NATURAL FIBRE REINFORCED COMPOSITES

STATISTICAL DATA ANALYSIS ON MECHANICAL PROPERTIES OF
NATURAL FIBRE REINFORCED COMPOSITES
ABSTRACT:
The use of natural fibres in reinforced composites has been rapidly increasing for structural
engineering applications in automotive and construction industries due to their high specific
strength, stiffness and sustainable benefits. However, natural fibres have limited range of real
applications and their performance has been questioned with a high variability in terms of their
mechanical properties and structural data analysis. A statistical study of strength and failure
strain on a set of samples of natural fibre composites might be helpful to design the
natural fibre composite structures. A deeper understanding on the variation of mechanical
properties of natural fibres provides scope for their reliability and future acceptance into
industries.
INTRODUCTION:
Recycling of plastics in automobile industries has gained importance [1] due to proposed
regulations demanding more eco-friendly products [2]. The use of natural fibres as reinforced
composites has been significantly increased in the previous decade [3]. Structural components
in automobile and civil industries demand materials with superior mechanical properties [4].
Natural fibres like jute, banana, flax, hemp and kenaf have high specific strength and stiffness
combined with less carbon footprint and biodegradable nature and are available at low cost [5].
But, the design data for structural analysis of natural fibre reinforced composites is limited and
their performance has been probed by a variability in their mechanical properties [6]. These
uncertainties resulted as the partial usage of natural fibre composites in commercial
applications. Hence, a deeper understanding of variation in mechanical properties of natural
fibres is necessary before they can be accepted for future applications in the industry. A basic
statistical data analysis based on behaviour of various samples of natural fibre composites
would reduce the time and cost for physical experimentations on prototype testing.
The mechanical properties of natural fibre composites show statistical tendency due to their
inherent uncertainties in desired design variables such as mechanical properties of fibre and
resin, void volume ratios of fibre dispersion, moisture content and temperature [7]. These
problems can be solved by studying the probabilistic design methodologies for the scattered
statistical distribution of these variables [8] and several algorithm codes have been developed
for the evaluation of mechanical properties of natural fibres [9]. In traditional practices,
material parameters are considered as known constants but the probabilistic design
methodologies enable us to quantify the inherent risk of failure of natural fibre composites.
Probabilistic design in composites has been predominantly used for carbon fibre composites
and that of natural fibre composites is still in the beginning stage [10]. However, natural fibre
composites are limited to their real engineering applications due to their high moisture content,
poor interfacial bonding properties with resin and hydrophilic nature of the fibre [11]. The
variability of mechanical properties of natural fibres depends upon the fibre geometry, fibre
loading and processing methods of fibre-resin matrix [12]. The natural fibre properties is also
influenced by external factors such as location of the fibre in the plant and environmental
conditions in the cultivated area [13]. These irregularities of natural fibre create experimental
difficulties while measuring the fibre parameters such as cross-section of fibre. Various
techniques have been used to quantify the variability of strength and stiffness using coefficient
of variation (Cv) [14]. The statistical analysis of mechanical properties of carbon fibres has
been investigated previously through the study of strength and failure strain distributions [15].
The present report studies the statistical behaviour of various natural fibre composites which
will further help in understanding the design requirements and by assessing their reliability we
can place them into commercial applications.
METHODOLOGY:
An experimental data is collected to determine the statistical distributions of mechanical
properties of natural fibre composites. The sample data is collected for several materials and
geometrical configurations. The natural fibre composites include flax and jute fibres with
variability in fibre orientation and weaving fabrication. These composites were manufactured
by vacuum assisted resin transfer moulding (VARTM) and resin used is epoxy. The sample
experimental data from the uniaxial tensile tests is noted. Engineering strain was measured
using optical extensometer whereas the strength and failure strain were measured at the point
corresponding to maximum axial load from stress-strain curves [14]. The statististical mean,
median and standard deviation of sample data is determined for various data sets. The
coefficient of variation of strength and failure strain is determined which is helpful to predict
the failure in material systems. Coefficient of correlation is determined between two parameters
among areal weight of the fibre, strength and failure strain. This is helpful to understand the
effect of one variable on other and the relation between two variables.
STATISTICAL DATA ANALYSIS:
SAMPLE DATA:
Statistical distributions are plotted for the sample data and the iteration is carried out for the
estimation of parameters in a chosen Probability Distribution Function (PDF). For each
estimated parameter, a graph is plotted for PDF to check the normal distribution of the sample
data.
Table 1: Parameters of Sample data [14]

Table 2: Sample data for Strength of Flax Twill Fibre

Table 3: Sample data for Failure Strain of Flax Twill Fibre

QUALITY OF SAMPLE DATA:
A sample data is collected from the population of strength and failure strain from the uniaxial
tensile tests. For each material system, strength and failure strain are determined for the
statistical analysis. The arithmetic mean, median and standard deviation is calculated for all
sets in the material system. One such operation is shown in Table 1 and Table 2. The critical
values (z values) and Probability Distribution Function (PDF) of each sample value is
calculated to check the normal distribution of the sample data.
Figure 1: Normal Distribution of Strength of Flax Twill fibre
Figure 2: Normal Distribution of Failure Strain of Flax Twill fibre
A set of sample data is said to be normally distributed when maximum number of values lie
closer to vertical axis or when the bell-curve have less width. For the set of data in Table 1 and
Table 2, most of the values in sample data lies within range of first standard deviation and the
rest within the range of second standard deviation.
For the selected set of sample data, the sample values are normally distributed and hence the
quality of the sample data is in good agreement for the Statistical analysis. The quality of other
sets of data in material system is determined and finally two sets of quality data is noted.
SAMPLING ERROR:
Sample data is set of values from the population, therefore the statistical analysis on sample
leads to certain margin of error which in turn depends on the normal distribution of the sample
data.
Margin of error, E = tα/2 √

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