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https://www.eduzhai.net International Journal of Composite M aterials 2013, 3(6A): 45-57 DOI: 10.5923/s.cmaterials.201309.05 Quantification of Matrix and Reinforcement Effects on the Young’s Modulus of Carbon Nanotube/Epoxy Composites using a Design of Experiments Approach Hossein Rokni1,2, Abbas S. Milani2,*, Rudolf J. Seethale r2, Meisam Omidi3 1Department of M echanical Engineering, University of M ichigan, Ann Arbor, M I 48109, USA 2School of Engineering, University of British Columbia Okanagan, Kelowna, BC V1V 1V7, Canada 3School of Science, Shahid Beheshti University, Tehran, Iran Abstract The focus of this work is to present a methodology to systematically study and classify the influence of a set of controllable parameters during the fabrication of carbon nanotube (CNT)/epoxy co mposites on the material’s e lastic modulus. The chosen factors include two types of poly mer matrices (i.e., LY 5052 and LY 564), two types of carbon nanotubes (i.e., single- and mult i-walled carbon nanotubes), functionalized and pristine carbon nanotubes, and different weight-percents (wt.%) of CNTs. A factorial design of experiment (DOE) with mixed levels has been employed to estimate the contribution of the aforementioned factors, along with their interactions, in the maximization of the Young’s modulus of the fabricated CNT/epoxy co mposites. Over 120 specimens were fabricated and tensile tests were carried out to obtain an optimu m Young’s modulus of the CNT/epo xy composite. The results indicate that among control parameters, the wt.% of CNTs and the type of CNTs have the highest effects, whereas their interaction has the least effect. It is also shown that the functionalized CNTs can significantly dimin ish the effect of noise factors, arising fro m the CNT wav iness, debonding between CNTs and polymer matrices, the random orientation of CNTs and non-uniform CNT d ispersion. Among tested material configurations, the highest Young’s modulus (4.135 GPa) was achieved on the functionalized single-walled carbon nanotube/amine resin LY5052 containing 1.5 wt.% of CNTs. This corresponded to a 33% imp rovement co mpared to the pure epoxy resin LY5052. The presented methodology is straightforward and can be applied to other types of CNT-reinforced co mposites. Keywords A. Poly mer-matrix co mposites (PMCs), B. Mechanical properties, C. Statistical p roperties/method, D. Mechanica l testing 1. Introduction After being recognized in 1991 by Iijima[1], carbon nanotubes (CNTs) rapidly attracted the attention of many res earch g roups d ue t o th eir except ion al mech an ical properties as reinforcing materials. Today CNTs are used in a wid e ran ge o f ap p licat ions in clud ing lig h t weig ht composite structures, field emission devices, electronics, micro/nano -elect ro -mechan ical system (M EM S/ NEM S) devices, sensors, actuato rs, nano -robot ics and med ical applications. CNTs can be classified into two most widely recogn ized cat egories: s ing le-walled carbon nanotubes (SWCNTs) and mult i-walled carbon nanotubes (MWCNTs). SWCNTs have mo re intimate contacts with the mat rix material, lead ing to more efficient load transfer between the composite constituents. On the other hand, MWCNTs can * Corresponding author: abbas.milani@ubc.ca (Abbas S. Milani) Published online at https://www.eduzhai.net Copyright © 2013 Scientific & Academic Publishing. All Rights Reserved be produced in much larger quantities at lower cost. The present literature reveals that the introduction of CNTs as reinforcing materials in poly mer matrices can significantly imp rove mechanical properties[2–12]. An excellent survey of the research studies on the mechanical and electrical properties of CNT-poly mer co mposites has been recently carried out by Ma et al.[13], Spitalsky et al.[14] and Sahoo et al.[15]. A mong earlier works published on the subject, only a few have specifically dealt with the effect of MWCNTs or SWCNTs on the Young’s modulus of epoxy-based composites and, hence, they will be addressed in the following rev iew sections. Table 1 summarizes highlights of this background work by other research groups. 1.1. Effect of MWCNTs One of the earliest reports on the Young’s modulus of CNT/epoxy co mposites dates back to the work o f Schadler et al.[16], in which the elastic modulus increased fro m 3.1 to 3.71 GPa (i.e., a 20% increase) by adding 5 wt.% of MWCNTs. Xu et al.[17] reported an increase in the Young’s modulus of MWCNTs-rein forced epoxy co mposites from 46 Hossein Rokni et al.: Quantification of M atrix and Reinforcement Effects on the Young’s M odulus of Carbon Nanotube/Epoxy Composites using a Design of Experiments Approach 4.2 to 5 GPa (19% increase) at only 0.1 wt.% of MWCNTs. Allaoui et al.[18] reported that the elastic modulus of the MWCNT/epo xy composites can be doubled when 1.0 wt.% of MWCNTs was mixed with a rubbery matrix. A double increase of the Young’s modulus fro m 1.2 to 2.4 GPa was also observed by Bai[19] for MWCNT/epo xy composites with 1.0 wt.% of CVD-MW CNTs. Li et al.[20] achieved 50% enhancement in stiffness by introducing 0.25 wt.% of copolymer-modified MW CNTs to the epo xy co mposite. Breton et al.[21] achieved a 32% increase in the Young’s modulus of o xidized MWCNT/epo xy co mposites with the addition of 6 wt.% CVD-MWCNTs. An experimental investigation for properties of MWCNT/epo xy co mposite was conducted by Ci and Bai[22]. They reported that only 0.5 wt.% MW CNT addition can increase the Young’s modulus of the epoxy composite up to 200%. Tseng et al.[23] showed an over 100% improvement of the Young’s modulus of functionalized MWCNT/epo xy co mposites with only 1.0 wt.% addition of MWCNTs. Yeh et al.[24] added MWCNTs to the epoxy resin E120-H100 and demonstrated that the addition of 5 wt.% MW CNTs increases the Young's modulus of MWCNT/epoxy co mposite up to 51.8%. Chen et al.[25] showed that the incorporation of 2 wt.% of MWCNTs led to an increase of the Young’s modulus of epoxy co mposites up to 17%. Sp italsky et al.[26] observed a two fold increase of the Young’s modulus of oxid ized MWCNT/epo xy composites by adding of 0.5 wt .% of MWCNTs. With 3 wt.% addition of MWCNTs, an enhancement of up to 27% in Young’s modulus of MWCNT/epo xy co mposite was observed by Montazeri et al.[27]. Recently, Omid i et al.[28] reported that only a 3 wt.% addit ion of MW CNTs enhanced the Young’s modulus of the epoxy co mposite up to 43.1%. 1.2. Effect of SWCNTs A review o f the past literature indicates that generally less attention has been devoted to SWCNT-reinforced epo xy composites as compared to MWCNT co mposites. A 30% improvement in the Young’s modulus was obtained by Zhu et al.[29] after adding 1.0 wt.% functionalized SW CNTs to the epoxy co mposite. Li et al.[30] also observed an increase up to 75% with 5 wt.% SW CNTs in epo xy co mposites. Valentin i et al.[31] reported that 56% imp rovement in the Young’s modulus of amino-functionalized SWCNT/epo xy composites was achieved by adding only 0.1 wt.% of SWCNTs. Zhu et al.[32] showed that up to 70% improvement in the Young’s modulus was found for epoxy composites with 4 wt.% of functionalized SW CNTs. 1.3. Moti vation and Organizati on of the Work In all studies reported in Table 1, a significant improvement in mechanical properties of epoxy composites has been obtained by means of varying different process parameters in the fabricat ion of specimens. However, there has been no systematic approach reco mmended to quantify the effect of each fabrication parameter and study potential interaction effects between them in controlling the mechanical response of the ensuing nanocompositesi. Table 1. Reported improvements in the Young’s modulus of CNT-based epoxy composites CNT type Purified MWCNT s CNT wt.% 5.00 Processing method Simple mixing %Imp 20 Mech an ical t est in g Tensile Ref. no. [16] Pristine MWCNTs 0.10 Solution mixing–spin co at in g 20 Shaft-loaded blister test [17] Pristine MWCNTs 1.00 Simple mixing 100 Tensile [18] Pristine MWCNTs 1.00 Simple mixing 100 Tensile [19] Copolymer-modified MWCNT s 0.25 Solvent mixing 50 Tensile [20] Oxidized MWCNT s 6.00 Simple mixing 32 Tensile [21] Pristine MWCNTs 0.50 Simple mixing 200 Tensile [22] Modified MWCNTs 1.00 Simple mixing 100 Tensile [23] Pristine MWCNTs 5.00 Simple mixing 52 Tensile [24] Pristine MWCNTs 2.00 Simple mixing 17 Tensile [25] MWCNT s 0.50 Solution mixing 54 Tensile [26] Pristine MWCNTs 3.00 Solution mixing 27 Tensile [27] MWCNT s 3.00 Solution mixing 43 Tensile [28] Fluorinated SWCNTs 1.00 Solution mixing 30 Tensile [29] Pristine SWCNT s 5.00 Simple mixing 75 Tensile [30] Modified SWCNT s 0.10 Simple mixing 56 Tensile [31] Modified SWCNT s 4.00 Solution mixing 70 Tensile [32] International Journal of Composite M aterials 2013, 3(6A): 45-57 47 As a result, this study aims at employing a statistical approach to quantify the influence of a set of control factors that have been commonly used by different research groups in the fabrication of CNT-reinforced co mposites. Namely, it is shown how a Taguchi method and the analysis of variance (ANOVA) can be employed to select an optimu m set of parameters that maximizes the elastic response of a CNT/epoxy co mposite. The selected study parameters include different epoxy and CNT types, different CNT states and various wt.% of CNTs. Namely, tensile tests of 128 specimens were carried out to obtain the Young’s modulus of different samples made of the resin LY 5052 or LY 564, reinforced with pristine or functionalized SW CNTs/ MWCNTs, and 0.25, 0.5, 1.0 or 1.5 wt.% of CNTs (Section 2). For the statistical analysis, a factorial design of experiment (DOE) with mixed levels has been chosen (Section 3) and the effect of above-mentioned control factors, together with their interactions, on improving the Young’s modulus of the tested composites is identified (Section 4). An aggregated effect of noise factors, stemming fro m the CNT waviness, debonding between CNTs and polymer matrices, the random orientation of CNTs and non-uniform CNT d ispersion, on the material elastic response has also been discussed. The concluding remarks are included in Section 5. 2. Experimental Procedure 2.1. Materials SWCNTs, MWCNTs and their functionalized counterparts, produced by chemica l vapor deposition (CVD), were purchased from Research Institute of Petro leum Industry (RIPI). The SW CNTs varied fro m 0.9 to 1.1 n m in diameter with the average length of 10 μ m while the MWCNTs were characterized by an average outer wall diameter of 20-50 n m and an average length of 20 μm with a carbon purity of 96%. In order to prepare functionalized SWCNTs/MWCNTs, the oxid ized SWCNTS/MW CNTs (SWCNTS/MWCNTs-COOH) were first achieved according to the HNO3 washing procedure; 8 g of pristine SWCNTS/MWCNTs were boiled in 400 ml of concentrated HNO3 for 40min . Then, SWCNTS/MWCNTs-COOH were filtered, washed with 600ml distilled water for several times to remove acid, and dried at 105◦C in an oven. During the second step, SWCNTS/MWCNTs-COOH was converted to acid chloride-functionalized SW CNTS/MWCNTs by reflu xing in thionyl chloride for 72 h. Figure 1 shows the Fourier t ransform infrared spectroscopy (FTIR) of carboxy lated MWCNTs, which peaks at 1704cm-1, 1206 cm-1 and 1079 cm-1 corresponding to C=O, C-O-C asymmetric, and C-O-C sy mmetric stretches, respectively. These peaks indicate successful generation of – COOH groups on the CNTs. The CNTs were embedded in t wo commercially availab le thermosetting polyester epoxies LY 5052/ LY 564 with a lo w viscosity and HY 5052/HY 560 hardeners, respectively. 2.2. Preparation of the CNT/epoxy Composite Speci mens SWCNTs and MWCNTs were init ially dispersed into hardener by tip sonication for 30 min to achieve a good dispersion. The sonication process was carried out in pulse mode and sonication power was adjusted at 60% amp litude to avoid over-heating the samp les. The epo xy resin and hardener were mixed at a weight ratio of 100:30. Subsequently, the mixture was stirred with high-speed dispersant under 900rp m for 15 min. The mixture was cast into a metallic mold and cured at 50°C for 15 hour. The prepared composite samp les were then mechanically polished to form s mooth surfaces. Another thermal curing procedure for each samp le was conducted at 100°C for 4 hours to achieve higher mechanical properties of the CNT/epoxy co mposites. Here the assumption is that both SWCNT and MW CNT nanocomposites have been prepared under the same chemical procedure, hence allowing the subsequent statistical analyses to be unbiased. Figure 2 shows a typical Transmission Electron Microscope (TEM) image of MW CNTs. 2.3. Micrography of Tested CNT/epoxy Composites Based on the ASTM D 638 (Type I), unia xia l tensile tests were performed at roo m temperature using Zwick Roel/A msler under a crosshead speed of 1 mm/ min. The dimensions of the specimens were 168 mm in length, 13 mm in width and 5 mm in thickness. Samp les without CNT addition (pure polymer samples) were also fabricated for comparison purposes. To achieve more reliable experimental results, four samples were fab ricated and tested for each wt.% of MWCNTs. Scanning electron microscopy (SEM) was employed to observe the fracture surface of the samples after the tensile tests. Figures 3(a) and 3(b) show the SEM micrographs of fractured surface of the pristine epo xy LY 564 and the 0.5 wt.% functionalized MWCNT/epoxy co mposite, respectively. The fracture surface of the epo xy resin LY 5052 reinforced with 0.5 and 1.0 wt.% of functionalized MWCNTs are also shown in Figures. 4(a) and 4(b), respectively. Figures 3 and 4 indicate that functionalized MWCNTs have been reasonably well d istributed and dispersed in the pure epoxy resin and the original traces of the imbedded MWCNTs can be clearly distinguished from the pattern of the fracture surfaces. In addition, a good interfacial adhesion can be observed due to the extremely low pull out of functionalized MWCNTs fro m the pure polymer matrix. 2.4. Mechanical Properties of the Tested Composites Mechanical properties of CNT/epoxy co mposite specimens made of LY564 and LY5052 poly mers reinforced with 0.25, 0.50, 1.00 and 1.50 wt.% of pristine and functionalized SWCNTs/MWCNTs are plotted in Figure 5, where the average values of four samples are taken into 48 Hossein Rokni et al.: Quantification of M atrix and Reinforcement Effects on the Young’s M odulus of Carbon Nanotube/Epoxy Composites using a Design of Experiments Approach account for each composition. The Young’s modulus of each material configuration is calculated as the average of the slope of the stress–strain curve in the linear reg ion (<2% strain). Figures 5(a) and 5(b) show that the addition of CNTs resulted in an increase in both the Young’s modulus and the tensile strength for all wt.% of CNTs, when compared with the pure polymer samples made of LY5052 and LY564. It should be noted that PSWCNT, FSWCNT, PMWCNT and FMWCNT in Figure 5 represent pristine SWCNT, functionalized SW CNT, pristine MWCNT and functionalized MWCNT, respectively. Figure 1. FTIR spectrum of functionalized CNT s (MWCNT-COOH) Figure 2. TEM micrographs of MWCNT s: (a) low magnification micrograph; (b) high magnification micrograph International Journal of Composite M aterials 2013, 3(6A): 45-57 49 Figure 3. SEM micrographs of fracture surface of (a) pure polymer matrix LY 564, and (b) 0.5 wt.% functionalized MWCNT /epoxy LY 564 composites Figure 4. SEM micrographs of fracture surface of (a) 0.5 wt.% functionalized MWCNT/epoxy LY 5052 composites, and (b) 1.0 wt.% functionalized MWCNT /epoxy LY 5052 composites (a) (b) Figure 5. Mechanical response of the CNT/epoxy composites vs. CNT weight percentage: (a) Young’ modulus, (b) tensile strength. The dashed and solid lines represent the properties of pure epoxy LY5052 and LY564, respectively. PSWCNT, FSWCNT, PMWCNT and FMWCNT represent pristine SWCNT, functionalized SWCNT, pristine MWCNT and functionalized MWCNT, respectively 50 Hossein Rokni et al.: Quantification of M atrix and Reinforcement Effects on the Young’s M odulus of Carbon Nanotube/Epoxy Composites using a Design of Experiments Approach 3. Methodology: Design of Experiments (DOE) DOE is a widely used technique to study different factors affecting the output of an experiment. In fact, DOE helps experimenters conduct a set of experiments strategically in such a way that they can gain the most possible information with min imal effort. 3.1. Mixed-level Factori al Designs One of the most used techniques in DOE is the factorial design in which all the possible comb inations of variables and levels are experimented. In a standard factorial design, all factors (study parameters) have an identical number of levels. If the number o f levels fro m one factor to another is different, however, mixed -level designs should be adapted [33]. In the present study, the two types of polymer matrix (i.e., LY 5052 and LY 564), the two types of CNTs (i.e., SW CNTs and MWCNTs), the two CNT states (i.e., pristine and functionalized SW CNTs/MWCNTs) along with four wt.% of CNTs are considered as the main (controllab le) factors. Table 2 summarizes the chosen two-level DOE used for the first three factors. Each factor takes coded values of –1 and +1 for its low and high levels, respectively. The wt.% of CNTs, on the other hand, is considered to have four possible levels as shown in Table 3. As a result, a mixed-level design of 41×23 (indicating 32 nominal experiments) should be considered. During subsequent statistical analyses, in order to accommodate the latter four-level factor (X) next to the other two -level factors (A, B, C in Tab le 2), an equivalent 22 design with pseudo factors D and E has been used to represent X (Table 3). Taguchi’s approach in the field of DOE is frequently used for robust optimization problems by means of distinguishing between controllable and uncontrobale factors. In the Taguchi approach, experiments are performed at pre-specifed combinations of design runs (e.g., using orthognal arrays, facoraial designs, etc). Results of the experiments are then analysed and compared via the so-called signal-to-noise (S/N) ratios. Formally, a S/N rat io is the measure of the mean square deviation fro m the ideal reposne[33]. A higher S/ N ratio renders a higer robustness in a design. Since the objective of the present work is to maximize the Young’s modulus of the CNT/epo xy co mposites, a “larger-the-better” type of S/N is adapted as follows[34]. ∑ S N = −10 log 1 n n i=1 1 yi2 (1) where yi denotes the individual response variable at the i-th experimental point and n is the number of test repeats. The effect of noise factors is embedded in the non-repeatability of data observed during repeats of a test. 3.3. Designing and Running the Experi ments In view of descriptions in Sections 3.1 and 3.2, the test matrix along with the obtained experimental results for the Young’s modulus of the CNT/epo xy co mposites for all factor co mbinations are summarized in Table 4. A total of 128 experiments (32 runs mult ipled by 4 repeats) were run in a random order as indicated in the table footnote. The high resolution of the 25 factorial design[33] allows us to estimate all main and interaction effects during the subsequent statistical analysis as follows. 3.2. A Taguchi Analysis Method Table 2. DOE used for two-level control factors Fact ors Labels Factor levels Low level (–1) High level (+1) Polymer type A LY 564 – HY 560 LY 5052 – HY 5052 CNT type B CNT state C MWCNT Prist in e SWCNT Fun ct ion alized Table 3. The equivalent 22 design used the four-level factor Four-level factor Wt .% of CNTs (X) x1=0.25 x2=0.50 x3=1.00 x4=1.50 T wo-level pseudo factors D E –1 –1 +1 –1 –1 +1 +1 +1 International Journal of Composite M aterials 2013, 3(6A): 45-57 51 Table 4. Young’s modulus (GPa) of CNTs-reinforced polymer composites Control factors Run A B C (D E) = X 1 –1 –1 –1 –1 –1 ????????1 2 +1 –1 –1 –1 –1 ????????1 3 –1 +1 –1 –1 –1 ????????1 4 +1 +1 –1 –1 –1 ????????1 5 –1 –1 +1 –1 –1 ????????1 6 +1 –1 +1 –1 –1 ????????1 7 –1 +1 +1 –1 –1 ????????1 8 +1 +1 +1 –1 –1 ????????1 9 –1 –1 –1 +1 –1 ????????2 10 +1 –1 –1 +1 –1 ????????2 11 –1 +1 –1 +1 –1 ????????2 12 +1 +1 –1 +1 –1 ????????2 13 –1 –1 +1 +1 –1 ????????2 14 +1 –1 +1 +1 –1 ????????2 15 –1 +1 +1 +1 –1 ????????2 16 +1 +1 +1 +1 –1 ????????2 17 –1 –1 –1 –1 +1 ????????3 18 +1 –1 –1 –1 +1 ????????3 19 –1 +1 –1 –1 +1 ????????3 20 +1 +1 –1 –1 +1 ????????3 21 –1 –1 +1 –1 +1 ????????3 22 +1 –1 +1 –1 +1 ????????3 23 –1 +1 +1 –1 +1 ????????3 24 +1 +1 +1 –1 +1 ????????3 25 –1 –1 –1 +1 +1 ????????4 26 +1 –1 –1 +1 +1 ????????4 27 –1 +1 –1 +1 +1 ????????4 28 +1 +1 –1 +1 +1 ????????4 29 –1 –1 +1 +1 +1 ????????4 30 +1 –1 +1 +1 +1 ????????4 31 –1 +1 +1 +1 +1 ????????4 32 +1 +1 +1 +1 +1 ????????4 Young’s modulus (GP a) 3.1641* 3.27110 3.45123 3.56119 3.2191 3.4729 3.6760 3.7759 3.3812 3.5279 3.7397 3.8643 3.4877 3.784 3.8822 3.9336 3.5865 3.7815 4.0453 4.1292 3.7738 3.8871 4.1010 4.2085 3.8520 3.99102 4.10117 4.2370 3.9118 4.11107 4.1533 4.2456 3.1454 3.25127 3.335 3.5125 3.1935 3.3881 3.5878 3.68103 3.3780 3.5013 3.6832 3.8257 3.461 3.6961 3.84128 3.9172 3.548 3.7245 3.9668 4.0827 3.7187 3.8496 4.093 4.14125 3.7749 3.95120 4.026 4.1093 3.8963 4.0552 4.1175 4.2017 3.1288 3.2346 3.31104 3.5050 3.16109 3.3066 3.4731 3.5773 3.3548 3.45105 3.582 3.6830 3.4167 3.55108 3.70113 3.85111 3.5234 3.6295 3.7324 3.9462 3.6742 3.7014 3.95106 4.0476 3.7269 3.81112 3.8683 3.9786 3.83114 3.9521 3.9784 4.0694 * Superscript numbers represent the (random) order of experimentation used 3.0211 3.13116 3.2716 3.4982 3.1526 3.26122 3.4440 3.5490 3.349 3.44115 3.4355 3.6789 3.4039 3.5398 3.6947 3.8319 3.51118 3.46124 3.7099 3.937 3.65121 3.6951 3.9164 4.0023 3.6374 3.7958 3.60100 3.7244 3.81101 3.9137 3.95126 4.0428 Eavg (GP a) 3.1100 3.2200 3.3400 3.5150 3.1775 3.3525 3.5400 3.6400 3.3600 3.4775 3.6050 3.7575 3.4375 3.6375 3.7775 3.8800 3.5375 3.6450 3.8575 4.0175 3.7000 3.7775 4.0125 4.0950 3.7425 3.8850 3.8950 4.0050 3.8600 4.0050 4.0450 4.1350 Estd (GP a) 0.0622 0.0622 0.0775 0.0311 0.0275 0.0929 0.1055 0.1055 0.0183 0.0386 0.1323 0.0967 0.0386 0.1187 0.0967 0.0476 0.0310 0.1399 0.1682 0.0967 0.0529 0.0967 0.0967 0.0915 0.0922 0.0998 0.2205 0.2176 0.0476 0.0915 0.0998 0.0998 S/N ratio (dB) 9.8512 10.1534 10.4698 10.9177 10.0410 10.5000 10.9715 11.2139 10.5265 10.8241 11.1246 11.4915 10.7236 11.2057 11.5377 11.7752 10.9732 11.2192 11.7076 12.0735 11.3621 11.5377 12.0626 12.2402 11.4573 11.7814 11.7776 12.0224 11.7303 12.0470 12.1324 12.3238 4. Results and Discussion 4.1. The Effect of Control Factors and Checking the Model Assumpti ons The standard analysis of variance (ANOVA )[33] was emp loyed to determine factors that have had statistically a significant effect on the Young’s modulus of the tested CNT/epoxy co mposites. Before any inferences are drawn fro m the analysis, however, let us check the main assumptions underlying standard ANOVA processes. The two main assumptions in this regard are the normality and randomness of the measurements to ensure the independence of test data (for more details of underly ing assumptions in a standard ANOVA, p lease see[33]). Figures 6 and 7 depict the normal probability plots and the random distribution of data for the Young’s modulus response on the basis of the S/N ratio and mean values responses, respectively. It should be noted that the S/N response is normally used in robust design/optimization practice, whereas the mean response (i.e., signal only ) is normally used in the absence of large noise effects. For co mparison purposes in the present case, we emp loy both of these response types. The distributions of obtained residual errors along the (theoretical) normal line, and also the random distribution of data points versus the run order, ensure the reliability of the performed ANOVA. Next, to study the significance of control factors and their interactions, results of ANOVA fo r the S/ N ratio and the mean response of the Young’s modulus are summarized in Tables 5 and 6, respectively. The analysis is undertaken for a minimu m confidence level of 95%. Any p-value less than 52 Hossein Rokni et al.: Quantification of M atrix and Reinforcement Effects on the Young’s M odulus of Carbon Nanotube/Epoxy Composites using a Design of Experiments Approach 0.05 in the ANOVA table indicates that the effect o f the respective factor is significant, with a 95% confidence at least. The sum of squares (SS) for the factors including the mixed-level factor X were obtained as follo ws, SSX = SSD + SSE + SSDE SSAX = SSAD + SSAE + SSADE SSBX = SSBD + SSBE + SSBDE (2a -d) SSCX = SSCD + SSCE + SSCDE The primary conclusion fro m Tables 5 and 6 is that the contributions of the main factors and the interactions obtained on the basis of the S/N ratio and mean responses are in close agreement. Fro m a DOE analysis point of view, this suggests that in the present case study, the effect of noise (random/uncontrollable) factors have been min imal. Hence, in the subsequent sections the S/N response is followed only. The obtained percentage contribution values in Table 5 (or Table 6) can be used to evaluate the importance of a change in the main and interaction factors on the Young’s modulus response. It can be observed that the main effects, including the types of poly mer (factor A), the types of CNTs (factor B), functionalized/pristine CNTs (factor C) and different wt.% of CNTs (factor X), significantly affect the Young’s modulus of the CNT/epo xy co mposite. All factors interactions, except for the interaction BX, have almost no effect on the Young’s modulus of the composite. The main factor effects together with the BX interaction effect account for mo re than 99% of the variability in the material’s elastic modulus. It is clear, however, that factors B and X are dominant and they can be primarily used during the fabrication of the CNT/epoxy co mposites to control their Young’s modulus by more than 85%. This result is also in accordance with earlier results in Table 1. Additionally, the fact that the interaction between these factors is found to be minimal, means that the analyst for the stiffness improvement of the nanocomposite can confidently vary a main factor without concerning about the effect fro m the other factor. The ‘adequate precision’ values reported in Tables 5 and 6 compare the range of the predicted values at the design points to the average prediction erro r. A ratio greater than 4 indicates adequate model discrimination[33]. In the conducted ANOVAs, the adequate precision values were well above this threshold. Tables 5 and 6 also include other adequacy measures, namely R2 and adjusted R2 , to confirm the significance of the statistical models emp loyed. Table 5. Result s of the ANOVA on the Young’s modulus based on S/N rat ios Fact or A B C X AB D.O.F. 1 1 1 3 1 Sum of Square 0.7435 3.0680 0.7918 9.0390 0.0034 Variance 0.7435 3.0680 0.7918 3.0130 0.0034 Fratio 165.22 681.78 106.84 175.96 0.76 AC 1 AX 3 BC 1 BX 3 0.0031 0.0208 0.0030 0.2659 0.0031 0.0069 0.0030 0.0886 0.69 1.53 0.67 19.69 CX 3 Error 13 Tot al 31 0.0014 0.0586 13.9985 0.0005 0.11 0.0045 R2 = 0.907; Adjusted R2 = 0.877; Adequate precision = 20.026 P-value 0.000 0.000 0.000 0.000 0.398 0.419 0.123 0.432 0.000 0.745 Co ntribut io n% 5.3113 21.9168 5.6564 64.5717 0.0243 0.0221 0.1486 0.0214 1.8995 0.0100 0.4186 Significance level Significant Most significant Significant Most significant No effect No effect No effect No effect Least significant No effect Table 6. Results of the ANOVAon the Young’s modulus based on mean values Fact or A B C X AB AC AX BC BX CX Error Tot al D.O.F. 1 1 1 3 1 1 3 1 3 3 13 31 Sum of Square 0.13101 0.54928 0.13814 1.58852 0.00033 0.00033 0.00171 0.00083 0.03847 0.00001 0.01001 2.45864 Variance 0.13101 0.54928 0.13814 0.52951 0.00033 0.00033 0.00057 0.00083 0.01282 0.00001 0.00077 R2 = 0.990; Adjust ed R2 = 0.981; Adequat e precision = 40.313 Fratio 87.01 364.81 91.75 350.67 0.22 0.22 0.74 0.55 16.65 0.00 P-value 0.000 0.000 0.000 0.000 0.647 0.647 0.403 0.470 0.000 0.991 Co ntribut io n% 5.329 22.341 5.619 64.610 0.013 0.013 0.070 0.034 1.565 0.000 0.407 Significance level Significant Most significant Significant Most significant No effect No effect No effect No effect Least significant No effect International Journal of Composite M aterials 2013, 3(6A): 45-57 53 4.1.1. Main and Interaction Effect Plots: Determining the Optimu m Material Configuration The average of S/N ratios at each factor level fro m Table 5 were calculated and listed in Table 7. Delta values (absolute difference between the responses at high and low levels) are used in Table 7 as a criterion fo r ran king the control factors. The factors with higher delta values indicate greater impact on the response. Accordingly, the ma in factors can be ranked as E > B > D > C > A. Th is ranking could also be made through the percentage contribution of each factor, given in Tables 5 and 6. Next, using the values in Table 7, the main effect plots were established as shown in Figure 8(a). The plots indicate that all the four factors A, B, C and X (which is represented by a combination of D and E) have positive effects (positive slopes). Hence, if only the main effects are taken into account, they should be set at their high level to maximize the Young’s modulus of the CNT/epoxy co mposites. This means that the highest Young’s modulus (i.e., 4.135 GPa) is obtained for functionalized SWCNT/epo xy-LY5052 composites with 1.5 wt.% of CNTs. Based on Figure 8(a) for factor C, the improvement seen in response of the functionalized CNT/epo xy co mposites compared to the ones with pristine CNTs would also prove a better dispersion of the functionalized CNTs in the poly mer matrix. Similarly, all possible two-factor interactions are plotted in Figure 8(b). It is seen fro m this figure that there are so me interactions between the main factors B and D, B and E as well as D and E, though statistically they are not of high significance as measured by the ANOVA analysis in Table 5. It is worth noting from the BD and BE interactions that the effect of wt.% of CNTs is small when the SWCNTs are used, and is large when the MWCNTs are introduced to the polymer matrix. Although Tables 5 and 6 show that the BC interaction factor has a very low contribution, Figure 8(b) reveals the fact that the functionalizat ion has less effect on the enhancement of the Young’s modulus in the MWCNT/epo xy co mposites, when co mpared to the SWCNT/epoxy co mposites. Similarly, in spite of the lack of statistically significant interaction between factors A and E, it can be deduced from the A E interaction plot in Figure 8(b) that the effect of wt.% of CNTs on the pure polymer LY5052 is smaller than that of LY564. Finally, it is worth recalling that a main advantage of Taguchi DOE is that it relies on a robust optimization approach by taking into account both controllable and uncontrollable (noise) factors. This is done through making use of statistical information fro m repeats of a test and defining a signal-to-noise index as in Eq. (1). Revisiting Table 4, it is noticed that the highest Young’s modulus (4.1350 GPa) has been obtained for the factor co mbination (run) #32 where all the experimental factors are set at level ‘+1’. Ho wever, this point has also had the highest standard deviation in the corresponding column. Thus for the analyst to make a final decision regarding both the average performance and robustness of the design points, S/N ratios should be employed. If the analysis only relies on the average response, non-robust points/material factors may be ch os en . Table 7. Average S/N ratios of Young’s modulus at each factor level S/N levels Low level A 11.15 Control factors B C D 11.00 11.15 11.08 E 10.83 High level 11.46 11.62 11.46 11.53 11.78 Delt a 0.31 0.62 0.31 Rank 5 2 4 0.45 0.95 3 1 4.2. A more in-depth Discussion on the Effect of Noise Factors Section 4.1 presented the analysis of test data regarding the effect of controlled parameters during the fabrication of CNT/epoxy co mposites. As shown through the obtained ANOVA results in Tables 5 and 6, the overall effect of noise factors (aggregated in the error term in ANOVA ) have been insignificant for the performed experiments. Pract ically speaking, a variety of factors includ ing the CNT waviness, the random orientation of CNTs, inappropriate CNT dispersion within the matrix, and debonding between CNTs and the matrix can be sources of erro r and cause variab ility in the Young’s modulus of the CNT/epo xy co mposites. Since these factors have been uncontrollable during the manufacturing process of the tested specimens, they are considered as noise. To exemplify the presence of these effects, Figure 9(a) shows a typical non-uniform dispersion of PMWCNTs 1.0 wt.% embedded in the epoxy LY 564 due to the van der Waals interactions. Similarly, TEM micrograph of the d ispersed MWCNTs in ethanol shows the presence of waviness of the CNTs, Figure 9(b). Often experimenters are curious to know which ‘control’ factor would result in the highest or lowest magnitude of variability in the material response through its possible interactions with uncontrollable noise factors. Subsequently, appropriate control factors can be chosen to min imize data variability wh ile imp roving the mean response of the material. In order to quantify the effect of noise factors on the Young’s modulus of the tested composite samples, the standard deviation values of Table 4 may be used as a measure of variability. For a given combination of control factors (i.e., each ro w in Table 4), a higher standard deviation indicates a higher variab ility in the mean Young’s modulus response. Consequently, Table 8 was established to present the mean standard deviation of the Young’s modulus over low and high levels of each control factor. It is noteworthy from Table 8 that the variability seems to be the highest when the type of CNT (factor B) is set at its high level (i.e., SW CNT). Similarly, it can be seen that the variability is the least when the type of the polymer (factor A) is set at its lo w level (i.e., LY 564 – HY 560 resin). Finally, Figure 10 was plotted based on the values of Table 8, to 54 Hossein Rokni et al.: Quantification of M atrix and Reinforcement Effects on the Young’s M odulus of Carbon Nanotube/Epoxy Composites using a Design of Experiments Approach further indicate the positive effect of functionalization of the variability in the material response. CNT surface (i.e., high leve l of factor C) in yie lding a lower Mean levels Low level High level Delt a Rank Table 8. Mean standard deviation of Young’s modulus at each cont rol factor level A 0.08547 0.09542 0.00996 5 B 0.06941 0.11148 0.04207 1 Control factors C 0.09905 0.08184 0.01721 3 D 0.08362 0.09727 0.01364 4 E 0.07199 0.10890 0.03691 2 (a) (b) Figure 6. (a) The variation of residuals versus observation order, and (b) the normal probability plot of residuals based on the S/N ratios (a) (b) Figure 7. (a) The variation of residuals versus observation order, and (b) the normal probability plot of residuals based on the mean response (a)

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