masses of the two new models, together with the [CMMMM] and [MMMMM] models, are tabulated in Table 6.1. The comparison with the baseline [MMMMM] model is useful to demonstrate the benefits of adding hard ceramics to ballistic performance. The two new models were tested with a 1200 m/s impact.

Table 6.1: Geometries and masses of four models.

Model SiC diameter Target thickness Target mass

Z 80 mm 6.5 mm 62.21 g

Vo WC SiC

X Y

Steel

64 mm 6 mm 61.90 g Z

Vo WC SiC

X Y

Steel

42 mm 5.5 mm 62.43 g Z WC

Vo SiC X Y Steel

N/A 5 mm 61.33 g Z Vo WC Steel

X Y

Figure 6.1 shows the kinetic energy of the projectile over time with an initial impact velocity of 1200 m/s for the four configurations described in Table 6.1. The best configuration (i.e., with the smallest residual kinetic energy) was the [CMMMM] model with a continuous layer of SiC as the front layer. As the diameter of the SiC disk was decreased, the performance also decreased, and converged towards an all-metal design

(the [MMMMM] model), which is consistent with the fact that for smaller inclusions, the thickness of the backing steel layer was also smaller. Figure 6.2 shows that the

[CMMMM] model was the only one which could survive a 1200 m/s impact, and the others failed with complete penetration.

200 MMMMM, 61.33 g CMMMM, 62.21 g 64 mm, 61.90 g 42 mm, 62.43 g 150

100 kinetic energy (J) energy kinetic 50

0 0 10203040 time (s)

Figure 6.1: Kinetic energy of the projectiles over time after a 1200 m/s impact.

(a) (b) Z

6.5 mm SiC Y 5 mm

Steel WC

6 mm 5.5 mm

Figure 6.2: 30 μs after a 1200 m/s impact on a quarter (a) [CMMMM] (b) [MMMMM] (c) 64 mm in diameter SiC disk and (d) 42 mm in diameter SiC disk targets.

6.2 Steel targets with hexagonal SiC plates

In this section, hexagonal plates were introduced to replace the homogeneous ceramic front layer considered in the last section. Previous studies have shown that pores inside hard materials can prevent crack propagation (Hyun et al., 2004) and crack propagation is one of the most important fracture mechanisms for ceramics (Gandhi and

Ashby, 1979). In this section, the gaps between the hexagonal SiC plates were employed effectively as pores within the ceramic to limit crack propagation and pulverization area, thereby possibly leading to better ballistic performance.

Four models with SiC hexagonal plates were built based on the constant-mass

[CMMMM] model. The hexagonal plates were 2.5 mm thick. The vertical views of the four quarter models are shown in Figure 6.3, all with hexagonal packing. In Figures 6.3

(a) and (b), the diameter of the hexagonal plates is 16 mm. In Figures 6.3 (c) and (d), the diameter is 8 mm. In Figure 6.3 (a) and (c), the distance between hexagonal plates is 1 mm. In Figures 6.3 (b) and (d), the distance is 0.5 mm. Since the amount of ceramic material removed in the interstitial area between the hexagonal plates was relatively small, the thicknesses of both the SiC and steel layers were not adjusted.

(a) (b)

Steel

SiC Y

WC X

Figure 6.3: Quarter models with SiC hexagonal plates (a) 16 mm and 1 mm (b) 16 mm and 0.5 mm (c) 8 mm and 1 mm and (d) 8 mm and 0.5 mm in the diameter and plates distance.

Subject to a 1200 m/s impact, the differences in penetration behavior between the different configurations were fairly small, not only among the four models with hexagonal plates, but also compared with the [CMMMM] model. Accordingly, a higher impact velocity of 1500 m/s was tested with all the models. The projectile kinetic 93 energies over time after a 1500 m/s impact are shown in Figure 6.4. Even though the differences were still small, none of the models with SiC hexagonal plates demonstrated a better resisting performance compared to the [CMMMM] model with a homogeneous ceramic front layer. The performance of the model with 16 mm diameter hexagonal plates, and a 0.5 mm spacing between the plates, was found to be the best among the four models with hexagonal plates. Increasing the inter-plate distance to 1 mm degraded slightly the performance of the model with 16 mm diameter hexagonal plates, which was the 2nd best design. Contrary to the models with 16 mm diameter hexagonal plates, the performances for models with 8 mm diameter hexagonal plates were improved with larger inter-plate distance. Overall, the better results with larger hexagonal plates demonstrated the importance of a continuous ceramic front layer for superior armour performance. The models showed that segmenting the ceramic front to confine damage was not beneficial to the ballistic system.

100 CMMMM, 62.21 g 16/1 mm, 60.21 g 16/0.5 mm, 60.53 g 8/1 mm, 59.35 g 8/0.5 mm, 60.12 g

50 kinetic energy (J) energy kinetic

0 0 10203040 time (s)

Figure 6.4: Kinetic energy of the projectiles over time after a 1500 m/s impact.

6.3 Steel targets with spherical SiC inclusions

In the work of Meijer, Ellyin, and Xia (2000), spherical inclusions were found to lead to a more homogeneous plastic strain distribution at the interfaces between the matrix and inclusions, as compared with cubic inclusions. The improved distribution of plastic strain indicated better energy dissipation and a higher yield stress in the target during an impact (Arias et al., 2003). To study the effect of the shape of the ceramic inclusions on the armour performance, SiC spheres were introduced in our models. Four models were built with one layer of hexagonal close-packed SiC spheres embedded in a 95 steel target close to the impact surface, i.e., the distance between the SiC spheres and the impact surface was zero. The distance between the SiC spheres was 0.5 mm. Vertical views of the four quarter models are shown in Figure 6.5. In the models of figures 6.5 (a) and (b), the targets contained SiC spheres 6 mm in diameter. The model of figure 6.5 (a) was impacted exactly at the location of a sphere, while the model of figure 6.5 (b) was impacted between two spheres. In Figure 6.5s (c) and (d), the targets contained SiC spheres 3 mm in diameter, and were impacted exactly on a SiC sphere and between spheres, respectively. Since only particles on the top layer of the targets are shown, only the central parts of the spherical inclusions are shown in Figure 6.5. In addition, the WC projectiles impacted on the left bottom corner in the models, which are not shown in

Figure 6.5.

(a) (b) SiC

Steel

Figure 6.5: Quarter-models with SiC spherical iinclusions. The impact occurred at the center of the target (lower left corner of the quarter model) (a) 6 mm wide and impact on a sphere (b) 6 mm wide and impact between spheres (c) 3 mm wide and impact on a sphere (d) 3 mm wide and impact between spheres.

To keep the mass/areal density constant, the thicknesses of the steel matrices were adjusted in the four models. Targets with SiC spheres 6 mm in diameter were 6.5 mm thick and targets with SiC spheres 3 mm in diameter were 6 mm thick. Since the distance

97 between particles in the SPH models was fixed at 0.5 mm, one whole layer of steel particles could only to or removed from the target, i.e., ±0.5 mm thickness of the target.

Consequently, the masses of the four different targets configurations with SiC spheres were slightly different. The other simulation settings were kept the same, and the four models were tested with a 1200 m/s impact.

The energy absorption efficiency was again used as the indicator for evaluating the designs. As shown in Figure 6.6, the results were also compared with the [CMMMM] and [MMMMM] models. None of the models with SiC sphere inclusions had better resisting performance compared with the [CMMMM] model. The addition of small SiC spheres 3 mm in diameter enhanced the ballistic performance compared with the

[MMMMM] model. On the other hand, the configuration with SiC spheres 6 mm in diameter, even with slightly more weight, exhibited a weaker performance compared with the [MMMMM] model. The large size of the SiC spheres in the models with 6 mm spheres contributed to a higher efficiency in absorbing kinetic energy from the projectile in the early stage of impact. However, the structure of the backing layer was destroyed by the large ceramic inclusions, which ultimately led to worse ballistic performance. The differences between the models with different impact locations were relatively insignificant. In general, targets with an impact between two spheres had a slightly better performance than for the case of impact directly on a spherical inclusion.

200 MMMMM, 61.33 g CMMMM, 62.21 g 6 mm, centered, 59.98 g 6 mm, intermediate, 61.09 g 150 3 mm, centered, 64.64 g 3 mm, intermediate, 64.60 g

100 kinetic energy (J) energy kinetic 50

0 0 10203040 time (s)

Figure 6.6: Kinetic energy of the projectiles over time after a 1200 m/s impact.

Figures 6.7 and 6.8 show the sequential effective stresses in the models with SiC spherical inclusions. Even though generally the kinetic energy of the projectile was dissipated over a larger area across the whole target in the models with SiC spheres 6 mm in diameter, the high stress area over 7x108 Pa was larger in the models with 3 mm diameter spheres. In addition, more material detached and dispersed away from both the top and bottom target surfaces in the models with SiC 6 mm diameter spheres than for the

3 mm diameter spheres. Based on the above, the models containing SiC spheres 3 mm in diameter were better able to defeat the projectile and therefore demonstrated better ballistic performances. Configurations with finer embedded inclusions therefore appear to be more beneficial for high-velocity impact models. 99

t=5 μs t=10 μs Effective Stress (Pa) (v-m)

t=15 μs t=20 μs

Figure 6.7: Sequential effective stresses in the steel target with a 1200 m/s impact on a 3 mm in diameter SiC sphere.

t=5 μs t=10 μs Effective Stress (Pa) (v-m)

t=15 μs t=20 μs

Figure 6.8: Sequential effective stresses in the steel target with a 1200 m/s impact on a 6 mm in diameter SiC sphere.

100

6.4 Steel targets with chains of spherical SiC inclusions

The studies in this section were inspired by the work of Daraio et al. (2006), in which the propagation of solitary waves in chains of spherical particles was observed, and the sound speed was found to be tunable by changing the static compressive force.

Accordingly, cubic packed SiC spheres were introduced to see if the configuration with spherical chains would improve the ballistic performance. Two models were built with a

1200 m/s impact, one with the impact directly on a SiC sphere and the other with the impact location between four spheres. Figure 6.9 shows vertical views of the two models with chains of spherical SiC inclusions. Since the SiC spheres were close packed, the distance between spheres was zero, and only the central parts of the spheres on the top layer of the targets is shown in Figure 6.9. The WC projectiles impacted on the left bottom corner in the models, which are not shown in Figure 6.9.

(a) (b) SiC

Steel

Figure 6.9: Quarter models with cubic packing spherical SiC inclusions with an impact (a) right on a sphere and (b) between four spheres.

101

The lateral view of a quarter model with an impact exactly on a sphere is shown in Figure 6.10. Three layers as chains of SiC spheres were embedded in the steel target.

The cylindrical steel target was fixed at 80 mm in diameter, but increased to a thickness of 9 mm, as the SiC spheres were 3 mm in diameter each. Consequently, the targets weighed more than the constant-mass targets in section 5.3.

WC Steel SiC Vo 3 mm Y

9 mm Plane of symmetry

Figure 6.10: A quarter model with chains of SiC sphere inclusions.

As the result, the design with chains of SiC sphere inclusions was not superior to the best constant-mass [CMMMM] model. Even with a higher energy absorption efficiency in the early stage of the impact, the models with chains of SiC spheres were completely penetrated by a 1200 m/s impact, due to the lack of ductile backing material to fully stop the projectile. After the impact, a considerable amount material was detached and scattered from the bottom of the targets.

The projectile kinetic energies for the [MMMMM], [CMMMM] models, and the two models with chains of SiC spheres are shown in Figure 6.11. Compared with the

[MMMMM] model, the energy absorption efficiency was higher in the models with chains of SiC spheres. However, the target with embedded chains of SiC spheres weighed

102 more than the constant-mass targets. Therefore, we could not conclude the models with chains of SiC spheres had better performance than the [MMMMM] target. The model had slightly better performance with an impact between four spheres compared to the model with an impact directly on a SiC sphere.

200 MMMMM, 61.33 g CMMMM, 62.21 g Centered, 73.01 g Intermediate, 73.37 g 150

100 kinetic energy (J) energy kinetic 50

0 0 10203040 time (s)

Figure 6.11: Kinetic energy of the projectiles over time after a 1200 m/s impact.

In summary, the ballistic impact event was over within a hundred microseconds, and was too fast for the propagation of solitary waves to influence the penetration dynamics. The design with chains of spherical inclusions was not superior to the one with a hard front layer and ductile backing layer. 103

6.5 Steel targets with chains of hollow of filled spherical SiC inclusions

The numerical studies discussed in this section were inspired by the work of Gu and Nesterenko (2007), and Ngo et al. (2013). In the work of Gu and Nesterenko (2007), powder-filled voids and rods were used in the ballistic target to reflect and stop a long rod projectile. In the work of Ngo et al. (2013), chains of hollow spheres were excited by an impulse for studying the highly nonlinear solitary waves and tunable dynamic response between the spheres. Accordingly, three models were built with hollow SiC spheres to study the effect of weight and properties of the spherical inclusions on the whole target performance. The three new models were built based on the model with solid chains of

SiC spheres in the previous section. The lateral view of the structure with hollow inclusions is shown in Figure 6.12. Since differences in impact results were small with different impact positions, as shown in section 6.3 and 6.4, all three models were tested with the projectile impact directly on one of the spherical inclusions in this section. The ratio of the inner to outer radius of the spheres was 0.5, i.e., the inner sphere diameter was

1.5 mm. In two of the models, the hollow central region of the SiC spheres was filled with B4C and steel, respectively. B4C is not only lighter but also harder than SiC, while steel is heavier but more ductile than SiC. B4C fillings were chosen to amplify the ceramic properties while steel fillings were chosen to amplify the metallic properties of chains of SiC. The Johnson-Holmquist material model was applied to B4C, and the property variables of the ceramics (Cronin et al., 2004) are tabulated in Table 6.2. The models were tested with a 1200 m/s impact.

104

WC SiC B4C/steel Steel Vo 1.5 mm 3 mm Y

9 mm Plane of symmetry

Figure 6.12: A quarter model with chains of hollow SiC sphere inclusions filled with

either B4C or steel.

105

Table 6.2: Properties variables of the ceramic inclusions.

JH variables SiC B4C

Mass density (kg/m3) 3163 2510

Shear modulus (GPa) 183 197

A 0.96 0.927

B 0.35 0.7

C 0.00 0.05

M 1.00 0.85

N 0.65 0.67

HEL (GPa) 14.57 19

PHEL (GPa) 5.9 8.71

D1 0.48 0.001

D2 0.48 0.5

S1 (GPa) 204.79 233

S2 (GPa) 0 -593

S3 (GPa) 0 2800

The ballistic performance of models with chains of hollow SiC spheres fell between the [MMMMM] and the best constant-mass [CMMMM] model. All the models with chains of hollow SiC spheres failed with a 1200 m/s impact, and a considerable amount of material detached from the bottom of the targets. 106

In Figure 6.13, the projectile kinetic energies of the three models with chains of hollow or filled SiC spheres are compared with the [MMMMM] and [CMMMM] models, and the model in the previous section with solid SiC spheres with an impact right on a sphere. All three models with hollow/filled SiC spheres had lower energy absorption efficiency, even with more mass compared to the [CMMMM] model. Differences between the two models with and without filling of B4C in the hollow SiC spheres were insignificant. The addition of B4C contributed little to the ballistic performance. The model with the SiC spheres filled with steel had the highest energy absorption efficiency, but it also had the highest mass among the four models with SiC sphere inclusions. Here the target mass was the key to the final ballistic performance, compared with other material properties. Again, we could not conclude definitively whether or not the models with chains of hollow/filled SiC spheres had a better ballistic performance than the

[MMMMM] target, since the total mass for the models with spherical inclusions was greater.

107

200 MMMMM, 61.33 g CMMMM, 62.21 g hollow, 70.29 g B4C, 71.47 g 150 SiC, 73.01 g steel, 73.98 g

100 kinetic energy (J) energy kinetic 50

0 0 10203040 time (s)

Figure 6.13: Kinetic energy of the projectiles over time after a 1200 m/s impact.

The effective stresses on the steel matrices were similar in the four models with chains of SiC spheres. As expected, the effective stresses on the steel matrix could only attain the yield stress, specified as 730 MPa. The effective stresses were larger near the top and bottom surfaces than in the middle of the targets in all four models. We observed stress concentrations on the interfaces between the matrix and outermost spherical inclusions. As shown in Figure 6.14 and 6.15, a larger area was affected by highly concentrated effective stresses adjacent to the impact site in the matrix for the hollow SiC spheres than in the matrix containing SiC spheres filled with steel. More steel was ejected from the top surface of the matrix with hollow SiC spheres, as compared to the other three matrices with SiC spheres. 108

t=5 μs t=15 μs Effective Stress Steel (Pa) (v-m)

t=25 μs t=40 μs

Figure 6.14: Sequential effective stresses on the steel matrix in the model with hollow SiC sphere inclusions with a 1200 m/s impact.

109

t=5 μs t=15 μs

Steel Effective Stress (Pa) (v-m)

t=25 μs t=40 μs

Figure 6.15: Sequential effective stresses on the steel matrix in the model with spherical steel-filled SiC inclusions with a 1200 m/s impact.

In the early stage of the impact, the effective stresses were larger near the impact site, towards outer fringe, and bottom surface of the target on SiC inclusions in all four models with SiC spheres. As shown in Figure 6.16, the model with hollow SiC spheres had the most fluctuations of stress waves reflecting across the SiC inclusions, compared with the other three models with filled SiC spheres.

110

t=5 μs t=15 μs

Effective Stress SiC (Pa) (v-m)

t=25 μs t=40 μs

Figure 6.16 Sequential effective stresses on the SiC spheres in the model with hollow SiC sphere inclusions with a 1200 m/s impact.

111

t=5 μs t=15 μs

Effective Stress SiC (Pa) (v-m)

t=25 μs t=40 μs

Figure 6.17: Sequential effective stresses on the SiC spheres in the model with steel-filled SiC spherical inclusions with a 1200 m/s impact.

Figure 6.18 shows the effective stresses on the B4C and steel fillings at 5 and 15

μs after impact. The stress patterns remained similar afterwards, and the only difference was the particles near the impact site moved outwards during the penetration. Only the particles of fillings near the impact site experienced effective stresses during the impact.

It was clear that the B4C fillings had higher stresses in the early stage of the impact, as compared with the effective stresses on the steel fillings which only attained values up to

730 MPa. However, the B4C ceramic fillings were brittle and fractured later during the

112 impact, which then relieved the applied stress. Even though the effective stresses on the particles of steel fillings were less compared to the B4C fillings, there were more particles involved with the energy dissipation even after being deformed. The results corresponded to the experimental penetration tests, which will be described in the next chapter, in which ceramics were pulverized while metals deformed and stayed intact during an impact event.

(a) t=5 μs t=15 μs B4C B4C Effective Stress (Pa) (v-m)

(b) t=5 μs t=15 μs Steel Steel

Figure 6.18: Sequential effective stresses on the (a) B4C and (b) steel fillings in the model with spherical filled SiC inclusions with a 1200 m/s impact. 113

In summary, the benefits of forced shear localization from the deformation of inclusions to reduce momentum transfer, as mentioned by Gu and Nesterenko’s (2007), was not evident in the models with a spherical projectile. The design with chains of hollow spherical inclusions was not superior to the one with a hard front layer and ductile backing layer. More work could be done by studying different inclusion geometries (e.g., different ratios of inner to outer radius of the spherical inclusions), combinations of different materials, and using other material models for the powder fillings.

6.6 Steel targets with staggered spherical SiC inclusions

The models built in this section were inspired by the work of Lyons (2000), in which the method of overlaying structures in a target influences the joints and free-edge areas inside the target, and may enhance the ballistic performance of the target.

Accordingly two models were built based on the models with chains of SiC spheres in section 6.4. To generate a staggered configuration, all of the SiC spheres in the middle layer were displaced one-half of the sphere diameter towards both the x and y axis, with the top and bottom layers remaining in the original position. As illustrated in Figure 6.19, the green circles represent the top and bottom layers of SiC spheres, and the blue circles represent the shifted middle layer. Since the diameter of the SiC spheres was 3 mm, the displacement was 1.5 mm in both the x and y directions. The two new models had the impact either directly on a SiC sphere, or between four spheres. The two models were tested with a 1200 m/s impact.

114

(1.5 mm, 1.5 mm)

displacement

Figure 6.19: The staggered configuration of SiC sphere inclusions.

As a result, the staggered structure strengthened the target and enhanced the ballistic performance, compared with the models with chains of solid SiC spherical inclusions. The projectile kinetic energies of the two new models with staggered SiC spheres are shown in figure 6.20, together with the [MMMMM] and [CMMMM] models, and the two models with chains of solid SiC spheres. Differences of target mass between the models with SiC spheres were insignificant. The energy absorption efficiency was found to be higher in the models with the staggered configuration. Both models with cubic packing or staggered SiC spheres had a better performance with an impact between four spheres compared with the models with an impact directly on a SiC sphere.

115

50 MMMMM, 61.33 g CMMMM, 62.21 g Staggered, centered, 73.13 g Staggered, intermediate, 73.25 g Chain, centered, 73.01 g Chain, intermediate, 73.37 g kinetic energy (J) energy kinetic

0 0 10203040 time (s)

Figure 6.20: Kinetic energy of the projectiles over time after a 1200 m/s impact.

In summary, the staggered configuration was beneficial to the ballistic performance, and more work could be done by studying different inclusion sizes and displacements in the staggered structure.

6.7 Steel targets with tilted SiC plates

The impact angle between a projectile and target is a key issue for armour design

(King, 1969). Since the projectile used in this study was a WC sphere, the impact angle 116 was introduced by tilting the front ceramic layer, based on the best constant-mass

[CMMMM] model.

In this last section, four models were built with the tilt angles of the SiC plates varying from 15 to 30 to 45 to 60 degrees. The lateral views of the four models are sshown in Figure 6.21. The thicknesses of the targets were all 6.5 mm, and the mass/areal density was not kept constant. The four models were tested with a 1200 m/s impact.

(a) Z (b) WC Steel Y Vo 15º 30º

SiC

45º 60º

Figure 6.21: Quarter models with SiC plates tilted (a) 15 (b) 30 (c) 45 and (d) 60 degrees from the impact ssurface.

The energy absorption efficiency was again used as the indicator for evaluating the relative performance of the designs. As shown in Figure 6.22, the results of the four models with tilted ceramic plates were also compared with the [MMMMM] and

[CMMMM] models. None of the models with tilting SiC plates had a better baallistic performance, even with a higher weight, as compared with the [CMMMM] model. The model with the SiC plate tilted 60 degrees with respect to the impact suurface had the best 117 performance among the four models with tilted ceramic plates. Tilting the SiC plates 30 or 45 degrees from the impact surface actually weakened the target, and therefore degraded the performance, even with more mass, as compared with the [MMMMM] model.

200 MMMMM, 61.33 g CMMMM, 62.21 g 15 degrees, 73.96 g 30 degrees, 78.41 g 150 45 degrees, 79.25 g 60 degrees, 79.55 g

100 kinetic energy (J) energy kinetic 50

0 0 10203040 time (s)

Figure 6.22: Kinetic energy of the projectiles over time after a 1200 m/s impact.

To conclude the studies presented in this chapter, the addition of ceramic inclusions enhanced the ballistic performances in most of the designs, compared with a pure metal target. However, the constant-mass [CMMMM] model from the previous chapter was the best model among all constant-mass designs. Sufficient backing material 118 was critical for superior ballistic performance. Including gaps between ceramic plates did not significantly affect the resisting performance as compared with a continuous front ceramic layer. Using embedded spherical ceramic inclusions improved the steel target performance, but was still not comparable with the [CMMMM] model performance. A staggered structure was beneficial to the target performance, and is worthy of further studies. An embedded ceramic plate with a 60 degrees tilt angle outperformed the other designs with 15, 30, and 45 degree tilt angles, but was still not superior to the

[CMMMM] model.

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Chapter 7: Cr-CrS cermets and ballistic penetration tests

This chapter describes actual ballistic experiments on fabricated armour materials.

We focus on Cr-CrS cermets containing aluminum oxide inclusions. The ceramic inclusions provide high hardness and resistance to penetration, while the cermets provide some amount of ductility and energy dissipation. The first section in this chapter discusses the methods of manufacturing the Cr-CrS targets. The second section presents the measurement of mechanical properties of Cr-CrS cermets. The final section describes the results of the ballistic tests we performed on the materials.

7.1 Fabrication of Cr-CrS targets

As mentioned in the first chapter, a cermet was chosen for the tests since it combines the advantages of both ceramics and metals: high hardness and ductility to form a material with high toughness, yet remaining relatively lightweight. The Cr-CrS system was chosen especially for its attractive material characteristics, such as the high wettability for adhering to inclusions to form hybrid structures. In addition, the self- propagating high-temperature synthesis (SHS) process was used to fabricate the Cr-CrS specimens, which is a convenient method for systematically varying the composition of the cermet, such as the amount of Cr in the cermet matrix.

Chromium and sulfur powders were used as raw materials for manufacturing the

Cr-CrS cermets. The Cr powders were purchased from Atlantic Equipment Engineers

120

(NJ, USA) with a purity of 99.8%. The average size of the Cr powders was 1-5 μm. The sulfur powders were purchased from Alfa Aesar (MA, USA) with a purity of 99.5%. The average size of the sulfur powders was under 150 μm, although the size was not relevant to the synthesis process as the sulfur powder was melted prior to reaction.

The Cr-CrS cermet fabrication process began with mixing the appropriate quantities of Cr and S powders in a roller mill with a grinding media for approximately twelve hours. Afterwards, the powder mixture was heated above the melting point of sulfur (115.21). The molten mixture was then degassed in a vacuum chamber with a pressure of 95 kPa, and then cast into a preheated stainless steel mold with the desired geometry, which was lined with an alumina isolation layer. After solidification of the molten mixture, the SHS method was used for synthesizing the Cr-CrS products in a pressurized reactor vessel. A tungsten coil was used to initiate the SHS reaction. The green mixture was ignited under a high ambient pressure of pure argon gas. The self- sustained flame then propagated through the sample and converted the green mixture into the corresponding Cr-CrS compound within seconds. Finally, the products were slowly cooled with a one-dimensional directional solidification method. Figure 7.1 shows a macro- and micrograph (Hitachi S-3000N VP-SEM) of the synthesized Cr-CrS cermet products.

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(a) (b) Cr

CrS

100 µm 3 cm

Figure 7.1: The (a) macro- and (b) micrograph of Cr-CrS cermet products (Navabi et al., raw data).

To minimize the percentage of porosity inside the Cr-CrS cermets, 4 methods were found to be beneficial for manufacturing high quality specimens: (1) vacuum degassing of the molten mixture before pouring the mixture into a mold, to remove dissolved hydrogen, water, and low melting point impurities, (2) preheating the mold, stirring the molten mixture inside, slowly cooling, then refilling the mold, to prevent pore formation inside the mixture during the solidification shrinkage, (3) applying static pressure of inert gas inside the synthesis chamber, to decrease the amount of gas products based on the stoichiometric reaction, and (4) using an electrically-heated tungsten coil rather than a Zr-Fe2O3 thermite mixture to initiate the SHS reaction.

The hexagonal abrasion-resistant alumina plates used as ceramic inclusions incorporated within the Cr-CrS targets were purchased from CerCo Corporation Specialty

Ceramics Division (OH, USA). The diameter of the hexagonal alumina plates was 9.53 mm, and the thickness of the plates was 3.18 mm. A single alumina plate was placed at the central bottom of the casting mold before pouring the molten chromium-sulfur mixture into the mold. The hybrid target with the alumina plate was fabricated after the 122 synthesis and quenching processes.

7.2 Mechanical properties

As given in the Taylor impact simulations in chapter 3, the property variables used in the cylindrical impactor were obtained by measuring the Cr-CrS samples.

The density of the Cr-CrS cermets was measured by taking the average of eight block samples. The volumes of the rectangular samples shown in Figure 7.1 (a) were obtained by measuring the length, width, and thickness of each sample. After dividing the mass by the volume, the average density of the cermets was found to be 3850 kg/m3.

The Poisson’s ratio and shear modulus of the Cr-CrS cermets were obtained by performing a flyer plate impact test. The flyer plate impact test applied dynamic stress loadings to allow the measurement of the elasto-plastic properties of the sample material with the use of embedded gauges (Rosenberg and Partom, 1985a and 1985b). An illustration of the experiment settings and test sample are given in Figure 7.2.

123

Given impact velocity (a) (b)

Mounted sample

Figure 7.2: A (a) schema of the flyer plate impact test and (b) photograph of a Cr-CrS cermet with the two Manganin gauges (Petel et al., 2014).

As a result of the test, the average principal stresses measured in the samples were found to be 6.0±1 GPa in the longitudinal direction, and 1.9±0.4 GPa in the lateral direction. The Poisson’s ratio could be calculated by the equation below:

0.24 (7-1).

And the shear modulus could be calculated by the equation below:

2.05 (7-2).

The Young’s modulus of the Cr-CrS cermets could then be calculated by the relation between elastic constants.

21 5.084 (7-3).

7.3 Ballistic impact tests with the Cr-CrS targets

The ballistic impact tests of the hybrid cermet targets were carried out using the 124 ballistic test range at Allen Vanguard Ltd. Allen Vanguard (AV) is an engineering company in Ottawa (ON, Canada) developing and providing equipment, services, and training to protect against hazardous threats. The details and results of the impact tests are given in the next two sub-sections.

7.3.1 Studies on the addition of ceramic inclusions in the Cr-CrS cermets

Three types of targets were considered in the first round of ballistic impact tests.

The first type of targets consisted of pure Cr-CrS cermets. The second type was comprised of Cr-CrS cermets with an embedded hexagonal alumina plate. The last type consisted of pure alumina. The dimensions of the three types of targets are shown in

Table 7.1. For the compositions of the Cr-CrS cermets, the molar ratio of chromium over sulfide was 1:3. As shown in Figure 7.3 (a), the hexagonal alumina plates were embedded in the Cr-CrS cermets as inclusions on the impact surface. For comparison, the pure alumina targets were purchased from McMaster-Carr (IL, USA) with a compressive strength of 172 MPa, and 2-3% porosity. The alumina targets were made with a larger diameter, as shown in Figure 7.3 (b), to maintain a constant areal density.

Table 7.1: The dimensions of the cermet and alumina targets.

Targets Diameter (mm) Thickness (mm)

Cr-CrS cermet 44.45 12.70

Cermet with alumina inclusion 44.45 12.70

Alumina 50.80 12.70 125

The targets were further inlaid in the top plate of a stack of seven polycarbonate

(PC) plates clamped together. The PC plates served as backing plates to capture the projectile debris. The penetration depth of the projectile into the stack of PC plates was a measure of the ballistic performance of the targets. The PC plates were bolted together with four steel screws, as shown in Figure 7.3. The PC plates were purchased from Sabic

(TX, USA) with the grade of Lexan 9034. The geometries and dimensions of the PC plates are shown in Figure 7.4.

(a) (b)

Figure 7.3: An inlaid (a) cermet with alumina inclusion and (b) pure alumina targets.

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12.70 mm

146.05 mm

38.10 mm X4 R 12.70 mm X4 PL

Ø 9.53 mm X4 PL

146.05 mm

Figure 7.4: Geometries and dimensions of the PC backing plates.

The inlaid target assemblies were placed on an elevated platform against a steel rod, and fastened in place with a fabric belt, as shown in Figure 7.5.

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Figure 7.5: The arrangement of the ballistic impact tests.

A variety of fragment-simulating projectiles (FSP) with different geometries and sizes is shown in Figure 7.6. The projectile used in our ballistic impact tests was a 44- grain, .30 caliber FSP, representing a typical threat from an improvised explosive device

(IED). The geometry and dimensions of the .30 caliber FSP are shown in Figure 7.7. The projectile was manufactured from cold rolled and annealed steel conforming to compositions 4337H or 4340H, and fully quenched and tempered to a Rockwell hardness value of 30±2 (MIL-DTL-46593B (MR), 2008). The projectiles were fired with powder charges to achieve the impact velocities approximately ranging from 1300 to 1700 m/s, as measured during the tests with a Doppler radar system.

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Figure 7.6: Fragment-Simulating Projectiles (FSP) with different geometries and sizes.

Figure 7.7: The geometries and dimensions of the caliber .30 Fragment-Simulating Projectile (in mm) (MIL-DTL-46593B (MR), 2008).

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Figure 7.8 (a) shows the settings of the gas gun and metal partitions for firing the projectile in the ballistic impact tests. Figure 7.8 (b) shows the front view of the aligning metal partition in front of the gas gun with a hole to allow the projectiles to pass through.

(a) (b)

Figure 7.8: The settings of the (a) gas gun and (b) aligning partition in the ballistic impact tests.

Photographs of an alumina target before and after the ballistic impact are shown in Figure 7.9. The targets were quite brittle under the high velocity 1354 m/s impact, and fractured locally into small pieces of scattered fragments, allowing the projectile to penetrate into the PC backing plates, as shown in Figure 7.9 (b). The experimental result was consistent with the simulation result in chapter 5, in which the whole ceramic target was pulverized after a high velocity impact. As indicated by the model calculations, a 15 mm thick alumina target was fully penetrated with an impact velocity above 1000 m/s.

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(a) (b)

Figure 7.9: A target (a) before and (b) after a ballistic impact.

Figure 7.10 shows a side view of the stack of PC backing plates after a ballistic impact. Since the PC materials are translucent, the penetration depths may be directly measured by visualizing the backing plates from the side, as shown in Figure 7.10. For a precise measurement of the penetration depth, the stack of PC plates may also be disassembled.

Penetration depth

30 mm

Figure 7.10: The PC backing plates after a ballistic impact.

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Three specimens of each type of targets were tested, and the results of the first round of ballistic impact tests are shown in Figure 7.11, giving a plot of the penetration depths for each specimen with different impact velocities. In general, the penetration depths were smaller in the specimens with the Cr-CrS cermet targets, as compared with the specimens with pure alumina targets. A smaller penetration depth indicates a greater degree of absorption of the projectile kinetic energy by the target, and therefore a better ballistic resistance performance of the target. For the specimens with Cr-CrS cermet matrices and alumina inclusions, a 1367 m/s impact resulted in a smaller penetration depth as compared with the specimens with pure Cr-CrS cermets under approximately equal impact velocities. However, the specimens with Cr-CrS cermet matrices and alumina inclusions had larger penetration depths with a 1721 m/s impact, and worse ballistic performances, as compared to the specimen with pure Cr-CrS cermets with a

1719 m/s impact.

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50 Cermet targets Cermet with inclusion Alumina target 40

20 penetration depth (mm) depth penetration 10

0 1300 1400 1500 1600 1700 1800 impact velocity (m/s)

Figure 7.11: Penetration depths of the first round of ballistic impact tests.

In summary, the Cr-CrS cermets had a superior ballistic performance as compared with the pure alumina targets. However, the alumina adopted in the first round tests was not comparable to the high-grade ceramics used as inserts in actual commercial ballistic vests. As a result, the absolute ballistic penetration performance of the Cr-CrS cermets, relative to ballistic-grade ceramics, could not be determined. In the future work, higher quality ballistic ceramic plates should be used to provide an appropriate baseline performance for the tests with the cermets. To determine the effect of changing the

133 composition of the cermet, further ballistic tests were carried out in which the properties of the cermet were varied by systematically changing the metallic content of the cermet.

7.3.2 Studies on different compositions of the Cr-CrS cermets

In the second round of ballistic impact tests, four types of Cr-CrS cermet targets with different chemical compositions were prepared to compare with the two-layer alumina and steel targets. Recalling the simulation results in previous chapters, the hard- soft two-layer design had the best ballistic performance among all the configurations explored. For the Cr-CrS cermets, samples were synthesized with the molar ratios of Cr:S ranging from 1.15:1, to 2:1, to 3:1, finally to a maximum of 4:1. The excessive and unreacted Cr remaining in the products increased the density and ductility of the Cr-CrS cermet by increasing the metallic content of the cermet. The density of the Cr-CrS cermets increased from 4040±50 to 5370±40 kg/m3 with the higher molar ratio of Cr:S.

The dimensions of the targets are shown in Table 7.2. The thicknesses of the targets were adjusted to maintain an approximately constant areal density. Alumina disks were purchased from McMaster-Carr (IL, USA) with a Young’s modulus of 372 GPa. To fabricate the steel target, a low-carbon steel rod was purchased from McMaster-Carr with a Rockwell hardness of B53-B62, and cut into a thin disk with a diamond saw. The alumina and steel disks were glued together with a 3M DP100 epoxy adhesive to form the two-layer target. In the second round of tests, to determine the residual kinetic energy of the projectiles, the targets were embedded in the top of a polyethylene (PE) backing rod, which was held clamped between two steel plates, as shown in Figure 7.12. The PE rods

134 were used for capturing the projectile, and obtaining penetration depth as a performance indicator. The cylindrical PE rods were purchased from McMaster-Carr with a diameter of 76.2 mm and length of 152.4 mm, as shown in Figure 7.12 (a).

Table 7.2: The dimensions of the cermet and two-layer targets.

Targets Diameter (mm) Thickness (mm)

Cr:S 1.15:1 63.5 8.13

Cr:S 2:1 63.5 6.86

Cr:S 3:1 63.5 6.35

Cr:S 4:1 63.5 5.84

Alumina 63.5 3.18

steel 63.5 1.57

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(a) (b)

Figure 7.12: Photographs of a (a) Cr-CrS cermet target with a PE backing rod and (b) clamped target.

As shown in Figure 7.13, the alumina-steel two-layer targets were clamped with the PE rods, with the ceramic layer facing the impact end as a front layer.

(a) (b)

Figure 7.13: Photographs of a (a) two-layer target with a PE backing rod and (b) the clamping settings for the target.

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The fixation of the target and the other impact settings were kept the same, as in the first round of ballistic tests. Figure 7.14 (a) shows how the target illuminated with a laser beam which was used to align the target before each test. In the second round tests, the projectiles were all fired with a velocity approximately of 1700 m/s.

(a) (b)

Figure 7.14: (a) front and (b) side views of a fixed target.

After the ballistic impacts, both the Cr-CrS cermets and alumina disks were shattered into small fragments, and only the steel disks remained on the platform with the

PE rods. The front and back views of a deformed steel disk after a ballistic impact are shown in Figure 7.15. The dimple shaped deformation indicates the ductile deformation of steel disks during the impact event.

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(a) (b)

Figure 7.15: The (a) front and (b) back views of a deformed steel disk after a ballistic impact.

Figure 7.16 (a) shows a PE rod after the impact with a penetration crater. To measure the penetration depth, the PE rods were cut in half, as shown in Figure 7.16 (b).

(a) (b)

Penetration depth

50 mm

Figure 7.16: (a) A PE rod before the test and (b) the PE rod cut into two sections after the

ballistic impact.

Three specimens of each type of targets were tested, and the results of all the second round tests are shown in Figure 7.17, which gives a plot of the penetration depths in each specimen with different impact velocities. In general, the Cr-CrS cermets exhibited smaller penetration depths as compared with the alumina-steel two-layer 138 targets, which is an indication of greater kinetic energy absorption by the Cr-CrS targets.

The penetration depths decreased with the higher molar ratio of Cr in the cermets, which indicated better resistance performance with the higher ductility and density in the Cr- enriched Cr-CrS cermets.

80 Cr:S 1.15:1 Cr:S 2:1 Cr:S 3:1 Cr:S 4:1 alumina-steel 70

60 penetration depth (mm) depth penetration

50 1690 1700 1710 1720 1730 impact velocity (m/s)

Figure 7.17: Penetration depths of the second round of ballistic impact tests.

In summary, the second round tests demonstrated superior ballistic performances of the Cr-CrS cermets, as compared with the alumina-steel two-layer design. The increase of the molar ratio of Cr:S in the Cr-CrS cermets enhanced the resistance against ballistic impacts. It is difficult to produce a Cr-CrS cermet with a Cr:S ratio greater than 4:1 since 139 the excess Cr acts as an inert diluent, and it is difficult to ensure flame propagation during the synthesis process for higher degrees of Cr dilution.

To conclude the studies and tests in this chapter, the evaluation of ballistic performances should be compared with high quality ceramic targets. The Cr-CrS cermets demonstrated better resistance performances, compared with an alumina-steel two-layer design with a similar areal density. Increasing the molar ratio of Cr:S in the cermet improved the ballistic performance. Since the hard-soft two-layer design had the best performance among all the simulation models, and the Cr-CrS cermets had a superior performance to the two-layer targets in the impact tests, the Cr-CrS cermet material has a high potential as a relatively lightweight material for incorporation into ballistic protection systems.

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Chapter 8: Conclusions

8.1 Summary of accomplishments

Research in this thesis presented design guidelines for hybrid configurations in ballistic protection systems. In particular, the integration of computational modeling and experimental results was achieved. The ballistic performance of layered structures was systematically explored with computational modeling. Designs with hard ceramic inclusions in a ductile matrix with various geometrical configurations were modeled, based on previous work by other scholars. It was shown that a two-layer design consisting of a hard ceramic front layer and a ductile backing layer had the best ballistic performance among the configurations studied, based on the ability of the target to attenuate the kinetic energy of projectile during ballistic impact. The findings led to a development of protocols for the actual ballistic impact tests. In the experimental tests, the ballistic performance of Cr-CrS cermets was tested and compared with a two-layer target comprised of alumina and steel disks. The experimental results demonstrated that the high density Cr-CrS cermets showed better resistance performances, as compared with the two-layer design.

In chapter 3, the Taylor impact test was used to validate the SPH method. The simulation models were built and analyzed using the software LS-DYNA and Matlab.

The use of symmetry planes to save computational power and time for the SPH simulation models was validated by comparing the final cylinder lengths in full and quarter models. The simulations were further validated by comparing the stress amplitudes and velocities of elastic stress waves between the SPH simulations and 141 theoretical calculations. As in one dimensional compression, the shear stresses were relatively small in the cylindrical impactor, and σxx and σyy were equal during the impact, given the axisymmetric geometry and boundary conditions of the cylindrical impactor. As expected, the effective stresses reached a maximum value equal to the given yield stress.

The ratio of the final to original cylinder length was not affected by different ratios of the original length over diameter, over the range of aspect ratios explored. The velocities of the elastic stress waves propagating in the cylindrical impactor from the simulations were close to the theoretical values. The final length of the cylindrical impactor was used to evaluate the parameters used in the SPH simulations. The default values for the smoothing length (CSLH) and neighbours per particle (NNP) were found to be appropriate for the simulations. A value of 0.5 mm was found to be the most appropriate value for the distance between particles (PD). Overall, the SPH method was found to be an accurate and useful method for modeling problems with the high strain rates and large deformations representative of ballistic impacts.

In chapter 4, the effect of geometry on the ballistic simulations was studied, and the performance of combinations of hard and soft materials was presented. The simple ballistic simulation models were built based on the work of Martineau, Prime, and Duffey

(2004), and the results were compared to their impact tests. The penetration depth was found to decrease with an increase of target diameter and thickness. The geometry was found to have a smaller influence at higher impact velocities. The simulation results deviated from actual impact tests with higher velocity impacts, although the experimental results exhibited a degree of scatter. In the second section, the whole target was assigned to consist of either SiC or steel to validate the materials models used in the SPH

142 simulations. From the results, the SiC target was pulverized after impact, and demonstrated brittle ceramic characteristics with the Johnson-Holmquist (JH) material model. The steel target deformed to a lesser degree than the SiC target, and demonstrated ductile metallic characteristics with the plastic kinematic (PK) material model. The results demonstrated the choice of the two material models was appropriate to depict the different behaviors of the two materials.

In chapter 5, the ceramic-metal layered target was systematically studied for optimization of the design. The target was divided into five layers and each assigned to be either silicon carbide (SiC) or steel. The ballistic performance of 32 combinations of different layers was systematically explored. Firstly, the targets were maintained with a constant volume with constant layer thickness. By using the critical velocity for penetration of the target with the projectile as an indicator, the [CCMMM] model exhibited the best ballistic performance, and survived a 2500 m/s impact. Models that survived a 2000 m/s impact, but failed with a 2500 m/s impact, were further differentiated by considering their energy absorption efficiency. The [CCCMM] model ranked second, and the [CMMMM] model was the third best design with constant volume. All three of the best-performing models had a consecutive two material design, consistent with the work of previous researchers (Lee and Yoo, 2001; Arias et al., 2003;

Gonçalves et al., 2004; Übeyli, Yıldırım, and Ögel, 2008). With a thin layer of steel at the impact surface, even though this led to effective confinement of ceramic fragments, the reduction of either the ceramic or metallic materials as backing layers weakened the performance. The five-layer design was further studied with the strength of the metallic layers reduced by a factor of 2 while maintaining the volume constant. The best design

143 was still the [CCMMM] model. However, the relative ranking of the other configurations changed, with the [CCCMM] model now with the second-best performance, and the

[MCCMM] model with the third best design. To compare targets in which the total mass was held constant, the thickness of the steel layers was adjusted to be 0.4 times that of a

SiC layer due to the different material densities. In this case, the three best designs were the [CMMMM], [CCMMM], and [CMCCC] models. Finally, a reduction in the strength of the metallic layers with constant total mass was applied to the five-layer designs. The best two designs were the [CCMMM] and [CCMMC] models. All the computation results indicated the two-layer and sandwich structures as being the best designs for ballistic protection systems. Different fixed factors and material properties will, in general, influence the relative ranking of the multilayered designs.

In chapter 6, different target configurations with SiC inclusions embedded in a steel matrix were explored. Seven types of arrangements for hard inclusions in soft matrices, inspired by previous work by other researchers were studied numerically with the SPH method. The absorption rate of the projectile kinetic energy was used as an indicator for the evaluation of the designs. A larger ceramic disk in diameter placed at the impact surface demonstrated better performance, as a thicker backing material was considered in the model to maintain the mass constant between the designs. The benefits of gaps between ceramic plates to prevent crack propagation and contain damage were not evident in our models, and the differences in the performances were insignificant.

Finer spherical inclusions in a steel target showed better resistance against ballistic impact, while large inclusions with insufficient backing material weakened the performance. Solitary waves, postulated to propagate through the connected inclusions

144 appeared to have an insignificant effect on the ballistic performance, since the timescale of the impact process was on the order of microseconds, significantly shorter than the time for solitary wave propagation. Even with insufficient backing materials, the designs with chains of SiC spherical inclusions had similar performances, compared to the two- layer design. Filling hollow spherical SiC inclusions with either another ceramic or steel had a significant effect on ballistic performance. Staggering the layers of spherical inclusions led to better ballistic performances, as compared with a regular array of spherical inclusions. Placing the SiC plates at an angle relative to the projectile impact was found to have no benefit for defeating and reflecting the projectile. Overall, the two- layer design studied in chapter 5 had superior performance to all the targets with different configurations investigated in this chapter, subject to the limiting factor of constant mass.

In chapter 7, the manufacturing, properties measurements, and experimental impact tests of chromium-chromium sulfide (Cr-CrS) cermets were presented. The Cr-

CrS specimens were synthesized by the self-propagating high-temperature synthesis

(SHS) method. The density of Cr-CrS cermets increased with higher molar ratio of Cr:S.

The first round of ballistic impact tests showed that the Cr-CrS cermets had a better ballistic performance than the alumina targets, although the alumina targets used were not of ballistics grade. In the second round of tests, the Cr-CrS cermets were shown to perform better than a two-layer design comprised of alumina and steel layers, with the performance improved when excess chromium was added to the sample. In summary, the ballistic tests with the Cr-CrS cermets demonstrated that this material has a high potential for incorporation into armour systems.

145

The integration of computational modeling and experimental tests is a two-way process. Simulations require material properties from actual experimental tests. In addition, simulation models should be built based on the conditions in actual impact tests.

The simulation outputs will later be adopted to manufacture and test real specimens. As an alternative, the best design in simulations can be used as a comparison with other target samples.

8.2 Original contributions

The following list summarizes the original findings in this thesis:

 The smoothed particle hydrodynamics (SPH) method has been validated by

studying the stress waves in a Taylor impact test, and shown to be a robust tool for

modeling ballistic impacts (Shiue et al., in preparation).

 The parameters used in the SPH simulations were studied by studying the final

impactor length in a Taylor impact test, and the default values for smoothing

length (CSLH) and neighbours per particle (NNP) were demonstrated to be

adequate for the computational study.

 The use of the plastic kinematic (PK) and Johnson-Holmquist (JH) material

models in the SPH method was investigated and validated as appropriate for

modeling metallic and ceramic materials, respectively.

146

 The effect of target geometry was studied by modeling ballistic impacts with the

SPH simulations, and the results were compared with experimental data.

 A multilayered structure was systematically explored for optimization of ballistic

performance by using the SPH simulations (Shiue et al., in preparation).

 Different configurations of ceramic-metal hybrid targets were explored by

incorporating hard ceramic inclusions into a ductile metal matrix to achieve the

best ballistic performance.

 Results from the SPH simulations were integrated into actual ballistic impact

tests, and identified the Cr-CrS cermet as an attractive ballistic material for use in

armour systems.

8.3 Pathways towards ballistic protection design optimization

In the present work, a finite design space was examined with respect to ballistic performance. The modeling software or similar tools used in the present study can be further integrated into a powerful tool for simulation optimization. Finer layered structures can be studied to tailor the relative proportions of the ceramic and metal materials to optimize the ballistic performance. Other types of target configurations can also be systematically explored. For example, the performance of functionally-graded materials may be studied, in which the properties of the material vary continuously from that of a ceramic to that of a metal (the Cr-CrS system studied in the current experimental work is such a system that be used to prepare a functionally-graded system). The 147 integration of simulation and experimental tests can also be further established. At present, the number of experimental configurations investigated is limited, and needs to be compared with the materials with the best current ballistic performance. Further experimental measurements can be performed to provide more precise material properties which are required as inputs to the simulations.

The modeling and optimization techniques explored in this thesis can be used for the development of other types of hybrid composites, not only other types of materials, but also innovative configurations. With better understanding of the damage mechanisms in ballistic impacts, more work can be done by using other structural shapes, such as I- beams, tubular members, and honeycomb structures, to achieve a reduction weight while maintain the high mechanical properties appropriate for armour design.

148

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