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Politecnico Di Milano Facoltà di Ingegneria dei Processi Industriali
Degree in Materials Engineering
3D Reinforcement of Composite Materials
Supervisors: Valter Carvelli (Politecnico di Milano) Giulio Ventura (Politecnico di Torino) Carlo Poggi (Politecnico di Milano)
Corinna A Conway 750155
Academic Year 2010 -‐ 2011
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Dedicated to my little brother, Michael Conway Who taught me how precious life truly is and what it means to follow
your dreams.
And to My Parents, Robert and Theresa Conway Who made this all possible through their love and
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Table of Contents
Abstract 13
Summary 14
Chapter 1 Introduction to Composites 16
1.1 Introduction 16
1.2 Fiber Reinforced Composites (FRC) 16
1.2.1 The Matrix 17
1.2.2 The Fibers 17
1.3 Reinforcement Architectures 19
1.3.1 2D Composites 20
1.3.2 3D Composites 21
References 22
Chapter 2 Reinforcement Fabric Manufacturing 23
2.1 Introduction 23
2.2 Weaving 23
2.2.1 2D Weaving 23
2.2.2 3D Weaving 25
2.2.3 3D Orthogonal Non-‐Woven, Multiaxial Weaving
and Distance Fabrics 26
2.3 Braiding 27
2.3.1 2D Braiding 27
2.3.2 Two and Four Step 3D Braiding 27
2.3.3 Multilayer Interlock Braiding 28
2.4 Knitting 28
2.5 Stitching 29
2.6 Z-‐Pinning 30
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References 31
Chapter 3 Composite Manufacturing 32
3.1 Introduction 32
3.2 Composite Consolidation techniques 32
3.2.1 Resin Transfer Molding 32
3.2.2 Resin Film Infusion 32
3.2.3 SCRIMP 34
3.3 Consolidation Equipment 34
3.3.1 Tooling (mold) 35
3.3.2 Heating and Cooling 35
3.3.3 Injection Equipment 36
3.4 Optimization 36
References 39
Chapter 4 Textile Fiber Reinforcement Properties 40
4.1 Introduction 40
4.2 In-‐Plane Shear 40
4.3 In-‐Plane Biaxial Tension 42
References 44
Chapter 5 Composite Modeling 45
5.1 Introduction 45
5.2 Fundamentals 46
5.3 Representative Volume 48
5.4 Rule of Mixtures 50
5.5 Basic Models for 2D Woven Composites 51
5.5.1 Mosaic Model 51
5.5.2 Undulation Model 53
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5.6 Models for 3D Woven Composites 56
5.6.1 Orientation averaging 57
5.6.2 Iso-‐Strain and Iso-‐Stress Model 57
5.6.3 Finite Element Model 60
References 61
Chapter 6 3D Woven Composites 63
6.1 Introduction 63
6.2 3D Woven Composites 63
6.2.1 Microstructure Features and Crimp 63
6.2.2 Tensile Properties 66
6.2.3 Compressive Properties 67
6.2.4 Flexural and Interlaminar Shear Properties 68
6.2.5 Interlaminar Fracture 68
6.2.6 Impact Damage Tolerance 69
References 71
Chapter 7 3D Braided, Knitted, Stitched and Z-‐Pinned Composites 72
7.1 Introduction 72
7.2 3D Braided Composites 72
7.2.1 In-‐Plane Properties 72
7.2.2 3D vs. 2D Braided Composites 73
7.3 3D Knit Composites 73
7.3.1 In-‐Plane Properties 73
7.3.2 Interlaminar Fracture and Impact Toughness 75
7.4 Stitched Composites 75
7.4.1 In-‐Plane Mechanical Properties 76
7.4.2 Fracture Toughness and Impact Damage Tolerance 76
7.5 Z-‐Pinned Composites 77
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7.5.1 Tensile and Compressive Strength 77
7.5.2 Delamination Resistance 78
References 79
Chapter 8 Concluding Remarks 80
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Figures
Figure 1.1: Depiction of fiber type, and non-‐woven composite architectures 18
Figure 1.2: Layup sequence 18
Figure 1.3: Stress vs. Strain graph comparing Carbon (green), Glass (purple) and Aramid (red) fiber properties 19
Figure 1.4: Braided, woven and knit fabric structures 20
Figure 1.5: Comparison of in-‐plane and through-‐thickness Properties 21
Figure 2.1: Traditional weaving loom 24
Figure 2.2: Illustration of yarn structure, and common weave Patterns 25
Figure 2.3: 3D weave geometries 26
Figure 2.4: Illustrating the ability to weave slits into the fabric capable of creating three-‐dimensional structures 26
Figure 2.5: Multilayer interlock braided fabric 28
Figure 2.6: 3D knit fabric 29
Figure 2.7: Stitched fabric 30
Figure 2.8: Z-‐pinning process 30
Figure 3.1: RTM 33
Figure 3.2: RFI 34
Figure 3.3: Autoclave for composite consolidation. Image provided by AAC research 35
Figure 3.4: Viscosity vs. Time – temperature dependence of thermoset TGDDM resin. Image taken from Understanding of Rheology of Thermosets 37
Figure 4.1: Biaxial tension test (left) and Picture frame test (right) 41
Figure 4.3: Illustrating non-‐linear behavior of woven fabric 42
Figure 4.4: Biaxial testing Machine 42
Figure 4.5: Biaxial testing sample 43
Figure 4.6: Clamps 43
Figure 5.1: Illustrating the microscopic heterogeneity of a composite structure. Fibers shown in grey and matrix in blue. 45
Figure 5.2: Illustrating the three planes of symmetry that make composites orthotropic materials. Planes are shown in yellow. 46
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Figure 5.3: Examples of common weave geometries 51
Figure 5.4: CLT modeling of a layered composite 52
Figure 5.5: Fiber undulation model 54
Figure 5.6: Types of 3D woven fabrics 57
Figure 5.7: a) Unit cell for the mixed iso-‐strain and iso-‐stress model. b) Division of the unit cell into 4 blocks 58
Figure 5.8: Possible assembly directions of block A and B 58
Figure 5.9: Example of a 3D FE model of a unit cell of a 3D orthogonal Woven composite material 60
Figure 6.1: Tensile strength at different stages of the weaving Process 64
Figure 6.2: Illustration of the crimping in 2D woven fabrics 65
Figure 6.3: difference between Idealized z-‐binder geometry (a) and actual (b) 65
Figure 6.4 Top and cross sectional view 66
Figure 6.5: Kinking failure in compression 67
Figure 6.6: Mode I delamination cracking 68
Figure 6.7: Effect of impact velocity on delamination damage of 2D and 3D woven composites 69
Figure 6.8: Effect of impact energy on flexural strength 70
Figure 6.9: Effect of impact energy on the compressive strength 70
Figure 7.1: Warp knit (a) Denbigh, (b) 1x3 single cord, and (c) 1x4 single cord architectures 74
Figure 7.2: Wale and course directions as well as warp and weft fabric structure. 75
Figure 7.3: Illustrating mode I interlaminar toughening mechanism of stitched composites 76
Figure 7.4: Depiction of z-‐pinned architecture at insertion site 77
Figure 7.5: Depiction of weaving and deflection caused by z-‐pins 78
Tables Table 1.1: Matrix materials costs, application temperature and
toughness. (TP – thermoplastic and TS – thermoset) 14 17
Table 1.2: Glass type and defining characteristics 19
Table 7.1: Reported results from Macander et al. for effects of braid
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pattern and edge conditions 73
Table 7.2: Tensile properties of warp knit with varying knit architectures 74
Table 7.3: Tensile properties of weft knit with varying knit architectures 74
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Abstract
Composite materials present a unique opportunity to engineer a material in order to optimize its physical, thermal and mechanical properties for specific applications. Offering many advantages such a relatively high specific strength, stiffness, fatigue resistance and corrosion resistance with respect to weight. Due to their exceptional qualities, composites can be found in many applications, from aircrafts, helicopters and spacecrafts to submarines, automobiles and sporting goods. However their wide spread use has been inhibited by their high cost, poor delamination toughness, and poor impact damage resistance. Many prospects have been investigated as methods for improving these characteristics, however composites reinforced with 3D fabric architectures appear to be the most promising solution. Here an investigation of 3D fabric architectures (3D woven, braided, knit, stitched and z-‐pinned), manufacturing methods, and composite properties are reviewed in order to have a better understanding of the pros and cons of such a material as well as potential improvements and opportunities. As expected 3D composites solve many of the problems faced by 2D composites, however these improvements are accompanied by the deterioration of in-‐plane properties. Many 3D composites show potential for applications unsuited for 2D composites, however optimization of 3D fabric manufacturing, composite production, and in-‐ and out-‐of-‐plane properties needs further investigation.
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Summary
I materiali compositi presentano una opportunità unica per progettare un materiale in modo da ottimizzare le sue proprietà fisiche, termiche e meccaniche per applicazioni specifiche. Questi materiali offrono molti vantaggi come: una relativamente alta resistenza specifica, rigidezza, resistenza a fatica e resistenza a corrosione se confrontati col peso. A causa delle loro qualità eccezionali, i compositi possono essere trovati in molte applicazioni: dagli aeroplani, elicotteri e veicoli spaziali ai sottomarini, automobili e merci sportive. Purtroppo la loro larga diffusione è limitata dal loro alto costo, piccola durezza alla laminazione e piccola resistenza all'impatto. Molti aspetti sono stati investigati come metodi per migliorare queste caratteristiche, comunque i compositi rinforzati con architetture di tessuti 3D appaiono essere la soluzione più promettente. Un approfondimento sui metodi di produzione, modellazione, e le proprietà dei compositi di tessuti 3d, 3d intreccaiti, cuciti e z-‐appuntati architetture di rinforzo è stata eseguita in modo da capire meglio i pro e contro di questi materiali così come possibili miglioramenti e opportunità.
Molti miglioramenti sono ancora necessari per la produzione di tessuti di rinforzo 3D. I tessuti e i tessuti intrecciati possono essere prodotti usando speciali macchine o modificando i tradizionali macchinari 2D. Comunque le architetture e i costi e i volumi di produzione sono correntemente limitati dalle tecnologie disponibili. RTM (Resin transfer molding) and RFI (Resin film infusion) or SCRIMP sono i metodi più efficienti per la corrente produzione di compositi 3D. Ogni metodo ha diversi benefici e limitazioni. Una revisione di base degli attuali metodi di prova e modellazione per i compositi 3D è presentata nei capitoli 4 e 5.
Come ci si aspetta i compositi 3D risolvono molti dei problemi che hanno i compositi 2D, comunque questi miglioramenti sono accompagnati dalla deteriorazione delle proprietà nel piano. L'ottimizzazione della manifattura dei tessuti 3D, la produzione di compositi, e le proprietà nel piano e fuori dal piano hanno bisogno di ulteriori investigazioni, comunque molti compositi 3D mostrano potenzialità per diverse applicazioni per cui non possono essere usati compositi 2D. Per esempio, cuciture e z-‐pinning mostrano eccezionali potenzialità per il rinforzo dei giunti, mentre I tessuti a maglia 3D mostrano un eccellemte resistenza all'impatto e sono di particolare interesse per l'uso nelle protesi ma non sono utilizzabili per applicazioni strutturali.
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1 Introduction to Composites
1.1 Introduction
Over the past years composites have become increasingly popular. Their
popularity is due to their ability to be manipulated and engineered in order to optimize physical, thermal and mechanical properties for specific applications. The mechanical properties of a composite depend on both the material selection as well as the orientation of the reinforcements within the component. For example, fiber direction may be dictated in order to optimize the mechanical properties of the material in a given direction and materials can be selected to optimize performance in diverse environments. Composites are also advantageous from a weight perspective, as they display a relatively high specific strength, stiffness, fatigue resistance and corrosion resistance with respect to weight. Therefore they are usually chosen for applications where high operational properties are crucial and weight management is critical. Due to their exceptional qualities, composites can be found in all types of applications, from aircrafts, helicopters and spacecrafts to submarines, automobiles and sporting goods.1,2 1.2 Fiber Reinforced Composites (FRC)
The definition of a composite material is that it must be made up of at least two distinguishable constituents demonstrating significantly different chemical or physical properties. The combination of these constituents into a composite creates a new material that displays a set of properties different from the individual properties of each of the constituent materials. There are many different composite types, however for the purpose of this thesis we will focus on Fiber Reinforced (FR) Composites. FR composites consist of a matrix, usually a rigid polymeric material embedded with fiber reinforcements. The polymeric material of the matrix is made from either a thermoplastic (e.g. polyamide, polypropylene, etc) or a thermoset (e.g. polyimides, epoxy, etc.) material, while the reinforcing fibers are usually made from glass, carbon or aramid.1,2
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1.2.1 The Matrix
Selection of the constituent materials depends on the desired properties of the final product. The two most common matrix materials for FR composites are thermoplastics and thermosets. Thermoplastics are characterized by: high application temperatures, high toughness and ease of repair. On the down side thermoplastics require high processing temperatures, and can be difficult to handle due to their high viscosity. Thermoset matrix materials are characterized by their low viscosity and low processing temperature with drawbacks in application temperature, and toughness (see Table 1.1). Matrix Material Cost Application Temperature Toughness PAI (TP) >25 €/kg > 300°C Medium-‐High PEEK (TP) >25 €/kg > 300°C High Polyimide (TS) 10-‐25 €/kg 200-‐300°C High PES (TP) 10-‐25 €/kg 200-‐300°C Low-‐Medium Epoxy (TS) 2.5 – 10 €/kg 120-‐200°C Low Phenolic (TS) 2.5 – 10 €/kg 120-‐200°C Low PBT (TP) 2.5 – 10 €/kg 120-‐200°C Low-‐Medium PA (TP) 2.5 – 10 €/kg 120-‐200°C Medium-‐High Polyester (TS) <2.5 €/kg <120°C Low PP (TP) <2.5 €/kg <120°C Table 1.1: Matrix materials costs, application temperature and toughness. (TP – thermoplastic
and TS – thermoset) 3 1.2.2 The Fibers The fibers of the FR composite can be varied in size, shape, length, direction, architecture, and material in order to engineer a composite to the have specific properties. The length of the reinforcing fibers can be whiskers (short/staple) or continuous (filament) (Figure 1.1), and usually have an ovular or circular cross-‐sectional shape, although almost any shape is possible. Whisker reinforcement fibers are used to create non-‐woven, non-‐structural composites. When randomly oriented in the matrix material they create an isotropic composite, while orienting the fibers can give more strength in the orientation direction, generating an anisotropic composite.
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Figure 1.1: Depiction of fiber type, and non-‐woven composite architectures
On the other hand, using filament fibers makes it possible to engineer the
reinforcement architecture. This can be achieved through the prepreg lay-‐up, or by using woven, braided, stitched, or z-‐pinned fabrics. A prepreg is a unidirectional fiber sheet impregnated with uncured matrix resin. The layup of the prepregs determines the fiber orientations within the composite (see figure 1.2). Fibers may be oriented in one direction (e.g. 0°/0°/0°/0°) giving unidirectional characteristics, or in multiple directions (e.g. 0°/+45°/-‐45°/90) creating quasi-‐isotropic properties.1
Figure 1.2: Layup sequence3
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The fiber material is also very important. Glass fiber reinforcements are the most common due to their low cost and high strength, however limitations are found in the low modulus, high density/weight, low fatigue and wear resistance, and sensitivity to humid environments. Within the glass fibers there are different types that can be selected based on the desired properties and environmental conditions (see Table 1.2)
Type General Characteristics E Low cost, General purpose S/R High stiffness and strength D Good dielectric properties A/AR Alkali resistance E-‐CR Acid Resistance C Good chemical resistance
Table 1.2: Glass type and defining characteristics Carbon fibers are becoming more popular and are of high interest due to their high modulus, high strength, and low density/weight, however they are still extremely expensive.
Figure 1.3: Stress vs. Strain graph comparing Carbon (green), Glass (purple) and Aramid (red)
fiber properties. 3 Aramid fibers have advantages in its high toughness, high strength and low cost, but suffer from low UV resistance, and low compressive strength (although the low compressive strength can be used to an advantage in certain applications). These are the three most common fiber reinforcement materials, whose tensile behavior are compared in Figure 1.3. However it is important to note, that boron, basalt and ceramic fibers have also been used to a much lesser extent.1,2 1.3 Reinforcement Architectures
Using more complex reinforcement architectures gives another engineering possibility. Woven, knit, braided, stitched, and z-‐pinned architectures provide
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the most interesting opportunities at the moment (figure 1.4). Within each fabric production process there are many different architectures that can be achieved. For example with 3D weaving we can produce angle interlock weaves, orthogonal weaves or through-‐thickness interlock weaves. The properties of each of these fabrics differ greatly, therefore the fabric itself can be engineered for the desired properties.1,2
Figure 1.4: Braided, woven and knit fabric structures
1.3.1 2D Composites 2D laminated composites are among the most common composites used in the
market today. In applications requiring high performance properties filament fibers are selected over whiskers and are oriented in the x-, y-directions of the composite. Some of the major disadvantages of 2D composites lie in their high cost, and low through-thickness mechanical properties due to the lack of z-directional fibers. Therefore the mechanical properties in the through-thickness direction are determined by the mechanical properties of the resin and the fiber-resin interface. A comparison of the in-plane and through-thickness strengths of 2D laminates, seen in figure 1.5 below, reveals that the through-thickness properties are usually less than 10% of the in-plane properties and therefore cannot be used in applications supporting high through-thickness or inter-laminar shear loads.2
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Figure 1.5: Comparison of in-plane and through-thickness properties1
Another issue with 2D composites is their poor impact damage resistance, delamination and the loss in mechanical properties caused by impact. A composite subjected to an impact in the through-thickness direction can suffer from degraded in-plane mechanical properties under tension, compression, bending and fatigue. Due to the threat of delamination, composite parts are often over-engineered by adding thickness, resulting in increased costs, weight and volume.2
Alternatives to improve through-thickness delamination resistance and post-impact mechanical properties include chemical and rubber toughening of resins, chemical and plasma treatment of fibers, and interlaying using though thermoplastic films. They have all shown improvements in low energy impacts but have other drawbacks, which have lead to the limitation of their use in large structures.2
1.3.2 3D Composites 3D composites were introduced as a solution to the main disadvantages of 2D composites: high fabrication costs, proneness to through-‐thickness delamination and low impact damage tolerance. Unlike the 2D composites, 3D composites have fibers in the x-‐, y-‐, and z-‐directions. The z-‐directional or z-‐binder yarn is responsible for the increase of these out-‐of-‐plane mechanical properties. 3D composites can be made from 3D woven, braided, or knit fabrics as well as stitched and z-‐pinned fabrics. The rest of this thesis will cover 3D composites and their reinforcements. The following chapters will review their manufacturing, composite consolidation, modeling and properties.2
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References 1. M. Sc. Badawi, Said Sobhey A. M. Development of the Weaving Machine
and 3D Woven Spacer Fabric Structures for Light Weight Composites Materials. Dresden Technical University. 2007
2. Tong, L. Mouritz, A.P. and Bannister, M.K. 3D Fibre Reinforced Polymer Composites. Elsevier Science Ltd. Oxford, UK. 2002.
3. Poggi, Carlo. Composites For Structural Application. Politecnico di Milano. Course, 2nd Semester 2011
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2 Reinforcement Fabric Manufacturing
2.1 Introduction
The manufacturing of the 3D fabric reinforcement plays a very important role in the growth of the 3D fiber reinforced composite industry. It is only through economical production of the 3D reinforcement that wide spread use can be achieved. There are many different ways in which to manufacture a 3D fabric reinforcement, however the most common methods, and those that will be discussed here, are: weaving, braiding, knitting, stitching, noobing, and z-‐pinning. 2,3 2.2 Weaving Weaving is one of the oldest forms of fabric production and is already used extensively within the composite industry. However, the fabrics currently being used are mostly 2D and not 3D. The weaving process, at the moment, allows for the production of fabric widths between 1.8 – 2.5 meters at a rapid production rate making this type of reinforcement good for components requiring large surfaces and fast production rates. An appealing aspect of the current weaving process is that the 2D weaving equipment can be easily altered, at little cost, to attain the ability of producing 3D fabrics, however yarn directions are restricted to 0 and 90 degree directions. 1,3 2.2.1 2D Weaving Let us begin with a description of the traditional 2D weaving process, as the 3D process is based off of its simpler counterpart. Weaving is the act of interlacing two sets of yarns to produce a fabric2. The steps of weaving are in the order of shedding, picking, beating up and taking up3. At this point it is important to note that there are different types of weaving looms, the traditional looms (Figure 2.1) that can produce fabrics of plain weave, twill and satin, and those called, jacquard looms, which can produce complicated fabric patterns. Jacquard looms have a lifting mechanism controlled by a computer in which individual warp yarns can be lifted at any time allowing for intricate patterns to be woven into the fabric, these are of particular interest in the 3D weaving process. 1,2,3
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Figure 2.1: Traditional weaving loom3
The weaving process starts by threading or feeding the warp yarns, those
that run in the machine direction – 0 degrees, into the loom from the source yarns. The source yarns are run through a series of rollers in order to maintain and control the tension. These yarns are then fed through the lifting mechanism. The lifting mechanism lifts the warp yarns in order to create a space, or shed, for the weft yarns to be inserted. The weft yarns are those running horizontal to the machine, or in the 90 degree direction. The sequence in which the warp yarns are lifted and the weft yarns inserted creates the pattern of the fabric (see Figure 2.2). It is important to note that the fabric architecture greatly influences the mechanical properties and drapability of the fabric and is highly dependent on the weave pattern, fiber or tow size, weft and warp yarn concentration, yarn tension, and tightness of the tows.1,2,3 Plain weave being the stiffest (least drapable) and weakest, while satin is the strongest and most drapable.3
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Figure 2.2: Illustration of yarn structure, and common weave patterns
Picking is the process of inserting the weft yarns in the shed created by the lifting mechanism.2 This can take place in a number of different ways. The oldest technique for insertion of the weft yarns is through the use of a shuttle to transport the yarns through the shed. This technique is slow, but creates a closed edge fabric. Open edged fabrics can be produced at much quicker rates, using a mechanical arm, rapier, or high-‐pressure air or water to transport the weft yarns through the shed.3 The next step is the beating up process, in which the inserted weft yarns are compacted using a comb-‐like devise, the reed. Finally, in order to have a continuous process the fabric is advanced forward by a series of positively driven rollers, this is called take-‐up. This process is continued until the desired length of fabric is created. The fabric can be produced continuously and cut into the lengths needed. Also different types of yarns can be used for warp and weft to help created a fabric better suited for the intended use. 1,2,3 2.2.2 3D Weaving The major difference between 2D and 3D woven fabrics is the need of multiple layers of warp yarns in the 3D fabrics. This tends to be a major disadvantage, as the need for a large number of warp-‐ends and the time required to prepare the loom can be very costly. Therefore, at the moment, most 3D woven fabrics are used in the production of narrow products reducing the number of warp yarns required. As stated above, the traditional weaving equipment can be easily altered to create a 3D woven fabric. The first modification is to use a lifting mechanism with multiple eyes, allowing for layered warp yarns. Jacquard looms are normally selected for the production of 3D woven fabrics, given the distinct advantage of improved control of the lifting mechanism. With the multiple layers of warp yarns, comes the creation of multiple sheds. This allows for multiple insertions of the weft yarns at the same time, and is the second modification needed in order to have 3D weaving. 1,2,3 In the formation of a 3D woven fabric, pockets are formed between any four adjacent warp yarns. These pockets can be filled with stuffer yarns that do not interlace with the weft yarns. The pockets can be filled according to mechanical needs and in this way the fabric can be further engineered to specific applications. In order to maximize performance, majority of the yarns are designed to lay flat, and only select warp yarns are used to bind the layers together. Examples of the weaving architectures capable of being produced using the 3D weaving procedure are given in the figure 2.3. Please note that
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these fabric architectures are idealized and not possible in reality. Woven materials can be produced in types of solid, shell, tubular and/or combinations of these. 1,2,3
Figure 2.3: 3D weave geometries2
As with 2D weaving, 3D weaving is limited to yarn placement in the 0 and 90 degree directions. Therefore its use is limited to components that are not subjected to extensive shear and torsion stresses. An advantage of the weaving loom is its capability of producing fabrics with slits that can then be opened into three-‐dimensional structures (see figure 2.4). This can be used to produce I beams and boxes using flat fabric and have already been used in civil engineering components. 3
Figure 2.4: Illustrating the ability to weave slits into the fabric capable of creating three-‐
dimensional structures.3
Examples of 3D weaving equipment include, 3WEAVE created by 3tex. This machine allows for the use of multiple filling layers at a time, use of carbon, aramid, glass, polyethylene, steel fibers, etc., produce a fabric thickness up to 25.4 mm, and a fabric width of 1830mm. 2 2.2.3 3D orthogonal Non-Woven, Multiaxial Weaving, and Distance Fabrics 3D orthogonal non-‐wovens are those fabrics produced from the same equipment used to produce 3D woven fabrics, but that do not contain interlacing
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yarns. A clear advantage of the 3D orthogonal non-‐wovens is that they are easier to produce close to the ideal architecture. 3 Multiaxial weaving allows for the placement of yarns in directions other than the traditional 0 and 90 degrees. However it is not suited for large scale production and the equipment tends to be much more expensive. Currently this type of technology is still in the development stages and much research is needed to discover to true potential. 3 Distance fabrics are produced using a similar processed used in the production of velvet. There are two sets of warp yarns, spaced at specified distance apart, that are woven as separate fabrics and at the same time interlinked by transferring specific warp yarns, pile yarns, between the layers. This fabric is important for the production of peel-‐resistant and delamination resistant sandwich composites. 3 2.3 Braiding Braiding is also commonly found in the production of many composite components: golf clubs, yacht masts and aircraft propellers. Unlike weaving, braiding allows for a much larger selection of shapes, however is not capable of producing large volumes of wide fabrics, therefore is better suited for the production of highly specialized parts. The disadvantages of braiding fall in the limited size of performs compared to the size of the equipment as well as the limited length of the preform before the yarns need to be refilled. 3 2.3.1 2D Braiding 2D braiding is usually preformed by a set of yarn carriers that counter rotate around a circular frame to form the braided fabric. Braided fabric is characterized by the high level of yarn interlinking and is formed as either a tubular or flat fabric. A large benefit of the braiding process is that braiding can be preformed over a mandrel in order to produce intricate perform shapes. The shapes achievable can have varying cross sectional shapes, varying dimensions along their length, and attachment points or holes can also be incorporated into the preform. By incorporating holes and attachment points it is possible to cut costs in component finishing as well as improve mechanical performance by allowing for unbroken fibers at the attachment sites. Another large benefit of the braiding process is the ability to produce fabric, containing yarns at angles other than 0/90 degree directions.3 2.3.2 Two and Four-Step 3D Braiding The 2D braiding equipment is insufficient to produce 3D braided fabric. One of the first 3D braiding processes, was developed by General Electric and is known as the four-‐step or row and column braiding. This process involves a flat bed containing rows and columns of yarn carriers that form the preform shape. The name comes from the requirement of four separate sequences of row and column motion in order to produce the braided fabric or perform. In this process, the yarns are mechanically compacted after each step, similar to the
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weaving process. The braiding process can be controlled in order to produce diverse braid patterns and allows for high control over mechanical properties of the preform in the three principal directions.3 Later the technology was developed into a cylindrical configuration known as, Through-‐the-‐Thickness braiding. This is achieved by having identical rings arranged side by side in an axial arrangement. The rings allow the yarn carriers to move from ring to ring in the axial direction while the rings rotate to perform braiding. Cylindrical braiding equipment is advantageous in space saving.3 Another form of braiding exists in the two-‐step process. In this process majority of the yarns are fixed in the axial direction, and a small number of yarns are used to braid. The shape of the perform can be controlled by the arrangement of the axial carriers. Here the braiding carriers move completely through the structure between the axial yarns. It is advantageous in that any shape can be achieved, and there is no need for mechanical compaction of the yarns reducing the risk of damage.3 2.3.3 Multilayer Interlock Braiding This method of 3D braiding is most similar to the traditional 2D braiding processes. The equipment is comprised of a cylindrical braiding frame containing parallel braiding tracks with yarn carriers that can be transferred between the tracks, allowing for the interlocking of the adjacent layers. This version of 3D braiding is advantageous in that the interlocking yarns are in the plane of the structure and therefore allow the preform to maintain most of the in-‐plane properties. However, to achieve the same number of yarn carriers the multilayer interlocking braiding equipment needs to be larger, and the equipment is less adaptable. Figure 2.5 illustrates multilayer interlock braided fabric.3
Figure 2.5: Multilayer interlock braided fabric3
2.4 Knitting At the moment knitting is the least known and studied of the fabric production techniques for use as composite reinforcements. However, current conventional knitting machines are already capable of producing 3D
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architectures as well as very detailed and intricate shapes and geometries. A downside to the knitting process is the high level of curvature of the fibers, which is one of the main causes for loss in mechanical (see figure 2.6). However, this high degree of curvature can be beneficial for non-‐structural components that require complex shapes or require the preform to be stretched over a complex geometry. Also, the knitting pattern can be greatly varied in order to engineer the fabric properties, it is even possible to knit fabrics with large sections of straight yarns to improve in plane mechanical properties. Further developments in the electronic control of the needles have allowed for the component to be knit in a way that allow for the final 3D shape to be formed automatically without further alteration after the knitting process, without excessive waste. 3
Figure 2.6: 3D knit fabric3
The traditional forms of knitting are either warp of weft knitting. In weft knitting there is only a single yarn fed into the machine at a 90-‐degree direction with respect to the fabric production. The yarn forms a line of interlocking loops to form the knit fabric. While with warp knitting, there are a number of yarns feed into the machine at the 0 degree direction with respect to the fabric production. With warp knitting, multiple types of yarns can easily be knit together, however more yarn bundles will be needed and therefore can be more costly. The interlocking of the loops is achieved through a needle bed, a row of closely spaced needles that pull the yarns through the previously knit loops. Machines with two or more needle beds are capable of creating 3D knit fabrics. 3 2.5 Stitching
Stitching is the simplest and cheapest of the methods for producing a 3D
fabric architecture. The process involves the insertion of a needle carrying a z-‐directional yarn through layers of 2D fabric, in effect stitching the layers together and creating a 3D architecture (see figure 2.7). The z-‐binding yarns are most commonly aramid. This is due to their high toughness as well as equipment requirements. Current stitching machinery may be used with aramid yarns
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without further alterations. However attention must be given to their tendency to absorb moisture and insufficient binding to many common polymer resins.3
Figure 2.7: Stitched fabric3
Creating 3D architectures through stitching provides many benefits.
Among those is the possibility to use the process with traditional 2D woven, braided, knit, etc. prepregs. This allows for a great degree of flexibility in the fabric lay-‐up; using different material layers, as well as different yarn directions. Also, stitching can be placed only in the areas that require reinforcement in the z-‐direction, as well as complex stitching patterns by using current embroidery machinery and software. Another great advantage is the ability to create complex 3D shapes by stitching different component parts together.3
The main disadvantages with this process lay in the reduction of the in-‐plane properties. This is due to local fiber damaged caused by the needle insertion, increased crimp induced by the z-‐directional yarns, and resin-‐rich pockets formed by the bunching of fibers contained by the stitching yarns.3 2.6 Z-pinning Z-‐pinning is used as an alternative method to stitching. The process uses pre-‐cured reinforcement fibers, which are embedded in a thermoplastic foam and placed on top of the prepreg or dry fabric. The prepreg and foam are then prepared for curing. During the curing process, the thermoplastic foam collapses and the pressure slowly drives the reinforcing fibers into the component (see figure 2.8). With z-‐pinning, there is less crimping induced by the z-‐directional reinforcing fibers as well as less damage to the yarns in the prepreg, while still maintaining the high level of control over reinforcement placement.3
Figure 2.8: Z-‐pinning process3
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References 1. Long, A.C. Design and Manufacture of Textile Composites. Woodhead
Publishing Limited, Cambridge England. 2005. 2. M. Sc. Badawi, Said Sobhey A. M. Development of the Weaving Machine
and 3D Woven Spacer Fabric Structures for Light Weight Composites Materials. Dresden Technical University. 2007
3. Tong, L. Mouritz, A.P. and Bannister, M.K. 3D Fibre Reinforced Polymer Composites. Elsevier Science Ltd. Oxford, UK. 2002.
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3 Composite Manufacturing
3.1 Introduction
There are many different ways in which to consolidate the preform to create the final composite component, however not all of these processes are suited for 3D preform consolidation. Methods such as hand impregnation, pultrusion, and commingled yarns greatly distort the fabric architecture during composite consolidation, significantly diminishing the final mechanical properties of the component. Therefore, in order to reap the benefits of the 3D preform production technologies, the correct consolidation technology must be chosen. At this moment the only manufacturing process that is successful in consolidating 3D fiber performs is Liquid Molding (LCM). This is due to its high flexibility regarding component shape. For preforms of complex geometries LCM offers opportunity to produce a high quality component for a relatively low cost. 1,2
LCM consists of a family of processes, which involves the impregnation of a dry reinforcement with a liquid thermosetting resin. The most widely used processes of the LCM family are: resin transfer molding (RTM), SCRIMP, and resin film infusion (RFI). Here we will review the different processes and the opportunities and challenges that they each provide with respect to the formation of 3D composites. 1,2 3.2 Composite Consolidation Techniques 3.2.1 Resin Transfer Molding Resin transfer molding is the most commonly used of the liquid molding techniques. It consists of a closed mould system, which produces components with excellent surface finishes and fiber volume ranging between 50-‐60%. It is perfect for production of high quality automotive and aerospace components. In this process the preform is place between a closed mould, and the resin is pumped into the mould at pressures ranging from 2-‐20 bar (see figure 3.1). The resin travels in the in-‐plane direction to the preform, this is a distinguishing feature of this process. This makes impregnation time and maximum injection length (of the resin) important factors and considerations, both being determined by pressure gradient, resin viscosity, permeability of the fiber bed,
32
and resin polymerization rate. Using these variants, injection time and length can be determined and maximized with economical considerations. However, the tooling used in RTM is often expensive due to the high-‐pressure requirements, and component size is limited due to maximum injection length (two meters is generally the limit) and financial considerations. 1,2
Figure 3.1: RTM
Variations to RTM include Vacuum assisted RTM (VARTM) where a vacuum is applied to aid in consolidation, air removal and increase the velocity of resin infiltration, and Structural Reaction Injection Molding (SRIM) where higher injection pressures are used to decrease production time. 1,2 3.2.2 Resin Film Infusion Resin Film Infusion (RFI) is an alternative to the RTM method. In RFI the resin is present in the form of a film instead of a liquid. The resin film is placed on the tool surface, over which the preform is placed. On top of the preform a release film (to allow for easy component removal) and breather material (in order to form a vacuum) are added. Everything is bagged, vacuumed and placed in an autoclave to be heated under pressure (see figure 3.2). The resin film melts and is sucked up into the preform through capillary action, thus being absorbed in the thickness direction. The pressure can be varied in order to compact the component to the desired fiber volume fraction. 1,2
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Figure 3.2: RFI2
RFI has many advantages and disadvantages of RTM. The advantages of RFI consist of the relatively low tooling costs and the loss of the maximum injection length limitations. However, RFI has limitations in the thickness of the component. Therefore RFI is usually used with thinner larger components while RTM is suited for smaller thicker components. Another disadvantage of RFI is the relatively high costs of the resin film, which can cost up to two times the price of the pure resin, as well as their difficulty to handle. 1,2 3.2.3 SCRIMP Seemann Composite Resin Infusion Process (SCRIMP) is a mixture of both the RTM and the RFI consolidation processes. SCRIMP uses a liquid resin from an external source, like with RTM, and impregnates the preform in the thickness direction, like with RFI. To achieve resin absorption in the thickness direction, a resin distribution medium is used. This medium allows the resin to flow quickly over the preform surface, spreading over the entire surface and then being absorbed in a similar fashion to RFI through the thickness of the component. The preparation is similar to RFI, with the layering of the components and sealing in a vacuum bag. The prepared setup is then placed under vacuum and the resin is sucked into the freeform through a resin inlet port. The vacuum created pressure gradient provides the driving force for resin infusion and no other injection equipment is needed. This process has an advantage in that tooling costs are cut similar to RFI, as well as cost reductions in the raw materials as in RTM. The limitations of thickness and maximum length are also overcome in this process. 1,2 3.3 Consolidation Equipment Just as for the selection of consolidation techniques, the selection of equipment to optimize composite consolidation is based off of many variants such as production quantities and qualities, material selection, process, etc. In
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this section we will briefly discuss the equipment used for the three main processes described above. 3.3.1 Tooling (mold)
For the RTM process a closed mold is used, meaning that the preform is completely enclosed by a mold, while for the RFI and SCRIMP processes a one sided mold or open mold is used. The most important consideration is the material used to produce the mold. This depends on cost and production volume. For low production volume, wood and plaster are generally used to make the mold due to the ease of mold production and low costs. However for large production volumes (10,000s) metals such as steel and aluminum are chosen. For high production volumes, it is more cost efficient to use metals due to their high durability the need for repair or replacement is greatly reduced. Also metals tend to produce higher quality surface finishes and allow for a wider range of processing temperatures.
3.3.2 Heating and Cooling As with all the other equipment, the heating and cooling systems are
dependent on the consolidation process. For RFI and SCRIMP, using an open mold, it is more cost effective to use an external heating sources, such as a convection oven, autoclave (figure 3.3) or other similar heating devices. The heating system selected will depend on component size, shape, required heating rate and curing temperature. Cooling is generally achieved through air-‐cooling. 2,4
Figure 3.3: Autoclave for composite consolidation. Image provided by AAC research
For RTM heating using external sources becomes too expensive. Here it becomes more cost effective to use an integrated heating system. This system consists of a series of internal channels that allow for temperature controlled
35
water or oil to flow through the mold. The heat is transferred between the water and the mold to control the temperature of the mold. 2 3.3.3 Injection Equipment Injection equipment is specific to the RTM process as it is the only process requiring the pressurized injection of resin into the mold. This equipment generally consists of a resin storage area, resin feed apparatus and delivery nose and is highly dependent on resin choice and resin handling requirements. The first option to consider is whether to have the resin injection controlled by constant pressure or constant flow rate. Constant pressure injection is beneficial in the sense that pressures can be controlled and therefore will not exceed equipment capabilities, however with constant pressure the flow rate will decrease as the preform becomes impregnated with resin and if resin cure rates are not controlled defects may form in the final component. Constant flow rate ensures that the preform is impregnated at a constant rate and therefore pre-‐curing is no longer a problem, however pressures required to maintain flow rate may be extremely high, requiring expensive equipment. 2 The second option to consider is whether to have resin and hardener injected together or separately. Premixed and simultaneously injected resin and hardener have better mixing and curing control. The equipment is simpler and cheaper with a higher flexibility to change between resins and lower maintenance costs. However, having the resin and hardener premixed runs the risk of curing occurring in the reservoir, therefore only limited amounts can be stored in the reservoir at a time and often leads to excess waste. Therefore it is generally better suited for components produced in low volume or using different resin systems. On the other hand, separately injected resin/hardener systems reduce waste as this system mixes only the required amounts at any given time. However it is difficult to switch between different resins and due to the increased complexity of the equipment, maintenance costs are increased. Therefore this system is generally used in production lines where large numbers of components are produced and flexibility is not as important.2 3.4 Optimization Optimization of the consolidation process is very important to maintain product quality, reduce waste, and reduce costs. Optimization involves the correct selection of materials, equipment, and processing requirements. As stated above, resin selection is the most important determinant of injection equipment. The selection of a resin is based off of both component requirements (mechanical, environmental, health, and costs) and the manufacturing process. Here we will focus on the consideration given to the manufacturing process when selecting a resin. The fist most important consideration is the viscosity of the resin. The viscosity must allow for complete infusion of the preform without the need of excessive pressure. Generally the pressure range must fall between 100kPa – 700kPa, and obviously pressure is determined by the viscosity of the resin combined with the permeability of the preform which is a factor of fiber
36
volume and injection distance, however it is a general rule that resin viscosity should not exceed 500cps during molding.2 Using Darcy’s law we can relate pressure, flow rate and resin viscosity, preform permeability, pressure gradient, and injection distance.1,2 Flow Rate = [(Permeability x Cross Section)/Viscosity] x (Pressure drop/Length) Re-‐written in variables: 〈u〉 = (-‐K/η)⋅∇〈P〉f (eq. 3.1)
〈u〉 = resin velocity vector averaged over fluid volume K = permeability tensor of the textile preform η = resin viscosity ∇〈P〉f = pressure gradient averaged over the fluid volume As thermosets are the most commonly used resins for LCM another important factor to consider is the relationship between viscosity, temperature and setting time. This plays an important role in the selection of pressure vs. flow rate injection equipment.1,2
Figure 3.4: Viscosity vs. Time – temperature dependence of thermoset TGDDM resin
Image taken from Understanding of Rheology of Thermosets3
As seen in the illustration (Figure 3.4), initial viscosity of thermoset resins decrease with increasing temperatures, however curing rate increases with increasing temperature, causing the viscosity to increase over time. Therefore it is important to find the correct balance between the viscosity, temperature and curing time.2,3 The architecture of the textile preform forms a complex network of channels through which the resin flows. Certain architecture types can create preferential flow directions, which can lead to entrapped air. Using equation 3.1 above it is possible to derive an equation describing the mold filling process by taking the partial derivative of flow rate with respect to time:1,2
37
The resin is assumed incompressible, therefore:
δ〈u〉/δt = 0
Viscosity is assumed constant, therefore:
δ(K⋅∇〈P〉f)/δt = (δK/δt)⋅∇〈P〉f+ K⋅(δ∇〈P〉f/δt) = 0
Boundary Conditions: Mold walls: n (K∇) = 0 Flow front: P = 0 Injection gates: P=Pi
In order to minimize defects in the resin injection process it is common to us Liquid Molding Simulation (LIM). LIMs use the above equations with boundary conditions to preform a finite element analysis simulating resin flow in the mold cavity. The variables are most often: Mold geometry, resin and preform properties, gate location, and injection conditions. Using LIMs it is possible to optimize resin, gate location, and determine minimum fill time, possible disturbances and problems in the filling process and injection conditions to cut costs and reduce defects.1
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References
1. Long, A.C. Design and Manufacture of Textile Composites. Woodhead Publishing Limited, Cambridge England. 2005.
2. Tong, L. Mouritz, A.P. and Bannister, M.K. 3D Fibre Reinforced Polymer Composites. Elsevier Science Ltd. Oxford, UK. 2002.
3. Franck, A.J. Understanding the Rehology of Thermosets. TA Instruments 2004.
4. http://www.aac-‐research.at/products/products_AAC_CompositePolymer_de.html
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4 Textile Fiber Reinforcement Properties
4.1 Introduction
The characterization of textile reinforcement properties, especially those of biaxial tension and shear, is important in the prediction of reinforcement drapability during composite forming and the determination of the final composite characteristics.5, 7 Some of the composite forming process are similar to those used for metal forming, however the discontinuous nature of fabric structures cause it to act differently than continuous materials such as plastic sheets and sheet metal.1 The drapability of the textile limits the 3D composite geometries that can be produced. Therefore having a good understanding of textile reinforcement drapability is essential when designing and choosing the components of the composite. In this section we will discuss the different methods available for analyzing the biaxial and shear behavior of 3D woven textile reinforcements.1, 5, 7 4.2 In-Plane Shear In-‐plane shear is considered the primary deformation mechanism of the textile reinforcement during composite forming. This is of great importance, as it will be the main determining factor in the limitations to the final 3D composite shape. The main objective of in-‐plane shear testing is to determine the limit to deformation, which is characterized by the locking angle, or maximum level of shear deformation before wrinkling occurs. Among the testing methods available we will discuss bias extension and picture frame.7, 8, 10 Bias extension tests have been popular due to their simple procedures and useful measure of the lock angle, which can then be used to determine the deformation limit. In this test, rectangular samples are cut in the bias direction and placed between two vertical clamps (see figure 4.1). The sample is then subjected to uniaxial extension. Some of the drawbacks of this test are that the deformation field within the sample is non-‐uniform, with maximum shearing occurring in the center of the sample, therefore visual monitoring is needed to determine the shear angle as it cannot be determined by crosshead displacement.7, 8, 10
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Figure 4.1: Biaxial tension test (left) and Picture frame test (right).8
The picture frame test is usually employed to test high shear angles and produces uniform shear throughout the sample. The fabric sample is mounted into a hinged frame paying close attention to ensure the fibers are parallel to the frame, as a slight variation in fiber direction will cause drastically different results (see figure 4.1). The two opposite corners are pulled in opposite directions. In order to achieve pure shear the yarns in the frame should be free to rotate, however this is extremely hard to achieve and therefore in most cases the fabric edges are held with a firm grip. Having a firm grip causes the fibers near the frame to bend leading to a difference between the shear angle in the fabric and in the frame. In order to reduce the effects of the firm grips, it is common to use a cross-‐shaped sample and remove the parallel yarns near the frame. Direct measurement of axial load and shear angle is possible through the following relationships:7, 8, 10
(4.1)
(4.2)
Shear force (Fs) is determined by the axial force (Fx), the slide length of the shear frame (l) and the frame angle (Φ). While frame angle can be determined directly from crosshead displacement (Dx). Shear angle can then be determined from the frame angle.
(4.3)
Photo camera and video cameras are employed to measure yarn width, pitch and estimate lock angle. As mentioned above, lock angle characterizes the deformation limit, or the maximum deformation before wrinkling occurs. In
41
order to determine the wrinkling point, samples are marked with horizontal lines, wrinkling occurs when the lines buckle.7, 8, 10 4.3 In-Plane Biaxial Tension
Woven fabrics are composed of perpendicular interlacing yarns, which are in turn composed of fibers. The cross sectional area of the fibers is so small that it is assumed they are only subject to tensile stress in the fiber direction. The interlacing of the yarns causes them to become wavy, or crimped. When placed under tension the yarns begin to straighten. If tension is applied in only one direction the yarns in that direction will straighten completely while the crimp of the interlacing yarns will increase to accommodate the straightening of the other yarns. On the other hand, if both sets of yarns are placed under tension a crimp equilibrium will be reached. This is a biaxial phenomenon. Due to the biaxial behavior and yarn undulations the tensile behavior of a woven fabric is non-‐linear at low tensions (see figure 4.3).1, 3, 5, 7, 8
Figure 4.3: Illustrating non-‐linear behavior of woven fabric8
Characterization of the biaxial tension behavior of woven fabrics is achieved using a biaxial testing machine. The machine is equipped with four independently controlled axes. These axes are computer directed allowing for independent control of direction, distance and speed of axes displacement.
Figure 4.4: Biaxial testing Machine10
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Figure 4.5: Biaxial testing sample8
The fabric sample, in the shape of a cross, is attached using free moving clamping rigs (figure 4.4 and 4.5). The clamps are equipped with load cells to record forces (see figure 4.6). Deformations are recorded using optical techniques. A common technique is to use a monochromatic CCD video camera to record the changes in fabric geometry and use digital image correlation (DIC) to quantify the data. DIC requires a camera to be positioned perpendicular to the fabric surface and the assumption that there are no out of plan deformations. DIC records the change in the surface of the sample by a series of images taken of the sample at different deformation stages. This requires points of reference, with textiles this can be naturally created from weave and surface textures, or a speckled paint pattern can be applied. 6
Figure 4.6: Clamps10 In the end, the DIC and the forces recorded on by the clamps gives a mapping of the deformation concentrations for the induced stresses. This data is important in knowing how the fabric reacts under biaxial tension, and can lead to a better understanding of how the fabric will behave both in the composite as well as during forming.
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References
1. Buet-‐Gautier, K. and Boisse, P. Experimental Analysis and Modeling of Biaxial Mechanical Behavior of Woven Composite Reinforcements. Experimental Mechanics. Vol. 41, No. 3, September 2001.
2. Bogdanovich, A.E., and Pastore, C.M. Mechanics of Textile and Laminated Composites. Chapman & Hall, 1996.
3. Gasser, A., Boisse, P., Hanklar, S. Mechanical Behavior of dry Fabric Reinforcements. 3D Simulations Versus Biaxial Tests. Elsevier. Computational Material Science 17 (2000) 7-‐20.
4. Ko, Frank K., and Chou, Tsu-‐Wei. Textile Structural Composites North Holland, 1989.
5. Launay, Jean, Lahmar, Fathia, Boisse, Philippe, Vacher, Pierre. Strain Measurement in tests on Fibre Fabric by Image Correlation Method. Advanced Composites Letters, Vol. 11, No. 1, 2001.
6. Lomov, S.V., Boisse, Ph., Deluycker, E., Morestin, F., Vancloster, K., Vandepitte, D., Verpoest, I., Willems, A. Full-field strain measurements in textile deformability studies. Composites: Part A 39 (2008) 1232-‐1244.
7. Lomov, S.V., Willems, A., Barburski, M., Stoilova, Tz., Verpoest, I. Experimental Textile Mechanics: Characterization of Deformability of Reinforcements for Textile Composites. http://www.mtm.kuleuven.ac.be/research/c2/poly/index.htm
8. Long, A.C. Design and Manufacture of Textile Composites. Woodhead Publishing Limited, Cambridge England. 2005.
9. Luo, Y. and Verpoest, I. Biaxial tension and ultimate deformation of knitted fabric reinforcements. Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, Belgium. Composites: Part A 33 (2002) 197-‐203.
10. Quaglini, Virginio, Corazza, Carola, Poggi, Carlo. Experimental Characterization of Orthotropic Technical Textiles Under Uniaxial and Biaxial loading. Composites: Part A 39 (2008) 1331-‐1342.
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5 Composite Modeling
5.1 Introduction
Composites are composed of a reinforcing textile or fiber and matrix materials. Their properties depend on the mechanical properties of each individual component as well as the interaction between them. For simplicity sake let us consider a composite embedded with unidirectional parallel fibers. On a microscopic scale the composite would be considered heterogeneous, due to the alteration between sections of fiber and matrix (see figure 5.1). However, due to the scale in which composites are used and the impracticality of modeling a heterogeneous microstructure, composites are usually assumed to have a homogeneous macrostructure. Therefore, when modeling composite behavior, it is extremely important to select a representative volume that accommodates all demonstrated properties of the composite on the microscopic level.12, 18, 23
Figure 5.1: Illustrating the microscopic heterogeneity of a composite structure. Fibers shown in
grey and matrix in blue. It is also important to distinguish between isotropic, anisotropic and orthotropic behaviors. Composites are known for their anisotropy or differing mechanical properties depending on orientation, and fall under orthotropic materials as they generally have three axes of symmetry around which the properties remain the same (see figure 5.2). 12, 23
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Figure 5.2: Illustrating the three planes of symmetry that make composites orthotropic
materials. Planes are shown in yellow.
Modeling of composite materials is a very useful tool in determining the mechanical properties, as experimental methods tend to be extremely expensive and impractical. In this chapter we will review the fundamentals on which composite modeling is based as well as some of the more widely used methods for modeling 3D woven composites. 12,23 5.2 Fundamentals To begin let us review the fundamentals that are required for composite modeling. The first being the generalized Hooke’s law -‐ the linear constitutive relationship between stress and strain. It is represented by the following:
[σ] = [C][ε] (5.1)
(5.2)
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[C] is the elastic stiffness constant and [S] is the inverse matrix of [C]. Leading to the following relationships:
(5.3)
(5.4)
(5.5)
Where ui (i=1,2,3) are the displacements in Cartesian coordinates and xj (j=1,2,3) are the coordinates.
The above relationships can be further simplified for orthotropic
materials as they have the three planes of symmetry. Becoming:
(5.6)
(5.7)
47
Where E1, E2, E3 are the three elastic moduli, G12, G23, G31 are the three
shear moduli, and ν12, ν23, ν31 are the three independent Poisson’s ratios. Remember that:
(5.8)
Therefore the constitutive relationship for elastic behavior of orthotropic materials becomes:
ε1 = 1/E1 (σ1 -‐ ν12σ2 -‐ ν13σ3)
ε2 = 1/E2 (σ2 -‐ ν21σ1 -‐ ν23σ3)
(5.9) ε3 = 1/E3 (σ3 -‐ ν31σ1 -‐ ν32σ2)
γ12 = τ12/G12 γ23 = τ23/G23 γ13 = τ13/G13
5.3 Representative Volume As discussed previously, it is very important to select a good representative volume. The representative volume must be large enough to include all microstructural features. Think of it as a type of monomer, or building block that when replicated is capable of reconstructing the composite. By determining the mechanical properties of the representative volume, we can use continuum mechanics to reproduce the properties of the material as a whole.12, 23 For a representative volume subject to a homogeneous macroscopic stress or strain and no body forces, the average stress and strains are defined as the sum of the micro-‐stresses and micro-‐strains in the representative volume, divided by the volume and can be represented by the following equations:
(5.10)
σij and εij are the true stresses and strains (micro stresses and strains) in the representative volume V. 12, 23 The boundary conditions for iso-‐strain and iso-‐stress on the representative volume are expressed by the following: Iso-‐strain: (5.11)
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Iso-‐stress: (5.12)
When there is perfect interfacial bonding between the representative volumes, then = and intrinsically = . nj is the unit normal vector pointing away from the surface of the representative volume. 23 By applying the homogeneous boundary conditions to the stress-‐strain relationship we can define the effective properties of the representative volume as follows: Iso-‐strain: (5.13)
(5.14)
Iso-‐stress: (5.15)
(5.16)
Solutions for true stress and strain can be obtained with either analytical or numerical approaches. Analytical approaches are cheaper and faster, but require a large number of assumptions and therefore may exclude certain characteristics and their input. Finite element methods (numerical) allow for more accurate modeling, however can be quite expensive.12, 23
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5.4 Rule of Mixtures The rule of mixtures is very useful in many analytical approaches for determining the longitudinal modulus of unidirectional composites and the major Poisson’s ratio from the properties of the individual components. However for determining the transverse and shear moduli modifications must be made. The assumptions made with the rule of mixtures are that the composite is subject to uniform or iso-‐stress and iso-‐strain conditions, no transverse stresses, and that the load carried by the fiber and matrix is proportional to both their moduli and cross-‐sectional area. For determining longitudinal modulus it is also assumed that the fiber and matrix are elastic bodies acting in parallel resulting in the following relationships: (5.17)
(5.18)
Vf and Vm representing the volume fractions of the fiber and matrix respectively, and Ef, Em, νf, νm represent the elastic moduli and Poisson’s ratios of the fiber and matrix components.13, 23
To approximate the transverse elastic properties of a composite, the fiber and matrix components are assumed to be elastic bodies in series, however this is an inaccurate method for approximation because in reality the transverse elastic properties lay between the series and parallel models.12, 23
(5.19)
In order to better approximate the transverse properties of a composite
from the individual component properties, Halpin-‐Tsai equations offer a good approximation by taking into account the fact that the properties lay somewhere between a parallel and series model.12, 23
(5.20)
(5.21)
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Where: M represents E2, G12, G23 of the composite Mf/m represents Ef/m or Gf/m of the fiber or matrix Vf is the fiber volume fraction
ξ is a constant representing the way the load is shared between the fiber and the matrix. (ξ=0 series, ξ=∞ parallel)
5.5 Basic Models for 2D Woven Composites The first step to applying a model is to choose the representative volume of a woven composite. Fortunately woven textiles are formed by a repetitive geometric pattern represented by the weave pattern. This makes selection of the representative volume, or unit cell, relatively easy as it is the smallest volume that represents the weave pattern. This pattern is represented by the number of interlacing weft ( ) and warp ( ) yarns. 23
For plain weave = =2 For twill weave = =4 For Satin weave (5-‐harness) = =5 This pattern or weave geometry can be seen in figure 5.3 below, demonstrating the most common weave geometries.
Figure 5.3: Examples of common weave geometries
Let us begin by discussing several basic 1D methods for modeling 2D woven composites: Mosaic model and Fiber Undulation model. These methods are considered 1D as they either do not consider fiber undulation or consider fiber undulation in only one direction. 12, 23 5.5.1 Mosaic Model
The mosaic model idealizes the composite as a grouping of asymmetrical cross-‐ply laminates that can then be modeled using the classical laminate theory (CLT) neglecting shear deformation in the thickness direction.
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CLT assumes that the composite is composed of thin sheets or layers of composites with unidirectional fiber reinforcements. Due to the thinness of each individual layer we can assume for each layer to be in a plane stress state or in other words that σ3=0. With these assumptions we can simplify equation 5.6 into the following:
(5.22)
(5.23)
Figure 5.4: CLT modeling of a layered composite
Using the above assumptions the constitutive equations are given by the following:
(5.24)
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(5.25)
N – Stress resultant
M – Bending moment ε -‐ In-‐plane strains (mid-‐plane) k – Curvature (mid-‐plane) Aij – In-‐plan stretching stiffness Bij – Bending/stretching coupling Dij – Bending stiffness Qij – Elastic constants of a lamina Subscript k referring to the kth layer and z referring to the distance between the mid-‐plane and the layers boundary as seen in figure 5.4. If we assume an iso-‐strain field in the middle plane, and that our composite can be modeled as an idealized asymmetrical cross-‐ply laminate, then we can express the stiffness constants by the following equations: (the simplification is only applicable for uniform weave geometries and not hybrid weaves) 2, 3, 11, 16, 18, 23
(5.26) 5.5.2 Undulation Model While the mosaic model is good for predicting the upper and lower bounds for effective stiffness and compliance constants for a unit cell of a woven composite, it does not take into consideration non-‐uniform stresses and strains that tend to concentrate in the fiber interlacing regions or fiber undulation. The fiber undulation model was created as a more accurate prediction model. 2, 3, 23
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Figure 5.5: Fiber undulation model
It is assumed that the fiber undulation in weft and warp yarns can be expressed using the following sinusoidal equations:
Weft: (5.27)
Warp: when a0 < x < a/2
(5.28)
when a/2 < x < a2
au representing the length of the undulation and a0=(a-‐ au)/2 and a2=(a+ au)/2. Undulation in the warp direction is neglected. Refer to figure 5.5 for definitions of other variables. As can be seen in figure 5.5, the unit cell in the fiber undulation model consists of two straight cross-‐ply regions and one undulated region. The two straight cross-‐ply regions can be model as before, while the elastic stiffness constants of the undulated weft yarns can be expressed in terms of weft elastic constants (Qij) and the undulation angle θ. The undulation angle is represented by the following equation:
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(5.29) And the elastic stiffness constants of the undulated weft yarn are expressed by:
(5.30)
(5.31)
Ishikawa and Chou6 obtained the following formulas:
(5.32) where superscripts F, W and M represent weft, warp and matrix respectively. The average effective properties of the unit cell can be determined by the sum of the average straight cross-‐ply regions and the average undulated region. Here we have the average compliance equations, inverted matrices:
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(5.33)
It is important to note that this model only takes into consideration
undulation in the weft yarn, not in the warp direction. To take into consideration yarn undulation in both directions a 2D model is needed. Further, to take into consideration yarn undulation in both directions as well as out-‐of-‐plane elastic constants a 3D model is needed. Reviews of 2D models can be found in work completed by Naik and colleagues14, 15 and for 3D models in work completed by Hahn and Pandey16 and Vandeurzen et al.24, 25, 26 for 3D models. 5.6 Models for 3D Woven Composites There are many different ways to model 3D woven composites, many depend on the geometry of the woven fabric, be it 3D orthogonal interlock, 3D through-‐thickness angle interlock or layer-‐to layer interlock (see figure 5.6). The three main models we will be discussing here will be the orientation averaging model, mixed iso-‐stress and iso-‐strain, and finite element applications.2, 3, 11, 12, 16, 23
Figure 5.6: Types of 3D woven fabrics
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5.6.1 Orientation averaging For Orientation averaging models the composite is regarded as a collection of small volumes, each volume being modeled as a unidirectional composite with transversely isotropic properties. This model has been applied to all three fabric geometries mentioned above. Each composite is divided into suffer (s), filler (f) and warp weavers (w1 and w2). The effective elastic properties are modeled using the simplified 3D model for 2D woven composites for non-‐mixed yarn systems:
(5.36)
As ideal geometry differs from the true geometry, it is necessary to take into consideration the effect of tow waviness on the elastic properties. Therefore a normal distribution is calculated for the out-‐of-‐plane alignment angle, ξ:
(5.37)
With a density function of:
(5.38)
Where σξ is the width of the distributions. In order to reduce the Young’s modulus and Poisson ratio caused by waviness, a waviness knockdown factor is introduced:
for σξ less than 10° (5.39)
This method provides respectable predictions of the in-‐plane macroscopic elastic constants and a reasonable estimation of the through-‐thickness elastic constants. 2, 3, 22
5.6.2 Iso-strain and Iso-stress model For prediction of mechanical and thermo-‐elastic properties of 3D orthogonal and angle-‐interlock composite materials, Tan et al.20, 21, 22 proposed a mixed iso-‐stress and iso-‐strain based unit cell modeling method. For a 3D orthogonal fabric we consider the structure to be simplified into rectangular cross-‐sectional shapes in three mutually orthogonal directions. An example of a unit cell is shown in figure 5.7 (a).
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Figure 5.7: a) Unit cell for the mixed iso-‐strain and iso-‐stress model. b) Division of the unit cell
into 4 blocks The Unit cell is further divided into smaller blocks, which can then be divided again to create individual unidirectional composite blocks (see figure 5.7 (b)). The properties of each unidirectional block, A, B, C, D, E, F, G can be determined using methods described previously. To determine the overall properties of the unit cell it is possible to assemble the blocks individually in the x-‐, y-‐ , and z-‐directions (see figure 5.8)
Figure 5.8: Possible assembly directions of block A and B
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For an x-‐assemblage of NA number of A blocks and NB number of B blocks in the strip, the overall material properties are represented by the following equations:
(5.40)
Where VA and VB are the volume fractions of block A and block B in the strip, and subscripts S, A, B refer to strip, block A and block B respectively. For a y-‐assemblage of A and B blocks:
(5.41)
For a z-‐assemblage of A and B blocks:
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(5.42)
In figure 5.7 b) it is seen that the blocks A and B, D and E, and F and G can be evaluated using the x-‐assembly equations. Strips 1 and 2, and 3 and 4 can then be modeled using the y-‐assembly equations. Finally the top and bottom planes can be evaluated using the z-‐assembly equations, estimating the overall properties of the complete unit cell. 2, 3, 12, 23 5.6.3 Finite Element Model Finite Element Modeling (FEM) is probably the most accurate method for predicting elastic and failure behavior of textile composites. It allows for detailed modeling of complex geometries and varying material properties. FEM works by breaking down the composite structure into small regions whose constitutive properties can be easily evaluated. Using brick, wedge and tetrahedral elements it is possible to generate a mesh depicting in detail the true geometry of the unit cell as seen in figure 5.9. Determination of true fabric geometry in the composite is of course is limited by current measurement technologies and may not be cost effective.
Figure 5.9: Example of a 3D FE model of a unit cell of a 3D orthogonal Woven composite
material.22 Yarns are modeled as orthotropic, with respect to the principle axes, with cross sectional shapes of rectangular, circular, elliptical or lenticular, while the matrix is assumed homogeneous and isotropic. It is important to note that accuracy of FEM depends on how accurately the fabric geometry is modeled. 2, 3, 11, 33
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References 1. Aboudi J., 1991, Mechanics of Composite Materials -‐ A Unified
Micromechanical Approach, Elsevier, Amsterdam, The Netherlands. 2. Ansar, mahmood, Wang Xinwei, Zhou Chouwei, 2011, Modeling strategies
of 3D woven composites: A review. Cmoposite structures 93, Elsevier. 3. Bogdanovich, A.E., and Pastore, C.M. Mechanics of Textile and Laminated
Composites. With applications to structural analysis. Chapman & Hall, London, UK 1996.
4. Chou T.W. and F.K. KO,1989, Textile Structural Composites, Volume 3 Composite MaterialsSeries,ElsevierSciencePublishers,Amsterdam,NewYork,U.S.A., 1989.
5. Hahn H.T. and R. Pandey, 1994, A micromechanics model for thermoplastic properties of plain weave fabric composites, J. Eng. Mat. & Tech., 116: 517-‐423
6. Ishikawa T. and T.W. Chou, 1982a, Elastic behavior of woven hybrid composites, J. Comp. Mat. 162-‐19.
7. Ishikawa T. and T.W. Chou, 1982b, Stiffness and strength behavior of woven fabric composites, J. Mat. Sci., 17:3211-‐3220.
8. Ishikawa T. and T.W. Chou, 1983a, One-‐dimensional Micromechanical analysis of Woven Fabric Composites, AIAA J., 21:1714-‐1721.
9. Ishikawa T. and T.W. Chou, 1983b, In-‐plane thermal expansion and thermal bending coefficients of fabric composites, J. Comp. Mat. 17:92-‐104.
10. Ishikawa T. and T.W. Chou, 1983c,Nonlinear behavior of woven fabric composites, J. Comp. Mat. 17:399-‐413.
11. Ko, Frank K., and Chou, Tsu-‐Wei. Textile Structural Composites 12. Long, A.C. Design and Manufacture of Textile Composites. Woodhead
Publishing Limited, Cambridge England. 2005. 13. Mori T. and Tanaka K., 1973,Average stresses in matrix and average
elastic energy of materials with misfitting inclusions, Acta Metalurgica, 21571-‐574.
14. Naik N.K. and V.K. Ganesh, 1992, Prediction of on-‐axes elastic properties of plain-‐weave fabric composites, Comp. Sci. & Tech., 45:135-‐152.
15. Naik N.K. and P.S. Shembekar, 1992a,Elastic behavior of woven fabric composites: I-‐ lamina analysis, J. Comp. Mat. 26:2197-‐2225.
16. Onate, Eugenio and Kroplin, Bern. Textile Composites and Inflatable Structures. Springer, The Netherlands. 2005.
17. Shembekar P.S. and N.K. Naik, 1992,Elastic behaviourof woven fabric composites: II-‐ Laminate analysis, J. Comp. Mat., 26:2226-‐2246.
18. Stig, Fredrik. An Introduction to the Mechanics of 3D-Woven Fiber Reinforced Composites. KTH School of Engineering Sciences, Stockholm, Sweden. April 2009.
19. Tan P., L. Tong and G.P. Steven, 1997a, Modeling for predicting the mechanical properties of textile composites -‐ A review, Composites, 28A:903-‐922.
20. Tan P., L. Tong and G.P. Steven, 1998,Modelling approaches for 3D orthogonal woven composites, J. Rein. Plastics & Comp., 17545-‐577.
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21. Tan P., L. Tong and G.P. Steven, 1999a, Models for predicting thermo mechanical properties of 3D orthogonal woven composites, J. Rein. Plastics & Comp., 18:151.
22. Tan P., L. Tong and G.P. Steven, 1999b,Micro-‐mechanics models for mechanical and thermo-‐mechanical properties of 3D angle interlock woven composites, Comp., 30A:637-‐648.
23. Tong, L. Mouritz, A.P. and Bannister, M.K. 3D Fiber Reinforced Polymer Composites. Elsevier Science Ltd. Oxford, UK. 2002.
24. Vandeurzen P., J. Ivens and I. Verpoest, 1996a, A three-‐dimensional micromechanical analysis of woven fabric composites: I. Geometric analysis, Comp. Sci. & Tech., 56: 1303-‐1315.
25. Vandeurzen P., J. Ivens and I. Verpoest, 1996b, A three-‐dimensional micromechanical analysis of woven fabric composites: 11. Elastic analysis, Comp. Sci. & Tech., 56: 1317-‐1327.
26. Vandeurzen P., J. Ivens and I. Verpoest, 1998, Micro-‐stress analysis of woven fabric composites by multilevel decomposition, J. Comp. Mat., 32:623-651.
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6 3D Woven Composites
6.1 Introduction
3D composites have been developed in order to combat the problems faced by 2D composites: reduce fabrication costs, increase through-‐thickness mechanical properties and improve impact damage tolerance. In 3D composites, fibers are aligned not only in the x-‐, y-‐direction, but also in the through-‐thickness (z-‐) direction. By placing fibers in the z-‐direction mechanical performance, impact damage and ease of processing can all be improved.14 3D composites consist of several types, including woven, knit, braided, stitched, and z-‐pinned. The first 3D composite to be manufactured was a braided carbon-‐carbon composite in the 1960s to be used in rocket motor components. Soon after 3D woven carbon-‐carbon composites were used for the brake components of jet aircrafts. 3D composites were meant to replace high-‐temperature metal alloy parts to improve durability, heat distortion and weight. These early 3D composites may not have been FR composites, however the idea still remains valid.14 6.2 3D Woven Composites At the moment 3D woven composites are used in only a few niche markets. They show a great potential for applications in the aerospace, marine, infrastructure, military and medical fields, due to their benefits: potential reduced fabrication costs, increased design flexibility, improved impact resistance and through-‐thickness mechanical properties. However there are still many challenges impeding their application, such as current production cost due to small scale production, cost of certification of new materials for load-‐bearing structures, and uncertainty of benefits. Only once these barriers are overcome will 3D woven composites make a name for itself in the world of composites. Here in this section we will discuss microstructural features and their effect on mechanical properties, delamination resistance, impact damage, as well as the different failure mechanisms.14 6.2.1 Microstructure Features and Crimp The microstructure is determined mainly by the fiber architecture of the
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preform and the weaving process. Defects in composite microstructure come mainly from the weaving of the fabric reinforcement and include abrasion, breakage, and distortion of yarns.9 However unequal distribution of resin during the composite forming stage can also pose a problem. Defects, such as these, can significantly degrade the composite properties. Abrasion and breakage caused by weaving cause large reductions in tensile strength of the yarns.14
Figure 6.1: Tensile strength at different stages of the weaving process9
This degradation of tensile strength is seen in figure 6.1 above. A reduction in tensile strength of about 30% is seen at the later stages of the weaving process. The extent of damage and reduction of properties depends on the weave, loom, as well as yarn material, type (twisted or untwisted), and diameter. Glass fibers display the highest loss of strength in comparison with carbon or Kevlar.14 Distortion of fibers from their idealized architecture is due to the interlacing of the yarns during weaving. Misalignment and waviness in 3D performs is much higher than that of the 2D performs, as much as 25% higher, and can cause a large degradation in composite properties.5 Crimping, or yarn waviness, is possibly the most important factor in determining the mechanical properties of the final composite. The more crimped the yarns, the lower the strength of the composite. When a crimped structure is subject to a tensile force the yarns begin to straighten, however the yarns do not straighten at the same rate, as the crimping is not uniform throughout the fabric. Therefore stress concentrate in specific regions causing those regions to fail earlier than others. Crimping also introduces shear stresses into the matrix (see figure 6.2).11, 14 Crimp has been defined in several ways from crimp %, crimp angle as well as defining the geometry of crimp. Describing the geometry of crimp is important when modeling the composite properties as discussed previously in chapter 5. The simplest definition of crimp is the crimp % or the ratio of the difference between the yarn length and fabric length over fabric length:
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An additional concern for 3D woven composites is the crimp induced by the z-‐binder yarns. They cause excess bunching of the surface fibers where they cross over the in-‐plane yarns. This reads to regions rich in fiber content and creates problems for the resin to enter. These regions lack resin and have increased porosity. At the same time, the fiber bunching creates spaces fiber poor that allow for excess resin to enter. The result is fiber rich and resin rich areas on the composite surface.14
Figure 6.2: Illustration of the crimping in 2D woven fabrics5
Figure 6.3: difference between Idealized z-‐binder geometry (a) and actual (b)14
Misalignment of the z-‐binder can also occur due to high tensile stresses during weaving as well as excessive pressure during consolidation. As can be seen in figures 6.3 and 6.4 the actual z-‐binder geometry is much different than the idealized. This is important to note, as tensile behavior is greatest when the fiber direction, so if the fiber is not aligned properly, the mechanical behavior will be greatly reduced.14
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Figure 6.4: Top and cross sectional view 12
6.2.2 Tensile Properties The tensile properties of 3D woven composites are only recently
beginning to become understood, and are often compared with those of 2D woven composites with similar fiber content. The Young’s modulus of 3D woven composites is commonly lower than the modulus of the equivalent 2D composite, however other studies show the modulus being higher.1,9 It is important to note that the Young’s modulus is not significantly influenced by the z-‐binder content or fiber structure, and is most probably influenced by the fiber content (increasing with increasing fiber content) and degree of fiber waviness (decreasing with increasing waviness), and can be accurately predicted using the block laminate and unit cell models.14 A feature displayed by 3D woven composites, but not by 2D, is an onset of plastic deformation at relatively low tensile stresses, displaying a reduction of stiffness from 20-‐50%. This softening is due to the onset of plastic deformation in the most heavily distorted load-‐bearing tows, distortion of yarns being caused by the z-‐binders. The critical tensile stress at which plastic deformation of these yarns occurs can be estimated by the following equation:14
€
σa =fs τ13[ ]ξ[ ]
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Where fs is the volume fraction of the load-‐bearing tows, τ13 is the axial shear strength of the tow, and ξ is the fiber waviness parameter, defined as the average misalignment angle for 90% of all load-‐bearing tows. In order to minimize softening it is necessary to minimize the in-‐plane fiber waviness or use a high yield shear strength resin.14 As tensile stresses increase above the critical value, the matrix of 3D woven composites begin to crack, z-‐binders begin to de-‐bond. Failure occurs though rupture of load-‐bearing tows. 3D woven composites generally have a lower tensile strength compared with 2D. The lower tensile strength is most likely due to fiber damage from weaving, fiber waviness and pinching of the surface tows. Prediction of tensile failure strength of 3D woven composites is difficult as it relies heavily on fiber damage and crimping which are hard to accurately measure.14 6.2.3 Compressive properties
In most cases it has been found that the compression modulus of 3D is lower than that of 2D woven laminate with similar fiber content, due to higher crimping and increased waviness of the 3D fibers.3 Studies for compressive strength determination are inconclusive as they show both an increase and a decrease in strength. The cause of the increased compressive strength is unclear. However the decreased compressive strength is due to kinking of the load-‐bearing tows (see figure 6.5). Kinking initiates in regions with low resistance to permanent shear deformation such as defects or misalignments, which are much more prevalent in 3D woven composites. Kinking arises when plastic shear flow of the matrix surrounds the axial tow, causing a rotation until break of the individual tows.14
Figure 6.5: Kinking failure in compression
Kinking in 3D woven composites is usually concentrated in the surface regions, where the most severely distorted tows are located. Kink bands develop as discrete geometric flaws, which inhibit catastrophic failure and instead cause the material to fail gradually under increasing strain, leading to significantly higher
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strains at ultimate failure. 3D woven composites have shown to have significant strength even after being exposed to compressive strains of more than 15%.14 6.2.4 Flexural and Interlaminar Shear Properties In most cases, the flexural properties of 3D woven composites have been found to be lower than those for 2D. This is due to crimping and increased misalignment of the tows by the z-‐binder.4,14 On the other hand, the interlanimar shear strength of 3D woven composites is generally the same or slightly higher than that for 2D composites. 3,4,13,14 6.2.5 Interlaminar Fracture The advantage of 3D woven composites lies in their high resistance to delamination cracking. 2D laminates are prone to delamination when subject to out-‐of-‐plane loads or impacts. The delamination tendencies of some 2D laminated composites significantly inhibit their use in many structures such as aircrafts, drawing attention to 3D woven composites.14 There are three modes in which a composite can delaminate. Mode I occurs through tensile crack opening (see figure 6.6), mode II through shear crack sliding and mode III through tearing. Mode I is the most studied and well know of the three delamination modes, and it has been found that delamination resistance of 3D woven composites in this mode is superior to those of 2D laminates.10,13 This improvements in delamination resistance can be achieved with small amounts of z-‐binder reinforcements, and delamination toughness increases with increasing volume content, elastic modulus , tensile strength and pull-‐out resistance of the z-‐binders. Guenon6 found the delamination toughness of a 3D woven composite with z-‐binder content of 1% to be 14 times higher than for 2D laminates.
Figure 6.6: Mode I delamination cracking14
This dramatic increase in delamination toughness is caused by the necessity for the crack tip to pass through the z-‐binders. The de-‐bonding of the z-‐binders as the crack propagates absorbs a small amount of energy. The majority of the toughening is caused by the bridging zone (figure 6.6), where the z-‐binders support a large portion of the applied force in turn reducing the stresses acting on the crack tip and increasing de-‐bonding toughness. Further toughening occurs from crack branching, due to the induced toughness of the z-‐binders, and the energy absorbed due to z-‐binder fracture and de-‐bonding.
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Delamination toughness decreases with decreasing misalignment of the z-‐binders, as tow strength is greatest in the fiber/yarn direction.14 6.2.6 Impact Damage Tolerance The impact damage tolerance of 3D woven composites is of particular interest to the aerospace industry as aircrafts are subject to impact loading conditions, such as hail, bird strikes and for military armored planes, bullet fire. Testing under lightweight, low speed projectiles was carried out to evaluate their potential use in commercial planes, while high-‐velocity bullets were used to evaluate impact damage tolerance for military aircraft applications. 4,7,8,14 The impact damage caused to 3D woven composites is less than that for 2D laminates with the same fiber volume content (see figure 6.7). This resistance to impact damage is due to the high delamination toughness, which impedes the spread of the delaminations from the impact site. This results in higher post-‐impact mechanical properties (see figures 6.8 & 6.9).1,3,14,15
Figure 6.7: Effect of impact velocity on delamination damage of 2D and 3D woven composites2
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Figure 6.8: Effect of impact energy on flexural strength15
Figure 6.9: Effect of impact energy on the compressive strength1
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References 1. Arendts F.J., K. Drechler and J. Brandt, 1993, Advanced textile structural
composites – status and outlook, Proc. Of the Int. Conf. on Advanced Composite Materials, ed.T. Chandra and A.K. Dhingra, 409-‐416.
2. Billaut F. and 0 . Roussel, 1995, Impact resistance of 3-‐D graphite/epoxy composites, Proc. of the 11” Int. Conf. on Comp. Mat., Vol. 5, Ed. A. Pourartip and K. Street, Whistler, BC, Canada, 14-‐18 August 1995, Woodhead Publishing Ltd., 551-‐558.
3. Brandt J., K. Drechsler and Fa-‐J.Arendts, 1996, Mechanical performance of composites based on various three-‐dimensional woven-‐fibre preforms, Comp. Sci. & Tech., 56: 381-‐386.
4. Chou S., H.-‐C. Chen and H.-‐E. Chen, 1992, Effect of weave structure on mechanical fracture behavior of three-‐dimensional carbon fiber fabric reinforced epoxy resin composites, Comp. Sci. & Tech., 45: 23-‐35.
5. Cox B.N., M.S. Dadhkak, W.L. Morris and J.G. Flintoff, 1994, Failure mechanisms of 3D woven composites in tension, compression and bending, Acta Metal. et Mat., 42:3967-‐3984.
6. Guenon V.A., T.-‐W. Chou and J.W. Gillespie, 1989, Toughness properties of a three-‐dimensional carbon-‐epoxy composite, J. Mat Sci., 24:4168-‐4175
7. James B. and Howlett S., 1997, Enhancement of post impact structural integrity of GFRP composite by through-‐thickness reinforcement, Proc. of the 2ndEuropean Fighting Vehicle Symposium, 27-‐29 May, Shrivenham, UK.
8. KO F.K. and D. Hartman, 1986, Impact behavior of 2-‐D and 3-‐D glass/epoxy composites, SAMPE J., July/August, 26-‐30.
9. Lee B., K.H. Leong and I. Herszberg, 2001, The effect of weaving on the tensileproperties of carbon fibre tows and woven composites, J. Rein. Plastics & Comp.,20: 652-‐670.
10. Mouritz A. P., C. Baini and I. Herszberg, 1999, Mode I interlaminar fracture toughness properties of advanced textile fibre glass composites, Composites,30:859-‐870.
11. Stig, Fredrik. An Introduction to the Mechanics of 3D-Woven Fiber Reinforced Composites. KTH School of Engineering Sciences, Stockholm, Sweden. April 2009.
12. Tan P., L. Tong, G.P. Steven and T. Ishikawa. 2000a. Behavior of 3D orthogonal woven CFRP composites. I: Experimental investigation, Composites, 31A:259-‐271.
13. Tanzawa Y., N. Watanabe and T. Ishikawa, 1997, Interlaminar delamination toughness and strength of 3-‐D orthogonal interlocked fabric composite, Roc. of the Eleventh Int. Conf. on Composite Materials, Ed. M.L. Scott, 14-‐18 July, Gold Coast, Australia, V-‐47 to V-‐57.
14. Tong, L. Mouritz, A.P. and Bannister, M.K. 3D Fibre Reinforced Polymer Composites. Elsevier Science Ltd. Oxford, UK. 2002.
15. Voss S., A. Fahmy and H. West, 1993, Impact tolerance of laminated and 3-‐ dimensionally reinforced graphite-‐epoxy panels, Proc. of the Int. Conf. on Advanced Composite Materials, Ed T. Chandra and A.K. Dhingra, 591-‐596.
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7 3D Braided, Knitted, Stitched, and Z-pinned
Composites
7.1 Introduction
In this section we will briefly review the mechanical properties of 3D braided, 3D knit, stitched, and z-‐pinned composites. This is meant to be a brief review and therefore data is not presented in a detailed manner. This should be used as a reference of the general knowledge of properties concerning these composites architectures. 7.2 3D Braided Composites Braided fabric is second most common fabric reinforcement architecture, after woven. 2D braided carbon and glass fabrics have been used in products such as golf clubs, yacht masts and aircraft propellers. Just like 3D woven fabrics, 3D braided fabrics show a number of advantages over 2D fabrics, such as higher levels of conformability, increased drapability, torsional stability and structural integrity. Other advantages include the ability to form intricately shaped performs, including changes in cross-‐sectional shape, tapers, holes, bends and bifurcations. Here in this section we will review the mechanical properties that have been studied in regards to composites made from 3D braided fabric reinforcement.15 7.2.1 In-Plane Properties There are many factors affecting the in-‐plane properties of composite materials. For 3D braided materials studies have been performed to study the effect of braid pattern and level of machining. Macander et. al examined the effect of braid pattern and edge condition on the performance of 3D braided composites. The results are found in table 7.1 below. The number, e.g. 1x1, denotes the braid pattern. The first number represents the number of spaces the yarn carrier advances in the x-‐direction. The second represents the number of spaces the yarn carrier advances in the y-‐direction. The final number indicates the number of carriers fixed in the axial direction (1/2F=50%). As can be seen from the data in table 7.1, there is a large difference between the properties of cut and uncut fabrics of the same braid pattern. This shows a high dependence
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on machining damage, as cut edged fabrics undergo further machining. Another large difference can be seen between weave geometries. The 1x1 weave geometry creates a much tighter weave than that produced for the 3x1. The tighter weave results in a higher yarn angle or crimping. As discussed in the previous chapter, crimping is one of the most important factors in determining the composite properties.11,15
Table 7.1: Reported results from Macander et al. for effects of braid pattern and edge
conditions11 7.2.2 3D vs. 2D Braided Composites It is often beneficial to compare the properties of new materials to older materials in order to have a better idea of the benefits and challenges presented. However, this often difficult as it is can be unclear as to what variables should be considered. Gause tested a 1x1 and 1x1x1/2F 3D braided composite against a 24-‐ply laminate of AS1/3501 prepreg designed to mimic the 3D architecture. The results for the 3D composite were as follows: decreased tensile strength in all directions, increase in longitudinal compressive properties and tensile modulus, and increased ability to retain tensile properties in fabrics containing open holes. Further studies are needed to further characterize 3D braided composites.15 7.3 3D Knit Composites
Of all the fabric reinforcements used for composite construction, knit fabric is
the least understood. Knitting creates a fabric by looping yarns together, creating a highly curved yarn structure, a structure with relatively low structural strength. The advantages of 3D knit performs lie in their high drapability and impact damage resistance. They are ideally suited to produce non-‐structural parts with complex geometries. Due to its exceptional impact damage resistance, it is being considered for the potential use in medical prosthesis, bicycle helmets, and automobile doors.15
7.3.1 In-Plane Properties The in-‐plane tensile properties of 3D knit composites have been studied the most. However, little information was given on knit architecture regarding
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loop length, shapes and densities, which could give valuable insight into the mechanisms behind the outcomes. Tests have shown that the tensile strength of knitted composites is similar to those of composites constructed with non-‐woven randomly oriented fibers, and that increases in fiber volume increased tensile strength.8,9,13 Wu and Leong studied the effect of knit architecture on the mechanical properties.10,16 They found that it was possible, to change the tensile properties from quasi-‐isotropic to strongly anisotropic by changing the knit geometry. The tensile properties increased with increasing fiber orientation, as expected. The results are listed in tables 7.2 and 7.3 below, and figure 7.1 depicts the fiber architectures used in the tests. 15
Table 7.2: Tensile properties of warp knit with varying knit architectures16
Table 7.3: Tensile properties of weft knit with varying knit architectures 10
Figure 7.1: Warp knit (a) Denbigh, (b) 1x3 single cord, and (c) 1x4 single cord architectures15
The tensile properties can also be controlled by changing the loop length or stitch density (as loop length increases stitch density decreases). Leong10 found that the modulus is dependent on fiber volume fraction, while tensile strength and failure stain, in course and wale directions, decreases with decreasing loop length for both weft and warp knit (see figure 7.2). On the other hand Wu16 found the exact opposite; in the course direction he found that tensile strength increases with decreasing loop length and that loop length had no effect
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in the wale direction. This shows that the properties of the knit fabric are dependent on many parameters and further testing is needed.10,15,16
Figure 7.2: Wale and course directions as well as warp and weft fabric structure.
There has not been much investigation on the compressive properties of knit composites. However, with what little has been done, it has been found that knit composites have a compressive strength better than the tensile strength, while compressive modulus is about the same. The compressive properties do not depend on loop length and are much more isotropic compared to tensile properties.15 7.3.2 Interlaminar Fracture and Impact Toughness Here is where the true benefits of 3D knit fabrics lie. Mouritz12 found the fracture toughness of the knit fabrics to be significantly higher than that for 2D and 3D woven, 2D braided and stitched composites. This is due to the looped yarn structure, which causes crack deflection and excessive crack branching, consequently increasing the toughness. This can be controlled through stitch density, as density increases toughness decreases, due to the tighter structure of densely stitched knit fabric. Tight structures do not allow for intermingling, which is responsible for crack deflection.11,12,15 The impact performance of knit composites under low to medium energy is also of great interest. Chou3 found that knit composites are capable of absorbing up to 2.4 times more impact energy than woven composites. This makes knit composites attractive candidates for components requiring high impact absorption or non-‐structural damage prone parts.3,15 7.4 Stitched Composites Stitching involves sewing the laminates in the z-‐direction with a high strength thread. The high strength thread is inserted through a stack of fabric using an industrial grade sewing machine. The through-‐thickness reinforcement of stitched composites is between 1-‐5% and is comparable to woven, braided and knitted 3D composites. The act of stitching the fabric prepregs together improves the delamination resistance, and impact damage tolerance. Stitching can also be used to connect separate composite components together,
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eliminating the need for mechanical fasteners, reducing costs and improving the joints mechanical properties. Due to the simple nature of stitching, it is possible to only stitch the areas that would benefit from the z-‐direction reinforcement, further reducing costs. Up to this point stitching has proven to be a simple, flexible and low-‐cost method for producing 3D composites, however there are limitations to the complexity of the components.15 7.4.1 In-plane Mechanical Properties During the stitching process damage can occur. This damage is the most important factor to consider when considering the mechanical properties. The most common forms of damage are fiber breakage, fiber misalignment, and crimping, all causing sever decreases in mechanical properties. Other damage can occur from micro cracking at stitch insertion sites and fiber compaction. Due to the increase in fiber damage caused by stitching, stitched composites tend to have slightly lower tension, compaction and flexural properties than unstitched composites, although there are many contradictions between data. As stitched composites have been extensively studied, there are databases containing detailed information on tension, compression, and bending modulus and strength of various materials.15 The interlaminar shear properties of stitched composites have not been extensively studied. The few studies that have been carried out show contradicting results and are therefore inconclusive.15 7.4.2 Fracture Toughness and Impact Damage Tolerance Stitched composites show a large improvement in mode I delamination resistance. The mechanism behind the fracture toughness is similar to that for 3D woven composites (see figure 7.3). When a crack forms and propagates through the stitches a bridging zone is formed, where the stitches exert a closing force, lowering strain in the crack tip. Stitched composites also show a large increase in mode II delamination toughness, however not as great as in mode I.7,15
Figure 7.3: Illustrating mode I interlaminar toughening mechanism of stitched composites7
Due to the high fracture toughness of stitched composites it is not surprising that they have good impact damage tolerance. Most studies for
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impact damage tolerance have been for ballistic projectiles and explosion shock wave as stitched composites have been of particular interest to the military. In both cases an increase in post-‐impact mechanical properties was observed.15 7.5 Z-Pinned Composites Z-‐pinning involves the insertion of short metal wire or pultruded composite pins in the z-‐direction. The pins can be inserted in uncured prepreg taps or dry fabrics (see figure 7.4). For further details on the z-‐pinning process please refer to Chapter 2. As this is a relatively new technology the full potential and application possibilities are currently being investigated. At this point z-‐pinning has demonstrated the ability to increase joint strength, remove the need for fasteners and create a more evenly distributed the load over a join region. However, there is not much data on mechanical properties such as flexural strength, shear strength, fatigue, etc. The data that will be reported here will consist of tensile and compressive strength, and delamination properties.15
Figure 7.4: Depiction of z-‐pinned architecture at insertion site14
7.5.1 Tensile and Compressive Strength Steeves and Fleck investigated the effect of z-‐pinning on tensile and compressive strength.14 Their results showed an average decrease in tensile strength of about 27%, while the modulus remained same. This decrease in tensile strength is believed to be caused by the stress concentration and fiber damage at the pin insertion sites. Freitas showed the same results for z-‐pinned materials containing more than 1.5% pinning. Below 1.5% the tensile properties remained almost unchanged.4,5,6,14,15 The effect of z-‐pinning on compressive properties has proven to be very similar that of tensile, with a 30% decrease in strength.14 However, it was also found that there is a strong correlation between fiber misalignment and decrease in composite strength. This correlation is caused by weaving of in-‐plane yarns around the z-‐pin (see figure 7.5), as weaving increases, compressive strength decreases. Weaving increases as the insertion angle of the z-‐pin increases. Insertion angles of 0° showed the least weaving, while weaving increased for 23° and 45° specimens.4,5,6,14,15
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Figure 7.5: Depiction of weaving and deflection caused by z-‐pins14
7.5.2 Delamination resistance Z-‐pinned composites show a high resistance to interlaminar cracking and through-‐thickness failure. Cartei and Partridge investigated the properties under mode I and II failure. For mode I failure the composite showed a rapid increase in delamination resistance with increasing z-‐fiber content and decreasing pin diameter.1,2,15 The mechanisms behind the increased resistance are similar to that of 3D woven and stitched composites. The presence of the z-‐directional fibers creates the bridging zone, which relieves strain from the crack tip. For more details on the mechanism see chapter 6.15
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References
1. Cartei D.D.R. and I.K. Partridge, 1999a, Delamination behavior of Z-‐pinned laminates, Proc. 12* Int. Conf. Comp. Mat., 5-‐9 July, Paris.
2. Cartei D.D.R. and I.K. Partridge, 1999b, Delamination behavior of Z-‐pinned laminates, Proc. 2"' ESIS TC4 Conf., Ed. J. G. Williams, 13-‐15 Sept., CH-‐ Les Diablerets, Elsevier.
3. Chou S. and C-‐J. Wu, 1992, A study of the physical-‐properties of epoxy-‐resin composites reinforced with knitted glass-‐fiber fabrics, J. Reinforced Plastics & Comp., 11:1239-‐1250.
4. Freitas G., T. Frusco, T. Campbell, J. Harris and S. Rosenberg, 1996, Z-‐Fiber technology and products for enhancing composite design, Proc. of the 83' Meeting of the AGARD SMP on "BoltedKionded Joints in Polymeric Composites", Sep. 2-‐3, Florence, Italy, pp.17-‐1 -‐ 17-‐8.
5. Freitas G., C. Magee, P. Dardzinski and T. Fusco, 1994, Fiber insertion process for improved damage tolerance in aircraft laminates, J. Advanced Mat., 25:36-‐43.
6. Freitas G., C. Magee, J. Boyce and R. Bott, 1991, Service tough composite structures usingz-‐fiberprocess,Proc.9" DoD/NASA/FAAConf.FibrousComp.,LakeTahoe, Nevada, Nov.
7. He M. and B.N. Cox, 1998, Crack bridging by through-‐thickness reinforcement in delaminating curved structures, Comp. 29:377.
8. Hohfeld J., M. Drews and R. Kaldenhoff, 1994, Roc. of the 31d Int. Conf. of Flow Processes in Composite Materials, July 7-‐9, 120.
9. Huang Z.M., Y. Zhang and S . Ramakrishna, 2001, Modeling of the progressive failure behavior of multilayer knitted fabric-‐reinforced composite laminates, Comp. Sci. & Tech., 61:2033-‐2046.
10. Leong K. H., P. J. Falzon, M. K. Bannister and I. Herszberg. 1998, An investigation of the mechanical performance of weft-‐knit Milano-‐rib glass/epoxy composites, Comp. Sci. &Tech., 58:239-‐251.
11. Macander A.B., R.M. Crane and E.T Camponeschi, 1986, Fabrication and mechanical properties of multidimensionally (X-‐D) braided composite materials, Composite Materials: Testing and Design (7 Conf.), ASTM STP 893, American Society for Testing and Materials, Philadelphia, 422-‐443.
12. Mouritz A. P., C. Baini and I. Herszberg, 1999, Mode I interlaminar fracture toughness properties of advanced textile fibre-‐glass composites, Composites, 30:859-‐870.
13. Ramakrishna S., N. K. Cuong and H. Hamada, 1997, Tensile properties of plain weft knitted glass fiber fabric reinforced epoxy composites, J. Rein. Plastics & Comp., 16:946-‐966.
14. Steeves A., Craig, Norman A. Fleck, 2006, In-‐plane properties of composite laminates with through-‐thickness pin reinforcement, International journal of solids and structures 43: 3197-‐3212.
15. Tong, L. Mouritz, A.P. and Bannister, M.K. 3D Fibre Reinforced Polymer Composites. Elsevier Science Ltd. Oxford, UK. 2002.
16. Wu W-‐L., M. Kotaki, A. Fujita, H. Hamada, M. Inoda and Z-‐I. Maekawa, 1993, Mechanical-‐properties of warp-‐knitted, fabric-‐reinforced composites, J. Reinforced Plastics & Comp., 12:1096-‐1110.
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8 Concluding Remarks
In this work the different 3D reinforcement architectures have been discussed in some detail. As a concluding remark, it is helpful to summarize the pros and cons associated with them. In General, 3D reinforcement architectures are characterized by reduced in-‐plane mechanical properties, increased delamination toughness and increased impact damage resistance. The reduction of the in-‐plane mechanical properties is due to increased fiber damage during processing (especially for stitching) and increased crimp. The improved out-‐of-‐plane mechanical properties are attributable to the z-‐directional fibers. At this time, the manufacturing of 3D composites is still being explored, however there are high hopes for the future that this type of reinforcement architecture will be able to improve manufacturing efficiency and ease, eventually reducing costs. Some of the defining characteristics of specific 3D architectures should also be acknowledged. Knit fabrics are of particular interest due to their exceptional impact resistance, however are unsuitable for structural application. Stitched and z-‐pinned are among the simplest and most inexpensive methods for producing 3D architectures greatly improving mechanical properties in joints connections. While 3D braided and woven allow for 3D shapes to be produced inherently providing a means for enhanced production techniques. 3D composites and their reinforcement architectures need to be further studied and improvements to both the reinforcement as well as production techniques need to be investigated before wide spread adoption is possible. However, 3D composites are a very promising solution to many of the problems faced by 2D composites and can be expected to become more prevalent in the future.