Fibre microbuckling

Microbuckling is a deformation in which the fibres are considered to act individually as columns inside the matrix material [11]. It has been the most widely studied failure mode for composites made of strong fibres and matrices. For high volume fraction composites, microbuckling is expected to be controlled by the matrix stiffness in shear. Defects formed in the composite, such as fibre misalignment or waviness, porosity and residual stresses, can act as sites for microbuckling initiation [12]. Fibre microbuckling in the composite laminate is thought to start from elastic bending of the fibres and manifests itself in the fibres being pushed into a wave pattern causing subsequent stress on the surrounding matrix material [13].

The microbuckling problem was first analyzed in a systematic way by Rosen [14]. He proposed the existence of two possible microbuckling modes in composite laminates – the extension mode (symmetric) and the shear mode (asymmetric), as illustrated in Figure 2. 8.

In the extension mode, the matrix material is predominantly in extension and adjacent layers deform out of phase with each other, while for the shear mode they deform in phase and the matrix is predominantly in shear.

It was concluded that the nature of microbuckling depended on the distance of fibre separation and was associated with the level of interaction between the fibres in the composite laminate. From the view of microscopic analysis, adjacent fibres in the composite may buckle independently of one another or in a cooperative manner. Wave-like

bending of adjacent fibres in different directions is associated with microbuckling. In this case, the transverse deformation of the fibres is out of phase relative to each other, with the result that deformation of the matrix takes place between adjacent fibres. This form of buckling is referred to as the extension mode and involve s strain deformation in the matrix material.

Fig. 2.8 Initial configuration and buckling modes investigated by Rosen [14].

On the other hand, adjacent fibres may buckle cooperatively so as to be in phase with one another. As a result, the deformation of the matrix material between the fibres is primarily in the form of shear, and the mechanism is referred to as the shear mode. It is the more common of the two, as extension mode buckling only takes place when the inter-fibre distance is quite large , as in composites with a low fibre volume fraction. As a result the occurrence of shear mode buckling can be predicted simply from a knowledge of the fibre content in the composite.

2.2.2.2. Kinking (or kink-banding)

It is now widely recognized that kink formation and propagation is the dominant compression failure mechanism in unidirectionally fibre-reinforced composites. Kinking is a localized deformation band across the specimen in which the fibres have rotated by a large amount, and the matrix has undergone large shear deformation, Figure 2.9 [11, 15]. It is considered to be a final consequence of microbuckling, and is called a post-buckling event [16-20], although sometimes it is considered to be an independent failure mechanism [13, 21]. K inking depends on the matrix stiffness and yield behavior in shear, and possibly on the fibre strength as well [14].

Fig. 2.9 In-plane buckling of fibres and fibre kink band geometry [13].

As fibre misalignment occurs in the loaded composite, shear stiffness is lost as a result of matrix yielding. This occurs at a fraction of the stress required to buckle the fibres in a perfectly aligned composite and localized fibre bending then takes place in narrow inclined zones. The final result of local fibre bending is fibre breakage to form distinct kink bands [13, 22, 23].

Garland et al. [24], and Narayanan [25] envisioned a similar failure mechanism in which a small, slant-aligned sequence of fibre breaks develops in shear or crushing failures and

triggers kink-band formation through excessive overloading of adjacent fibres to the point of bending and failure, as illustrated in Figure 2.10.

Fig. 2.10 Schematic of fibre failure sequence in shear triggered kink-band formation [24].

Fibres outside the band above and below it are seen to be straight whereas inside it they are seen to be rotated. The fibres are clearly broken at the boundaries of the band while signs of fibre breaks are also seen inside the kink-band [26]. Once the kink-band forms in the material, the straight fibres adjacent to it tend to kink at a lower stress than was required to initiate the first kink-band. Contact of the straight fibres outside the band with the rotated fibres inside it tends to bend the straight fibres. Excessive bending results in breaking of a narrow strip of these fibres along the boundary. These then rotate further so as to conform with the deformation inside the original band, thereby increasing its width. The process is then repeated as shown in Figure 2. 11.

Fig. 2.11 Geometry of kink-band formation [16].

2.2.2.3. Shear cracking and delamination

According to Wu and Sun [27], microbuckling in the 0° plies caused the formation of kink-bands and was considered as the primary failure mode for damage initiation at the bearing surface. It initiated in the outer-most 0° plies near the laminate surface at around 77.5% of the ultimate failure load. At higher loads, the damage propagated at an angle of between 30° and 40° into the interior of the specimen until it reached a critical length, as seen in Figure 2. 12. This propagation of the damage was referred to as interlaminar shear cracking.

Fig. 2 .12 Micrograph of shear cracking in bearing failure [27].

Wang [28] also stated that local delamination would occur upon the formation of kink-bands. He identified two main mode s of damage to the laminate during bearing failure, as shown in Figure 2. 13.

Shear cracking often appeared in the area closest to the bearing surface and was formed due to the accumulation of compressive failure in each individual ply of the laminate. Lateral expansion of the laminate was caused by the shear stress under the compressive loading, promoting propagation of the shear cracks. From a microscopic view, shear cracking was comprised of fibre kinking, fibre-matrix shearing and matrix cracking.

The propagation of the shear cracks in the laminate ceased once converging cracks met, creating a larger scale unstable delamination [27, 28] , Figure 2.13. The formation of the delamination, or even laminar longitudinal splitting, occurred as a secondary damage mechanism.

2.2.3. Factors affecting bearing failure

2.2.3.1. Stacking sequence and percentage of 0° plies

The mechanical properties of composite laminates are strongly dependent on the stacking sequence [29]. The laminates are usually made up of plies in the 0°, 90° and ± 45°

directions. Park [30] stated that the stacking sequence had a great effect on delamination and the ultimate bearing strength of laminated composites. For both orthotropic and quasi-isotropic laminates, the delamination bearing strength of a lay-up with 90° layers on the surface was stronger than that of a lay-up with 90° layers located at the centre of the laminate. He suggested that 90° plies played an important role in the delamination bearing strength of the laminates. This result is similar to that reported by Quinn and Mathew [31]

in a previous study. They found that in a quasi-isotropic laminate, the bearing strength was improved by placing 90° plies at the surface and 0° plies towards the center. The constrainment of the 0° plies by the 90° plies in the outer layers resulted in a higher failure load being sustained by the laminate.

According to Colling [5] , bearing strength was significantly dependent on the ratio of 0°

fibres to fibres in other directions. It increased with the addition of additional 0° plies due to the higher compressive strength in the load direction. However, there was a maximum

percentage of 0° fibres that could be added. Once this percentage was exceeded, the failure mode changed, and a reduction in bearing strength occurred. Longitudinal splitting between the 0° fibres now took place because of the poor in-plane transverse restraint.

In contrast, Smith and Pascoe [32] concluded that there was only a minor influence of stacking sequence on the bearing strength of laminates. Only the location of the 0° fibres in the laminate was reported to significantly affect the failure mode. Splitting and breaking away of the laminate occurred with 0° fibres on the surface while more general delamination between layers was observed with 0° fibres towards the interior of the laminate. The bearing strength was higher in the latter case. The elastic stiffness of the laminate in the loading direction and the fracture strain were independent of the stacking sequence of the laminate [33]. However the stacking sequence played a major role in determining the nature of the laminate fracture surface.

2.2.3.2. Laminate thickness

An increase in the critical strain has been observed with decreased thickness [34]. More precisely, the transverse strain in the matrix became more important with reduced laminate thickness. Rosen [14] neglected the effect of transverse strain on microbuckling, but its effect should be included [34].

According to Wu and Sun [35] , the bearing strength increased significantly with increased laminate thickness. As the thickness increased, kink-bands , which originated from the outmost 0° plies on either side of the laminate, propagated deeper into the interior of the laminate to merge together. Consequently, a higher stress, as well as higher load, was required for a thicker laminate.

The effect of laminate thickness on the compression behaviour of composite laminates was investigated by Lee and Soutis [36]. They found that the strength of unidirectional laminates dropped by approximately 2-36 % in going from 2 to 8 mm thick specimens. But for open hole multidirectional specimens, the average strength increased with increasing

specimen thickness, except for the 8 mm thick specimen ([45n/0n/-45n/90n]s) that failed prematurely due to extensive delamination introduced by matrix cracking, as seen in Figure 2.14.

Fig. 2.14 Open hole average compressive strength as a function of specimen thickness for multidirectional laminates [36].

2.2.3.3. Hole machining defects

The mechanical performance of bolted joints can be affected by the quality, as well as the accuracy, of the hole [37]. The quality of the hole is determined by the roughness of the surface and the damage in the area adjacent to the hole. Traditional methods for machining of holes include grinding and drilling. When drilling composites, it is difficult to achieve good hole quality. Hole machining defects which reduce the strength of the laminates, such as delamination, chip-out of fibres or matrix, and degradation of the matrix due to overheating, can easily occur. For example, if the cutting angle is too small and the cutting edge is wedged between two laminae, delamination may occur. However, it usually occurs when the last plies of the panel do not withstand the force exerted by the drill edge [38, 39].

During drilling, fibres and matrix can be torn out of the hole surface, resulting in a rough surface which can generate crack initiation sites. In addition, if the drilling thrust or torque forces are too high, the matrix may be degraded by overheating produced as a result of the friction between the tool and the laminate [37].

Increasing attention has been paid to drilling quality recently. For example, a drilling process with a one shot drill bit to get high quality holes has been examined by Fernandes [40]. The process was modeled as five steps, each directly related to the various drilling and reaming processes.

2.2.3.4. Lateral clamping

Bearing strength is strongly influenced by lateral clamping which is produced by the pressure of the washer on both sides of the bolted region [41]. There are two mechanisms for explaining the increase in strength in a laterally constrained laminate. Firstly, for clamped bolted joints, failure occurs at the washer edge while it only happens at the pin-contact area of an unconstrained laminate. Stress levels at the washer edge are relatively low compared to the hole edge, allowing a greater overall induced stress from bearing in the specimen. Secondly, the frictional force at the interface of the washer and laminate affect the load transfer across the laminate, influencing the distribution of the load over the larger area covered by the washer. The first mechanism often occurs in finger-tightened clamped specimens. The frictional forces in this case are relatively small. However, for a higher clamping torque, the friction between the clamp and the laminate is higher.

Consequently, the bearing strength is higher and this is explained by the second mechanism.

For clamped bolted joints, the clamping torque presses into the laminate under the washer [30]. Delamination on the loaded side of hole is therefore suppressed. The location of the delamination moves to the outer edge of the washer-constrained region. Clamping pressure of bolted joints suppresses the onset and propagation of laminate delamination, leading to a change in the failure mode. Consequently, the lateral clamping pressure increases both the delamination and ultimate failure strength of bolted joints in the laminate. With increased clamping pressure, a significant increase in ultimate bearing strength occurs while the delamination bearing strength shows a progressive increase.

2.2.3.5. Matrix stiffness

Wu and Sun [27] used Sun and Jun’s [42] microbuckling model to show that the critical stress in the direction of compression (σ_xx)_cris given by

) 1 /(

)

(σ_{xx cr} =G_m^ep −V_f (2)

where G_m^epis the elastic-plastic shear modulus of the matrix and V_f is the fibre volume fraction. This shows that the bearing strength is dependent on the shear modulus of the matrix indicating that the bearing strength should be increased by increasing the modulus.

2.2.4. Rationale for present study

As noted in Section 2.2.1 and shown in Figure 2.3 the joint efficiency for bolted composite laminates is substantially lower than for metals. Reinforcement of composite laminates in the vicinity of the hole using layers of steered fibres has been used successfully as a strategy for improving bearing performance. Several different methods have been used to define the trajectories for the steered fibres, as described in References 43-47. However although substantial improvements were achieved, the incorporation of steered fibres into the laminate clearly complicates the production process.

A review of the literature revealed two alternate strategies that might be effective in improving bearing performance and these were the focus of the work undertaken here. The findings of Wu and Sun [27] indicate that bearing strength should be improved by increasing the modulus of the matrix, as discussed in Section 2.2.3.5. However, increasing the modulus generally leads to a reduction in toughness for matrix resins but recent work has shown that simultaneous increases in both stiffness and toughness can be achieved in epoxy resin by incorporating nanoparticles into the resin [48]. Development of a nano particle reinforced matrix resin and its performance in a composite loaded in bearing was therefore the focus of the first part of the study. Accordingly, a detailed review of

Additionally, it has been reported that bearing strength is also strongly affected by lateral constraint (clamping force) at the loaded hole [9, 30, 41] as discussed in Section 2.2.3.4.

One benefit of lateral constraint is that it should oppose generation of the kink-bands since this involves outward lateral displacement of the material below the kink bands. This suggests that bearing performance may be improved by through thickness reinforcement, such as z-pins, and their use was examined as the second strategy trialed in this thesis. Z-pin reinforcement is a relatively new technology and is therefore reviewed in detail in Section 2.4.

2.3. EPOXY NANOCOMPOSITES

2.3.1. Definition and Composition

An epoxy nanocomposite is a composite material consisting of an epoxy resin matrix as the continuous phase, and nanometer-sized fillers, such as nanoparticles [49-55] and nanofibres [56-59], as the dispersed phase. The fillers must have at least one dimension in the order of nanometers (smaller than 100 nm) and can range from essentially isotropic elements to highly anisotropic needle-like or sheet-like elements [60].

2.3.1.1. Epoxy resins

Epoxy resins are used extensively in composite materials for a variety of demanding structural applications. The properties and structure of epoxy resins vary and strongly depend on the chemical structure of the resin and the curing agent, the presence of modifying agents and the curing conditions. All epoxy resins are characterized by the presence of a three-membered ring containing two carbon atoms and an oxygen atom. This is called an epoxy group or, less commonly, an epoxide or oxirane or ethoxylene ring:

C C

O R

where R represents the point of attachment to the remainder of the resin molecule. The epoxide function is usually a 1,2- or a-epoxide that appears in the form:

called the glycidyl group, which is attached to the remainder of the molecule by an oxygen, nitrogen, or carboxyl linkage, hence, the terms glycidyl ether, glycidyl amine, or glycidyl ester [61].

In spite of the diversity and complexity of the available epoxies, the majority of resins are based on only three compounds: TGMDA (tetraglycidyl methylene dianiline), also called TGDDM (tetra-glycidyl 4,4’-diamino-diphenylmethane resin), DGEBA (diglycidyl ether of bisphenol A), and phenol formaldehyde novolac epoxy. The major difference between the molecules is that the cross-link density of cured TGDDM and novolacs is higher than that of DGEBA, resulting in higher values of Young’s modulus and glass transition temperature (Tg) but lower values of failure strain [62, 63].

TGDDM is the major component of the high performance resin formulations. These are amongst the stiffest available, and as a result, laminates based on TGDDM are amongst the highest performing. These resins are often used as matrices for carbon and aromatic fiber reinforced composites in the aerospace industry because they fulfill the requirements of high modulus and high temperature performance [64, 65]. Well-known trade names of these resins are Alradite MY 0510 (TGAP), Alradite MY 720 (TGDDM), Alradite XVMY 0505 (all supplied by Ciba). The structure of TGDDM is:

H2C CH

There are drawbacks to the high cross-link density of TGDDM resins. The most disadvantageous feature is that the resin failure strain is low, approximately 1.5%. This leads to the development of large delaminations upon impact, and consequently, low compression strength after impact. A second problem is water absorption, as every epoxy amine reaction results in a hydroxyl group. This leads to a reduction in the glass transition temperature (Tg).

DGEBA is the most widely used resin, bearing common trade names such as EPON 828, EPON 826, EPON 825 (Shell), DER 332, DER 331, DER 323 (Dow), Alradite CY 225, CYD-128 (Ciba). Diglycidyl ether of bisphenol A made by reacting bisphenol A with epichlorohydrin is widely used in industry due to its fluidity, processing ease, and the desirable physical properties of the cured resin. The structure of the resin is as follows.

Compared with TGDDM, bisphenol A epoxy cures to a lower cross-link density. Thus the resin modulus and Tg are lower, and consequently, mechanical properties and high temperature performance are also reduced. However, the cured bis A epoxy has a higher failure strain and a lower water absorption.

Novolac epoxies are one of the most important classes of epoxy resins. They are products of the reaction of epichlorohydrin with various phenolic novolacs, cresol novolacs or bisphenol A novolacs. The structure of novolac epoxy is shown below.

H2C CH

Novolac epoxies have a higher functionality, and thus cure to a higher cross-link density than DGEBA. The addition of novolac to a formulation increases the resin Tg, but decreases the failure strain. These resins are extensively used in prepreg formulations.

Epoxy resin curing agents are divided into three technologically important classes: (a) active hydrogen compounds, which cure by polyaddition reactions; (b) ionic initiators,

Epoxy resin curing agents are divided into three technologically important classes: (a) active hydrogen compounds, which cure by polyaddition reactions; (b) ionic initiators,