Diameter dependence of the apparent tensile modulus of hemp fibres: A morphological, structural or ultrastructural effect?

Abstract

The aim of this paper is to investigate the origin of the diameter-dependence of Young’s modulus in hemp fibres. In view of the considerable experimental difficulties encountered when determining the 3D morphology of elementary fibres, the influence of the fibre morphology and size on the E-modulus is studied using a mathematical model. An approach based on the 3D elastic theory is used to construct a model of the fibre structure, and to predict its mechanical properties. We clearly show that the modulus is dependent on the size of the lumen and on the outer fibre diameter. This structural effect, induced by the cylindrical geometry, the multi-layered organisation, and the orientation of the cellulose microfibrils only partly explains the large, experimentally determined dispersion of apparent E-modulus, as a function of fibre diameter. Ultrastructural parameters, such as cellulose crystallinity and microfibril angles, are identified to be the main factors involved in this dependence.

Introduction

Cellulosic fibres originating from annual plant stems, such as hemp, flax, jute, kenaf and ramie, represent an interesting alternative to man-made fibres in composite applications, and can be competitive with glass fibres in particular. At the present time, natural fibres are used mainly in low performance applications, in the construction and automotive industries. Their specific mechanical properties, and full potential in composite applications, thus appear to be poorly exploited. However, before such fibres can be used for the reinforcement of organic matrices in high performance applications, it is essential to gain an accurate understanding of their micro-mechanical behaviour. This calls for the use of advanced, sophisticated experimental techniques, and also requires the development of theoretical tools, in order to correctly relate the microstructure, ultrastructure and complex organisation of such fibres to their mechanical properties.

Ligno-cellulosic fibres have an intricate structure and organisation. Stem fibres such as hemp are made up from single cells (unitarian or elementary fibres). The elementary fibres are glued together by a pectin interface, to form technical fibre bundles. These bundles are separated from one another through partial decomposition of the cell wall, induced by bacteria or mechanical processes. The elementary fibres have a typical cell plant structure, with a lumen and a particularly thick wall. They have a rounded polygonal outer shape, which is irregular and non-uniform along length of the fibre, and also varies from one fibre to another. Typically, the fibres have a diameter lying between 10 μm and 50 μm, and a length of approximately 8–14 mm [1]. The central cavity can be narrow, round or elliptical, with a diameter normally lying between 0.5 and 10 μm [1], [2] depending of the plant maturity [3]. Schäfer and Hornermeier [1] evaluated the cross-section of the lumen at approximately 70–130 μm², i.e. from 13% to 16% of the total cross-sectional area of the fibre. Thygesen [2] measured a mean lumen fraction of 9%. The cell wall is composed of two main layers: the primary wall, which is generally very thin (70–200 nm) according to Bergander and Salmén [4] and Thygesen [2]), and the secondary wall, which is subdivided into three sub-layers referred to as S₁, S₂ and S₃. S₂ is the main sub-layer of the cell wall, in terms of its thickness, which represents around 90% of the total wall thickness (Table 1). Each layer is comprised of a mixture of three main types of polymer, i.e. cellulose, hemicellulose and lignin. The cellulose unit cells are organised in a crystalline network, which forms microfibrils with a lateral thickness of about 2–5 nm and a length of 30 nm [5]. These microfibrils have been observed in the form of agglomerates which, in addition to their crystalline composition, contain amorphous cellulose and hemicellulose [6]. The remaining interstitial space between the agglomerates is filled with a continuous amorphous matrix, comprised of lignin and hemicellulose. The cellulose agglomerates and matrix appear to be grouped in the form of concentric lamellae, of around 20–30 nm repeat [6], see Fig. 1. The cellulose microfibrils are spirally wound, at an angle with respect to the fibre axis. This angle varies between layers (Table 1).

Natural fibres are characterised by a broad scattering of their mechanical properties, which is generally attributed to: the methods used for single fibre tensile tests and the computation of their mechanical properties [6], [7], [8], their morphology, the structure and composition of the fibres [7], [10], maturity of the plant [3], position of the fibre in the plant [10], [23], [29], preparation of the fibres (retting process and treatments) [11], [12], environmental conditions (temperature and humidity) [13], [14], [15], [16], [17], [18], and loading history [8], [19], [20]. It is very often noted that the mechanical properties, and more precisely the tensile strength and rigidity of such fibres, are highly dependent on their diameter [9], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34]. The ultimate tensile strength (UTS) is shown to decrease when the fibre diameter increases, for flax [9], [21], [22], [23], hemp [24], bamboo [25], jute [26], [33], [34] and sisal [27], [28]. The strength of natural fibres appears to be in agreement with Griffith’s theory [35], developed in the field of the mechanics of fracture in brittle materials. The main idea is that the strength of a material is dictated by the presence, and in particular the size, of microscopic defects. The larger the flaw in a fibre, the lower its tensile strength, such that when the fibre diameter increases, the probability of the presence of a critical defect increases, resulting in a higher probability of premature failure. In Fan [24], the author attributes the diameter dependence of the tensile strength of hemp fibres to the number of inherent joints, called defaults or dislocations, in the fibres. Whereas the UTS diameter dependence is well understood, the question of tensile elastic modulus still remains unresolved. In effect, a strong decline in modulus, associated with increasing fibre diameter, has been experimentally observed by various authors for the case of elementary flax [29], [30], hemp [31], stinging nettle [32] and jute [33], [34] fibres. Griffith’s theory does not provide a complete explanation for the observed behaviour: although flaws degrade a fibre’s strength, they should in no way affect their elastic modulus. In the literature, the diameter dependence of the fibres’ stiffness is often attributed to an over-estimation of their effective cross-sectional area, and more particularly the need to take the presence of the fibres central cavity into account. In practice, it is extremely difficult to experimentally determine the influence on stiffness of the lumen area in elementary fibres. Cutting techniques using microtome can induce damage and deformation. As pointed out by Abbey et al. [36], Focused Ion Beam (FIB) sectioning could also lead to ion implantation and structural modifications. SEM observations can induce deformation or shrinkage of a fibre, due to the use of low vacuum conditions, and produce significant surface modifications due to electron beam damage. The accurate determination of the lumen area of an isolated fibre requires the use of non-invasive, non-destructive techniques. Abbey et al. [36] proposed a technique based on the use of synchrotron X-ray tomography.

As a consequence of the experimental difficulties, in this paper, we propose an analysis of the influence of lumen size on the macroscopic mechanical properties of fibres, through the use of a comprehensive model. Most of the models available in the literature, developed over the past decades for wood or plant cells, are based on the classical laminated theory (CLT). Plate models, with an antisymmetric laminated structure, are somewhat different to the realistic structure of a natural fibre. Only more sophisticated tools, based on the thick laminated composite tube model, are able to take the hollow structure of the stem fibres into account, and more precisely to formulate the 3D stress–strain relationships in the laminate, under loading. Gassan et al. [37] proposed this type of model for ligno-cellulosic fibres to study the influence of a change in cross-sectional shape of a fibre (from elliptic to circular). Nilsson and Gustafsson [38] improved the model, by introducing an elastoplastic constitutive law for the matrix, together with some geometrical defects in order to fit the observed non-linear tensile behaviour of the hemp and flax fibres. For such 3D laminated composite tube models, the finite element method is required in order to compute the diameter–modulus relationship. Neagu and Gamstedt [39] described and precisely analysed the analytical and numerical solutions proposed in the literature to solve the elasticity problem of a cylindrically anisotropic circular tube subjected to axisymmetric loading. They underlined the influence of ultrastructural parameters, such as microfibril angle, on the hygroelastic properties of a typical softwood fibre. Marklund and Varna [40] proposed first a straightforward and transparent exact solution for the elasticity problem concerning multilayered concentric cylinder valid for orthotropic phase materials and for an arbitrary number of phases, particularly to study the influence of the restriction of rotation on longitudinal modulus of wood fibre. In the present study, we propose to use a 3D model for three-phase composites, together with an analytic approach to its solution, to investigate the origin of the diameter-dependence of elastic modulus in hemp fibres. A sensitivity analysis of the model parameters is also conducted to determine which parameters are significant and require additional research for strengthening the knowledge base, thereby reducing output uncertainty and which inputs contribute most to output variability.