Structure, morphology and mechanical properties of Rhectophyllum camerunense (RC) plant fiber. Part II: Computational homogenization of the anisotropic elastic properties

doi:10.1016/j.commatsci.2010.12.013

Computational Materials Science

Volume 50, Issue 4, February 2011, Pages 1550-1558

https://doi.org/10.1016/j.commatsci.2010.12.013 Get rights and content

Abstract

In part I of this paper, we used statistics to derive some parameters (actual area of the cross-section, polar moment of inertia) and Voronoi partitioning techniques to reconstruct the section of a plant fiber. The reconstructed geometry is used here to perform bottom-up predictive simulations of the anisotropic elastic properties of the fiber taking into account the underlying physics at the finer scales (thicknesses of the cell wall layers, microfibril angle). For this purpose, three load cases are considered and the overall response of the fiber is computed numerically at each material point by a detailed modeling of the microstructure at the point under consideration. The predicted longitudinal modulus is in good agreement with experimental results. Moreover, computational homogenization allow us to access to the overall elastic properties of the transverse isotropic material, which is very hard to do by direct measurement due to the minute cross-section of the fiber.

Research highlights

▸ Computational homogenization of a plant-fiber is performed. ▸ Overall anisotropic elastic properties of the fiber are computed. ▸ Computed and measured values of the longitudinal modulus are in good agreement. ▸ Coupling behavior of the fiber could be studied using the same geometry.

Introduction

Plant fibers are increasingly used as reinforcements in composite materials. They could be in the form of cellulose nanofibrils obtained by steam explosion for example [1]. Polymers reinforced with cellulose nanofibrils are mostly studied by chemistry scientists and one of the challenges they need to perform is a uniform dispersion of the nanofibrils in the matrix. Plant fiber reinforcement could also be used in the form of bundles of fiber cells also called tracheids [2], [3]. Fiber bundles are easier to handle and to disperse in a polymeric matrix than cellulose nanofibrils. They belong to the field of interest of material engineering scientists. Hybrid composites use both cellulose nanofibrils and tracheid bundles to combine the advantages of each of them.

It is well-known that the behavior of plant fibers depends on the different scale levels, from the cellulose microfibrils to the fiber bundle [4]. However, due to their minute cross-sections, direct measurement of the transverse properties of the fibers is a very difficult task. Multiscale modeling is therefore a suitable method allowing the derivation of material properties of natural fibers. In the earlier models, wood cells were represented as circular tubes allowing derivation of analytical solutions for the stiffness [5]. Then, wood cells were treated as parts of a hexagonal cellular structure [6] and analytical solutions were also derived. In the past few decades, progress has been made in the fields of physics, chemistry, material and computer sciences thus bridging the gap between the mechanics of materials and other disciplines. Today, it is generally admitted that computational homogenization incorporating fine-scale physical and chemical mechanisms in the macroscopic level is the most accurate approach for bottom-up predictive simulations [7], [8], [9]. Image-based geometry and physical parameters at a finer scale are the most important inputs needed for the implementation of the method. In the first part of this paper, statistics were used to derive certain event patterns of the cross-section of RC-fibers. The cross-section was also reconstructed by using Voronoi partitioning techniques. The objective of this second part is to perform bottom-up predictive simulations of the anisotropic elastic properties of the fiber taking into account the underlying physics at finer scales. Interactions between the structure, morphology and mechanical properties are then highlighted. For this purpose, three load cases are considered and the entire response of the fiber is computed numerically at each material point by a detailed modeling of the microstructure at the point under consideration. This paper is outlined as follows. In the first section the reconstructed image of the cross-section of the fiber will be recalled and will be extruded to obtain the geometrical model of the fiber. Next, laminate plate theory will be applied for modeling the cell wall. Numerical simulations will be performed in the third section and the results will be presented and commented in the fourth and final section.

Section snippets

Geometrical modeling of the fiber

The structure of natural fibers is very complex. The fiber cell consists of several layers (cell wall) surrounding an empty cavity in the middle Fig. 3a. Some morphological features including pits could also be observed [10]. Pits are important for water transportation and fracture initiation. In computational homogenization, it is not relevant to include these features in the geometrical modeling. The image-based reconstruction techniques developed in the first part of this paper are suited to

Mechanical behavior of the cell wall

In this chapter, we will briefly introduce the method used to describe the mechanical behavior of plant cell walls. Fig. 3a represents the image of the ultrastructure of the RC-fiber obtained by transmission electron microscopy. Details on material preparation and method are described in Ref. [11]. Fig. 3a confirms the generally accepted opinion on the multilayer structure of plant cell walls and especially those of wood, the most studied material [10]. According to this view, the tracheids are

Macroscopic modeling and extraction of the macroscopic elastic properties

The quasi-tubular shape of the RC-fiber leads us naturally to adopt a model of a thick cylinder for the identification of anisotropic elastic properties (Fig. 4a). It should be stressed that the microtome cutting of the fiber fixed in epon resin caused a slight ovality of this section. The problem of an elastic thick cylinder with monoclinic symmetry subjected to tension, torsion and pressure was solved analytically in the literature [14], [15], [17], [18]. Due to the very high number of

Numerical simulations

Both classical laminated theory of plates for the description of the mechanical behavior of the cell wall and macroscopic modeling of the fiber are integrated in a numerical model for the extraction of the macroscopic elastic properties of the RC-fiber. The geometrical model is described in Section 3. Layer properties, orientation angles of microfibril and thicknesses are reported in Table 1. A linear layered structural shell element (SHELL99) of ANSYS is used. The element has six degrees of

Results and comments

Numerical simulations using data in Table 1 allow us to calculate the overall transverse isotropic elastic properties of the RC-fiber. We must also recall that for 87% of the 11,051 elements, the layers on one side of the middle surface are counterbalanced by the corresponding layers on the other side with opposite microfibril angle such that the net shear force over the entire thickness is canceled out. Consequently, no twisting is observed in the deformed shape. First of all, the influence of

Conclusions

Material engineers’ approach to plant fibers is still mainly based on the utilization of bundles of fiber cells as reinforcement in composite materials. So they need to access their anisotropic properties for the design and analysis of structural parts. In the first part of this paper, we use statics to derive some parameters (actual area of the cross-section, polar moment of inertia) and Voronoi partitioning techniques to reconstruct the section of a plant fiber. Then the reconstructed

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Structure, morphology and mechanical properties of Rhectophyllum camerunense (RC) plant fiber. Part II: Computational homogenization of the anisotropic elastic properties

Abstract

Research highlights

Introduction

Section snippets

Geometrical modeling of the fiber

Mechanical behavior of the cell wall

Macroscopic modeling and extraction of the macroscopic elastic properties

Numerical simulations

Results and comments

Conclusions

Composites: Part A

Mechanics of Materials

Composites Part A: Applied Science and Manufacturing

International Journal of Solids and Structures

Carbohydrate Polymers

Canadian Journal of Botany

Annals of Forest Science

Philosophical Transactions of the Royal Society, London

Cellular solids