# Modelling of Natural Fibre Composites

## Introduction

The finite element method is popular in the design engineering community. Through finite element analysis (FEA), a model of any composite structure with its complexity in shape, material selection, boundary conditions, load-withstanding ability, and other influencing factors can be analyzed under specific conditions. Virtual experiments could be done and viewed via a graphical user interface. Researchers carry out many iterations using FEA to optimize the outcomes so as to attain higher accuracy in the structure, enhance its lifetime, account for uncertainties, and reduce downtime in the product development process.^{1}

FEA can be used to calculate the mechanical properties of discontinuous fibre composites and helps to determine the source of variability; in general, accuracy is imperfect owing to the quality of the fibre’s structural design considered at the meso-scale level as a representative volume element (RVE). Currently, numerical models are used to generate RVE, which can be categorized into three main groups - sedimentation, hard, and soft models - along with their limitations. Sedimentation algorithms are tough systems that impose restrictions on the fibre alignment distribution. While the restriction on the ceiling volume fraction is condensed, sedimentation algorithms are computationally costly, and forming meshes for rigid models would be problematic, due to the small distances between the bundles of the rigid structures. In a hard model, it prevents bundle-to-bundle penetrations; fibre volume fractions are restricted due to fibre jamming, and this is usually experienced when the pockets of free space are too small to accept other inclusions. In soft models, overlapping of fibre bundles is permitted to occur, and hence it is unrealistic, as there is no restriction on the fibre volume fraction that is imposed. Allowing bundle-to- bundle penetration also creates incorrect load transfer paths at bundle crossovers.^{2}

RVE size is linked to the fibre length and tow size and can be several orders of magnitude larger than the scale of the reinforcement. Computation time is one of the primary concerns in meso ranges discontinuous fibre composites materials. Two-dimensional (2D) models are a computationally inexpensive option, using a ID linear beam element to represent the fibre bundles, randomly distributed in 2D space. This overlooks fibre crimping and allows bundle-to-bundle penetration, as all bundles are deposited on the same plane, reducing the accuracy. 2D models are also inclined to be over-stiff, as interconnecting bundles are rigidly bonded at the intersection points, increasing as the RVE thickness increases.^{2} Three numerical algorithms - fibre kinematics, a custom Delaunay meshing algorithm, and tensile modulus predictions - were integrated to create a realistic simulation of the network of a composite structure. Fibre tortuosity was simulated using fibre bending and twist compaction of fibre kinematics. Compressive, tensile, and in-plane shear properties were simulated using a Delaunay meshing algorithm with respect to the RVE fibre architecture. Less than 5% error in was tensile modulus predicted on the basis of the realistic network of composite structure.^{3}

The contact and interaction between the polymer matrix and the discontinuous or continuous high stiffness natural fibres and particles play a vital role in determining the properties of the composite. The role of the matrix is chiefly to transmit the stresses to the reinforcement and protect the fibres’ surface from mechanical abrasion, retaining the characteristics required for the specific application of the composite.^{4}-^{5} The potential use of natural fibres along with polymer matrix composites is mostly in the area of aircraft and automobile interiors, called secondary structures, owing to the composites’ high specific stiffness, definite strength, light weight, high corrosion resistance, and fatigue resistance. Composites reinforced with natural fibres have been gaining increased consideration in numerous applications because of their availability, recyclability, biodegradability, and low material cost.^{6}

## Modelling and Simulation of Composite Structures

In order to generate an effective model of progressive failure in thermoplastic reinforced natural fibre composite structures, the damage behaviour should recognize various loading environments. In a compression test, stiffness degradation represents a response to damage and crack spreads in composite laminates. In complex structures, the composite failure mechanisms such as matrix cracking, fibre breaking, and delamination between adjacent plies are used to predict the damage in composite materials.^{7} Delamination growth in the matrix is related to various levels of damage such as fracture mechanics, damage mechanics, failure criteria, and dam- age/plasticity coupling. Continuum damage mechanics (CDM) models deliver a traceable outline for modelling damage initiation and evolution. The Matzenmiller, Lubliner and Taylor (MLT) model of growth for damage variables is sure to follow a Weibull distribution formulation, mainly appropriate for modelling damage propagation phenomena.^{8}

Four damage mechanisms for pliable matrix-reinforced fibre composites under compressive load can be distinguished: fibre crushness, resilience of the fibre, plies buckling strength with elastic matrix deformation, failure of the matrix and kink- band. The interfacial debonding is considered as an important degradation mechanism in the composite.^{9} The first phase of debonding is initiated by isolated fractures in the weak region.^{10} These fractures intensify the stress concentration under the shear effect, causing cyclical rotation of the plies, debonding of the interface, and cracking of the matrix. As the applied load increases, it creates additional cracks between the layers and leads to the ultimate failure of the fibre-reinforced thermoplastic matrix composites.^{11} The Cohesive Zone Model was introduced by Dugdale and Yielding and Barenblatt. This model is used for simulating delamination for a wide variety of heterogeneities material at various scales to form the laminate composite.^{12}

In the direction of the *x* axis, the (1 /E_{x}) compliance of an orthotropic unidirectional fibre reinforced lamina considered by its main axes oriented at an angle 0 to the coordinate axes would be assessed as^{1314}

In Equation 4.1, L and T denote the main material axes (longitudinal and transverse), while E_{x} represents Young’s modulus in the *x* axis direction. Shear modulus (E_{L}), Young’s moduli (E_{1}), shear modulus (G_{LT}), and Poisson’s ratio (v_{LT}) are unidirectional fibre-reinforced lamina phenomena. Elastic constants (E_{L}, E_{T}, v_{LT}, and G_{LT}) of a unidirectional fibre-reinforced lamina can be found using assumptions and micro mechanics, using known moduli, Poisson’s ratios, and volume fractions of the fibre (V_{f}) and the matrix (V_{m}) generated as

This Halpin-Tsai equation represents the fibre, ribbon or particulate composites and helps in designing composite materials with suitable macroscopic properties.^{15 }Dissimilar homogeneous isotropic materials and fibre-reinforced composite materials deliver the possibility of tailored mechanical properties by the proper selection of material constituents (matrix and fibre) and their volume amounts. Each lamina is considered as a building block; since several laminae may be stacked one upon another, its ply thickness, orientation of each and individual lamina, and the stacking sequences will decide its mechanical properties. Finally, we may obtain the constitutive calculations for n-layered laminates along with stress-strain relations of an individual fibre-reinforced lamina as per the classical lamination theory.^{1617} Continuous modulus loss owing to hydrolysis reactions of natural fibre-reinforced composites under hygrothermal ageing is considered in order to assess the long-term mechanical behaviour of composites.^{18}