Cellulose (2020) 27:6961–6976
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are greatly reduced. In such a situation, network deformations become non-affine (Picu 2011), so that local strains can differ greatly from the average behaviour. Moreover, the role of structural variations increases with reduced material density. With a low relative bonded area of a fibre network, heterogeneity of fibres becomes essential as well. The segment lengths between inter-fibre joints become longer [mean segment length can be 5–40 times greater than the fibre diameter (Ketoja et al. 2019)], and weak points along a fibre are not necessarily supported by other neighbouring fibres. Such features become increasingly important for compressive loads, for which a local network failure can simply mean that the associated fibre segment loses partly its ability to carry stress. This may happen not only by fibre bending, as shown in many previous models (Subra- manian and Picu 2011; Bergstro¨m et al. 2019), but also by sudden buckling or displacement of an individual fibre under compressive stress (Ketoja et al. 2019). This was noticed experimentally by Ketoja et al. (2019), who found abrupt displacements in fibre networks using an image cross-correlation technique. The possibility of a localizing failure in a heteroge- neous fibre has been omitted in previous simulation models (Alimadadi et al. 2018; Hossain et al. 2019; Bergstro¨m et al. 2019), which are based on uniform fibre segments without inherent structural unevenness inside a single segment between two joints. Ketoja et al. (2019) introduced a mean-field theory where the buckling of fibre segments was postulated to be an important deformation mechanism describing mean stress build-up during network compression. The theory explained the stress increase for intermediate compressive strains in varied well-bonded fibre mate- rials in the density range of 20–100 kg/m 3 . Ma¨kinen et al. (2020) provided further evidence for the theory by showing that acoustic energy emission could be directly correlated with the stress-compression beha- viour. Their cyclic measurements revealed another source of acoustic events than fibre bending. However, the theory was not able to explain the behaviour at very large strains because of collective softening of the material (Picu and Subramanian 2011). Moreover, the theory overestimated the stress when the strain was below 10% (Ketoja et al. 2019; Ma¨kinen et al. 2020) and when large amounts of cellulose microfibrils (CMF) were added to a fibre network (Ketoja et al. 2019). Added CMF seemed to increase strength at
intermediate compression levels by forming cellulose micro-scale sheets within the fibre network (Bossu et al. 2019). In the current study, we have taken the above considerations into account when improving the strength of lightweight natural fibre materials. The bond strength and total inter-fibre contact area (Sor- munen et al. 2019) can be increased with polymeric, fibrillar and fines materials. The strengthening mech- anisms are twofold: Firstly, fine components can build loose material bridges between fibres, which, during drying with the help of surface tension forces, drag fibres in contact with one another thus increasing the number of bonds and reducing the mean fibre segment length. Usually, this is associated with a higher density of the whole material as well. Secondly, polymeric and fibrillar components can strongly affect the strength of individual bonds by (a) enhancing the mechanical entanglement of the inter-fibre fibrils, (b) creating a larger microscopic contact area where short-range interactions become effective, or (c) by changing these chemical forces (Schmied et al. 2013). Overall mate- rial strength is further improved if the formed network is able to distribute local stresses evenly over the fibre network. For this reason, we explored multi-scale network structures by combining wood and hemp fibres with varying dimensions and flexibilities. The studied fibre and fine components covered the broad length (width) range from * 40 l m ( * 3 nm) up to * 15 mm ( * 50 l m). In addition to strength measurements, the micro-scale homogeneity of the structures was followed as well.
Materials and methods
Fibres and fine components
Hemp bast fibres were selected as the long fibre component in the furnish. The fibre length of a single hemp bast fibre can vary from 1 to 34 mm (average 8–14 mm) with a diameter between 17 and 23 l m (Shahzad 2012). The typical value of the longitudinal Young’s modulus of a hemp fibre is 30–60 GPa (Shahzad 2012). Finnish hemp bast fibres (Cannabis sativa, delivered by HempRefine Oy) with the chem- ical composition of 81% cellulose, 11% hemicellu- lose, and 5% lignin were treated with a Kvarn BAHS- 30 hammer mill (Kamas Industri AB). Fibres were
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