Size dependency of tension strength in natural fiber composites

Abstract

This paper reports on a combined experimental and theoretical study on the size dependency of tension strength of clear wood at loading parallel to fiber direction. The fracture behavior of the tested softwood specimens was found to be rather brittle with low precursory activity and a statistical variation of the strength. The distribution of the strength values can be well fitted with a Weibull distribution distinguished by a shape parameter ρ∼8−10. A significant dependency of the mean strength of the material on the cross-sectional size of the specimens was obtained. The range of load redistribution in clear wood subjected to tension parallel to fiber was assessed by the theoretical concept of fiber bundle models for fiber composites. Hereby the macroscopic behavior was modelled in terms of the microscopic damage process.

Introduction

The material wood is a natural unidirectional fiber composite. The fibrous character of softwoods can be found at two different length scales: On the micro-scale (some 10–$\text{100}\text{μm}$) softwood consists of hollow, unidirectionally aligned cells, in the following named ‘micro-fibers’, which are bonded in lateral direction by very thin layers of matrix material. On the ultra-scale (some 0.01-$\text{1}\text{μm}$) the walls of the hollow micro-fibers consist of bundles of very stiff and strong cellulose chains (ultra-fibers), being wriggled around the axis of the micro-fibers in different layers and mainly bonded by two matrix materials, lignin and hemicellulosis. The crystalline structure of the ‘ultra-fibers’ determines the brittle character of fracture at tension loading and the very high ratios of strength and stiffness vs. density. The unidirectional build-up at the micro-scale leads to a pronounced anisotropy in the directions parallel and perpendicular to the fiber; typically strength and stiffness values differ by a factor of 10–20 for the two directions. The natural growth process forwarding several kinds of defects and irregularities yields a high scatter of all material parameters; typically coefficients of variation are in the range of 15–30 percent.

Scale effects of wood strength are well known with respect to tension loading perpendicular to fiber direction. In this weak plane of wood, exhibiting the most brittle failure mode of splitting, the pronounced scale effect of the stressed volume can be modelled adequately by a simple weakest link approach for a purely serial system [1]. However, recent investigations showed that the purely serial system approach is not fully applicable for realistic length scales but that the stress redistribution effects of partial parallel systems have to be taken into account.

In case of bending and tension parallel to fiber direction scale effects of width and depth have been reported in several studies [2]. However, modelling of wood loaded parallel to fiber as a parallel system of fibers has not yet been performed to the knowledge of the authors. Existing models mostly treat all scale effects in the view of some modified weakest link approach thereby silently neglecting the effects of stress redistribution after the initial fracture of the weakest fiber [3].

In the presented study results of tension strength of wood parallel to fiber direction obtained from quasistatical ramp-loading are presented. As anticipated, the tested wood specimens exhibited a rather brittle fracture character with low precursory activity preceding final failure. Tension strength for the specimens of a fixed size can be described by a Weibull distribution. Furthermore, samples of larger cross-sectional dimensions have smaller average strength indicating the existence of a size effect of wood, when loaded in tension parallel to fiber direction.

In order to obtain an accurate prediction of the point of ultimate failure the statistical evolution of the damage across the entire macroscopic system and the associated stress redistributions have to be considered, being a demanding problem. One of the most important approaches to the strength and reliability of fiber composites reducing the complexity thoroughly are the Fiber bundle models (FBM). The basic concept of FBM was first introduced by Daniels [4] and Coleman [5] and in the following has been the subject to intense research efforts during the last decades [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]. Fiber bundle models are constructed so that a set of fibers is arranged in parallel, each one having identical elastic properties but statistically distributed strength values. The modelled specimen is loaded parallel to the direction of the fiber and the first fiber failure during the loading process occurs, when the load stress exceeds the tensile strength of the weakest fiber. Once the fibers begin to fail the released load of the broken fibers has to be redistributed to the intact fibers according to some specific interaction law between the fibers. A large amount of efforts have been devoted to understand the behavior of fiber bundles under various load sharing conditions [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]. Based on a novel fiber bundle model introduced recently [25] a theoretical interpretation of the experimental results obtained for tension strength of clear wood parallel to fiber direction is presented. The macroscopic strength data are explained in terms of the damage process occurring on the micro-fiber level, i.e., on the level of the wood cells. In order to provide a quantitative characterization of the load redistribution among fibers a power law load-transfer function is proposed and its effective exponent is assessed.

In Section 2 a detailed description of the experimental procedure used for the uniaxial testing of wood specimens is presented. The experimental results are summarized in Section 3 followed by the presentation of the theoretical approaches in 4 Modelling of damage development, 5 Fiber bundle model with variable range of interaction.