# Kenaf bast fiber bundle-reinforced unsaturated polyester composites. III: Statistical strength characteristics and cost-performance analyses.

Abstract

The tensile, flexural, and impact strength distribution and the cost-effectiveness of kenaf bast fiber bundle (KBFB)- reinforced unsaturated polyester composites were studied. Probability models including normal, two-parameter Weibull, gamma, lognormal, exponential, Burr, Pareto, and inverse Gaussian models were fitted against measured composite strengths. Taking the 5th percentile values as the composite's strength design values, the two-parameter Weibull model provided the most conservative composite strength design values. A cost-effectiveness analysis showed these composites were more cost-effective than glass fiber-reinforced sheet molding compounds (SMCs) for carrying tensile and flexural loads when their fiber loadings reached 51.2 and 56.3 percent (wt/wt), respectively. The KBFB-reinforced unsaturated polyester composites were less cost-effective than glass fiber-reinforced SMCs for carrying impact loads. This work suggests that natural fiber-reinforced composites have the potential to be viable replacement materials in applications where impact resistance is not critical.

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A high fiber loading kenaf bast fiber bundle (KBFB)-reinforced unsaturated polyester (UPE) composite fabrication process was previously developed (Duet al. 2010). The fabricated KBFB/UPE composites from the process possessed tensile modulus (12.1 GPa), specific modulus (9.92 GPa.[cm.sup.3]/g), and specific tensile strength (44.8 MPa.[cm.sup.3]/g) that met specification requirements for glass fiber-reinforced sheet molding compounds (SMCs): 9 GPa, 4.86 GPa.[cm.sup.3]/g, and 31.4 MPa.[cm.sup.3]/g, respectively. However, the tensile strengths (54.6 MPa) were slightly lower than the specification requirement (58 MPa) and exhibited large variations. Incorporation of these composites in automotive structural applications remains to be addressed, particularly where reliability in strength values is critical.

A number of statistical models can be used to study the distribution of composite strengths and estimate the reliability of composites. The Weibull distribution model (Weibull 1939) is the most widely used model for characterizing material strength distributions (Weibull 1951, Knight and Hahn 1975, Alqam et al. 2002, Dirikolu et al. 2002, Zureick et al. 2006, Rodrigues et al. 2008) and reinforcing fiber strength distributions (Luo and Netravali 1999; Bos et al. 2002; Andersons et al. 2005, 2009; Panthapulakkal et al. 2006; Xue et al. 2009). In addition to the Weibull model, applications of lognormal and gamma distribution models have also been reported (Wu et al. 2006, Basu et al. 2009).

Probability density functions for the two-parameter Weibull, lognormal, and gamma models are given in Equations 1 to 3, respectively. These three models assume that the location parameter is equal to zero.

f(x:[lambda],k) = k/[lambda] [(x/[lambda]).sup.k-1] exp [ - [(x/[lambda]).sup.k]] (1)

f(x:[lambda],k) = 1/[square root of (2[pi]kx)] exp [ - [(1n x - [lambda]).sup.2]] (2)

f(x:[lambda],k) = [x.sup.k-1] exp (- x/[lambda])/[GAMMA](k)[[lambda].sup.k] (3)

where [lambda], and k are scale and shape parameters, respectively. [GAMMA](k) is the gamma function defined as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

To date, there are no statistical and reliability analysis data available for natural fiber-reinforced thermoset polymer composites. There are a few published articles that study the statistical distribution and reliability of forest products. Guess et al. (2003) statistically studied the internal bond strengths of medium-density fiberboard, but the normal distribution was not suitable. Perhac et al. (2007) studied the probability of wood-plastic composite stiffnesses and flexural strengths using parametric and nonparametric probability plots. Using maleic anhydride grafted polypropylene as a coupling agent did not substantially alter the probability plots. Young et al. (2008) studied the reliability in modulus of elasticity and modulus of rupture for wood-plastic composites and provided three confidence intervals (CIs) for the product's lower percentiles for modulus of elasticity and modulus of rupture using bootstrapping methods. Young et al. (2009) reported that wood strand (raw material for oriented strand board) thicknesses were not normally distributed and the upper percentiles of strand thickness were estimated using bootstrapping methods. Weibull, normal, lognormal, exponential, and a few other quantitative statistical models were used in these studies. Yang et al. (2010) investigated the flexural fatigue behavior of wood flour-polypropylene composites and showed that a nondimensional fatigue model and the two-parameter Weibull probability distribution model could both be used for estimating fatigue life of these wood plastic composites.

Natural fiber-reinforced composites are potentially cost-effective because of their low densities and material costs despite their low absolute strengths. D'Almeida (2001) performed a cost analysis of composites made of sisal, jute, bagasse, and towel gourd fibers. These fibers have strengths ranging from less than 400 MPa to greater than 600 MPa. The cost-effectiveness of their composites for carrying the same flexural load was competitive with glass fiber-reinforced composites for certain fiber strength ranges and fiber volume fractions (percent, vol/vol). Specifically, the natural fiber composites were competitive at 70 percent (vol/vol) fibers with strengths less than 400 MPa, 50 percent (vol/vol) fibers with strengths between 400 and 600 MPa, and 40 percent (vol/vol) fibers with strengths greater than 600 MPa. A cost-effectiveness investigation of the KBFB-reinforced UPE composites prepared in our laboratory (Du et al. 2010) is of interest and highly desirable.

The objectives of this study were (1) to investigate the tensile, flexural, and impact strength statistical distributions and reliability of KBFB-reinforced UPE composites and (2) to analyze the cost-effectiveness of these composites compared with glass fiber-reinforced SMCs for automotive structural component applications.

Materials and Methods

Materials

KBFBs were supplied by Kengro Corporation. The UPE resin (Aropol Q-6585), provided by Ashland Chemical Company, was used as the matrix polymer. The diluent, styrene, and the free radical initiator, t-butyl perbenzoate, were purchased from Fisher Scientific Inc. A polyvinyl acetate (PVAc) water emulsion (solid content, 46%), provided by Tailored Chemical Products, Inc., was used as a mat preforming binder.

Composite fabrication

Composites were fabricated as previously described (Du et al. 2010). Long KBFBs were first ground into short fibers with an average length of 3.3 ram. Then, these short KBFBs were preformed into loose mats using the PVAc adhesive, and these preformed mats were infused with predetermined amounts of the UPE resin. The prepreg, assembled by five mats, was then compression molded into composite. The detailed process parameters for the UPE resin formulation, KBFB mat preforming, and compression molding were reported previously. The target fiber loadings were 50 to 60 percent (wt/wt). The composite fiber loadings were calculated after curing and all the squeezed-out resin was sanded off. A total of 25, 44, and 40 specimens were prepared for tensile, flexural, and impact testing, respectively.

Testing

The resultant composite samples were cut to tensile specimens using a CNC machine and were tested on an Instron 5869 universal testing machine under displacement control conditions in accordance with ASTM Standard D638-03 (ASTM International 2004). The cross head rate was set at 4 mm/min, and the tensile strain was recorded by an Instron 2630-100 series extensometer. Flexural test specimens were studied on the same Instron 5869 machine under displacement control conditions in accordance with ASTM Standard D790-03 (ASTM International 2003). The support span was set at 60 mm, and the testing speed was set at 4 mm/min. Impact properties were tested using an Izod fixture on an Instron Dynatup 9250HV Instrumented Drop Tower in accordance with ASTM Standard D256-06 (ASTM International 2006).

Results and Discussion

Statistical distributions

The experimental data analyses were performed using SAS statistical software, release 9.2 (SAS Institute Inc., Cary, North Carolina) and MATLAB 2009a. Table 1 summarizes the descriptive statistics of the measured tensile, flexural, and impact strengths. The experimental data histograms are plotted in Figures 1a, 1b, and 1c for the composites' tensile, flexural, and impact strengths, respectively. The skewness of the tensile strengths distributions is close to zero indicating that the tensile strengths were distributed nearly symmetrically. The skewness values of the flexural and impact strength distributions were -0.234 and -0.287, respectively, indicating the existence of a slightly left skewness. From the flexural and impact strength histograms, one can see the bulk of the flexural and impact strength values lie to the right.

Distribution models including normal, two-parameter Weibull, lognormal, gamma, and several other parametric models were fitted to the experimental data. Seven different statistics of goodness-of-fit for each distribution model for these three strengths were calculated and used as selection criteria. These statistics included-2LogLike, Akaike's information criterion (AIC), corrected Akaike's information criterion (AICC), Schwarz Bayesian information criterion (BIC), Kolmogorov-Smirnov statistic value (KS), Anderson-Darling statistic value (AD), and Cramer-von-Mises statistic value (CvM). The results are summarized in Tables 2, 3, and 4 for tensile, flexural, and impact strengths, respectively. In the tables, the lowest value of a given goodness-of-fit criterion was used to define the optimal distribution model.

The normal distribution model is the best for fitting the experimental tensile strengths (Table 2), followed by the Burr and Weibull distributions. The other six distribution models also show acceptable statistics of fit except the exponential and Pareto distributions. Similar results are observed for flexural strengths (Table 3). The normal distribution model provided the best fit to the measured flexural strengths followed by the inverse Gaussian, lognormal, and Weibull distribution models. The gamma model failed to converge for the given experimental flexural strength data. Hence, no goodness-of-fit statistics are reported for this model. In contrast to tensile and flexural strengths, the Weibull distribution model is the best model for fitting impact strengths (Table 4). The normal distribution ranks just below the Weibull model. These statistics suggest the normal distribution model works best for tensile and flexural strengths, while the Weibull distribution model works best for impact strengths. The exponential and the Pareto models are not appropriate for describing the strength distributions of KBFB-reinforced UPE composites. The remaining distribution models reasonably characterized the strength distributions. The scale and shape parameters and corresponding 95% CIs, based on the maximum likelihood methods, for the optimal distribution models for tensile, flexural, and impact strengths are summarized in Table 5.

[FIGURE 1 OMITTED]

Reliability analysis and design values

The fitted survival curves for composite tensile, flexural, and impact strengths, based on the relevant optimal distribution models, are plotted in Figures 2a, 2b, and 2c, respectively. The fitted survival curves for all these three strength properties closely matched the nonparametric Kaplan-Meier curves (Kaplan and Meier 1958). The estimated 95% CIs are also included in the figures. The 5th percentile values (95% probability of survival) have normally been chosen as design values in structural engineering (Ellingwood 2000). Table 6 summarizes the 5th percentile values estimated by the best distribution model (normal distribution for tensile and flexural strengths, and Weibull distribution for impact strengths). The values of the normal 5th percentile tensile and flexural strengths were 44.95 and 74.42 MPa, respectively. One can see that the normal 5th percentile tensile strength value was higher than the corresponding experimental tensile strength (44.50 MPa), which is not acceptable where a conservative estimate of strength is desired. However, values of the Weibull 5th percentile tensile and flexural strengths (43.15 MPa, 72.24 MPa) were both lower than the experimental data. Therefore, though the normal distribution model was the best fitting model for tensile and flexural strengths, the Weibull distribution model provided the most conservative strength estimates. The value of the Weibull 5th percentile impact strength was 4.75 kJ/[m.sup.2], which closely matched the experimental data (4.77 kJ/[m.sup.2]). Again, the normal distribution model provided a nonconservative 5th percentile impact strength value.

[FIGURE 2 OMITTED]

The conservative strengths obtained using the Weibull distribution model are consistent with results reported by Kam and Chang (1997) and Alqam et al. (2002). The estimated 5th percentile tensile, flexural, and impact strength values in this study using the Weibull distribution model, can be used as design strength allowable for the KBFB-reinforced UPE composites considered here. Based on this study, 95 percent of these laboratory-manufactured KBFB-reinforced UPE composites will conservatively survive when the tensile stress, flexural stress, and applied impact energy per square meter are lower than 43.15 MPa, 72.24 MPa, and 4.75 kJ/[m.sup.2], respectively. As part of future work, an investigation on the effect of sample size on the design strengths may be desirable.

Cost analysis

Although possessing lower absolute strengths, natural fiber-reinforced composite materials can compete with glass fiber-reinforced composites in terms of specific properties and costs. D'Almeida (2001) proposed a cost analysis model to calculate the price per unit length of a composite specimen, Q, subjected to an applied three-point bending load P.

Q = 3/2 L/t [[rho].sub.C]/[[sigma].sub.C] [X.sub.C]P (5)

In this equation, L and t are the test span and the specimen thickness, [[rho].sub.C] and [[sigma].sub.C] are the composite density and flexural strength, and [X.sub.C] is the price per unit of composite weight. Equation 5 can also be written as

Q = [beta] x P (6)

[beta] = 3/2 L/t [[rho].sub.C]/[[sigma].sub.C] [X.sub.C] (7)

Here, the cost parameter [beta] is a constant for a given composite geometry.

Similarly, the price per unit length of a composite tensile specimen can be calculated.

Q = [[rho].sub.C]/[[sigma].sub.C-Tension] [X.sub.C]P (8)

or

Q = [beta] x P (9)

Q = [[rho].sub.C]/[[sigma].sub.C-Tension] [X.sub.C] (10)

Q = 13" P (9)

Here, [[sigma].sub.C-Tension] is the composite tensile strength. The cost parameter [beta] for a composite subjected to a tensile load is independent of the composite's geometry.

In the same manner, the price per unit length of a composite can be calculated for the material subjected to impact loads.

Q = [[rho].sub.C] / [I.sub.C][X.sub.C]E (11)

or

Q = [beta] x E (12)

[beta] = [[rho].sub.C] / [I.sub.C][X.sub.C] (13)

In Equations 12 and 13, E is the absorbed energy and [I.sub.C] is the composite impact strength.

The composite with a lower value of the parameter [beta] will be more cost-effective to carry the same load or to resist the same amount of impact energy. A cost-effectiveness coefficient K is proposed to compare kenaf fiber-reinforced UPE composites with a type of commercial glass fiber-reinforced SMC-R25 of each type of load,

K = [[beta].sub.C] / [[beta].sub.SMC] (14)

Here, [[beta].sub.C] and [[beta].sub.SMC] are the cost parameters for the KBFB-reinforced composite and the glass fiber-reinforced SMC. The cost-effectiveness coefficients of kenaf fiber-reinforced UPE composites subjected to tensile ([K.sub.T]), flexural ([K.sub.F]), and impact loads ([K.sub.I]) can be calculated by Equations 15 to 17.

[K.sub.T] = ([[rho].sub.C] / [[sigma].sub.C-Tension]) x [X.sub.C] / ([[rho].sub.SMC] / [[sigma].sub.SMC-Tension]) x [X.sub.SMC] (15)

[K.sub.F] = ([[rho].sub.C] / [[sigma].sub.C-Flexure]) x [X.sub.C] / ([[rho].sub.SMC] / [[sigma].sub.SMC-Flexure]) x [X.sub.SMC] (16)

[K.sub.I] = ([[rho].sub.C] / [I.sub.C]) x [X.sub.C] / ([[rho].sub.SMC] / [I.sub.SMC]) x [X.sub.SMC] (17)

In these equations, [[rho].sub.SMC], [[sigma].sub.SMC-Tension], [[sigma].sub.SMC-Flexure], and [I.sub.SMC] are density, tensile strength, flexural strength, and impact resistance for glass fiber-reinforced SMC, respectively.

When a KBFB-reinforced composite is more cost-effective than the glass fiber-reinforced SMC, then the corresponding cost-effective coefficient is less than 1. The price per unit weight of SMC-R25, [X.sub.SMC] is determined at the 25 percent fiber loading. The price per unit composite weight, [X.sub.C] at various fiber loadings can be calculated by Equation 18:

[X.sub.C] = [x.sub.UPE] x [wt.sub.UPE]% + [x.sub.PVAc] x [wt.sub.PVAc]% + [x.sub.KBFB] x [wt.sub.KBFB]% (18)

Here, x and wt% are the unit price and weight percentage for each component.

Table 7 summarizes the price of each constituent in the kenaf fiber-reinforced composite and in a typical glass fiber-reinforced SMC (R25 SMC). Prices of UPE and filler for SMC were obtained from an automotive component manufacturer. The weight percentage of each component, as well as tensile, flexural, and impact strengths of R25 SMCs are listed in Table 7. These data were used to calculate the cost-effectiveness coefficients of kenaf fiber-reinforced composites for comparison to glass fiber-reinforced R25 SMCs. The cost coefficients [K.sub.T], [K.sub.F], and [K.sub.I] are plotted in Figures 3a, 3b, and 3c against fiber loadings for tensile, flexural, and impact loads, respectively.

In general, these coefficients decrease, i.e., KBFB composites become more cost-effective, with increasing fiber loading. KBFB-reinforced composites become more cost-effective than glass fiber-reinforced SMCs for tensile and flexural applications when the fiber loading exceeds 51.2 and 56.3 percent (wt/wt), respectively. These observations suggest kenaf fiber-reinforced composites are viable candidate replacement materials for glass fiber-reinforced SMCs that carry tensile or flexural loads, within the fiber weight fraction range from 50 to 70 percent (wt/wt).

[FIGURE 3 OMITTED]

KBFB-reinforced composites were less cost-effective than glass fiber-reinforced SMCs subjected to impact loads. The cost coefficient [K.sub.I] for composites carrying impact loads is always substantially higher than 1, although this coefficient decreased from 6.50 to 3.19 as the fiber weight percentage increased from 50 to 70 percent. This might be attributed to energy absorption due to the distributed brittle fracture of the glass fibers; KBFBs have no similar energy dissipation mechanism. Thus, kenaf fiber-reinforced com posites appear to be less cost-effective than glass fiber-reinforced SMCs for carrying impact loads.

Summary and Conclusions

The KBFB-reinforced UPE composite tensile, flexural, and impact strengths were studied statistically based on experimental results. The normal and two-parameter Weibull models were found to appropriately describe the distribution of the composite strengths. Other distribution models, gamma, lognormal, Burr, and Inverse Gaussian, provided reasonable characterization of composite strengths, with the exception of the exponential and Pareto models. The two-parameter Weibull model provided the most conservative 5th percentile design values for composite tensile, flexural, and impact strengths (43.15 MPa, 72.24 MPa, and 4.75 kJ/[m.sup.2], respectively). These values can be used as design strength allowable for KBFB-reinforced UPE composites.

The cost-effectiveness analysis suggested that KBFB-reinforced UPE composites were more cost-effective than glass fiber-reinforced SMCs for carrying tensile and flexural loads when their fiber loadings were higher than 51.24 and 56.29 percent (wt/wt), respectively. However, at these fiber loading levels, this class of composites were less cost-effective than glass fiber-reinforced SMCs for impact resistance applications.

Acknowledgments

The authors express appreciation for financial support by the US Department of Energy, the Center for Advanced Vehicular Systems (Grant No. DE-FC26-06NT42755) and the Forest Product Department at Mississippi State University. We also appreciate Kengro Corporation, Tailored Chemical Products, Inc., and Ashland Chemical Company for donated materials.

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The authors are, respectively, Graduate Student and Professor, Forest Products Lab., Mississippi State Univ., Mississippi State (yd33@ msstate.edu, jZhang@cfr.msstate.edu); Assistant Professor, Dept. of Mechanical and Aerospace Engineering, Utah State Univ., Logan (anna. xue@usu.edu); and Associate Professor, Dept. of Aerospace Engineering (lacy@ae.msstate.edu), Associate Professor, Dept. of Chemical Engineering (hossein@che.msstate.edu), Professor, Dept. of Mechanical Engineering (mfhorst@cavs.msstate.edu), and Professor, Dept. of Chemistry (CPittman@chemistry.msstate.edu), Mississippi State Univ., Mississippi State. This report was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof. Approved for publication as Journal Article no. FP564 of the Forest and Wildlife Research Center, Mississippi State Univ. This paper was received for publication in May 2010. Article no. 10-00007.

The tensile, flexural, and impact strength distribution and the cost-effectiveness of kenaf bast fiber bundle (KBFB)- reinforced unsaturated polyester composites were studied. Probability models including normal, two-parameter Weibull, gamma, lognormal, exponential, Burr, Pareto, and inverse Gaussian models were fitted against measured composite strengths. Taking the 5th percentile values as the composite's strength design values, the two-parameter Weibull model provided the most conservative composite strength design values. A cost-effectiveness analysis showed these composites were more cost-effective than glass fiber-reinforced sheet molding compounds (SMCs) for carrying tensile and flexural loads when their fiber loadings reached 51.2 and 56.3 percent (wt/wt), respectively. The KBFB-reinforced unsaturated polyester composites were less cost-effective than glass fiber-reinforced SMCs for carrying impact loads. This work suggests that natural fiber-reinforced composites have the potential to be viable replacement materials in applications where impact resistance is not critical.

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A high fiber loading kenaf bast fiber bundle (KBFB)-reinforced unsaturated polyester (UPE) composite fabrication process was previously developed (Duet al. 2010). The fabricated KBFB/UPE composites from the process possessed tensile modulus (12.1 GPa), specific modulus (9.92 GPa.[cm.sup.3]/g), and specific tensile strength (44.8 MPa.[cm.sup.3]/g) that met specification requirements for glass fiber-reinforced sheet molding compounds (SMCs): 9 GPa, 4.86 GPa.[cm.sup.3]/g, and 31.4 MPa.[cm.sup.3]/g, respectively. However, the tensile strengths (54.6 MPa) were slightly lower than the specification requirement (58 MPa) and exhibited large variations. Incorporation of these composites in automotive structural applications remains to be addressed, particularly where reliability in strength values is critical.

A number of statistical models can be used to study the distribution of composite strengths and estimate the reliability of composites. The Weibull distribution model (Weibull 1939) is the most widely used model for characterizing material strength distributions (Weibull 1951, Knight and Hahn 1975, Alqam et al. 2002, Dirikolu et al. 2002, Zureick et al. 2006, Rodrigues et al. 2008) and reinforcing fiber strength distributions (Luo and Netravali 1999; Bos et al. 2002; Andersons et al. 2005, 2009; Panthapulakkal et al. 2006; Xue et al. 2009). In addition to the Weibull model, applications of lognormal and gamma distribution models have also been reported (Wu et al. 2006, Basu et al. 2009).

Probability density functions for the two-parameter Weibull, lognormal, and gamma models are given in Equations 1 to 3, respectively. These three models assume that the location parameter is equal to zero.

f(x:[lambda],k) = k/[lambda] [(x/[lambda]).sup.k-1] exp [ - [(x/[lambda]).sup.k]] (1)

f(x:[lambda],k) = 1/[square root of (2[pi]kx)] exp [ - [(1n x - [lambda]).sup.2]] (2)

f(x:[lambda],k) = [x.sup.k-1] exp (- x/[lambda])/[GAMMA](k)[[lambda].sup.k] (3)

where [lambda], and k are scale and shape parameters, respectively. [GAMMA](k) is the gamma function defined as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

To date, there are no statistical and reliability analysis data available for natural fiber-reinforced thermoset polymer composites. There are a few published articles that study the statistical distribution and reliability of forest products. Guess et al. (2003) statistically studied the internal bond strengths of medium-density fiberboard, but the normal distribution was not suitable. Perhac et al. (2007) studied the probability of wood-plastic composite stiffnesses and flexural strengths using parametric and nonparametric probability plots. Using maleic anhydride grafted polypropylene as a coupling agent did not substantially alter the probability plots. Young et al. (2008) studied the reliability in modulus of elasticity and modulus of rupture for wood-plastic composites and provided three confidence intervals (CIs) for the product's lower percentiles for modulus of elasticity and modulus of rupture using bootstrapping methods. Young et al. (2009) reported that wood strand (raw material for oriented strand board) thicknesses were not normally distributed and the upper percentiles of strand thickness were estimated using bootstrapping methods. Weibull, normal, lognormal, exponential, and a few other quantitative statistical models were used in these studies. Yang et al. (2010) investigated the flexural fatigue behavior of wood flour-polypropylene composites and showed that a nondimensional fatigue model and the two-parameter Weibull probability distribution model could both be used for estimating fatigue life of these wood plastic composites.

Natural fiber-reinforced composites are potentially cost-effective because of their low densities and material costs despite their low absolute strengths. D'Almeida (2001) performed a cost analysis of composites made of sisal, jute, bagasse, and towel gourd fibers. These fibers have strengths ranging from less than 400 MPa to greater than 600 MPa. The cost-effectiveness of their composites for carrying the same flexural load was competitive with glass fiber-reinforced composites for certain fiber strength ranges and fiber volume fractions (percent, vol/vol). Specifically, the natural fiber composites were competitive at 70 percent (vol/vol) fibers with strengths less than 400 MPa, 50 percent (vol/vol) fibers with strengths between 400 and 600 MPa, and 40 percent (vol/vol) fibers with strengths greater than 600 MPa. A cost-effectiveness investigation of the KBFB-reinforced UPE composites prepared in our laboratory (Du et al. 2010) is of interest and highly desirable.

The objectives of this study were (1) to investigate the tensile, flexural, and impact strength statistical distributions and reliability of KBFB-reinforced UPE composites and (2) to analyze the cost-effectiveness of these composites compared with glass fiber-reinforced SMCs for automotive structural component applications.

Materials and Methods

Materials

KBFBs were supplied by Kengro Corporation. The UPE resin (Aropol Q-6585), provided by Ashland Chemical Company, was used as the matrix polymer. The diluent, styrene, and the free radical initiator, t-butyl perbenzoate, were purchased from Fisher Scientific Inc. A polyvinyl acetate (PVAc) water emulsion (solid content, 46%), provided by Tailored Chemical Products, Inc., was used as a mat preforming binder.

Composite fabrication

Composites were fabricated as previously described (Du et al. 2010). Long KBFBs were first ground into short fibers with an average length of 3.3 ram. Then, these short KBFBs were preformed into loose mats using the PVAc adhesive, and these preformed mats were infused with predetermined amounts of the UPE resin. The prepreg, assembled by five mats, was then compression molded into composite. The detailed process parameters for the UPE resin formulation, KBFB mat preforming, and compression molding were reported previously. The target fiber loadings were 50 to 60 percent (wt/wt). The composite fiber loadings were calculated after curing and all the squeezed-out resin was sanded off. A total of 25, 44, and 40 specimens were prepared for tensile, flexural, and impact testing, respectively.

Testing

The resultant composite samples were cut to tensile specimens using a CNC machine and were tested on an Instron 5869 universal testing machine under displacement control conditions in accordance with ASTM Standard D638-03 (ASTM International 2004). The cross head rate was set at 4 mm/min, and the tensile strain was recorded by an Instron 2630-100 series extensometer. Flexural test specimens were studied on the same Instron 5869 machine under displacement control conditions in accordance with ASTM Standard D790-03 (ASTM International 2003). The support span was set at 60 mm, and the testing speed was set at 4 mm/min. Impact properties were tested using an Izod fixture on an Instron Dynatup 9250HV Instrumented Drop Tower in accordance with ASTM Standard D256-06 (ASTM International 2006).

Results and Discussion

Statistical distributions

The experimental data analyses were performed using SAS statistical software, release 9.2 (SAS Institute Inc., Cary, North Carolina) and MATLAB 2009a. Table 1 summarizes the descriptive statistics of the measured tensile, flexural, and impact strengths. The experimental data histograms are plotted in Figures 1a, 1b, and 1c for the composites' tensile, flexural, and impact strengths, respectively. The skewness of the tensile strengths distributions is close to zero indicating that the tensile strengths were distributed nearly symmetrically. The skewness values of the flexural and impact strength distributions were -0.234 and -0.287, respectively, indicating the existence of a slightly left skewness. From the flexural and impact strength histograms, one can see the bulk of the flexural and impact strength values lie to the right.

Distribution models including normal, two-parameter Weibull, lognormal, gamma, and several other parametric models were fitted to the experimental data. Seven different statistics of goodness-of-fit for each distribution model for these three strengths were calculated and used as selection criteria. These statistics included-2LogLike, Akaike's information criterion (AIC), corrected Akaike's information criterion (AICC), Schwarz Bayesian information criterion (BIC), Kolmogorov-Smirnov statistic value (KS), Anderson-Darling statistic value (AD), and Cramer-von-Mises statistic value (CvM). The results are summarized in Tables 2, 3, and 4 for tensile, flexural, and impact strengths, respectively. In the tables, the lowest value of a given goodness-of-fit criterion was used to define the optimal distribution model.

The normal distribution model is the best for fitting the experimental tensile strengths (Table 2), followed by the Burr and Weibull distributions. The other six distribution models also show acceptable statistics of fit except the exponential and Pareto distributions. Similar results are observed for flexural strengths (Table 3). The normal distribution model provided the best fit to the measured flexural strengths followed by the inverse Gaussian, lognormal, and Weibull distribution models. The gamma model failed to converge for the given experimental flexural strength data. Hence, no goodness-of-fit statistics are reported for this model. In contrast to tensile and flexural strengths, the Weibull distribution model is the best model for fitting impact strengths (Table 4). The normal distribution ranks just below the Weibull model. These statistics suggest the normal distribution model works best for tensile and flexural strengths, while the Weibull distribution model works best for impact strengths. The exponential and the Pareto models are not appropriate for describing the strength distributions of KBFB-reinforced UPE composites. The remaining distribution models reasonably characterized the strength distributions. The scale and shape parameters and corresponding 95% CIs, based on the maximum likelihood methods, for the optimal distribution models for tensile, flexural, and impact strengths are summarized in Table 5.

[FIGURE 1 OMITTED]

Reliability analysis and design values

The fitted survival curves for composite tensile, flexural, and impact strengths, based on the relevant optimal distribution models, are plotted in Figures 2a, 2b, and 2c, respectively. The fitted survival curves for all these three strength properties closely matched the nonparametric Kaplan-Meier curves (Kaplan and Meier 1958). The estimated 95% CIs are also included in the figures. The 5th percentile values (95% probability of survival) have normally been chosen as design values in structural engineering (Ellingwood 2000). Table 6 summarizes the 5th percentile values estimated by the best distribution model (normal distribution for tensile and flexural strengths, and Weibull distribution for impact strengths). The values of the normal 5th percentile tensile and flexural strengths were 44.95 and 74.42 MPa, respectively. One can see that the normal 5th percentile tensile strength value was higher than the corresponding experimental tensile strength (44.50 MPa), which is not acceptable where a conservative estimate of strength is desired. However, values of the Weibull 5th percentile tensile and flexural strengths (43.15 MPa, 72.24 MPa) were both lower than the experimental data. Therefore, though the normal distribution model was the best fitting model for tensile and flexural strengths, the Weibull distribution model provided the most conservative strength estimates. The value of the Weibull 5th percentile impact strength was 4.75 kJ/[m.sup.2], which closely matched the experimental data (4.77 kJ/[m.sup.2]). Again, the normal distribution model provided a nonconservative 5th percentile impact strength value.

[FIGURE 2 OMITTED]

The conservative strengths obtained using the Weibull distribution model are consistent with results reported by Kam and Chang (1997) and Alqam et al. (2002). The estimated 5th percentile tensile, flexural, and impact strength values in this study using the Weibull distribution model, can be used as design strength allowable for the KBFB-reinforced UPE composites considered here. Based on this study, 95 percent of these laboratory-manufactured KBFB-reinforced UPE composites will conservatively survive when the tensile stress, flexural stress, and applied impact energy per square meter are lower than 43.15 MPa, 72.24 MPa, and 4.75 kJ/[m.sup.2], respectively. As part of future work, an investigation on the effect of sample size on the design strengths may be desirable.

Cost analysis

Although possessing lower absolute strengths, natural fiber-reinforced composite materials can compete with glass fiber-reinforced composites in terms of specific properties and costs. D'Almeida (2001) proposed a cost analysis model to calculate the price per unit length of a composite specimen, Q, subjected to an applied three-point bending load P.

Q = 3/2 L/t [[rho].sub.C]/[[sigma].sub.C] [X.sub.C]P (5)

In this equation, L and t are the test span and the specimen thickness, [[rho].sub.C] and [[sigma].sub.C] are the composite density and flexural strength, and [X.sub.C] is the price per unit of composite weight. Equation 5 can also be written as

Q = [beta] x P (6)

[beta] = 3/2 L/t [[rho].sub.C]/[[sigma].sub.C] [X.sub.C] (7)

Here, the cost parameter [beta] is a constant for a given composite geometry.

Similarly, the price per unit length of a composite tensile specimen can be calculated.

Q = [[rho].sub.C]/[[sigma].sub.C-Tension] [X.sub.C]P (8)

or

Q = [beta] x P (9)

Q = [[rho].sub.C]/[[sigma].sub.C-Tension] [X.sub.C] (10)

Q = 13" P (9)

Here, [[sigma].sub.C-Tension] is the composite tensile strength. The cost parameter [beta] for a composite subjected to a tensile load is independent of the composite's geometry.

In the same manner, the price per unit length of a composite can be calculated for the material subjected to impact loads.

Q = [[rho].sub.C] / [I.sub.C][X.sub.C]E (11)

or

Q = [beta] x E (12)

[beta] = [[rho].sub.C] / [I.sub.C][X.sub.C] (13)

In Equations 12 and 13, E is the absorbed energy and [I.sub.C] is the composite impact strength.

The composite with a lower value of the parameter [beta] will be more cost-effective to carry the same load or to resist the same amount of impact energy. A cost-effectiveness coefficient K is proposed to compare kenaf fiber-reinforced UPE composites with a type of commercial glass fiber-reinforced SMC-R25 of each type of load,

K = [[beta].sub.C] / [[beta].sub.SMC] (14)

Here, [[beta].sub.C] and [[beta].sub.SMC] are the cost parameters for the KBFB-reinforced composite and the glass fiber-reinforced SMC. The cost-effectiveness coefficients of kenaf fiber-reinforced UPE composites subjected to tensile ([K.sub.T]), flexural ([K.sub.F]), and impact loads ([K.sub.I]) can be calculated by Equations 15 to 17.

[K.sub.T] = ([[rho].sub.C] / [[sigma].sub.C-Tension]) x [X.sub.C] / ([[rho].sub.SMC] / [[sigma].sub.SMC-Tension]) x [X.sub.SMC] (15)

[K.sub.F] = ([[rho].sub.C] / [[sigma].sub.C-Flexure]) x [X.sub.C] / ([[rho].sub.SMC] / [[sigma].sub.SMC-Flexure]) x [X.sub.SMC] (16)

[K.sub.I] = ([[rho].sub.C] / [I.sub.C]) x [X.sub.C] / ([[rho].sub.SMC] / [I.sub.SMC]) x [X.sub.SMC] (17)

In these equations, [[rho].sub.SMC], [[sigma].sub.SMC-Tension], [[sigma].sub.SMC-Flexure], and [I.sub.SMC] are density, tensile strength, flexural strength, and impact resistance for glass fiber-reinforced SMC, respectively.

When a KBFB-reinforced composite is more cost-effective than the glass fiber-reinforced SMC, then the corresponding cost-effective coefficient is less than 1. The price per unit weight of SMC-R25, [X.sub.SMC] is determined at the 25 percent fiber loading. The price per unit composite weight, [X.sub.C] at various fiber loadings can be calculated by Equation 18:

[X.sub.C] = [x.sub.UPE] x [wt.sub.UPE]% + [x.sub.PVAc] x [wt.sub.PVAc]% + [x.sub.KBFB] x [wt.sub.KBFB]% (18)

Here, x and wt% are the unit price and weight percentage for each component.

Table 7 summarizes the price of each constituent in the kenaf fiber-reinforced composite and in a typical glass fiber-reinforced SMC (R25 SMC). Prices of UPE and filler for SMC were obtained from an automotive component manufacturer. The weight percentage of each component, as well as tensile, flexural, and impact strengths of R25 SMCs are listed in Table 7. These data were used to calculate the cost-effectiveness coefficients of kenaf fiber-reinforced composites for comparison to glass fiber-reinforced R25 SMCs. The cost coefficients [K.sub.T], [K.sub.F], and [K.sub.I] are plotted in Figures 3a, 3b, and 3c against fiber loadings for tensile, flexural, and impact loads, respectively.

In general, these coefficients decrease, i.e., KBFB composites become more cost-effective, with increasing fiber loading. KBFB-reinforced composites become more cost-effective than glass fiber-reinforced SMCs for tensile and flexural applications when the fiber loading exceeds 51.2 and 56.3 percent (wt/wt), respectively. These observations suggest kenaf fiber-reinforced composites are viable candidate replacement materials for glass fiber-reinforced SMCs that carry tensile or flexural loads, within the fiber weight fraction range from 50 to 70 percent (wt/wt).

[FIGURE 3 OMITTED]

KBFB-reinforced composites were less cost-effective than glass fiber-reinforced SMCs subjected to impact loads. The cost coefficient [K.sub.I] for composites carrying impact loads is always substantially higher than 1, although this coefficient decreased from 6.50 to 3.19 as the fiber weight percentage increased from 50 to 70 percent. This might be attributed to energy absorption due to the distributed brittle fracture of the glass fibers; KBFBs have no similar energy dissipation mechanism. Thus, kenaf fiber-reinforced com posites appear to be less cost-effective than glass fiber-reinforced SMCs for carrying impact loads.

Summary and Conclusions

The KBFB-reinforced UPE composite tensile, flexural, and impact strengths were studied statistically based on experimental results. The normal and two-parameter Weibull models were found to appropriately describe the distribution of the composite strengths. Other distribution models, gamma, lognormal, Burr, and Inverse Gaussian, provided reasonable characterization of composite strengths, with the exception of the exponential and Pareto models. The two-parameter Weibull model provided the most conservative 5th percentile design values for composite tensile, flexural, and impact strengths (43.15 MPa, 72.24 MPa, and 4.75 kJ/[m.sup.2], respectively). These values can be used as design strength allowable for KBFB-reinforced UPE composites.

The cost-effectiveness analysis suggested that KBFB-reinforced UPE composites were more cost-effective than glass fiber-reinforced SMCs for carrying tensile and flexural loads when their fiber loadings were higher than 51.24 and 56.29 percent (wt/wt), respectively. However, at these fiber loading levels, this class of composites were less cost-effective than glass fiber-reinforced SMCs for impact resistance applications.

Acknowledgments

The authors express appreciation for financial support by the US Department of Energy, the Center for Advanced Vehicular Systems (Grant No. DE-FC26-06NT42755) and the Forest Product Department at Mississippi State University. We also appreciate Kengro Corporation, Tailored Chemical Products, Inc., and Ashland Chemical Company for donated materials.

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The authors are, respectively, Graduate Student and Professor, Forest Products Lab., Mississippi State Univ., Mississippi State (yd33@ msstate.edu, jZhang@cfr.msstate.edu); Assistant Professor, Dept. of Mechanical and Aerospace Engineering, Utah State Univ., Logan (anna. xue@usu.edu); and Associate Professor, Dept. of Aerospace Engineering (lacy@ae.msstate.edu), Associate Professor, Dept. of Chemical Engineering (hossein@che.msstate.edu), Professor, Dept. of Mechanical Engineering (mfhorst@cavs.msstate.edu), and Professor, Dept. of Chemistry (CPittman@chemistry.msstate.edu), Mississippi State Univ., Mississippi State. This report was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof. Approved for publication as Journal Article no. FP564 of the Forest and Wildlife Research Center, Mississippi State Univ. This paper was received for publication in May 2010. Article no. 10-00007.

Table 1.--Statistical summary of tensile, flexural, and impact strengths, respectively. Tensile Flexural Impact strength strength strength (MPa) (MPa) (kJ/[m.sup.2]) Sample size 25 44 40 Fiber loading (wt%) 58-63 62-68 53-63 Mean 53.10 83.64 6.25 SD 5.05 5.67 0.79 COV (%) 9.52 6.78 12.71 Skewness -0.056 -0.234 -0.287 Table 2.--Goodness-of-fit criteria for each distribution model of the tensile strength data. Fit statistics Distribution -2 Log likelihood AIC AICC Normal 150.936 (a) 154.936 (a) 155.481 (a) Weibull 151.859 155.859 156.404 Gamma 151.077 155.077 155.622 Lognormal 151.228 155.228 155.774 Exponential 248.605 250.605 250.779 Burr 151.615 157.615 158.758 Pareto 248.726 252.726 253.272 Inverse Gaussian 151.215 155.215 155.760 Fit statistics Distribution BIC KS AD CVM Normal 157.374 (a) 0.825 0.359 0.064 Weibull 158.296 0.694 (a) 0.388 0.060 Gamma 157.515 0.879 0.384 0.070 Lognormal 157.666 0.905 0.403 0.075 Exponential 251.824 2.857 9.468 2.051 Burr 161.272 0.699 0.3471 0.056 (a) Pareto 255.164 2.858 9.472 2.052 Inverse Gaussian 157.653 0.905 0.403 0.075 (a) Indicates the best distribution model. Table 3.--Goodness-of-fit criteria for each distribution model of the flexural strength data. Fit statistics Distribution -2 Log likelihood AIC AICC Normal 276.499 (a) 280.499 (a) 280.792 (a) Weibull 277.405 281.405 281.698 Lognormal 277.428 281.428 281.721 Exponential 477.529 479.529 479.624 Burr 277.006 283.006 283.606 Pareto 477.758 481.758 482.051 Inverse Gaussian 277.429 281.429 281.722 Fit statistics Distribution BIC KS AD CvM Normal 284.067 (a) 0.571 0.2371 0.035 (a) Weibull 284.974 0.816 0.378 0.058 Lognormal 284.996 0.482 0.264 0.036 Exponential 481.313 3.779 17.600 3.826 Burr 288.358 0.775 0.315 0.049 Pareto 485.327 3.780 17.606 3.828 Inverse Gaussian 284.997 0.481 (a) 0.264 0.036 (a) Indicates the best distribution model. Table 4.--Goodness-of-fit criteria for each distribution model of the impact strength data. Fit statistics Distribution -2 Log likelihood AIC AICC Normal 94.051 98.051 98.375 Weibull 93.816 97.816 (a) 98.141 Gamma 95.301 99.301 99.625 Lognormal 96.209 100.209 100.534 Exponential 226.596 228.596 228.701 Burr 93.412 (a) 99.412 100.079 Pareto 226.657 230.657 230.981 Inverse Gaussian 96.21 100.210 100.534 Fit statistics Distribution BIC KS AD CvM Normal 101.429 0.723 0.433 0.058 Weibull 101.194 (a) 0.529 (a) 0.312 (a) 0.045 (a) Gamma 102.679 0.767 0.574 0.076 Lognormal 103.587 0.806 0.665 0.088 Exponential 230.285 3.313 14.047 3.013 Burr 104.479 0.625 0.318 0.048 Pareto 234.035 3.313 14.050 3.014 Inverse Gaussian 103.588 0.808 0.670 0.089 (a) Indicates the best distribution model. Table 5.--Summary of the best distribution parameters for composite tensile, flexural, and impact strengths, respectively. Scale parameter (mean) Predicted 95% CI Tensile strength (MPa), normal 53.10 51.01-55.18 Flexural strength (MPa), normal 83.64 81.91-85.36 Impact strength (kJ/ml), Weibull 6.59 6.36-6.83 Shape parameter (SD) Predicted 95% CI Tensile strength (MPa), normal 5.05 3.95-7.03 Flexural strength (MPa), normal 5.67 4.68-7.18 Impact strength (kJ/ml), Weibull 9.10 7.19-11.52 Table 6.--Fifth percentile values (95% probability of survival) for composite tensile, flexural, and impact strengths, respectively. 5th percentile value Normal Experimental Estimate 95% CI Tensile strength (MPa) 44.50 44.95 41.97-47.92 Flexural strength (MPa) 75.19 74.42 71.88-76.96 Impact strength (kJ/[M.sup.2]) 4.77 4.96 4.59-5.33 5th percentile value Weibull Estimate (a) 95% CI Tensile strength (MPa) 43.15 39.35-47.31 Flexural strength (MPa) 72.24 68.77-75.88 Impact strength (kJ/[M.sup.2]) 4.75 4.32-5.23 (a) The Weibull estimates were statistically significantly lower than the normal estimates. Table 7.--The component prices, densities, and mechanical properties of KBFB and glass fiber-reinforced UPE composites. Unit price and Material properties Source KBFB-reinforced composites Price (US$/kg) Kenaf fiber 0.44-0 Zampaloni et al. 2007 UPE 2.65 PVAc 1.30 Manufacturer Composite cost (US$/kg) 1.03 Density (g/[cm.sup.3]) 1.2 SMC (R25) Price (US$/kg) E-glass fiber (25%) 3.25 Mohanty et al. 2000 UPE (25%) 2.65 Filler (50%) 0.22 Composite cost (US$/kg) 1.59 Density (g/[cm.sup.3]) 1.85 European Alliance for SMC 2001 Tensile strength (MPa) 73 European Alliance for SMC 2001 Flexural strength (MPa) 178 European Alliance for SMC 2001 Impact (kJ/[M.sup.2]) 75 European Alliance for SMC 2001

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Author: | Du, Yicheng; Zhang, Jilei; Xue, Yibin; Lacy, Thomas E., Jr.; Toghiani, Hossein; Horstemeyer, Mark F. |
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Publication: | Forest Products Journal |

Date: | Sep 1, 2010 |

Words: | 5054 |

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