Tensile mechanical properties of natural fibre composites – a statistical approach

: The main objective and the originality of this work are to create a hybrid-natural fibre composite by the RMS method. Hybrid composites are manufactured by combining two or more dissimilar kinds of fibre in a single matrix. In the first section, Response Surface Methodology (RSM) using a Box-Behnken experimental design and the Analysis of Variance (ANOVA) are applied to investigate the effects of the type of fibres, chemical treatment, volume fraction and treatment time on the mechanical properties (ultimate tensile strength and Young’s modulus) in the tensile quasi-static loading when used two resins namely, epoxy and polyester. In the studied range, statistical analysis of the results showed that selected variables had a significant effect on the mechanical properties, except the treatment time that has a very weak significance effect on the mechanical properties. Then, to maximize the mechanical properties, the optimal conditions coded by RSM were found: the type of fibres (X 1 ) of [-0.28 and -0.33], the chemical treatment (X 2 ) of -1, the volume fraction of fibre (X 3 ) of 1 and the treatment duration (X 4 ) of [-0.97 and -1] for epoxy resin matrix. Similarly, when used the polyester resin matrix; the type of fibres (X 1 ) of -0.26, the chemical treatment (X 2 ) of -1, the volume fraction (X 3 ) of 0.99 and the sinking time (X 4 ) of [-0.94 and -0.93]. The obtained optimum parameters were confirmed experimentally in the second section.


Introduction
Natural fibres have been used to reinforce materials for over 3000 years. More recently, the natural fibre composites are receiving more attention during the last thirty years due to their ecologically friendly behavior [1]. Researchers focus their investigations on composite materials based on renewable resources with comparable properties to synthetic fibres for reducing petroleum consumption and pollution [2][3][4][5][6]. The natural fibres are lighter than synthetic fibres which revert as fuel reduction when this material is used by the automotive industry. Moreover, the natural fibres have low density, low cost, its availability, renewability, easy recyclability, low process energy, good thermal and acoustical insulation properties, acceptable specific strength and modulus, and reduced tool wear (non-abrasive) in machining operations [7][8][9][10]. Table 1 shows physical properties of some natural fibres used as reinforcement in composites materials [11][12][13][14][15][16].
The properties of the composite depend not only on the properties of the fibre but are also controlled by the properties of the matrix, interfacial adhesion between the fibre and matrix and the design of the hybrid system. In order to improve their properties researchers turned their focus on the study of effect on mechanical properties due to hybridization of naturalnatural fibres i.e. Hybrid composites consist of an amalgamation of two or more fibres to form a single matrix. The possible combinations of hybrid composites include artificial-artificial, natural-artificial and natural-natural fibre types [14,17]. In this paper, sisal, jute and flax fibres were used as reinforcements because they are abundantly found in nature.
There are few studies in the literature investigated and addressed the competitiveness, capabilities and suitability of hybrid natural fibres as reinforced fillers in polymeric matrices.
Since, Schneider and Karmaker [18] developed composites using jute and kenaf fibre and polypropylene resins and they reported that jute fibre provides better mechanical properties than kenaf fibre. Recently, Venkateswaran et al. [19] reported that sisal/banana hybrid natural fibre composite specimens were prepared with different rations by taking 0.4 volume fraction and tensile properties of these hybrid natural fibre composites are also examined using rule of mixtures (RoHM). In the next study, Venkateswaran et al. [20] studied the mechanical properties such as tensile strength, flexural strength, impact strength and water absorption rate of sisal and banana fibres reinforced epoxy composite materials. They have observed when the hybridization of the sisal fibre with banana/epoxy composites up to 50% by weight increases the mechanical properties and also decreases the water absorption properties.
Boopalan et al. [21] studied the mechanical and thermal properties of jute and banana fibre reinforced epoxy hybrid composites. Jute fibre was hybridized with banana fibre, in order to enhance the better mechanical properties of composites.
In other words, the adhesion between the reinforcing fibres and the matrix plays an important role in the final mechanical properties of the materials; when natural fibre used as reinforcement in composite materials, many problems occur at the interface due to incompatibility. Fibre-matrix interaction can be improved by surface or structural modification of the fibres using various processes such as alkali treatment, bleaching, acetylation and steaming. It is worth to mention that the chemical treatment of the fibres can either increase or decrease the strength of the fibres, and hence good understanding of what occurs structurally is required [22].
In this paper, we used two types of chemical treatment namely, alkaline (sodium hydroxide) NaOH and sodium bicarbonate NaHCO3. In alkaline treatment, fibres are immersed in NaOH solution for a given period of time. Ray et al. [23] and Mishra et al. [24] treated jute and sisal fibres with 5% aqueous NaOH solution for 2 h up to 72 h at room temperature. Similar treatments were attempted by Morrison et al. [25] to treat flax fibre. Asumani et al. [22] studied the alkali and silane treated kenaf fibre reinforced polypropylene composites. It has been noted that the tensile strength and modulus increased significantly by 25% and 11% respectively after treatment with 5% alkali. Another, Rajesh and Prasad [26] studied short jute fibre/PLA composites with different concentrations of NaOH and H2O2 treatments on jute fibres. The effect of fibre loading and alkali concentrations used for fibre treatment on the mechanical properties of the composites were investigated. It was reported that the tensile properties of composites with treated fibre at higher fibre loadings were better than those of untreated fibre.
Although we mentioned many studies about composites, there are few studies in literature studied the mechanical properties of natural-natural hybrid fibre reinforced polymer composites, i.e. The main goals of the first part of this work are to prepare natural hybrid composite plates using response surface methodology (RSM) and the desirability function approach. Then, the ANOVA study involves the effects of input parameters, namely and coded; type of fibre (X1), chemical treatment (X2), volume fraction of fibre (X3) and treatment duration (X4) on mechanical properties of composites. In the second part of this work, the different tests realized to characterize the mechanical properties of the optimal natural hybrid composite reinforced with polyester or with epoxy resins which were experimentally analyzed.

Materials
In this present investigation sisal (Agave sisalana), jute (Corchorus Capsularis of Tiliaceae) and flax (Linum usitatissimum) fibres are used for fabricating the composite specimens. The definitions of fibres are discussed in detail as follows:

Jute fiber
Jute is a bast fibre whose scientific name is Corchorus Capsularis of Tiliaceae family. Jute is a natural biodegradable fibre with advantages such as high tensile strength, excellent thermal conductivity, and coolness etc. Its abundance in availability with cheaper cost has acquired importance of its use in polymer composites [27]. Jute fibre extracted from the bark of jute plant has three major categories of chemical compounds namely cellulose (58-63 wt%), hemicellulose (20-24 wt%), and lignin (12-15 wt%) and some other small quantities of components like fats, pectins, aqueous extracts, etc [28].

Sisal fiber
Natural sisal fibre is a hard fibre extracted from the leaves of the sisal plant in the form of long fibre bundle. This plant, scientifically named Agave sisalana Perrine, is of Mexican origin and is grown in Brazil, East Africa particularly in Tanzania, Haiti, India, Indonesia and Thailand [29]. A sisal plant produces about 200-250 leaves and each leaf contains 1000±1200 fibre bundles which are composed of 4 wt% fibre, 0.75 wt% cuticle, 8 wt% dry matter and 87.25 wt% water [30]. So normally a leaf weighing about 600 g will yield about 3% by weight of fibre with each leaf containing about 1000 fibres. Sisal fibres with excellent mechanical property are mainly used as textiles, strings, mats, yarns, art ware and reinforced material [31].

Flax fiber
Flax, Linum usitatissimum, belongs to the best fibres. It is grown in temperate regions and is one of the oldest fibre crops in the world. It's an 80 to 120 cm high plant which possesses strong fibers all along its stem and contains 70% of cellulose. These cellulose based fibres have low density, good tensile strength, stiffness and high aspect ratio [32][33].

Fibre preparation methods
In order to improve the interfacial properties between the fibres (the sisal, jute and flax fibres) and the matrix, we were subjected to several surface treatments. The fibres were cut into 300 ±2mm long pieces, washed with distilled water and oven dried at 45 °C until obtaining a constant weight. In this study, fibres were treated with sodium hydroxide NaOH and sodium bicarbonate NaHCO3, with various times 4, 12 and 24 hrs.
The volume fraction of fibre (VF) is calculated by using the following relation [34][35].
VF is fiber volume fraction, Wf are the weight (g) of fibres ( sisal, jute and flax) and Wm is the weight (g) of matrix, ρf and ρm are the density (g/cm 3 ) of fibers and matrix, respectively. Also, the diameters of sisal, jute and flax fibres were evaluated by a Visual machine 250 tool makers microscope with ×4.5 magnifications and 1μm resolution at three different random locations along the single fibre and the average value is taken, as shown in Fig. 1. The average diameters detected of sisal, jute and flax fibres were 240±40 µm, 880±80 µm and 17±10 µm, respectively.  Table 1 shows the average values of physical and mechanical properties real of natural fibres (sisal, jute and flax) and resins (epoxy and polyester) used in this study. Ten identical specimens from each fibre and resin were tested and the average value is tabulated.

Table 1
Physical and mechanical properties of sisal, jute, flax fibres and resins used in this study. In this process untreated sisal, jute and flax fibres, they were respectively immersed in 7, 9 and 1 wt% NaOH solution for various times 4, 12 and 24 hrs at room temperature. Then, The fibres were washed several times with fresh water to remove any NaOH sticking on the fibre surface, neutralized with dilute acetic acid and after that, washed again with distilled water.
Finally, pH was maintained at 7. The fibres were then dried at room temperature until a constant weight was reached.

Treatment with NaHCO3
Similarly, the second treatment method consisted of soaking the raw of the sisal, jute and flax fibres in 25, 25 and 10 wt% NaHCO3 solution for various times 4, 12 and 24 hrs at room temperature, respectively. The fibres were then taken out of the solution, drained, and washed several times with tap water to remove any residual NaHCO3 traces sticking on the fibre surface. Then, fibres were neutralised with dilute acetic acid. After that, rinsed again with distilled water. Finally, the fibres were dried at room temperature until a constant weight was reached.

Mechanical properties
In order to evaluate the effect of the fibres' type, chemical treatment, volume fraction and treatment time on the mechanical properties (ultimate tensile strength and Young's modulus) the modified composites were measured using a Universal Testing Machine EZ20, equipped with a load cell of 20 KN. The clamps used during the tests have self-concentric alignment and are manually adjusted by mechanical springs. The tensile static tests were performed at a constant speed of 2 mm/min and the longitudinal strain was measured using an extensometer with 30 mm gauge length. All tests were conducted at a room temperature of 26°C and a relative humidity of approximately 30%. Tensile tests were conducted according to the ASTM D 3822-01 specifications. In each case, five specimens for each composite were tested and the average value is tabulated (Table 3).

RSM experimental design
The response surface methodology (RSM), firstly induced by Box and Wilson [36][37][38], is a method for the accurate prediction of engineering system input-output relationships by taking a full consideration for parameter interaction. It has been widely applied in numerous manufacturing fields for the design, development and formulation of new products, as well as in the improvement of existing product designs. RSM is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which a response of interest is influenced by several variables and the purpose is to optimize this response [37]. An important advantage of RSM is the reduced number of experimental trials A BBD was performed with four independent variables (X1, type of fibre; X2, chemical treatment; X3, volume fraction of fibre; and X4, treatment duration) at three levels. In addition, there are two qualitative variables (X1, type of fibre and X2, chemical treatment) and the other two are quantified (volume fraction of fibre and X4, treatment duration). The range of the independent variables, the levels of the independent variables and the results of the whole design consisting of 29 (calculated based on Eq. (2)) experimental points performed in random order were presented in Table 3; these conditions were based on the results of the preliminary experiments. N = 2 n + 2n +Nc = 2 4 + 2×4 + 5 = 29 runs (2) where N is the total experimental runs, n is the number of variables and Nc replicate runs at the centre. For statistical calculation, each variable was coded at three levels: "-1", "0" and "+1", where "-1" is the lowest level, "0" is the central level and "+1" is the highest level. And each combination was repeated five times.
A complete description of the process behavior requires a quadratic or higher order polynomial model. Hence, the full quadratic models were established by using the method of least squares, which included all interaction which is termed to calculate the predicted response. The quadratic model is usually sufficient for industrial applications. For n factors the full quadratic model is shown in Eq. (3): where Y is the response; Xi and Xj are the variables (i and j range from 1 to k); a0 is the model intercept coefficient; bi, bii and bij are the interaction coefficients of linear, quadratic and the second order terms, respectively; k is the number of independent variables (k = 4 in this study). The quality of the model was expressed by the adjusted-R 2 (R 2 adj), and predicted-R 2 (R 2 pred). The other important coefficient, R 2 , which is called coefficient of determination in the resulting ANOVA tables, is defined as the ratio of the explained variation to the total variation and is a measure of the fit degree. When R 2 approaches to unity, it indicates a good correlation between the experimental and the predicted values. The regression analyses, graphical analyses, analyses of variance (ANOVA) and analyses of response surfaces were carried out using Design Expert software V8 (Stat-Ease). The significance of the independent parameters and their interactions and the adequacy of the developed model were estimated by analysis of variance (ANOVA). The variables, units, symbol code and levels were shown in Table 2.      the corresponding response (i.e., α = 0.05, or 95% confidence level), this indicates that the obtained models are considered to be statistically significant, which is desirable; as it demonstrates that the terms in the model have a significant effect on the response, and the higher F-values for each coefficient suggest more significance of that term in the model [39].
As can be seen from Table 4, the regression model for ultimate tensile strength was found to be highly significant from the Fisher's test which had a high F-values (12.27 and 35.73) with very low probability (both P < 0.0001 and both p-values < 0.05) according to, epoxy and polyester resins, respectively. Judging by the F-values of the items in the regression models, the order in which the independent variables influenced the ultimate tensile strength degradation efficiency was: the volume fraction of fibre (X3) which is the most important factor affecting the tensile strength. Its contribution is (74.33% for σepoxy and 82.46% for σpolyester). Similar results were reported by Ben Brahim [40], when they study the effect of Similarly, results from ANOVA (Table 5) for the quadratic model showed that the polynomial models were highly statistically significant, as suggested by the high model F-values (10.15 for Eepoxy and 7.37 for Epolyester) and low P-values (both < 0.0001 for Eepoxy and Epolyester, both p-values <0.05). The F and P values are used to check the significance of each coefficient.
The lower P-value and higher F-value indicated the more significance of corresponding coefficient. The high values of determination coefficients (R 2 epoxy = 0.8024 and R 2 polyester = 0.7467), and adjusted determination coefficients (adj-R 2 epoxy = 0.7233 and adj-R 2 epoxy = 0.6454) showed a high degree of correlation between the experimental and the predicted values of Young's modulus. In addition, according to Table 5, it can be apparently the volume fraction of fibre (X3) which is the most important factor affecting on Young's modulus (E). Its contribution is (Cont. = 45.78 % and Cont. = 48.99 %) for epoxy and polyester resins, respectively. The next factor influencing E is the type of fibres (X1) with (Cont. = 7.50 % and Cont. = 12.35 %), there are lots of work that has been done to study the effect of fiber loading on the mechanical properties [42][43][44]. Whereas, the chemical treatment (X2) with (Cont. = 0.72 % and Cont. = 8.17 %) was found to be less significant on Young's modulus of epoxy and polyester resins, respectively. Similarly, the treatment duration (X4) has a very weak effect on the Young's modulus due to higher P-value (P > 0.05). Its contribution is (Cont. = 0.04 % and Cont. = 0.02 %) for epoxy and polyester resins, respectively.

Perturbation plots
The main effects of the single factor (X1, X2, X3 and X4) and the perturbation plots for both response parameters (σu and E) are illustrated in Fig. 4. They confirm the ANOVA results demonstrated in Tables 4 and 5. The x-axis in the graphs is the low and high level of the design factor and y-axis is the mean value of the response parameter at a specific design factor level. Fig. 4a illustrates the perturbation plot of σu for both resins. According to this plot, we

Effect of operating parameters on grafting
In order to present the relationship between independent variables (type of fibres (X1), types of chemical treatment (X2) and volume fraction of fibre (X3)) on response parameters (ultimate tensile strength (σu) and Young's modulus E), the response surface plots of the models were generated and illustrated on the three-dimensional space by varying two variables within the experimental range for both resins matrix tested (epoxy and polyester), while the treatment duration (X4) is kept at the middle level (12 hrs) and when using three different natural fibres, namely and coded; flax fibre (-1), jute fibre (0) and sisal fibre (+1). by improving the fibre-matrix interaction, subsequently, significantly increased the ultimate tensile strength and Young's modulus of the composites. Several authors [45][46][47][48], have focussed the studies on the treatment of fibres to improve the bonding with resin matrix. For example, Zou et al. [49] studied the effects of alkali and silane surface treatments on sisal fibre properties and they observed that the surface treatments facilitated good adhesion between fibers and thermoplastic matrix resulting in composites with improved mechanical properties.
Generally, the plots indicate that the highest ultimate tensile strength and Young's modulus can be achieved at the volume fraction of fibre is higher (level +1) with NaHCO3 chemical treatment (level -1), when using jute fibre (level 0) and when reinforcing composites with epoxy matrix. Also, for all types of fibres a quadratic increase in the response parameters with increasing the volume fraction of fibre were observed. This is due to the high fibres tensile modulus compared to resins matrix.

Multiple response optimizations
In this section, the statistical method of RSM was used to calculate desirability for the optimization analysis. This approach is a multi-criteria methodology often applied when various responses have to be considered at the same time and it is necessary to find optimal comprises between the total numbers of responses taken into account. The Derringer function or desirability (D) function is the most important and most currently used multi-criteria methodology in the optimization of analytical procedures [39]. The global D value was analyzed basing on individual desirability's. Statistical analyses were performed operating the Design Expert software V8 (Stat-Ease). The constraints used during the optimization process are summarized in Table 6. The best optimal values of independent variables and responses are reported in Table 7

Creation of the hybrid composites
Once the optimal level of the process parameters is selected, the final step is to predict and verify the improvement of the performance characteristics (ultimate tensile strength and Young's modulus) using the optimal levels of the process parameters presented in terms of coded factors in section 3.4. To make the confirmation tests, we converted the coded values presented in Table 8 to the actual values. The rule of mixture fibre has been presented in Fig.

Hybrid composites manufacturing methods
In this study the hybrid composites are fabricated by hand-lay up method. Composites were made using a wood mould measuring: 300 × 150 × 5 mm length, width and depth, respectively. Four beadings a glass plate were used to maintain a 5 mm thickness all around the mould plates. Initially, the moulds are cleaned, dried and silicon spray was used as releasing agent. Secondly, untreated jute, and flax fibres were, weighed, bagged and formulated according to the various fibre contents indicated in Table 8. In this section, fibres were treated with sodium bicarbonate NaHCO3, with various times 4 to 4.33 hrs (see Table 9).
Then, the fibres were mixed with resin matrices (epoxy or polyester) for the fabrication of composite. Then, uniform pressure of 5 Pa was applied over the mould plates (purpose of this is to maintain uniform thickness and to avoid void formation during curing) for 1 h at room temperature curing. Finally, the composites were cut and shaped in rectangular form (250 × 25 × 5 mm) according to ASTM standard by using a diamond saw blade. Four identical samples were prepared for each volume fraction of fibres and all the specimens were tested at a strain rate of 2 mm/min using an electronic tensometer.

Confirmation test results
The four different hybrid composite specimens: HCE1, HCE2, HCP1 and HCP2 (see Table 8) are tested in the universal testing machine to find the tensile properties. Each test was repeated four times and the results are displayed as strength against strain (Figure 3a-d). Also,  Table 1.  The average values of the ultimate tensile strength and Young's modulus of different composite formulations are plotted in Figure 10 for better comparison. It is observed that the hybrid composite HCE1 had the highest tensile properties (ultimate tensile strength and Young's modulus) especially when reinforced with epoxy. The lowest tensile properties were produced by jute composite when reinforced with epoxy. The modulus value for the hybrid composite HCP2 fell within these two values.

Conclusion
In this paper, the application of RSM for the tensile quasi-static loading of biocomposites was presented. Mathematical models of ultimate tensile strength and Young's modulus evolutions according to the influence of independent variables are tested through ANOVA and found to be adequate at 95% confidence interval. The following conclusions are drawn from the present investigation: 1) The ANOVA shows that: (e) The new hybrid material which is obtained by the optimisation of input parameters confirms the predicted results.
3) In addition, the hybrid composite specimens HCE1 when reinforced with an epoxy matrix possess good tensile strength and can withstand the strength up to 64.71 MPa; hence provide higher Young's modulus of 2.19 GPa.