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Vol. 8. Issue 4.
Pages 3517-3528 (July - August 2019)
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Vol. 8. Issue 4.
Pages 3517-3528 (July - August 2019)
Original Article
DOI: 10.1016/j.jmrt.2019.06.026
Open Access
Optimization of tensile behavior of banana pseudo-stem (Musa acuminate) fiber reinforced epoxy composites using response surface methodology
Mohamad Zaki Hassana,
Corresponding author

Corresponding author.
, S.M. Sapuanb, Siti Amni Roslana, Sa’ardin Abdul Aziza, Shamsul Saripa
a Razak Faculty of Technology and Informatics, Universiti Teknologi Malaysia, Kuala Lumpur, Jalan Sultan Yahya Petra, 54100 Kuala Lumpur, Malaysia
b Advanced Engineering Materials and Composites Research Centre, Department of Mechanical and Manufacturing Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Serdang, Selangor, Malaysia
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Figures (8)
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Tables (5)
Table 1. Properties of banana fiber and EpoxAmite-102 hardener.
Table 2. Actual and coded variable selected for the Box–Behnken design.
Table 3. Experimental and predicted tensile strengths.
Table 4. Initial analysis of variance results for acquired quadratic model.
Table 5. Analysis of variance results for acquired 2FI model.
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Banana pseudo-stem fibers used as a reinforcing material in synthetic matrix polymers have offered various advantages as they are environmentally friendly, have relatively low density and are abundantly available. The main factors that influence the mechanical behavior of natural composites are fiber length, fiber content, and chemical treatment. This study optimized the blending parameters of banana pseudo-stem epoxy composites through response surface methodology (RSM) based on Box–Benhken design. The predicted tensile strength value for these composites as a function of an independent variable was obtained from the ANOVA statistical approach. The analysis of the results showed that fiber length, fiber content and sodium hydroxide variables significantly in 2 factors interaction (2FI) model terms. This model was used to determine the maximum tensile stress and it was closely agreement with experimental finding with the value of R2 = 0.9973. The optimum conditions for tensile strength were identified as fiber length 3.25 mm, sodium hydroxide content 5.45 (wt%), and fiber loading 29.86 (wt%). The maximum tensile strength of optimum banana pseudo-stem epoxy composite was increased by 22% over the epoxy-resin system.

Banana fiber
Response surface methodology
Box–Behnken design
Full Text

In recent years, natural fibers have proven that they can replace their synthetic polymer counterparts. Natural fibers are cheap and bio-degradable while having good sound abatement capabilities, low abrasively, and no health hazards [1]. Natural fibers are extracted from various plant parts and are classified accordingly. Currently, natural fibers such as kenaf [2,3], rice husk [4], banana [5,6], and bamboo [7,8] are abundantly available in developing countries such as Malaysia, Indonesia, Thailand, and other Asian countries. They have not, however, been optimally utilized. At present these fibers are used as conventional products for the production of yarn, ropes, cordage [9], and matting as well as articles like wall table mats, handbags, and purses [10]. Among natural fibers, banana is one of the oldest cultivated plants in the world. The word ‘banan’ itself comes from the Arabic language, meaning ‘finger’, where it belongs to the Musaceae family and Musa genus [11]. There are approximately 300 species of banana, however, only 20 varieties are used for consumption [12]. Approximately 50 million metric tons of bananas are produced every year in the Asian, African, Chinese, and American subtropical regions [13]. Banana fiber has possible uses in composite structures and advanced technology.

To improve mechanical properties in composite structures, fiber loading, fiber length, and mercerization effect have been widely investigated. Phua et al. [14] investigated the mechanical properties of starch-grafted-polypropylene/kenaf fiber composites with fiber loadings of 10, 20, and 30 wt%. These biocomposites were prepared via the compound melting and compression molding processes. They found that mechanical properties improved with increased fiber loadings. The effect of fiber content on the mechanical properties of hemp and basalt fiber reinforced phenol formaldehyde composites was investigated by Öztürk [15], who fabricated fibers reinforced composites with fiber loadings of 20, 32, 40, 48, 56 and 63 vol%. He mentioned that tensile strength increased with increased fiber loadings of up to 40 vol%. However, mechanical properties decreased above this value. For both composites, elongation at break increased as the fiber volume fraction increased. Furthermore, the maximum tensile strength of Napier grass fiber/polyester composites increased with increased fiber loadings of up to 25%, providing an optimum volume fraction for a the fiber reinforced composite [16]. In addition, the reduced strength of the composite with a 30% fiber volume fraction resulted in fiber entanglements that created longer fiber lengths. The effect of different fiber weights on the mechanical properties of sisal fiber phenol formaldehyde composites was discussed by Maya et al. [17]. They found that as fiber content increased, the mechanical strength of the composite was also increased with an optimum value of 54 wt% fibers loading. Currently, the optimum findings on fiber loading are still inconsistent due to compounding parameters during composite preparation.

An experimental study was carried out to investigate and characterize the effect of fiber length on the mechanical properties of natural fiber composite structures. The effects of fiber length on the mechanical behavior of coir fiber-reinforced epoxy composites was conducted by Das et al. [18], who found that tensile strength reached its maximum value at 12 mm fiber length. The prediction of optimum fiber length for banana epoxy composites was discussed by Venkateshwaran et al. [19], who found that increases in fiber length and weight ratio increased tensile strength and modulus up to a 15 mm fiber length. The effect of fiber length on the tensile properties of epoxy resin composites reinforced with kenaf/PALF fibers was examined by Aji et al. [20], who revealed that an optimal maximum tensile strength was recorded at a fiber length of 0.25 mm, while a fiber length of 2 mm decreased tensile modulus performance due to weak interface bonding between the matrix and reinforcement.

Poor adhesion between fiber and matrix is generally a problem in natural fiber reinforced composites. The presence of waxy substances and pectin on the fiber surface leads to ineffective bonding [21]. Here, the hydroxyl group and moisture content of cellulose fibers cause poor surface wetting, resulting in dimension instability, composite microcracking, and mechanical behavior degradation. To overcome this issue, chemical treatments have been promoted to modify fibers surfaces. Mejia et al. [22] evaluated the influence of alkali treatments on banana fiber composites to reveal that matrix interactions were dependent on the polarity of the modified fiber surface. They also mentioned that treatments with 1% concentration NaOH produced the most effective conditions. Karthikeyan and Balamurugan [23] concluded that increases in chemical concentration resulted in a decrease in fiber diameter and fiber strength. They mentioned that 6% alkali treated coir fiber-epoxy resin composite showed a satisfactory fiber diameter reduction and better mechanical strength compared to untreated composites.

The response surface method is a tool that implements a statistical approach to optimize natural fibers experimental properties. Central Composite Design (CCD), Doehlert Design (DD), 3-level factorial, and Box–Benhken Design (BBD) are well known response surface methods. Aly et al. [24] studied the optimization of alkaline treatment conditions for flax fiber. They reported that BBD is an accurate tool for optimizing treatment conditions to obtain optimal fiber tensile strength and flexural modulus. This statement is in accord with other researchers who used BBD for the same purpose. Vardhini et al. [25] employed BBD to increase the lignin decomposition removal of banana fiber and found treatment conditions of 11 g/L NaOH concentration, 2.5 h treatment time and a temperature of 90 °C improved the rate in which lignin was removed from the banana fiber. Manzato et al. [26] used BBD to determine optimal conditions for cellulose extraction and suggested that 1.2 NaOH/NaClO ratios at 45 °C and 2 h were the best possible extraction conditions for jute fiber pulp using the response surface methodology.

When blending banana pseudo-stem fiber epoxy composites, there are a few factors that influence tensile strength. Thus, experiment design is being an effective tool for optimizing the final composite response. In this study, simultaneous parameter optimization was employed to characterize the tensile behavior of composites. The test run was based on the Box–Behnken design with three parameters, including fiber loading, sodium hydroxide concentration, and fiber length. Statistical approach and the accuracy of the parametric optimization was obtained using Design Expert Software 11.1.0. Furthermore, a series of optimum parametric mechanical behavior of composites were also evaluated.

2Materials and methods2.1Materials

An epoxy resin with the commercial name EpoxAmite was used as a polymer matrix and obtained from Kird Enterprise, Nilai Negeri Sembilan, Malaysia. The banana pseudo-stem (Musa acuminate) fiber was supplied by Innovative Pultrusion Sdn Bhd, Seremban Negeri Sembilan, Malaysia. The properties of both the banana fiber [27] and epoxy-resin are given in Table 1. The chemical used to treat the banana fiber was sodium hydroxide (NaOH), which was provided in pallet form by Orioner Hightech Sdn Bhd, Cyberjaya Selangor, Malaysia.

Table 1.

Properties of banana fiber and EpoxAmite-102 hardener.

  Banana fiber [27]  EpoxAmite-102 hardener 
Density (kg/m31350  1110 
Flexural strength (MPa)  2–5  84.25 
Tensile strength (MPa)  54.00  56.40 
Young's modulus (GPa)  3.49  3.10 
Cellulose (%)  63–64  – 
Hemicellulose (%)  19  – 
Lignin (%)  – 
Mixed viscosity (kg/ms)  –  0.65 
Specific volume (m3/kg)  –  9.03 × 10−4 
2.2Preparation of banana pseudo-stem fibers

Initially, the banana pseudo-stem fibers (Fig. 1(a)) were washed with distilled water to eliminate any surface impurities. Then, it was soaked in 3, 6, and 9 wt.% NaOH for 5 h as shown in Fig. 1(b). The fibers were left to dry at room temperature overnight before being placed into circulation oven at 80 °C for 6 h. These fibers were then grounded to 0.1–15 mm using a Cheso Model N3 crusher machine 0.3 mm, 1.8 mm and 3.3 mm. The chopped banana fibers were measured using a stainless steel sieve model BS410/1986 (Endecots Ltd.) and rotational shaker. Banana pseudo-stem fibers of different lengths were used as reinforcement as illustrated in Fig. 1(c). Epoxy-resin with fiber was gradually mixed to 10, 20, and 30 wt% fiber loading before being placed in the mold cavity as displayed in Fig. 1(d). Tensile specimens were cured overnight.

Fig. 1.

Photo of (a) banana fibers (b) chemically retted of fibers (c) banana fibers with different lengths and (d) molding parts of the tensile specimens.

2.3Experimental of Box–Benhken design

The BBD is a spherical and revolving design [28]. As illustrated in Fig. 2(a) the BBD consists of the central point and the middle points of the edges. It is depicted as a shape that consists of three interlocking 22 factorial designs [29] and a central point as showed in Fig. 2(b).

Fig. 2.

Geometric views of BBD as a (a) cube design and (b) three interlocked 22 factorial designs [28].


In this study, the design was obtained using Design Expert Software 11.1.0. It consisted of three variables of three levels (+1, 0, −1) for fiber length (mm), NaOH concentration (wt.%), and fiber loading (wt.%). In addition, fiber length (X1), NaOH content (X2), and fiber loading (X3) were elucidated in a range of 0.3–3.3 mm [30], 3–9 wt% [31], and 10–30 wt% [32], respectively, as tabulated in Table 2.

Table 2.

Actual and coded variable selected for the Box–Behnken design.

Variables  Code  Experimental valueReferences 
    Lower (−1)  Centre (0)  Higher (+1)   
Fiber length (mm)  X1  0.3  1.8  3.3  [30] 
NaOH concentration (%wt)  X2  [31] 
Fiber loading (%wt)  X3  10  20  30  [32] 

In experiment design, the N that is randomized and optimized by BBD is based on the cube design expressed according to Ref. [33].

N = 2k(k − 1) + cp
where k is the factor number and cp is the number replicated central points. This study’s experimental trial was randomized and did not depend on the antecedent conditions of previous and predicted runs. An important assumption is that all operating variables are continuous, measurable and controllable by experiments with negligible errors. To maximize the tensile strength of banana-epoxy composite, three-levels-factors, k = 3, and cp = 5 were used. This produced 17 experimental trials, five of which were replicated at the central points (0, 0, 0) as showed in Table 3. Similar conditions were also pointed out in Ref. [24].

Table 3.

Experimental and predicted tensile strengths.

Run std  Run no  Fiber length (mm)  NaOH concentration (wt%)  Fiber loading (wt%)  Tensile strength (MPa)Residual 
          Experiment  Predicted   
14  1.8  20  16.13  11.08  −0.0428 
0.3  20  11.21  15.80  0.3347 
3.3  30  23.55  15.05  −0.2390 
0.3  30  8.32  16.95  0.0685 
0.3  10  20.18  20.11  0.0747 
17  1.8  20  15.88  16.94  0.0960 
0.3  20  17.02  23.67  −0.1203 
12  1.8  30  14.81  17.36  −0.1490 
16  1.8  20  15.98  15.80  −0.1853 
10  1.8  10  11.91  15.80  0.1847 
10  11  1.8  10  18.98  11.89  0.0185 
12  3.3  20  17.21  11.48  −0.2665 
13  13  1.8  20  16.07  15.80  0.2747 
14  3.3  10  11.04  15.80  0.0847 
15  3.3  20  17.58  8.32  −0.0028 
15  16  1.8  20  15.61  17.39  0.1860 
11  17  1.8  30  17.04  19.30  −0.3165 
2.4Tensile test

The tensile test was carried out on flat samples using a 10 kN load cell in a Shimadzu AGX-S Universal Testing Machine with a crosshead displacement rate of 1 mm/min. A dog bone specimen was fabricated following ASTM D638 [34]. Tests were conducted for all three samples and their average were used as the final result.

3Results and discussion3.1Model fitting and ANOVA analysis for tensile strength

Table 3 shows the experimental finding and predicted responses following tensile tests and Box–Benken design formulation, respectively. The residual values were calculated between an experimental result and predicted response.

The tensile strength results for banana epoxy composites were further investigated using Analysis of Variance (ANOVA) to determine significant variables. By applying multiple regression analysis to the responses, the ANOVA quadratic models for the tensile strength of the three chosen factors is shown in Eq. (2)

Tensile Strength, σy = 15.934 + 1.58125 X1 + 1.3775 X2 + 0.20125 X3 − 1.36 X1X2 + 6.0925 X1X3 − 2.325 X2X3 − 0.0456 X12 − 0.13325 X22 − 0.11575 X3²
where X1, X2, and X3 are coded variables for fiber length (mm), NaOH concentration (wt%), and fiber loading (wt%), respectively. This quadratic equation was utilized to generate tensile strength predictions for each variable. Table 4 shows a F-value of 384.66, implying that the quadratic model was significant. The significant interaction between variables and tensile strength was evaluated based on their p-values. P-values less than 0.0500 were considered significant, which is reflected in model terms by X1, X2, X1X2, X1X3, and X2X3. Non-significant terms were removed and the final expression of the best fitting model was deducted.

Table 4.

Initial analysis of variance results for acquired quadratic model.

Source  Sum of squares  df  Mean square  F-value  p-Value   
Model  213.16  23.68  384.66  <0.0001  Significant 
X1-fiber length  20  20  324.88  <0.0001  Significant 
X2-Concentration  15.18  15.18  246.55  <0.0001  Significant 
X3-fiber loading  0.324  0.324  5.26  0.0555  Not significant 
X1X2  7.4  7.4  120.16  <0.0001  Significant 
X1X3  148.47  148.47  2411.44  <0.0001  Significant 
X2X3  21.62  21.62  351.18  <0.0001  Significant 
X12  0.0088  0.0088  0.1431  0.7164  Not significant 
X22  0.0748  0.0748  1.21  0.3069  Not significant 
X32  0.0564  0.0564  0.9162  0.3703  Not significant 
Residual  0.431  0.0616       
Lack of Fit  0.2641  0.088  2.11  0.2418  Not significant 
Pure Error  0.1669  0.0417       
Cor Total  213.59  16         
R² = 0.9980      Adjusted R² = 0.9954       
Predicted R² = 0.9790      Adequate precision = 80.6445       
C.V. % = 1.57      Mean = 15.80       

ANOVA was repeated to eliminate insignificant model terms and to find the tensile strength response as shown in Table 5. Here, ANOVA for the 2 factors interaction (2FI) model that fit the responses was suggested. As seen in Table 5, the predicted tensile strength values from Eq. (3) and the experimental responses were in a good agreement. To determine model precision, error percentages were calculated. The highest error percentage for experimental trial (Run No. 2) as shown in Table 3 was less than 4% [35], which is effectively accepted. It should be noticed that model term X3 was unreliable in the quadratic polynomial model (Eq. (2)), but was significant in Eq. (3). All variable square terms were not significant, so the nonlinear effect from final regression tensile strength was excluded. The 2FI model term described tensile strength regression as follows:

Tensile strength, σy = 15.80 + 1.58X1 + 1.38X2 + 0.2013X3 − 1.36X1X2 + 6.09X1X3 − 2.32X2X3

Table 5.

Analysis of variance results for acquired 2FI model.

Source  Sum of squares  df  Mean square  F-value  p-Value   
Model  213  35.5  607.44  <0.0001  Significant 
X1-fiber length  20  20  342.27  <0.0001   
X2-Concentration  15.18  15.18  259.74  <0.0001   
X3-fiber loading  0.324  0.324  5.54  0.0403   
X1X2  7.4  7.4  126.59  <0.0001   
X1X3  148.47  148.47  2540.52  <0.0001   
X2X3  21.62  21.62  369.98  <0.0001   
Residual  0.5844  10  0.0584       
Lack of fit  0.4175  0.0696  1.67  0.323  Not significant 
Pure error  0.1669  0.0417       
Cor. total  213.59  16         
R² = 0.9973      Adjusted R2 = 0.8826       
Predicted R² = 0.9909      Adequate precision = 98.9348       
C.V. % = 1.53      Mean = 15.80       

The tensile strength model afterwards was statistically inspected using the lack-of-fit value as tabulated in Table 5. The p-value of the F-test for lack-of-fit was 2.11, which is not significant, and the model was accepted relative to pure error. In addition, Table 5 lists the statistical data for tensile strength variance analysis. A coefficient of regression (R2) of 0.9973 suggests that the model competently represented the relationship between significant model terms. In fact, the closer the R2 value is to 1, the higher the reliability of empirical model data [36]. Again, a similar observation was noticed in that the Adjusted R-squared of 0.996 was close to 1. This indicates that the empirical model was significantly reliable. R2 and Adjusted R-squared were also in good agreement, with an approximately 95% confidence level [37]. Furthermore, the coefficient of variation (C.V.) implies the precision of the actual and predicted model, which must be lower than 10% [35]. A low C.V. of 1.53% was recorded, showing reliability of the experiment conducted in this study. Adequate Precision, which measures the signal to noise ratio, was greater than 4. This ratio for the studied model was equal to 82.783, showing an adequate signal and this model was utilized to navigate the design space.

3.2Adequacy of residual plots analysis of composites

Model adequacy was inspected to verify if the suggested model provided a sufficient approximation of actual systems. To evaluate model satisfaction, internal studentized residuals were verified with the assumption of ANOVA values. The studentized residual was used to obtain the standard deviation between experimental and predicted values. Fig. 3(a) presents the relationship for normal probability distribution and internal residuals with tensile strength. All residual points showed a likely ‘s’ curve closer to the line that fit model data. As shown in from Fig. 3(a), the residual value did not display any apparent problem with normality [38].

Fig. 3.

Typical (a) normal probability — residual (b) residual — run (c) externally studentized residuals — predicted response and (d) predicted — actual values traces following tensile test of banana epoxy composites.


Fig. 3(b) displays the correlation between residual and experimental runs for tensile strength behavior. The data point fell inconstantly close to ‘0’, which the lowest value of 2.125 demonstrating constant variance in experimental observations. It was suggested that no transformation response is required for the experimental design of this study [39].

Fig. 3(c) shows the relationship between studentized residuals and predicted tensile strength responses. As can be seen from this curve, studentized residuals were randomly scattered in a constant range across plot “0”. This indicates that was no clear pattern, validating the initial assumption of constant variance. In addition, all residual data points fell between +3 and −3 [35], proving the adequacy of the model.

Fig. 3(d) presents a linear plot for predicted and experimental values for banana pseudo-stem epoxy composite tensile strength. All scatter points were correctly distributed close to the line, which suggests a high degree of correlation between the experimental and predicted values. Qiu et al. [40] reported that the closer data points are to the reference line, the greater the accuracy of the model. All fundamental analyses were closely fitted, reflecting the suitability of the selected empirical model.

To attain a better understanding of the results, the perturbation plot in Fig. 4 provided a correlation for all process parameters at the center point on the tensile strength response. The perturbation plot demonstrates the response of a particular variable in movement from the chosen reference point while all the other variables remain fixed [41]. In this study, the reference point was set in the center of the design space, which was the zero-coded level of each variable. It was seen that tensile strength increased with increases in fiber length (X1) due to greater fiber strength and matrix bonding. It is also evident from the plot that tensile strength increased with increases in concentration (X2) due to the removal of waxes and cellulose from the fiber interface. It can be noticed that fiber loading (X3) showed a similar effect due to bonding. In contrast, an increase in the fiber loading (X3) marginally increased tensile strength. As seen in Eq. 3 and Table 5, tensile strength was most effected by fiber length (F = 342.27, p < 0.0001) and concentration (F = 259.74, p < 0.0001). The interaction between parameters X1X2 (F = 126.59, p < 0.0001), X1X3 (F = 2540.52, p < 0.0001), and X2X3 (F = 369.98, p < 0.0001) was significant. Quadratic parameters were determined to not have a significant effect on these interacting coefficients.

Fig. 4.

Main effect perturbation plot of banana epoxy composites following tensile test.

3.3Response surface contour plots of tensile strength

Fig. 5 shows the three dimensional (3D) response and two dimensional (2D) contour effects of the input parameters on tensile strength behavior. Fig. 5(a) illustrates the interaction effect of concentration and fiber length on tensile strength. It can be ascertained from the silhouette view of all process parameters in the 3D surface plot that an increase in fiber length increased tensile strength by up to 30%. In addition, an increase in NaOH concentration also increased composite tensile strength due to better interlocking between the fiber and matrix [42]. This effect is clearly seen in the 2D contour plot, where the tensile strength was lowest at 3 wt% and increased steadily up to 20 MPa with respect to sodium hydroxide concentration. Karthikeyan et al. [43] reported that increased NaOH concentrations of up to 4 wt% and fiber lengths up to 30 mm increased tensile strength and elongation, with any further increases in NaOH concentration reducing tensile strength.

Fig. 5.

Typical 3D and 2D plots of (a) concentration (wt.%) versus fiber lengths (b) fiber loading (wt. %) versus fiber length (mm) and (c) fiber loading (wt.%) versus concentration (wt.%) on tensile strengths.


Fig. 5(b) shows a silhouette view for all fiber loading (wt%) and fiber length (mm) process parameters and tensile strength. The 3D surface plot confirms that an increase in tensile strength with increases in fiber length up to 3.3 mm and increases in fiber loading. The 2D contour plot illustrates that tensile strength value was highest at 3.3 mm and lowest at 0.3 mm with respect to fiber length. The effect of fiber length and fiber loading on biocomposites was studied by Basiji et al. [44], who suggested that increases in fiber length and fiber loading significantly increased composite mechanical properties. As seen in Fig. 5(b), a fiber length of 3.3 mm and a fiber loading of 30 wt% provided optimum conditions for tensile strength.

The interaction effect for the response surface plot of fiber loading (wt.%) versus concentration (wt.%) on tensile strength is represented in Fig. 5(c). Tensile strength was slightly increased by increases in NaOH concentration at a lower fiber loading (wt%) under conditions of 18 MPa or higher as viewed in the 2D plot of Fig. 5(c). Ng et al. [45] proposed that high concentrations of alkali treatment (5 wt.%) and high fiber loadings (30 wt.%) improved biocomposite tensile strength due to low hemicellulose levels. Akhtar et al. [46] revealed that the tensile and flexural properties of kenaf-polypropylene composite could be ascribed to strong bonds between the fiber and matrix due to wax removal.

Fig. 6 reveals the effect of sodium hydroxide concentration on tensile tests. Tests were conducted with a constant fiber length and fiber loading of 3.3 mm and 20%, respectively. The results for NaOH concentration showed that with 6% of alkaline mercerization, composite mechanical behavior, including tensile strength and Young’s modulus, increased. Natural fibers composites treated with 6% concentration sodium hydroxide for 24 h showed improvements in tensile strength [47]. This finding indicates good adhesion between natural fibers and polymer matrixes.

Fig. 6.

Typical stress-strain of banana epoxy composites for different sodium concentration following tensile test.

3.4Optimization and confirmation test of composites

After studying what variable parameters influenced the tensile strength of banana epoxy composites, the optimal parameter that offered the highest tensile strength was determined. As observed from Fig. 5 and Table 5, when NaOH concentration and fiber length increased, tensile strength increased up to a certain limit, whereas fiber loading had a minimal effect. To optimize tensile strength, a maximum targeted goal between 8.32 and 23.55 MPa was set as optimal values, with the three variables adjusted in the ranges under study. The typical ramp and cube for optimization are shown in Fig. 7. Desirability was computed by multiplying the individual desirability of each response from zero to one at the goal. As can be observed from Fig. 7(a), the optimal operating conditions for tensile strength were a fiber length (X1) of 3.25 mm, a NaOH content (X2) of 5.45 (wt%.), and a fiber loading (X3) of 29.86 (wt%.).

Fig. 7.

Typical (a) ramp and (b) cube for numerical optimization of fiber length (mm), concentration (wt%) and fiber loading (wt%).


According to the BBD results, the predicted tensile strength was 23.73 MPa as shown in Fig. 7(b). Desirability values close to 1 were selected as the most effective parameters value with respect to the response factor [48]. In this study, desirability was equivalent to 1. To confirm the validity of the statistical experiment strategies, tensile tests were performed under the optimized conditions. Here, five samples were tested and an average of tensile strength of 22.86 MPa was recorded. The results demonstrated that the percentage error between the measured and predicted values was well within 3.7%, suggesting that model adequacy was reasonable for approximately 96% of the prediction interval. Good agreement was found between the predicted and experimental results, verifying model validity and confirming existence of the optimal point.

Fig. 8 shows the stress-strain curves of neat epoxy-resin and optimum banana pseudo-stem epoxy composites for tensile strength. Tensile strength increased by 22% from 18.12 MPa to 23.30 MPa with the addition of banana fibers and treatment with sodium hydroxide at optimum levels. In addition, the tensile modulus of neat epoxy increased nearly two fold from 931 MPa to 1628 MPa. Previous studies have recorded a similar trend [49].

Fig. 8.

Stress-strain curves of neat epoxy-resin and optimum banana-epoxy composites following tensile strength.


The effect of fiber loading, fiber length, and alkaline treatment content on banana fiber reinforced thermoset was evaluated using the Box–Benhken design. In this study, three independent variables were considered and fitted using a 2 factor interaction model. The results showed good agreement between tensile strength experimental and predicted values for R2, predicted R2, and adjusted R2. The maximum tensile strength was obtained with optimum conditions with a fiber length of 3.25 mm, NaOH content of 5.45 (wt%.), and fiber loading of 29.86 (wt%.). The predicted tensile strength was 23.73 MPa, close to its experimental value of 22.86 MPa. In addition, maximum composite tensile strength was increased up to 22% by the epoxy-resin system. The present paper has showed that the BBD method is an economical way of gathering optimum values of mechanical behavior in the shortest period of time. In addition, an optimization of the matrix modification especially the effect of nano-fillers on the mechanical and physical properties of the natural fiber polymer composites using BBD technique is interesting to discover.

Conflicts of interest

The authors declare no conflicts of interest.


Appreciation is given to Universiti Teknologi Malaysia under the 'Dana Penyelidikan UTM RAZAK', R.K.130000.7740.4J297 and 'PRGS-ICC', R. K130000.2540.4J381 grants for the financial support provided throughout the course of this research project. The authors would like to thank Ministry of Education Malaysia and Universiti Putra Malaysia for the financial support through the Visiting Scholar (Post-Doctoral) scholarship.

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