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\title{Analysis of Tensile Strength of Bamboo Reinforced Polyester Composite}
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             \author[1]{Alimasunya  Elizabeth}

             \author[2]{Alimasunya  Elizabeth}

             \affil[1]{  Nnamdi Azikiwe University}

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\date{\small \em Received: 11 December 2015 Accepted: 1 January 2016 Published: 15 January 2016}

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\begin{abstract}
        


Nigerian grown species of bamboo called bambusa vulgaris which was examined to analyze its tensile strength. The fibre characteristics and tensile strength were investigated at three different fibre lengths and fibre loadings i.e 10, 30,50mm and 10, 30, 50 wt.% respectively. Fibre length was varied in each fibre loading from 10mm to 50mm, the tensile strength of the three different series of composites varies from 28.32Mpa to 38.10Mpa. The predicted optimum tensile strength is 44.51Mpa. Generated results have been validated by the confirmation of experiments at three replications, when the control factors were set at 30mm and 30% wt or (level 2, level 2), using Taguchi?s design of experiments approach. It was observed from the analysis of variance of the samples that there is a variation in the increase of tensile strength of the bamboo that are dependent on the fibre length and fibre loading used. The percentage contributions of parameter according to the pooled ANOVA for signal-to- Noise ratio showed that the fibre length (36.61%) in controlling variation and mean strength is significantly smaller than the fibre loading (44.15%).

\end{abstract}


\keywords{bamboo, bambusa vulgaris, tensile strength, taguchi?s experimental design, fibre length, fibre loading.}

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\let\tabcellsep& 	 	 		 
\section[{I. Introduction}]{I. Introduction}\par
omposites can be defined as materials that consist of two or more chemically and physically different phases separated by a distinct interface. The different systems are combined judiciously to achieve a system with more useful structural or functional properties no attainable by any of the constituent alone  {\ref [Shaw et al. 2010}]. The strength of bamboo is greater than many timber products, but lesser than the tensile strength of steel. Bamboo is readily available and is emerging as low cost, light weight, and environmentally friendly. Tensile test is the most basic type of mechanical test. It is not difficult to perform and it is not expensive compared to other mechanical tests. 
\section[{II. Materials and Methods}]{II. Materials and Methods} 
\section[{General}]{General}\par
purpose grade unsaturated orthophathalic polyester resin (RGP 67G), was obtained from Center for Composite Research and Development, JuNeng Nigeria Limited, Nsukka. The bamboo fibres were extracted mechanically from the young stem of bamboo plant, shredded and air-dried for young stem of bamboo plant, shredded and air-dried for about a week until constant mass. The dried fibres were chopped into 10mm, 30mm and 50mm fibre lengths and 10\%, 30\% and 50\% weight fraction used as reinforcement materials in the composite preparation, by hand lay-up method using a three-piece stainless s t e e l mould having dimensions 200x 150x30mm. Methyl ethyl ketone p er o x i d e (MEKP) and cobalt napthenate of commercial grade were used as the catalyst and accelerator respectively for resin curing. 
\section[{a) Volume Fraction and Density of Fibre}]{a) Volume Fraction and Density of Fibre}\par
The density and volume fraction of fibres used for the sample preparation was calculated by a method which enables the rule of mixtures analysis of measured composite properties. The picnometric procedure was adopted for measuring the density pc of the composite of mass M c at a given mass fraction of resin M r . Volume fraction V r of resin was calculated using the following relationships:?? ?? = ?? ?? ?? ?? ?? ?? ?? ?? [1]\par
Where ?? ?? is the resin density then, the volume fraction ?? ð??"ð??" and density ?? ð??"ð??" of fibre where calculated using the following equations: [1]?? ð??"ð??" + ?? ?? = 1 [2] ?? ?? = ?? ð??"ð??" ?? ?? ?? ?? ?? ð??"ð??" [3]\par
The density of fibre was also measured using archimedes principle. Both results produced similar results and an average value of 960kg/m 3 was obtained as fibre density. b) The Taguchi Approach to Robust Parameter Design In the early 1980s, Genichi Taguchi, a Japanese engineer, introduced his approach to using experimental design for: designing products or processes so that they are robust to environmental conditions; designing/ developing products so that they are robust to component variation; and minimizing variation around a target value.\par
In parameter design, there are two types of factors that affect a product's functional characteristic: control factors and noise factors, at this stage of design, the specific values for the system parameters are determined. Usually, the objective is to specify these nominal parameter values such that the variability transmitted from uncontrollable or noise variables is minimized. 
\section[{III. Selection of an Orthogonal Array}]{III. Selection of an Orthogonal Array}\par
In selecting an appropriate OA, the prerequisites are: (a) selection of process parameters and interactions to be evaluated and (b) selection of number of levels for the selected parameters [2] The process parameters were already decided and are given in Table \hyperref[tab_0]{1}. It was also decided to study each selected parameter at three levels. With two parameters each at three levels, the total degree of freedom (DOF) required is 4 [= 2(3-1)]. As per Taguchi's DOE approach, the total DOF of t selected OA must be greater than or equal to the total DOF required for the experiment. So, an L 9 (2 3 ) orthogonal array was selected for the present work. 
\section[{IV. Experimental-Analysis and Discussion}]{IV. Experimental-Analysis and Discussion}\par
The tensile tests were performed according to ASTM D638 standard using Universal Testing Machine at a crosshead speed of 5 mm/min. Specimens for each sample were tested and the tensile strength and tensile modulus were expressed as:\par
Tensile strength (MPa) = P/bh  {\ref [4]} Where; P = Pulling force (N), b =Specimen width (m), and h = Specimen thickness (m) Robust design is an "engineering methodology for improving productivity during research and development so that high-quality products can be produced quickly and at low cost"  {\ref [3]}. The idea behind robust design is to improve the quality of a product by minimizing the effects of variation without eliminating the causes (since they are too difficult or too expensive to control). Nine trial conditions with three repetitions are used in this work. The selected quality characteristic, tensile strength, is 'higher the better' (HB) type, the S/N (signal to noise) ratio, for 'higher the better' type of response was used as given in the following equation:(S/N) HB = ?10?????? ? 1 ?? ? 1 ?? 1 2 + 1 ?? 2 2 + ? 1 ?? ?? 2 ?? [5]\par
Where y 1 , y 2 ??y n are the responses of quality characteristic for a trial condition repeated n times. The S/N ratios were computed using equation 5 for each of the 9 trials and mean response for each factor at the three levels is presented in Table \hyperref[tab_2]{3}.  {\ref [4]} Along with the raw data. The average value of the tensile strength for each parameter at levels 1, 2 and 3 are plotted in figure  {\ref 2}. The average values of S/N ratios of various parameters at levels 1, 2 and 3 are plotted in figure  {\ref 1}.\par
The summary of the responses and ranking for tensile strength of bamboo fibre reinforced Polyester composites on the bases of the larger the better quality, for Signal to Noise Ratio, and mean of means lead to the conclusion that factor combination of A 1 B 1 gives the minimum strength while A 2 B 2 gives the maximum strength as shown in Figure  {\ref 1} and Figure  {\ref 2}. It is found that as far as the tensile strength is concerned; B and A have significant effect on the composite. The range (Delta) is the difference between higher and lower response. The larger the (Delta) value for a parameter, the larger the effect the variable has on the tensile strength of the composites. This is because the same change in signal causes a larger effect on the output variable being measured. It is clear from table 4 and 5 that the fibre weight fraction is ranked 1 st and fibre length 2 nd .In order to confirm Taguchi's design of experiment and to study the significance of the parameters in affecting the quality characteristic of the mechanical properties analysis of variance (ANOVA) was performed. The pooled ANOVA of the raw data (tensile strength) is given in Table \hyperref[tab_6]{6}. The S/N ANOVA (pooled version) is given in Table \hyperref[tab_7]{7}. It is clear from ANOVAs that the parameters A and B (fibre length and fibre weight) significantly affect both the mean value as well as the variation of the tensile strength because these are significant in both the ANOVAs. The percent contributions of parameters as quantified under column P of Table \hyperref[tab_6]{6} and Table \hyperref[tab_7]{7} reveal that the fibre weight (B) in controlling the mean and variation is significantly larger than the fibre length (A). [5] Software MINITAB 16 was used to analyze the Taguchi design of experiment, and the linear regression equations.    The optimal tensile strength (?TS) is predicted at the selected optimal setting of process parameters. The significant parameters with optimal levels are already selected as: A2B2. The interaction effects are not being considered in estimating mean and confidence interval around the estimated mean due to poor additivity between parameters and interactions. The estimated mean of the response characteristic can be computed as  {\ref [4]}:?TS = A ? 2 + B ? 2 ? T ? Ts [6]\par
Where:\par
T ? Ts = overall mean of Tensile strength = 37.83 Mpa From (Table \hyperref[tab_2]{3})  The predicted optimal Tensile strength is: ?TS = 44.51MpaA ? 2 =\par
The 95\% confidence interval of the predicted optimal tensile strength is:\par
( ?????? ? ??. ??) < ??????(??????) < (?????? + ??. ??).\par
40.401 < ?TS (Mpa) < 48.619 
\section[{b) Experimental Validation}]{b) Experimental Validation}\par
The last stage of Taguchi's robust technique is the confirmation of the experiment. Three confirmation experiments were conducted at the optimal setting of the process parameters. The average value of tensile strength was found to be 44.54Mpa. This result was within the confidence interval (95 \%) of the predicted optimal tensile strength.  
\section[{V. Conclusions}]{V. Conclusions}\par
The experimental investigations on the analysis of tensile strength of bamboo reinforced polyester composites were conducted. The experiments lead us to the following conclusions obtained from this study:\par
The successful fabrication of a new class of polyester based composites reinforced with short bamboo fiber is possible by simple hand lay-up technique; and The bamboo reinforced composite has an optimum tensile strength of 44.51MPa when the control factors (Fibre length, Fibre loading) are set at (30mm and 30\%wt) or (level 2, level 2); Global Journal of Researches in Engineering ( ) Volume XVI Issue III Version I\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.010897435897435897\textwidth}P{0.8391025641025641\textwidth}}
C\tabcellsep Journal of Researches in Engineering ( ) Volume XVI Issue III Version I\\
\tabcellsep Global\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.032196969696969696\textwidth}P{0.39280303030303027\textwidth}P{0.14166666666666666\textwidth}P{0.18674242424242424\textwidth}P{0.06439393939393939\textwidth}P{0.032196969696969696\textwidth}}
S/N\tabcellsep Processing Factors\tabcellsep Factor's designation\tabcellsep \tabcellsep Level\tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep 1\tabcellsep 2\tabcellsep 3\\
1\tabcellsep Fibre Length (mm)\tabcellsep A\tabcellsep 10\tabcellsep 30\tabcellsep 50\\
2\tabcellsep Fibre Weight Fraction (\%)\tabcellsep B\tabcellsep 10\tabcellsep 30\tabcellsep 50\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{3}{l}{Source: Field experiment}\end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.11393298059964725\textwidth}P{0.05246913580246913\textwidth}P{0.06746031746031746\textwidth}P{0.03597883597883598\textwidth}P{0.14091710758377424\textwidth}P{0.07645502645502644\textwidth}P{0.01948853615520282\textwidth}P{0.07645502645502644\textwidth}P{0.09894179894179893\textwidth}P{0.1679012345679012\textwidth}}
Expert. Run\tabcellsep Fibre Length (mm)\tabcellsep \multicolumn{2}{l}{Fibre Weight. Fraction (\%)}\tabcellsep \multicolumn{4}{l}{Measure Response (Mpa) Trial 1 Trial 2 Trial 3}\tabcellsep Mean Tensile Response\tabcellsep SN Ratio (dB)\\
1\tabcellsep 10\tabcellsep 10\tabcellsep \tabcellsep 28\tabcellsep \multicolumn{2}{l}{27.83}\tabcellsep 29.13\tabcellsep 28.32\tabcellsep 29.03655249\\
2\tabcellsep 10\tabcellsep 30\tabcellsep \tabcellsep 41.40\tabcellsep \multicolumn{2}{l}{39.50}\tabcellsep 39.70\tabcellsep 40.20\tabcellsep 30.07877224\\
3\tabcellsep 10\tabcellsep 50\tabcellsep \tabcellsep 37.80\tabcellsep \multicolumn{2}{l}{37.51}\tabcellsep 35.69\tabcellsep 37.00\tabcellsep 31.34769209\\
4\tabcellsep 30\tabcellsep 10\tabcellsep \tabcellsep 38.80\tabcellsep \multicolumn{2}{l}{38.40}\tabcellsep 38.30\tabcellsep 38.50\tabcellsep 31.70880621\\
5\tabcellsep 30\tabcellsep 30\tabcellsep \tabcellsep 45.20\tabcellsep \multicolumn{2}{l}{44.92}\tabcellsep 44.88\tabcellsep 45.00\tabcellsep 33.06412024\\
6\tabcellsep 30\tabcellsep 50\tabcellsep \tabcellsep 41.60\tabcellsep \multicolumn{2}{l}{40.32}\tabcellsep 41.08\tabcellsep 41.00\tabcellsep 32.25352731\\
7\tabcellsep 50\tabcellsep 10\tabcellsep \tabcellsep 35.80\tabcellsep \multicolumn{2}{l}{35.00}\tabcellsep 34.20\tabcellsep 35.00\tabcellsep 30.87682137\\
8\tabcellsep 50\tabcellsep 30\tabcellsep \tabcellsep 38.33\tabcellsep \multicolumn{2}{l}{37.00}\tabcellsep 36.63\tabcellsep 37.32\tabcellsep 31.43392063\\
9\tabcellsep 50\tabcellsep 50\tabcellsep \tabcellsep 39.20\tabcellsep \multicolumn{2}{l}{38.20}\tabcellsep 36.90\tabcellsep 38.10\tabcellsep 31.61049495\\
Total\tabcellsep \tabcellsep \tabcellsep \tabcellsep 346.13\tabcellsep \multicolumn{2}{l}{338.68}\tabcellsep 336.51\\
\multicolumn{3}{l}{?? ? TS = Overall mean of TS =}\tabcellsep \multicolumn{3}{l}{346.13+338.68+336.51 3×9}\tabcellsep \multicolumn{2}{l}{= 37.83??????}\\
\multicolumn{3}{l}{TS= Tensile strength.}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_2}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.32602739726027397\textwidth}P{0.523972602739726\textwidth}}
\tabcellsep Year 2016\\
\tabcellsep 23\\
\tabcellsep Journal of Researches in Engineering ( ) Volume XVI Issue III Version I A\\
Source: Field experiment\tabcellsep Global\\
© 2016 Global Journals Inc. (US)\tabcellsep \end{longtable} \par
 
\caption{\label{tab_3}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.11818181818181818\textwidth}P{0.20454545454545453\textwidth}P{0.1393939393939394\textwidth}P{0.06515151515151514\textwidth}P{0.08787878787878788\textwidth}P{0.031818181818181815\textwidth}P{0.051515151515151514\textwidth}P{0.001515151515151515\textwidth}P{0.12575757575757576\textwidth}P{0.02424242424242424\textwidth}}
\tabcellsep \tabcellsep \tabcellsep \multicolumn{6}{l}{Main Effect Plot (data means) for SN Ratio}\\
\tabcellsep 32.6\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 32.4\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 32.2\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 32\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
SN Ratio\tabcellsep 31.2 31.4 31.6 31.8\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 31\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 30.8\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 30.6\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 30.4\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 0\tabcellsep 0.5\tabcellsep 1\tabcellsep 1.5\tabcellsep 2\tabcellsep 2.5\tabcellsep 3\tabcellsep 3.5\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Factor levels}\tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \multicolumn{2}{l}{Responses}\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Means}\\
\tabcellsep \tabcellsep \multicolumn{2}{l}{Levels}\tabcellsep \multicolumn{3}{l}{A:FibreLength (mm)}\tabcellsep \tabcellsep B: Weight Fraction (\%)\\
\tabcellsep \tabcellsep 1\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{35.17}\tabcellsep \tabcellsep 33.94\\
\tabcellsep \tabcellsep 2\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{41.50}\tabcellsep \tabcellsep 40.84\\
\tabcellsep \tabcellsep 3\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{36.81}\tabcellsep \tabcellsep 38.70\\
\tabcellsep \tabcellsep \multicolumn{2}{l}{Delta}\tabcellsep \tabcellsep \multicolumn{2}{l}{6.33}\tabcellsep \tabcellsep 6.90\\
\tabcellsep \tabcellsep \multicolumn{2}{l}{Rank}\tabcellsep \tabcellsep 2\tabcellsep \tabcellsep \tabcellsep 1\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep Source: Field experiment\\
\tabcellsep \multicolumn{8}{l}{Fig. 2 : Graph of Mean of Means against Factor Levels (1, 2 and 3) for Tensile Strength}\\
\multicolumn{3}{l}{The regression equation is}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{5}{l}{Tensile strength = 33.0 + 0.0408 A + 0.119 B}\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \multicolumn{2}{l}{Predictor}\tabcellsep Coef\tabcellsep \tabcellsep \multicolumn{2}{l}{SE Coef}\tabcellsep T\tabcellsep P\\
\tabcellsep \tabcellsep \multicolumn{2}{l}{Constant}\tabcellsep 33.032\tabcellsep \tabcellsep 4.303\tabcellsep \tabcellsep 7.68\tabcellsep 0.000\\
\tabcellsep \tabcellsep A\tabcellsep \tabcellsep 0.04083\tabcellsep \tabcellsep \multicolumn{2}{l}{0.09465}\tabcellsep 0.43\tabcellsep 0.681\\
\tabcellsep \tabcellsep B\tabcellsep \tabcellsep 0.11900\tabcellsep \tabcellsep \multicolumn{2}{l}{0.09465}\tabcellsep 1.26\tabcellsep 0.255\\
\tabcellsep \tabcellsep \multicolumn{5}{l}{S = 4.63692 R-Sq = 22.7\% R-Sq(adj) = 0.0\%}\tabcellsep \end{longtable} \par
 
\caption{\label{tab_4}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6} \par 
\begin{longtable}{P{0.17809523809523808\textwidth}P{0.056666666666666664\textwidth}P{0.16190476190476188\textwidth}P{0.1376190476190476\textwidth}P{0.12952380952380954\textwidth}P{0.18619047619047618\textwidth}}
source\tabcellsep DOF\tabcellsep SS\tabcellsep V\tabcellsep F ratio\tabcellsep P(\%)\\
A\tabcellsep 2\tabcellsep 64.72\tabcellsep 32.36\tabcellsep 1.90\tabcellsep 38.75\\
B\tabcellsep 2\tabcellsep 74.86\tabcellsep 37.43\tabcellsep 2.44\tabcellsep 44.83\\
Total\tabcellsep 8\tabcellsep 167\tabcellsep -\tabcellsep -\tabcellsep 100\\
e(pooled)\tabcellsep 4\tabcellsep 27.42\tabcellsep 6.855\tabcellsep \tabcellsep 16.42\end{longtable} \par
 
\caption{\label{tab_6}Table 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7} \par 
\begin{longtable}{P{0.13453237410071942\textwidth}P{0.04280575539568345\textwidth}P{0.13453237410071942\textwidth}P{0.1039568345323741\textwidth}P{0.28129496402877696\textwidth}P{0.1528776978417266\textwidth}}
source\tabcellsep DOF\tabcellsep SS\tabcellsep V\tabcellsep F ratio\tabcellsep P(\%)\\
A\tabcellsep 2\tabcellsep 3.620\tabcellsep 1.810\tabcellsep 1.73\tabcellsep 36.61\\
B\tabcellsep 2\tabcellsep 4.366\tabcellsep 2.183\tabcellsep 2.37\tabcellsep 44.15\\
Total\tabcellsep 8\tabcellsep 9.889\tabcellsep -\tabcellsep -\tabcellsep 100.0\\
e(pooled)\tabcellsep 4\tabcellsep 1.903\tabcellsep 0.476\tabcellsep \tabcellsep 19.24\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Source: ANOVA generated output}\end{longtable} \par
 
\caption{\label{tab_7}Table 7 :}\end{figure}
 			\footnote{© 2016 Global Journals Inc. (US)} 		 		\backmatter  			 \par
The predicted optimal range at 95\% confidence interval of the Tensile strength is: 40.401 < ?TS (Mpa) < 48.619\par
References Références Referencias   {\ref computer scientists 2008} {\ref vol 11 IMECS 2008} {\ref , 19-21 March, 2008, Hong Kong} 			 			  				\begin{bibitemlist}{1}

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