Evaluation of the Diameter Influence on the Tensile Strength of Pineapple Leaf Fibers ( PALF ) by Weibull Method

Since the past century, composites became the fast growing class of materials for engineering applications. They can be projected through the combination of distinct phases, to attend specific requirements not possible to be achieved by a single conventional ceramic, polymer or metallic alloy1. In particular, polymer composites reinforced with strong synthetic fibers such as glass, carbon and aramid are nowadays extensively used in practically all engineering sectors, from simple surfboards and house appliances to high-tech medical prosthesis and aerospace components2-4. Synthetic fibers, however, are associated with some environmental and economical disadvantages. For instance, their production is costly and energy-intensive, which might be related to CO2 emission in the case of consuming electricity from thermoelectric power. Moreover, synthetic fiber-based products cannot be easily recycled and, thus, may be responsible for long-term pollution after their discard at the end of operational life. Both CO2 emission and worldwide pollution are becoming serious environmental problems affecting global warming and climate changes5. In addition, glass fiber processing and handling, as leftover, are hazardous procedures that may cause lung diseases. In this decade, investigations and engineering application on natural lignocellulosic fibers extracted from cultivated plants have challenged the predominant use of synthetic fibers6-17. While still today carbon fibers in high-tech composite applications such as aircrafts cannot yet be substituted, glass fiber in common polymer composites are being successfully replaced by lignocellulosic fibers18-20. Indeed, automobiles are increasingly using lignocellulosic fiber composites not just as an environmentally friendly advertising but mainly because of technical advantages21-23 and restricted legislation24. Figure 1 illustrates a modern automobile together with several of its components made of polymer matrix composites reinforced with lignocellulosic fibers. The current preference for lignocellulosic fiber composites is justified by their comparatively lower cost and density. Moreover, technical reasons such as less damage to processing tools and molding equipments as well as better finishing of automobile parts, Figure 1, favor the engineering application of these composites. In addition, relatively higher toughness and superior strength in comparison with the polymer matrix motivate their use as structural parts12. Many well known lignocellulosic fibers have, in recent years, been extensively investigated and applied as polymer composite reinforcement. These investigations and applications initiatives were discussed in review articles and book chapters9-17. In particular, it was reported for sisal, ramie, curaua, jute, bamboo, coir, piassava and buriti fibers that the tensile strength varies with the inverse of the diameter13. A simple mathematical hyperbolic correlation was found to provide a reasonable adjustment between the ultimate tensile stress σ and the fiber equivalent diameter d : Evaluation of the Diameter Influence on the Tensile Strength of Pineapple Leaf Fibers (PALF) by Weibull Method


Introduction
Since the past century, composites became the fast growing class of materials for engineering applications.They can be projected through the combination of distinct phases, to attend specific requirements not possible to be achieved by a single conventional ceramic, polymer or metallic alloy 1 .In particular, polymer composites reinforced with strong synthetic fibers such as glass, carbon and aramid are nowadays extensively used in practically all engineering sectors, from simple surfboards and house appliances to high-tech medical prosthesis and aerospace components [2][3][4] .Synthetic fibers, however, are associated with some environmental and economical disadvantages.For instance, their production is costly and energy-intensive, which might be related to CO 2 emission in the case of consuming electricity from thermoelectric power.Moreover, synthetic fiber-based products cannot be easily recycled and, thus, may be responsible for long-term pollution after their discard at the end of operational life.Both CO 2 emission and worldwide pollution are becoming serious environmental problems affecting global warming and climate changes 5 .In addition, glass fiber processing and handling, as leftover, are hazardous procedures that may cause lung diseases.
In this decade, investigations and engineering application on natural lignocellulosic fibers extracted from cultivated plants have challenged the predominant use of synthetic fibers [6][7][8][9][10][11][12][13][14][15][16][17] .While still today carbon fibers in high-tech composite applications such as aircrafts cannot yet be substituted, glass fiber in common polymer composites are being successfully replaced by lignocellulosic fibers [18][19][20] .Indeed, automobiles are increasingly using lignocellulosic fiber composites not just as an environmentally friendly advertising but mainly because of technical advantages [21][22][23] and restricted legislation 24 .Figure 1 illustrates a modern automobile together with several of its components made of polymer matrix composites reinforced with lignocellulosic fibers.
The current preference for lignocellulosic fiber composites is justified by their comparatively lower cost and density.Moreover, technical reasons such as less damage to processing tools and molding equipments as well as better finishing of automobile parts, Figure 1, favor the engineering application of these composites.In addition, relatively higher toughness and superior strength in comparison with the polymer matrix motivate their use as structural parts 12 .
Many well known lignocellulosic fibers have, in recent years, been extensively investigated and applied as polymer composite reinforcement.These investigations and applications initiatives were discussed in review articles and book chapters [9][10][11][12][13][14][15][16][17] .In particular, it was reported for sisal, ramie, curaua, jute, bamboo, coir, piassava and buriti fibers that the tensile strength varies with the inverse of the diameter 13 .A simple mathematical hyperbolic correlation was found to provide a reasonable adjustment between the ultimate tensile stress σ and the fiber equivalent diameter d : where A and B are characteristic constants for each type of fiber.The reason for a general relationship specified by Equation 1 was given in terms of defects and flaws, typical of a lignocellulosic structure 13 .This inverse correlation, so far, has not been investigated for the fiber extracted from the pineapple plant (Ananas comosus) and generally known as PALF.
Despite a number of works on the properties of PALF and reinforced polymer composites [25][26][27][28][29][30][31][32] , limited information exist regarding its engineering applications.In fact, the pineapple is better known as a tropical fruit, illustrated in Figure 2, associated with drinks and a fibrous edible pulp.
Table 1 presents some relevant mechanical properties and structural composition reported for PALF in recent overview papers on lignocellulosic fibers 15,30 .In this table, there is apparently a mistake concerning the elastic modulus of 1.44 GPa presented by Faruk et al. 15 .The values of 25-82 GPa of Satyanarayana et al. 30 appear to be the correct ones.It is important to notice in Table 1 that the PALF tensile strength was found to vary within a great dispersion  The possible use of PALF as an engineering material depends on the precise identification of its mechanical properties, especially the tensile strength.Since no investigation has been conducted so far on the diameter influence, the objective of the present work was to determine with statistical precision the PALF correlation between its ultimate tensile strength and equivalent diameter by means of Weibull analysis.

Experimental Procedure
The basic material used in this work was untreated PALF, illustrated in Figure 3.These fibers were donated by the Brazilian firm Permatec Triangel.The lot of as-received PALF was cleaned and dried in a stove at 60 °C for 24 hours.A diameter analysis was performed on one hundred fibers randomly removed from the as-received lot.Each fiber was measured in five different points along the length and then 90° rotated to be measured again, assuming a cylindrical shape.The rotation guarantees an equivalent value of the mean diameter for each fiber.Figure 4 shows the histogram for the distribution of PALF diameters by conventionally considering 6 diameter intervals.
In addition to the one hundred fibers initially considered in the histogram, for each interval in Figure 4 of equivalent diameter, 20 other fibers were selected.All these fibers were then individually tensile tested at 25 ± 2 °C in a model 5582 Instron machine.Specials grips were used to avoid both fiber slippage and damage.The test length was 10 cm and the strain rate 2.1 × 10 -4 s -1 .Values obtained for the tensile strength, i.e. the ultimate stress, were statistically interpreted by means of the Weibull Analysis computer program.
The Weibull statistical analysis is based on a cumulative distribution function: where θ and β are mathematically known as the shape and scale parameters.Equation 2 can be conveniently modified into a linear expression by double application of logarithm: ( ) In the present case of PALF strength dependence with diameter, β is the slope of Equation 3 and indicated as Weibull modulus, while θ is the characteristic strength.Using the 20 experimental strength data for each interval in Figure 4 associated with an average equivalent diameter, the computer program constructed the linear graph of Equation 3 and calculated the Weibull parameters.

Results and Discussion
Based on the maximum load (L) obtained from curves such as those illustrated in Figure 5, the tensile strength (σ m ) was determined for each fiber by the following equation: where d is the equivalent diameter in Figure 4.
The values of σ m were then statistically analyzed by means of the Weibull method applied for the 20 fibers associated with each of the six diameter intervals shown in the histogram of Figure 4.As aforementioned, the Weibull Analysis program provided the probability diagram plots of reliability vs. location parameter associated with Equation 3 for all diameter intervals.These Weibull linear plots are shown in Figure 6.Here it should be noted that all plots in Figure 6   are unimodal, i.e., with just one single straight line fitting the points at each interval.This indicates similar mechanical behavior of all fibers within the same diameter interval.
The Weibull Analysis program also provided the corresponding characteristic strength (θ), the Weibull modulus (β) and the precision adjustment (R 2 ) parameters.The values of these parameters as well as the average mechanical strength and associated statistical deviations, based on the Weibull distribution, are presented in Table 2.Here it is important to mention that the average strength and deviation are determined within the Weibull statistic and not as a simple sum of values divided by the number of the samples with corresponding standard deviation.
The variation of the characteristic strength with the average fiber equivalent diameter for each one of its intervals is shown in Figure 7.In this figure, there is a clear tendency for the θ parameter to vary inversely with the average PALF fiber diameter.This means that the thinner the fiber the higher tends to be the characteristic strength.Furthermore, the corresponding values of β and R 2 , shown in Table 2, statistically support the inverse correlation between θ and the average diameter d (mm).By means of a mathematic In order to analyze the physical meaning of Eq. ( 5), the Weibull average tensile strength, m σ , presented for the PALF in Table 2 was plotted as a function of the equivalent diameter in Figure 8.In this figure, an apparent hyperbolic inverse correlation also exists between m σ and d within the error bars (Weibull statistical deviations) and investigated limits.
One should note that the large dispersion (error bars) in the values of the tensile strength in Figure 8, particularly for the thinner fibers, is due to the heterogeneous and random structural aspects of the biological process of formation of   any lignocellulosic fiber [7][8][9][10][11][12][13][14][15][16][17] , such as the PALF fibers in this work.As a consequence, one might also consider a straight line passing within the error bars as a possible correlation between m σ and d.In this case, the tensile strength could be interpreted as varying linearly with the diameter.However, the variation of θ with d in Figure 7, suggests that an inverse correlation fits better the experimental results for the PALF fibers.Based on Equations 5 and 6 it is suggested that, as in others lignocellulosic fibers 15,16 , a hyperbolic type of mathematical equation is the best statistical correlation between the tensile strength and the diameter of PALF.
The microfibrillar nature of the PALF could also be responsible for the results in Figure 8.As illustrated in Figure 9a, the thinner fiber, with d = 0.11 mm display a more uniform structure with simultaneous rupture of its microfibrils, shown in Figure 9b.By contrast, the thicker fiber with d = 0.25 mm in Figure 9c has more defects and microstructural porosity associated with heterogeneous rupture of microfibrils, Figure 9d.In other words, the thinner fibers tend to be more uniform with more close packed microfibrils.This contributes to fiber resisting cross section areas with less empty spaces and, consequently, should display higher strength.As a final remark, it should be mentioned that an inverse correlation such as that in Equations 5 and 6 could allow, in practice, a selection of stronger thinner PALF to effectively reinforced polymer composites with improved mechanical properties.

Conclusions
• A Weibull statistical analysis of tensile-tested pineapple leaf fibers (PALF) revealed an inverse correlation between the tensile strength and the fiber diameter.This correlation indicates a possible hyperbolic mathematical equation to associate the PALF strength with its diameter.
• SEM observations provided evidences that a thicker PALF, with more microfibrils as well as defects and porosity than a thinner one, could undergo rupture at a comparatively lower stress.
• Statistically, the larger distribution of micro fibrils mechanical resistances of the thicker fiber also provides a higher chance that a weaker fibril to rupture shortly than any of the fewer fibrils of the thinner fiber.

Figure 1 .
Figure 1.Automobile components based on polymer composites reinforced with lignocellulosic fibers.

Figure 4 .
Figure 4. Histogram of the statistical frequency of fibers within six conventional diameter intervals.

Figure 6 .
Figure 6.Weibull diagrams for PALF tensile strength in different intervals of diameter.

Figure 7 .
Figure 7. Variation of the PALF Weibull characteristic strength with the corresponding fiber equivalent diameter for each interval in Figure 4.

Figure 8 .
Figure 8. Variation of the PALF Weibull average strength with the corresponding fiber equivalent diameter for each interval in Figure 4.

Table 1 .
Mechanical properties and structural compositions of pineapple leaf fibers.

Table 2 .
Weibull parameters for the tensile strength of PALF fibers associated with different diameter interval.