Bamboo fibres for reinforcement in composite materials: Strength Weibull analysis

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Abstract

A recently developed mechanical method for extracting long bamboo fibres opens the possibility to exploit this new material as reinforcement in composite materials for high end uses. The strength distribution of the fibres was characterized in a novel approach to evaluate the effect of defects introduced by the extraction process as function of different scale variables: fibre length, fibre surface area and fibre volume. The modified Weibull distribution, a practical model requiring only three parameters, described accurately the fibre strength distribution of the fibres at different gauge lengths. The average fibre strength decreased with increasing gauge length, from 943 MPa at L = 1 mm to 733 MPa at L = 40 mm and it was nearly independent of the mean fibre volume. The Weibull shape parameter was found to be 7.6 for all tested fibres, showing low strength variability in comparison with other natural fibres and some synthetic fibres, indicating their high quality.

Introduction

Bamboo Guadua angustifolia as other cellulosic materials is an abundantly present form of biomass and it is the most important bamboo species of the Americas due to its size, high growth rate, good mechanical properties and the impact it has for the local economy where it grows [1]. This giant grass-type plant, being one of the three largest bamboos in the world, has been used for centuries in construction and a wide range of handicrafts.

The cylindrical shape of the bamboo culm is, however, a limitation for its direct use in several engineering systems [2]. A more flexible alternative is extracting the bamboo fibres from the culm and using them as reinforcement of polymeric matrices. Bamboo fibres, more specifically the technical fibres that are composed of elementary fibres, can be an attractive alternative to other natural fibres and glass fibres in composite applications. Bamboo fibre can be used for a variety of structural and semi-structural applications due to its good specific properties, renewability and other environmental benefits, which include a large CO2 capture and low energy consumption per kg of fibres [1], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12].

In spite of these benefits, studies on bamboo fibre reinforced plastics (BFRP) are relatively scarce because fibres are not readily available [3], [4], [5]. Little effort has been devoted to the extraction of long bamboo fibres because of the difficulty of separating the fibres [7], [8], [9]. Table 1 shows an overview of the applied extraction methods and the corresponding physical and mechanical properties of the fibres. In steam explosion techniques, bamboo strips are saturated with overheated steam in an autoclave and suddenly depressurized to atmospheric pressure. This process has to be repeated several times in order that microsteam explosions occur inside the soft cells, facilitating the extraction of the fibres. In chemical extraction, bamboo pieces are soaked in a chemical solution (e.g. NaOH) at a relatively high concentration with the purpose of dissolving the soft tissue that binds the technical fibres together. Finally, mechanical methods usually use hammer mills, roller mills, toothed rollers, etc., to detach the fibres from the culm.

From this comparison, it is clear that the fibre separation process determines the morphology and mechanical properties of the extracted fibres. The fibre’s aspect ratio for example influences the final properties of bamboo fibre reinforced polymers (BFRP). Defects introduced by the extraction method reduce the tensile strength of all fibres [13], [14], [15], [16]. For instance, unretted flax fibres were found to have lower tensile strength compared to dew retted flax because less damage was introduced in the extraction after retting, as it required lower mechanical force [17].

The industrial adoption of natural resources for reinforcing composites is an active subject of research. The acceptance of natural fibre reinforced plastics in technical applications depends on the availability of material data and specific design information. Establishing the reliability needed for final product applications requires extensive testing and a substantial amount of research [18]. In fact, one of the main concerns for massive industrial application of natural fibres is their variability in mechanical properties [19], [20], [21]. In comparison with synthetic fibres, natural fibres have a significantly higher variation in diameter between fibres and within a fibre [2], [13], [20], [21], [22], [23], [24]. In addition, fibre strength was found to be negatively correlated to fibre diameter and gauge length [2]. Nevertheless, this variation in fibre properties can be characterized and predicted when quality management is used [25], but also controlled when this information serves as a feedback for optimizing the extraction and further fibre preparation.

Osorio et al. [26] published a significant step forward in the extraction of high quality, long bamboo fibres. Characterizing completely the strength of these fibres is the subject of this study. To obtain a realistic estimate of the fibre properties a large population of fibres was tested (Sections 2 Experimental, 3 Results and discussion) and statistically analyzed (Sections 1.2 Effect of defect density distribution, 1.3 Effect of within-fibre diameter variation, 3 Results and discussion). This should provide a better understanding of the material and a more accurate appreciation of its potential. The generated data can further be used in design and in modelling of BFRP properties in order to fulfil the correspondent safety demands for end products.

The Weibull distribution [27] is a widely used statistical tool for describing the tensile strength of brittle materials such as carbon and glass fibre [28], [29], [30]. As shown in Table 2, it was also applied to a wide range of natural fibres such as jute, hemp, sisal, flax, coconut and bamboo. Two assumptions that underlie the theory are that the material is brittle and that the strength is governed by the most serious flaw [31], [32]. The brittleness assumption is satisfied if the material has linear-elastic behaviour up to failure. The weakest link character for a technical bamboo fibre can be assumed as a chain consisting of several segments with certain strength. These segments can be regarded not only as a concatenation of elementary fibres as shown in Fig. 1, where the fibre ends are considered as “weak points”, but also, as the minimum length or volume where a defect is found. Elementary fibres have an average length of 2.1 mm and an average diameter of 17 μm [33]. Their pentagonal or hexagonal cross-sections are arranged in a honeycomb pattern [34].

Strength distribution of technical natural fibres is usually described by means of two parameter Weibull distribution [35]. To improve the accuracy of the prediction, a modified Weibull model had been introduced by the implementation of a third parameter [36], [37]:P=1-exp-VV0βσσ0mwhere P is the probability of failure of a fibre of volume V at a stress less than or equal to σ. The parameters of the distribution are the scale parameter σ0, the shape parameter m and the volume sensitivity β. The scale parameter σ0 is a measure of the characteristic strength. It corresponds to the fracture stress with a failure probability of 63.2% of a unit of material with reference volume V0. The shape parameter m mainly defines the variability of the distribution. The higher m, the more narrow and right-skewed the distribution, and thus more consistent quality of the fibres. For natural fibres this value ranges between 1 and 6 and synthetic fibres usually have shape factors between 5 and 15 [38], [39]. Andersons et al. [29] found a shape factor between 5.1 and 5.4 for glass fibres. The strength variability was caused by the inherent flaw distribution along a fibre and by the fibre-to-fibre strength variability within a batch, due to variations in processing and damage introduced by the handling of the fibres.

The parameter β is a measure of the sensitivity of the strength to the volume V. It is an empirical parameter that was introduced to improve the predictive power of the Weibull model with respect to experimental data [36], [37]. The implementation of this parameter was found in several studies [22], [36], [38], [40] with positive results. If β = 1, the conventional Weibull distribution is obtained, in which each part of volume V contributes equally to the failure probability. Choosing β between 1 and 0 weakens the volume-dependency: the lower β, the lower the decrease of strength for increasing volume V. The volume dependency entirely disappears if β = 0 [41]. A final parameter is the reference volume V0. V0 is independent of the other parameters and therefore has to be selected arbitrarily. Some studies based the selection on the dimensions of an elementary fibre [39], [42]. More commonly, V0 is chosen to correspond to a standard unit. The latter convention is also adopted in this work, which uses a reference volume V0 of 1 mm3.

From Eq. (1) the average strength (σv), the standard deviation (σsd) and the modus (Ms) can be calculated respectively with Eqs. (2), (3), (4) [39]. Γ corresponds to the gamma function.σv=σ0VV0-βmΓ1+1mσsd=σ02Γ1+2m-σv2Ms=σ0m-1m1mV-βmAccording to Eq. (1), for a constant fibre diameter the average strength (σ2) at certain volume (V2), can be estimated from a known strength (σ1) at its corresponding volume (V1) and shape parameter (m) as follows [36]:σ2=σ1V2V1-βmThis equation has been useful for predicting fibre strength [22], especially in analyses of the micromechanical fibre fragmentation test, commonly used to evaluate the shear strength at extremely short fibre lengths [43].

Eq. (1) assumes that the defect density is homogeneously distributed over the volume of the material. Weibull [27] noted, however, that other defect density distributions are also plausible. In the fibre literature (see Table 2) it is commonly assumed that the defect distribution is only function of the length of the fibre. The resulting modified Weibull distribution is identical to Eq. (1) except that volumes are substituted by lengths (L):P=1-exp-LL0βσσ0mThe derived statistics (Eqs. (2), (3), (4), (5)) can similarly be adapted by substituting volume by length. While some studies use as reference length L0 the length of an elementary fibre [39], [42], this study uses 1 mm, as it is more practical.

For fibres with different diameters, the volume-based model and the length-based model lead to different strength predictions, as is illustrated in Fig. 2. The figure divides fibres into segments with equal failure probability for length-based defect densities (left) and volume-based defect densities (right). In case fibres have the same length, a length-based defect density predicts a failure probability that is independent of diameter, while a volume-based defect density gives rise to more defects for thicker fibres and thus to a higher probability of failure. In case fibres have the same volume, wider fibres are also shorter, leading for the length-based model to less defects and thus to higher strength.

The defect distribution within bamboo fibres can be affected by their morphology and by the extraction process. When the length and diameter of elementary fibres are homogeneously distributed within the fibre, the fibre ends are also distributed homogeneously (see Section 3.2). Since the fibre ends form “weak links” between the elementary fibres, this fibre architecture suggests a volume-based defect distribution [39], [42], [44]. The extraction process, however, may add defects that are distributed differently. For example, certain compression, rubbing or combing-based extraction steps may systematically introduce damage every certain distance along the fibre length, thus favour a length-based defect distribution. In combing processes involving needles, thicker fibres may have a higher probability of needle-attack. Some chemical processes may introduce damage on the fibre surface. The latter two processes thus favour yet another defect distribution: a surface-based one. Given that the bamboo fibre diameter can range between 150 and 250 μm for the same batch [26], it is thus meaningful to consider how defects are distributed within the fibres and to relate this to the fibre extraction method.

Some studies [22], [45] argue that the reduction in mechanical properties in wool fibres with increasing fibre length is not only caused by the accumulation of defects along the fibre but also by diameter variations along the length of a fibre. Therefore, Zhang et al. [22] and Xia et al. [46] incorporate in their studies on respectively wool and jute fibres a within-fibre diameter variation parameter λ that replaces β in Eq. (6):P=1-exp-LL0λσσ0mThe parameter λ is the slope of the line obtained when plotting the logarithm of the coefficient of variation of the fibre diameter (CVFD) versus the logarithm of the measured fibre length. The parameter λ is positive, which reflects that there is an increase of the within-fibre diameter variation (CVFD) with increased fibre length.

This work presents geometrical and strength data for an extensive population of bamboo fibres, which were extracted using the high quality mechanical extraction process of Osorio et al. [26]. The bamboo fibres were individually tested in tension using various gauge lengths. To determine the strength distribution of the fibres, the fibre data are analyzed using the modified Weibull model. For that, the effect of representing the defect density distribution as function of the fibre length, fibre volume or fibre surface area is considered, to determine which one is more appropriate. The within-fibre diameter variation parameter λ is also determined. These results provide a practical, quantitative predictive model for the strength of the currently studied bamboo fibres.

Section snippets

Experimental

A first important source of uncertainties when obtaining the strength properties of the fibres is the methodology followed for determining the cross sectional area (due to the noncircular cross-section) that can lead to a large difference in the reported tensile strength measurements [47]. Other sources of uncertainty are particular test conditions and poor measurement techniques, which lead to a significant discrepancy between the experimental data and the calculated data obtained by the

Fibre cross-sectional area and perimeter

The cross sectional area of 15 fibres was determined using two methods. The first one (Aw), was based on the weight of individual fibres and the apparent average density of bamboo fibres. The second one (AS), was based on analysis of SEM images (Fig. 4a). The average relative error between both methods was 3.8 ± 1.5%. For the area determination for all tested fibres (420 specimens), only method Aw was used because of its practical simplicity. Fibre diameters were found to range from 100 to 220 μm,

Conclusions

Recently a promising mechanical method was developed for extracting high quality bamboo fibres from bamboo culms to be used as reinforcement in composite materials. In this work, the strength and geometry of the bamboo fibres obtained by this method were quantified in order to have a better understanding of the behaviour of the final composite material.

The modified Weibull distribution (length-based model), a practical model requiring only three parameters, was used to describe accurately the

Acknowledgements

This work was supported by the Belgian Science Policy Office (BelSPO) project BL/01/V20, in a cooperative project with Vietnam. MM acknowledges the agency for Innovation through Science and Technology in Flanders (IWT/OZM/080436).

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