Tensile characterization of unidirectional discontinuous bamboo fibre/epoxy composites
D. Perremansa*, E. Trujilloa, L. Osorioa, A.W. Van Vuurea, J. Ivensa, I. Verpoesta
aDepartment of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 44 bus 2450, 3001 Heverlee, Belgium
*Corresponding author. Tel. +3216321231; E-mail address:
ABSTRACT
Bamboo culms consist of a nodal structure in which the fibres are as long as the internode length (between 15 and 30 cm), limiting the length of the reinforcing fibres. The implementation of these fibres to reinforce polymers in large-scale applications leads to the production of discontinuous composites in unidirectional configuration. The influence of the average overlapping length between adjacent fibre layers on the mechanical characteristics of aligned “short“ (5 cm) fibre bamboo-epoxy composites is investigated using a tensile testing procedure. The overlapping patterns were predefined at certain regular positions. Aligned discontinuous bamboo-epoxy composites with different overlapping lengths are produced with a light RTM. Tensile testing results have indicated that the overlapping patterns have a significant influence on the tensile strength of the composite samples and low impact on the stiffness of the composite. A modified local load sharing model (LLS) was applied to simulate the tensile strength of an aligned short fibre bamboo-epoxy composite with the different overlapping patterns and also a random dispersion of fibre along the samples.
1. INTRODUCTION
1.1 General introduction and problem outline
Nowadays rational exploitation and use of sustainable natural resources are a necessity and they will play a crucial role in the near future. In recent years there has been an increasing interest to scientifically study the potential of bamboo fibre as reinforcing material for polymer matrix composites [1-3]. Bamboo (Guadua angustifolia) fibres,referred in this study as technical fibres or fibre bundles (composed of elementary fibres) and obtained after a standard extraction process, are becoming a real alternative for glass fibres as reinforcement for composite materials.
Bamboo fibres, amongst other natural fibres, have one of the most favorable combinations of low density (1.4g/cm³) and good mechanical properties that can compete with glass fibres in terms of specific properties, as visible in figure 1 [4]. Furthermore, bamboo fibres are an inexhaustible renewable bio-resource with high growth and CO2 fixation rate [5]. Theseadvantages make that bamboo fibres become a sustainable candidate to be exploited at larger industrial scale and that they provide an alternative to reduce of the environment impact of composite structures by replacing less environment-friendly fibres (e.g. glass fibre).
Figure1: Representation of the specific mechanical characteristics of several natural fibres. Synthetic glass fibres are also included to allow a comparison. Due to their low densities, the specific longitudinal stiffness and tensile strength of natural fibres is similar to that of E-glass. Natural fibres can thus replace glass fibres in several applications. [4]
A large bottleneck that impeded the introduction of bamboo fibres as composite reinforcing materials for many years has been the extraction of undamaged long fibres, but recently, a new environmental friendly mechanical process was developed by KU Leuven to produce high quality long bamboo fibres suitable to be used as a reinforcement in polymeric matrices [6]. In this process, the use of high temperature, high pressure or chemicals is avoided, reducing both the damage introduced to the fibres and the amount of energy required for the extraction of bamboo fibres, while at the same time as well decreasing the environmental impact of the extraction method.
A second drawback towards the large-scale industrial application of bamboo fibre composites is the discontinuous structure of the bamboo fibre culm, as visible in figure 2. The bamboo culm is divided in internodes, in which the reinforcing fibres are well aligned, and nodes, where the reinforcing fibres entangle and contribute as such to the buckling strength of the culm [7-8]. This structure, inherent to the bamboo fibre plant, limits the extraction length of the reinforcing bamboo fibres to the internode length. For a 48-month-old culm, the internode length of Guadua angustifoliafibres varies between 20 and 35 cm [7]. The fibre diameter ranges between 90 and 250μm that in combination with its high modulus gives a high bending stiffness of the fibres impeding the production of endless bamboo yarns[7]. Therefore, an innovative approach towards the use of continuous bamboo fibre material is the development of a preform of unidirectionally aligned bamboo fibres that will allow the use of existing technology to produce high performance composite parts. The production of endless bamboo fibre preform, will help to overcome the actual restriction of having discontinuous fibres.
Figure 2: Guadua angustifolia culm showing its sectioning into nodes and internodes. In the nodes, the reinforcing fibres are entangled, while in the internodes they are severely aligned [7-8].
To bring this to reality, is the aim of this current study; to perform a systematic characterization of the effect of the overlapping length for a set of fibre bundles, but also to study the influence of a complete randomizedoverlapping patterns of unidirectional single fibres into the continuous perform. This characterization, benchmarked with the mechanical behaviour of a fully continuous UD fibre composite, will show the feasibility to use highly oriented discontinuous bamboo fibres in continuous preforms that can be applied in different existing manufacturing techniques.
1.2Scientific modelling background
In this paper, the mechanical characteristics of aligned short-fibre bamboo-epoxy composites are investigated using tensile test experiments. The experimental results are then compared with a series of models that allow a prediction of the mechanical characteristics of these composites. The upcoming paragraphs rally through the applied models to predict the longitudinal stiffness and tensile strength of aligned unidirectional short-fibre composites and set forth their mainassumptions.
1.2.1 Prediction of longitudinal stiffness of aligned UD short-fibre composites
The rule of mixtures is the simplest mechanical model to estimate the properties of a multiple component system. It estimates the composite material properties by taking a volume weighed average of the corresponding properties of the individual constituents.Concerning the prediction of the longitudinal stiffness of a composite, this model assumes the presence of continuous aligned fibres through-out the entire length of the composite. Furthermore, it adapts the isostrain assumptionthat reflects the necessity that planar cross-sections remain planar during loading conditions. Applying Hooke’s law and previous assumptions yields the following formula to estimate the longitudinal stiffness of a composite:
(1)
The shear lag theory considers a single cylindrical linear elastic and isotropic fibre of finite length Lsf and radius rsf that is encased in a concentric cylindrical shell of linear elastic, isotropic matrix with radius Rm.A unidimensional stress-state situation is applied in which the matrix tensile strain becomes equal to the applied strain () at a radial distance Rm from the fibre axis. Furthermore, it assumes that the fibre axial stress vanishes at the fibre ends and that the shear force is constant at concentric cylindrical surfaces around the fibre [9]. Full analysis of the model results in a length depending modified rule of mixtures, as given in equations 2-4.
The Halpin-Tsai equations are a series of semi-empirical equations to determine the different moduli of composites. Originally, they are developed to predict the entire set of moduli of continuous fibre composites. However, by applying a number of restrictive assumptions, the results can be extended towards short-fibre composites.The Halpin-Tsai equations are deduced from the work of Hermans and Hill. They assume a composite in which the embedded phase consists of continuous and perfectly aligned cylindrical fibres. The fibres are modelled as transversely isotropic and linearly elastic. The matrix phase is considered to be linearly elastic and isotropic. Hermans analytically establishes the strain field in the embedded system under an applied stress by assuming displacement and stress continuity at the fibre radius. The stress and strain field are then volume averaged to yield one of the stiffness tensor terms. By varying the applied stress, the entire stiffness tensor can thus be deduced. Halpin and Tsai argue that these results (for the continuous fibre) can be written in a more general form by the insertion of two variables, η and ζ, and two additional assumptions. The first approximation yields that ζ is insensitive to the matrix Poisson coefficient. The second, more inaccurate one, states that the composite contraction coefficient and longitudinal stiffness must follow the rule of mixtures relations. The general form is shown in equations 5 and 6, in which Z represents one of the composite moduli [10-12]. Equation 7 visualizes the necessary assumptions.
The Mori Tanaka model embroiders on the concept of an equivalent inclusion. In this case, an infinite solid body with stiffness Cm that is initially in a stress-free state is considered.An inhomogeneous inclusion with different material properties compared to the solid body is then introduced and the entire system is subjected to a uniformly applied strain at infinity εA. The idea is to homogenize the inhomogeneous inclusion by compensating for the material properties with the introduction of a virtual transformation strain that leads to same stress state in the inclusion.In the Mori-Tanaka method the influence of multiple inclusions on the strain field, compared to the one-inclusion system, is included in an image strain. This image strain is approximated by its mean value, which is the same anywhere, in all the inclusions and in the matrix. This mean field assumption implies that each inclusion only feels the presence of the other inclusions indirectly through the total strain in the matrix.To obtain the homogenized stiffness of a composite using the Mori-Tanaka method, the volume average of the composite stresses is rewritten using Hooke’s Law. The strains in inclusions and matrix are then linked to the externally applied strain using strain concentration tensors.The model assumes that the total disturbance strain in the composite should be absent, which leads to equations 8-10, in which represents the strain concentration tensor that links the total strain in the inclusion to the applied strain. It can be stated in terms of the dilute strain concentration tensor that relates the total strain in the inclusion to the average matrix strain (which is the sum of the applied strain and the image strain) [13].
It is remarked that this model additionally assumes that fibre and matrix are linearly elastic and perfectly bonded through the entire deformation state. The matrix is usually considered isotropic, whereas the fibres are modelled as transversely isotropic. The Mori-Tanaka algoritm does not depend on the size of the inclusion, nor on their positional coordinates. It does depend on shape and orientation of the inclusions, as well as their volume fraction [13].
1.2.2 Prediction of longitudinal tensile strength of aligned UD short-fibre composites
The rule of mixtures applies the iso-strain assumption, indicating that the component with the lowest breakage strain will fail first. Since bamboo fibres,utilized in this research, are more brittle than the epoxy matrix and since the produced composites contain high fibre volume fractions, they will break at the breakage strain of the fibres, reducing the rule of mixtures to equation 11, in which indicates the longitudinal fibre tensile strength, the longitudinal tensile stress in the matrix at fibre failure and Vf and Vm the volume fractions of respectively fibre and matrix This explanation further assumes that the stress concentration around one broken fibre initiates an avalanche of other fibre failures (at the same strain) and that no mechanisms of crack propagation deceleration are present.
The Kelly-Tyson model is based on the shear lag theory and therefore puts forth the same assumptions as previously described in paragraph 1.2.1. It embroiders on the interaction between axial tensile stresses in the fibre and shear stresses at the interface of the fibre.The Kelly-Tyson model further assumes interface failure to occur first and models the shear stress at the interface as a constant in the debonded or yielded area [14]. By introducing the critical aspect ratio Sc as the smallest fibre aspect ratio at which the axial fibre tensile stress can just reach the fibre strength and by assuming that fracture occurs when the axial fibre tensile stress reaches the fibre strength, the composite strength is determined as stated in equation 12.
The global load sharing model (GLS), invented by Curtin, incorporates statistics in the estimation of composite tensile strength. The model builds further on the pioneering work of Weibull, who deduced a semi-empirical expression for the strength distribution of brittle materials based on a chain-of-links system, and Rosen, who introduced the weakest-link theory in the prediction of the tensile strength of fibre reinforced plastics. Curtin modifies Rosen’s chain-of-bundles idea by accounting for load contributions of broken fibres. He argues that stress recovery occurs in the ineffective length due to the presence of a presumed constant interfacial shear stress. In his model, the ineffective length is calculated using the Kelly-Tyson approximations, leading to equation 13 for the longitudinal tensile strength of composites [15-17].
The local load sharing (LLS) model deroutes from the intention to predict the composite tensile strength in an analytical way. It incorporates matrix shear loading to re-distribute the applied load between adjacent fibres and therefore can account more accurately for fibre breakages. Usually, a spring element model is considered in which the fibre is represented by axial springs in the longitudinal direction and the matrix by shear springs in the transverse direction. Each of the spring elements is assigned a stiffness matrix. Strength variation is included through a Weibull distribution. At each strain increment, the stresses in the springs are compared to the fibre strength. If the fibre strength is exceeded, the spring element stiffness is removed and a stress re-distribution is performed. At each step the normalized composite stress is also calculated. This iterative scheme is repeated until the relative difference in two subsequent composite stress values is larger than a pre-set value. Monte Carlo simulation is then performed and the composite strength is taken as the average of the simulated values [18].
2. MATERIALS AND METHODS
Bamboo culms (Guadua angustifolia) are extracted from a typical bamboo plantation in Colombia, specifically from the Coffee Region, at 1.300 meters above sea level. Technical fibres are extracted from the bamboo culms using a mechanical extraction process that neither uses chemicals nor high temperature. The maximum length of the extracted fibres is the internode length, which for 48 month culms is reported to be between 20 and 35 cm. The fibre diameter ranges between 90 and 280 µm.
The bamboo fibres are layer-wise positioned in a unidirectional way in a channel of predefined dimensions (28x2cm). In a first stage, discontinuities in the fibre preform are introduced by the application of a repetitive series of slits over half the width of each layer. The length between two half-width slits originating at the same side within one layer is referred to as the slit length and fixed at 5cm. Subsequently, a series of slits of which the initial position is shifted over a certain length, referred to as the overlapping length (LO), are applied within the same layer, but toward the other side. The overlapping length is varied as a function of the slit length and takes on the values of 0.5, 1.5 and 2.5cm respectively. For each stacking layer, the initial position of all the slits is shifted by half a slit length (LS) in order to reduce stress concentrations. No slits are inserted in the clamp area. The entire pattern construction is visible in figure 3.
Figure 3: The explanation of the inversion symmetry that exists between adjacent fibre assemblies. The left-hand side of the figure shows the upper view of the alternating fibre assemblies. The cuts that are made in one of the assemblies are also made in the neighbouring assemblies, but from the other edge on. The right part reveals the lateral view of the composite. Solid yellow lines indicate that the fibre cut is made to the viewer’s side. Dotted yellow lines represent fibre cuts to the back of the composite.
In a second stage, the effect of the slits is reduced by reducing the cutting length to one fifth of the composite width and by randomizing the overlapping length between different fibre bundles. To establish such a configuration, a random number generator (RNG) is asked to produce a collection of 20 numbers in between 0 and 250. The end value of the RNG expresses the length dimension of the fibre in mm, as given by the ASTM standard. The applied random number generator makes use of the random variation in atmospherical noise to bring forth the desired set of values. The values are linked to the fibre bundles in the order they are generated, starting from the bottom wall of the mould channel and continuing until a fibre layer is completely filled. This numbering sequence is visualized with red indices for the bottom fibre assembly in figure 4. The collection of RNG values expresses the distance between the cuts and the left side of the fibre bundles. To avoid breakage of the composite samples in the clamped area during tensile testing, values that are located between the interval [0,50] are shifted 50mm to the right and values within the interval [200,250] are shifted 100mm to the left.
Figure 4: Schematic clarification of the linking procedure to relate the RNG-values to the fibre cuts in each assembly. The sequence is shown for the first 3 RNG-values. To highligth the cuts, the remaining side fibre bundles are not depicted.