On the Multi-Parameter Experimental Investigation of Curing Cycle for Glass Fabric/Epoxy Laminated Composites.
Epoxy matrix composites are of the most commonly used polymer matrix composites for all different types of reinforcement. In epoxy composites production the curing process plays a key role due to the great number of properties which are affected or controlled by this process [1, 2]. Therefore, the affecting parameters for the curing process, such as curing temperature and time, have been widely investigated [3, 4, 5, 6, 7, 8, 9] in research efforts to accurately control the result of a curing process. Moussa et al.  have extended an existing model for predicting temperature-dependent mechanical properties in order to additionally describe the recovery behavior of cold curing structural adhesives. Maljaee et al.  present an investigation addressing the effect of environmental conditions on the thermal properties of a cold curing epoxy resin used in repair and strengthening of masonry structures. The exposure conditions consist of laboratory indoor conditions (IC), long-term water immersion (WI), hygrothermal exposure (HG) and outdoor real exposure conditions (OC). It was observed that the changes of Tg in OC conditions in the studied environment have a good correlation with the moisture absorption level and the obtained results from WI tests. In another work conducted by Chang et al. , compression resin transfer molding (CRTM), combining resin transfer molding (RTM) and compression molding, have been developed to fabricate fiber reinforced plastic (FRP) components with large dimensions or high fiber volume content. Experimental results shown that the compression pressure and the resin temperature are significant variables for improvements in the mechanical properties of the part, while the effect of pre-heated mold temperature on the mechanical properties appears to be trivial. In a previous work of Oh and Lee , the temperature profiles of a 20 mm thick unidirectional glass/epoxy laminate during an autoclave vacuum bag process were measured and compared with the numerically calculated results. From the experimental and numerical results, it was found that the measured temperature profiles were in good agreement with the numerical ones, and conventional cure cycles recommended by prepreg manufacturers for thin laminates should be modified to prevent temperature overshoot and to obtain full consolidation. Finite element simulation of the heat transfer, curing reaction, and consolidation in the laminate was used by Li et al.  to find optimal autoclave temperature and pressure histories for curing of thermoset-matrix composite laminates. In this study the objective is to minimize the total time of the cure cycle, while the constraints include a maximum temperature in the laminate (to avoid thermal degradation) and a maximum deviation of the final fiber volume fraction from its target value. Another finite elements approach was presented by Yang and Lee  to calculate optimized cure cycles which can be developed for thick laminates. Additionally, several attempts have been made to optimize the applied curing cycles [10, 11, 12, 13].
The relation between the curing temperature ([T.sub.C]) and the glass transition temperature ([T.sub.g]) has been found to be of great importance for the curing process , since it controls the applied curing mechanism. However, the research in this field was not limited to the traditional curing processes. The use of alternative curing processes, such as curing with microwaves, was always part of the research in this field and can be found both in older  and recent studies [16, 17, 18, 19, 20, 21].
Taguchi analysis is one of the most commonly used techniques for prediction of the response of the examined composites. For instance, the Taguchi method has been used to investigate the influence of amount, size and presence of surface treatment on the performance of the examined materials . It also has been used together with finite element analysis in order to investigate the importance of V-ring indenter parameters . In another application, Taguchi method was used together with response surface method to determine the optimum machining conditions leading to minimum surface roughness in drilling of GFRP composite . Taguchi design has also seen service in the development of multiphase hybrid composites consisting of epoxy reinforced with glass-fiber and filled with rice husk particulates .
Taguchi method is followed by Analysis of Variance (ANOVA) and a calculation of Regression or Multiple Regression models in order to create an effective prediction model. Among the commonly used Multiple Regression Analyses, which occurs from many different regression models [22, 26, 27, 28], some efforts have been made to achieve highly accurate multiple regression models [28, 29]. However, the regression models used in the fields of composites manufacturing and machining are quite trivial and their accuracy is in most of the cases quite low.
In this study, a multi-parameter analysis, using Taguchi method for design of experiments, has been conducted to investigate the optimum curing conditions for E-glass fabric/epoxy laminated composites. The independent variables in the [L.sub.25] Taguchi orthogonal array were heating rate a, curing temperature [T.sub.C] and curing time [t.sub.C], addressing five levels each. Tensile and 3-point bending tests were performed for each experiment number (run number) of the Taguchi [L.sub.25]. According to the analysis of variance, the significant parameters for both tensile and flexural performance were [T.sub.C] and [t.sub.C], at a 95% confidence level. The estimated values of the curing parameters for optimum tensile and flexural performance were calculated with an estimation error considerably lower than 1%. Three different Multiple Regression models, combined with backward elimination, were examined. Two commonly used models were failed to accurately predict both tensile and flexural behavior of the cured composites ([R.sup.2] [approximately equal to] 65%). However, these widely used regression models achieved a quite low accuracy. The improvement of the regression models' accuracy came by introducing the use of a regression analysis method that is very common in epidemiology, sociology and psychology, i.e. Poisson regression. Therefore, in order to achieve a highly accurate regression model, a Poisson Regression model was introduced, [R.sup.2] of which was greater than 97% for the prediction of both tensile and flexural values.
The recorded accuracy of the currently used multiple regression models used in this field hardly achieve a value of 65%-70%. Therefore, in this study, the use of Poisson regression model is introduced to achieve considerably higher accuracy, which surpass in this case the value of 97%. Thus, such a regression model of such an accuracy could be a helpful tool for the researchers, in order to develop a reliable technique for the prediction of the mechanical properties of composite materials under development.
The Araldite GY 783 low-viscosity epoxy resin was used for the present study. In order to produce the matrix epoxy system for the composite specimens, it was combined with the low-viscosity, phenol free, modified cycloaliphatic polyamine hardener. The glass transition temperature ([T.sub.g]) was 100 [degrees]C and the pot life (i.e. the period during which viscosity is observed to be independent of time and, therefore, may be safely used) at 20 [degrees]C and 65% relative humidity (RH) was 35 min. The aforementioned conditioning requirements were obeyed during the preparation of all composites laminates. Woven E-glass fabric of 282 g/[m.sup.2] density was used for matrix reinforcement. The characteristics of the fabric used can be found in Table 1. An explosive view of the fabrication process, in which both layer sequence and fabric orientations of the composites laminates tested are presented, is shown in Figure 1. Since the warp direction is the enhanced one, see Table 1, it is clear that this is the main weave direction and, therefore, the laminae orientations in the stacking sequence of the composites were based on the warp direction.
Taguchi Design of Experiments
In order to study the entire process parameter space with a small number of experiments only, Taguchi's method uses a special design of orthogonal arrays . The Taguchi approach is a more effective method than traditional design of experiment methods such as factorial design, which is resource and time consuming. With this method the number of experiments to evaluate the influence of control parameters on certain quality properties or characteristics is markedly reduced compared to a full factorial approach.
In general, Taguchi method considers the interactions between all different parameters. In this case, the effect of these interactions is lower than 1% and, therefore, it should not be considered. Moreover, it is already known that it is more convenient, and almost equally effective, to use Taguchi method in order to determine the influence of the parameters (and the interactions between them, if they are significant), because the number of measurements is significantly lower in this case, as compared to the respective one in the case of the full factorial method .
In the calculation of the loss function there are three ways of transformation depending on the desired characteristic of the measured value. The characteristic of the desired value can either be the-lower-the-better, the-higher-the-better or the-nominal-the better. The loss function of the "the-higher-the-better" quality characteristic ([y.sub.k]), which was used for this study, with m as the mean of the target quality parameter is calculated as shown in Equation 1 where [L.sub.ij] is the loss function of the [i.sub.th] performance characteristic in the [j.sub.th] experiment.
[mathematical expression not reproducible] Eq. (1)
In the Taguchi method, the S/N ratio [n.sub.ij] for the [i.sub.th] performance characteristic in the [j.sub.th] experiment, which can be calculated using Equation 2, is used to determine the deviation of the performance characteristic from the desired:
[n.sub.ij] = - 10log([L.sub.ij]) Eq. (2)
Regardless of the category of the performance characteristic, a larger S/N ratio corresponds to a better quality performance. Therefore, the optimal level of the process parameters is the level with the highest S/N ratio [32, 33].
The most important step in a design of experiments is the selection of control factors. Factors such as heating rate (a), temperature ([T.sub.c]), time ([t.sub.c]) affect the mechanical behavior of an epoxy matrix and, consequently, of a laminated composite. The impact of these three factors on tensile and flexural strength of glass fabric/epoxy laminated composites is studied in this work using an [L.sub.25] orthogonal array design. The selected levels of the three control factors are listed in Table 2.
Preparation of E-Glass Fabric/Epoxy Laminated Composites
To create the matrix mixture, weighed amounts of hardener were added into the epoxy resin (monomer) at the manufacturer recommended monomer/hardener proportion, which was a 100:50 by weight ratio. Subsequently, the mixture was stirred gently using a laboratory mixer for mechanical stirring for 5 min at 200 rpm and, then, the matrix mixture was coated and hand-rolled on E-glass fabrics in layer sequence under constant stirring . For each hand lay-up procedure, four layers of E-glass fabric were employed in [[0[degrees]/45[degrees]/-45[degrees]/0[degrees]].sub.T] sequence. The surface on which the specimens were produced was covered by release paste wax, in order to facilitate the release of the laminated composites after solidification. Figure 1 shows the hand lay-up procedure applied in explosive view mode. All composite specimens of this study were of 40 [+ or -] 1% by volume epoxy proportion. To achieve this proportion in all specimens, both the fabric and the matrix mixture used for coating were weighed before each hand lay-up process and after solidification.
For each experiment number (run number) of the Taguchi design of experiments, see Table 3, five specimens were prepared and underwent each test (i.e. tensile and 3-point bending test). The specimens which underwent 3-point bending tests were 93.6 x 12.7 x 1.1 mm, as in accordance with ASTM D790-03 test method. The size of the specimens which underwent tensile tests was 102 x 6 x 1.1 mm according to ASTM D3039/3039 M. All specimens were cut at their testing dimensions using a Struers Discotom-2 along with a 40A25 cut-off wheel. To evaluate the necessity of tabs on the specimen regions which were held in the grips, the theoretical tab limits were marked on the specimens, as recommended from the ASTM standard tensile method used. Thus, if the failure was detected in the theoretical control area (between the two theoretical tab limits) no tabs were needed. As can be easily observed in Figure 2, the failure occurred into the theoretical control area and, therefore, no tabs were recommended by the ASTM standard used.
The pot life is the period during which the viscosity of the epoxy system (liquid mixture of epoxy resin and hardener) is observed to be independent of time and, therefore, it may be safely used. For the epoxy system used in this study, i.e. the Araldite GY 783 low-viscosity epoxy resin combined with a low-viscosity, phenol free, modified cycloaliphatic polyamine hardener at the monomer/hardener proportion of 100:50 by weight, the pot life at the preparation room conditioning (20 [degrees]C and 65% relative humidity) was 35 min. After the end of the pot life of the epoxy matrix a three-step curing cycle was applied. Specifically, before the curing conditions of the Taguchi design of experiments, as they are described in Table 3, were applied, all specimens were left in ambient temperature for 6 hours (step 1). Subsequently, a ramp step (step 2) was applied employing five different levels (values) for the first variable of the Taguchi design, which was the heating rate a [[degrees]C/min] of this step. It was expected that heating rate would be the less important parameter, since an epoxy system for general application was used in this study. However, as it will become clear during the following analysis, the use of this parameter in a regression model can significantly increase its accuracy. The final step of the curing cycle used (step 3) was the second curing plateau (the first was the 6 hours plateau of step 1 at ambient conditions). The temperature and the duration of this plateau were considered as independent parameter for the Taguchi design, employing five levels each. The importance of both parameters of this step was expected to be high, since both temperature and time of a curing process are the most effective parameters, as regards the mechanical properties of the cured composites. However, the use of only these two important parameters in a regression model will lead to a low accuracy prediction model. A general diagram describing the complete curing cycle applied is presented in Figure 3. Parameter a, [T.sub.C] and [t.sub.C] represent the heating rate [[degrees]C/min], the curing temperature [[degrees]C] and the curing time [h], respectively. The selected values (i.e. the levels) for each under study parameter are given in Table 2.
It is well known that three different curing mechanisms can be met. The existence of each mechanism is controlled by the correlation between the curing temperature ([T.sub.C]) and the glass transition temperature ([T.sub.g]) [3, 4, 5]. Specifically, curing temperature ([T.sub.C]) can be [T.sub.C] > [T.sub.g], [T.sub.C] = [T.sub.g] or [T.sub.C]<[T.sub.g]. For each correlation between curing temperature and glass transition temperature a different curing mechanism takes place. In the first case, i.e. when [T.sub.C] > [T.sub.g], the reaction is rapid and its rate is driven by chemical kinetics. In the second case, i.e. when [T.sub.C] = [T.sub.g], vitrification takes place (i.e. material solidifies). Finally, in the case of [T.sub.C] < [T.sub.g], the reaction rate decelerates and becomes diffusion-controlled. For the epoxy system used, the glass transition temperature ([T.sub.g]) was 100 [degrees]C. In order to include all the above mechanisms in the Taguchi design of experiments used in this study, the [T.sub.g] temperature as well as two different temperatures under [T.sub.g] and two different temperatures over it were selected.
Experimental Set-up and Tests
An Instron 4482 test machine of 100 kN capacity was used for both tensile and 3-point bending tests. In accordance with D790-03 and D3039/3039 M ASTM standard methods, all tests were performed in the standard laboratory atmosphere of 23 [+ or -] 1 [degrees]C and 50 [+ or -] 5% RH (Relative Humidity). Test conditioning was kept constant for 6 hours before each test. The support span was set at 52 mm for the flexural tests, in order to meet the test method's span-to-depth ratio requirement. The test speed of 2 mm/min was applied on both tensile and 3-point bending tests, as recommended from the ASTM methods used.
Analysis of Variance (ANOVA)
Analysis of variance (ANOVA) is a statistical tool by the use of which two tasks of great importance for a statistical analysis can be conducted. ANOVA examines the hypothesis that the means of two or more populations are equal and, subsequently, it evaluates the significance of one or more factors. For this reason, it compares the response variable means at the different factor levels.
In this study, the significant factors for both tensile and flexural performance were temperature and time at 95% confidence level, see Tables 4 and 5. Specifically, the tensile performance is affected almost equally by both curing temperature and time (32.71% and 35.89%, respectively). The flexural performance is mostly affected by curing temperature (44.02%) and secondarily by curing time (31.52%). The main effects plot for the main effect terms in tensile load and flexural strength for factors a, [T.sub.C], and [t.sub.C] are shown in Figures 4 and 5, respectively. The results of the above analysis were confirmed performing additional tests. The confirmation tests with the maximum error are presented in Tables 6 and 7. The maximum error achieved was considerably lower than 1% in both cases. The optimal values can be predicted using Equation 3 .
[mathematical expression not reproducible] Eq. (3)
where: [[eta].sub.m] is the total mean of the response (tensile load and flexural strength, respectively) and characteristic under consideration; [[eta].sub.i] is the mean values at the optimum level and q is the number of control factors that significantly affects curing process of composite.
Multiple Regression Analysis
Regression analysis is a statistical process for approximating the relationships between variables. It is a method for modelling different variables. It helps to understand how the dependent variable deviates when any one of the independent variables is changed . In this study, three different Multiple Regression Models (scenarios) were used for analysis and comparison: a commonly used multiple regression model involving only the significant factors, the same regression model as before involving all the factors this time and a Poisson regression model (which employees a logarithmic transformation and is widely used in epidemiology, sociology and psychology).
Backward elimination applied to all possible combinations (up to fourth order) of the variants included in the regression of each scenario. The effect of removing a variable on residual mean square ([MS.sub.re]) was assessed for each variable, and the variable with the least effect on increasing [MS.sub.res] was removed if it did not increase the [a.sub.out] ratio for removal. For all three scenarios [a.sub.out] was set equal to 0.1. The process continued until removal caused a significant change in [MS.sub.res], when that variant was left in and no further removals were done.
Results and Discussion
Scenario 1 (Commonly Used Regression Model Involving Only Significant Factors)
In this first Scenario, Multiple Regression Analysis was carried out for tensile load and flexural strength using a commonly used Regression method , i.e. using the model of Equations 4 and 5_ and taking only significant factors ([T.sub.C], [t.sub.C]) as independent variables. Normal probability of regression equations for tensile load and flexural strength are plotted in Figure 6.
Tensile load = 2439.95 + 8.86 x [T.sub.C]-0.26 x [T.sub.C] x [t.sub.C]+ 0.01 x [t.sub.C ]Eq. (4)
Flexural strength = 0.01 + 2.68 x [T.sub.C] + 32.37 x [t.sub.C] -0.20 x [T.sub.C] x [t.sub.C ]Eq. (5)
A comparison between the experimental results and the theoretical values (calculated using the Regression Models of Scenario 1) is provided in Figures 7 and 8. It is clear that, even if the trendline is almost the same in both cases and therefore the model can predict the trend for tensile and flexural performance, the accuracy of the Multiple Regression Models of this scenario is quite low. Specifically, in both the tensile and flexural case, [R.sup.2] is about 0.65 or 65%.
Scenario 2 (Commonly Used Regression Model Involving All Factors)
In this Scenario, Multiple Regression Analysis was carried out for tensile load and flexural strength using the same commonly used Regression method as in Scenario 1, but involving all the factors of the Taguchi [L.sub.25] (a, [T.sub.C], [t.sub.C]) as independent variables. The regression equations of this scenario are presented below, see Equations 6 and 7. Normal probability of regression equations for tensile load and flexural strength are plotted in Figure 9.
Tensile load = 2311-432 x a + 0.08 x [T.sub.C]+413 x [t.sub.C] + 6.63 x [T.sub.C] x a-45.4 x a x [t.sub.C]-2.53 x [T.sub.C] x [t.sub.C ]Eq. (6)
Flexural strength = 135 + 81.8 x a + 1.176 x [T.sub.C] + 51.4 x [t.sub.C]+0.781 x [T.sub.c] x a-0363 x [T.sub.c] x [t.sub.C ]Eq. (7)
A comparison between the experimental results and the theoretical values (calculated using the Regression Models of Scenario 2) is provided in Figures 10 and 11. It can be easily observed that the accuracy of the Multiple Regression Models of this scenario is considerably increased in comparison with the respective one of Scenario 1. Specifically, in both the tensile and flexural case, [R.sup.2] is about 0.70 or 70%.
Scenario 3 (Poisson Regression Model Involving All Factors)
Poisson regression is a regression method, which employees a logarithmic transformation that compensates for skewness, prevents a negative predicted value, and also includes the proportionality between variance and the mean .
Therefore, if a Poisson distribution is considered for Y, then a log-linear model can be constructed as
lnY = [alpha] + [[beta].sub.1][X.sub.1] +[[beta].sub.2][X.sub.2] + [[beta].sub.k ][X.sub.k] Eq. (8)
However, due to the fact that the prediction is in terms of log counts, this form can be difficulty used, because in practice actual counts are needed. In order to handle this difficulty, both sides have to be exponiated.
[mathematical expression not reproducible]
[mathematical expression not reproducible] Eq. (10)
In this form, the predicted value of Y is in counts.
Poisson regression analysis, together with backward elimination, was carried out for tensile load and flexural strength taking all factors (a, [T.sub.C], [t.sub.C]) as independent variables. In the case of flexural strength regression model, only the significant factors ([T.sub.C], [t.sub.C]) were kept, since the heating rate factor (a) was eliminated by the backward elimination process. Normal probability of regression equations for tensile load and flexural strength respectively are plotted in Figure 12.
The regression equations of this scenario are presented in Equations 11 and 12.
Tensile load = [mathematical expression not reproducible] Eq. (11)
[Y'.sub.1]=-0.3-8.8xa + 0.524x[T.sub.C]-0.83x[t.sub.C]+0.784 x [a.sup.2] -0.002901x[T.sub.C.sup.2] + 1.547x[t.sub.C.sup.2] + 5.31xax [t.sub.C] -0.1979 x [T.sub.C] x[t.sub.C] +0.000003 x[T.sub.C.sup.3]-0.285 x[t.sub.C.sup.3] -0.3327 xax[t.sub.C.sup.2] + 0.00099x[T.sub.C.sup.2]x[t.sub.C]+0.01975x[T.sub.C]x[t.sub.C.sup.2] + 0.0153x[t.sub.C.sup.4] + 0.03159x[a.sup.2]x[t.sub.C.sup.2] + 0.126xax[t.sub.C.sup.3] -0.000001x[T.sub.C.sup.3]x[t.sub.C]-0.000064x[T.sub.C.sup.2]x[t.sub.C.sup.2] -0.000481 x[T.sub.C]x[t.sub.C.sup.3] -0.00573xax[t.sub.C.sup.4]
Flexural strength = [mathematical expression not reproducible] Eq. (12)
[Y'.sub.2]=4.6336 + 0.009461x[T.sub.C]+0.1188x[t.sub.C]-0.000792x[T.sub.C]x[t.sub.C]
Taking this data into consideration it is obvious that the Poisson regression model is the regression model of the highest accuracy. Specifically, in the case of tensile model [R.sup.2] is equal to 97.05% and in the case of flexural model [R.sup.2] reaches the value of 98.11%. It can be easily observed in Figures 13 and 14 that the experimental and theoretical results always show a perfect correlation.
Woven E-glass fabric/epoxy laminated composites were produced using a hand lay-up process and underwent tensile and flexural testing according to a [L.sub.25] Taguchi design of experiments. The multi-parameter analysis followed was based on three different Multiple Regression models (scenarios): a commonly used multiple regression model involving only the significant factors, the same regression model as before involving all the factors this time and a Poisson regression model (which employees a logarithmic transformation and is widely used in epidemiology, sociology and psychology). In order to get the final form of the regression models, backward elimination was applied to all possible combinations (up to fourth order) of the variants included in the regression of each scenario.
Due to the form of the experimental results' curves, especially in the case of tensile testing where absolute lack of symmetry and a non-sinusoidal manner of the curve slope's change can be observed, the commonly used Multiple Regression model fails to predict the experimental results with high accuracy. Both in the case of the involvement of only significant factors in the aforementioned regression model and in the case where all factors were involved, the low accuracy of the regression model make it risky to further optimize the curing process, using, for instance, multi-objective optimization techniques. The use of Poisson regression method, combined with backward elimination, is introduced to increase the accuracy of the multiple regression model. In fact, the accuracy ([R.sup.2]) of the Poisson Regression model was about 97-98%, when the respective one of the commonly used Multiple Regression model tested was about 65%. Therefore, further process optimization based on such an accurate model would not be risky, since the correlation of the experimental results and the theoretical values of the Poisson Regression model was almost perfect.
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Georgios V. Seretis, Georgios N. Kouzilos, Dimitrios E. Manolakos, and Christopher G. Provatidis, National Technical University of Athens
Received: 01 Oct 2017
Revised: 05 May 2018
Accepted: 31 May 2018
e-Available: 08 Aug 2018
Polymer-matrix composites (PMCs), Laminated composites, Hand/Manual Lay-up, Cure behaviour, Mechanical Testing, Process optimization, Multiple Regression
Seretis, G., Kouzilos, G., Manolakos, D., and Provatidis, C., "On the Multi-Parameter Experimental Investigation of Curing Cycle for Glass Fabric/Epoxy Laminated Composites," SAEInt. J. Mater. Manuf. 11(3):193-203, 2018, doi:10.4271/05-11-03-0019.
TABLE 1 Characteristics of the E-glass fabrics. Warp Weft Fiber description Glass EC11 204 fiber Glass EC11 204 fiber Thread count (ends/cm) 8 6 Weight distribution (%) 57 43 TABLE 2 Design of experiments (DOE) factors and their levels. Level Control factor 1 2 3 4 5 A: Heating rate [[degrees]C/min] 1 2 3 4 5 B: Temperature [[degrees]C] 50 80 100 120 140 C: Time [h] 2 4 6 8 10 TABLE 3 Taguchi [L.sub.25] OA response values and S/N ratio for tensile and 3-point bending tests. Heating rate a Run number [[degrees]C/min] Temperature [T.sub.C] [[degrees]C] 1 1 1 2 1 2 3 1 3 4 1 4 5 1 5 6 2 1 7 2 2 8 2 3 9 2 4 10 2 5 11 3 1 12 3 2 13 3 3 14 3 4 15 3 5 16 4 1 17 4 2 18 4 3 19 4 4 20 4 5 21 5 1 22 5 2 23 5 3 24 5 4 25 5 5 Tensile S/N Run number Time [t.sub.C] [h] Tensile load [N] ratio [dB] 1 1 2612.0 68.34 2 2 3690.0 71.34 3 3 2797.5 68.93 4 4 3397.0 70.62 5 5 2971.0 69.46 6 2 2736.7 68.74 7 3 3059.0 69.71 8 4 3643.0 71.23 9 5 3275.0 70.30 10 1 3122.0 69.89 11 3 2894.0 69.23 12 4 3178.5 70.04 13 5 2831.0 68.75 14 1 3307.5 70.39 15 2 3309.0 70.39 16 4 2938.0 69.36 17 5 2769.0 68.85 18 1 3156.0 69.98 19 2 3862.3 71.74 20 3 3629.5 71.19 21 5 2526.0 68.05 22 1 2594.5 68.28 23 2 3409.5 70.65 24 3 3277.5 70.31 25 4 3542.5 70.99 Flexural Flexural S/N Run number strength [MPa] ratio [dB] 1 143.3 42.79 2 327.3 50.30 3 286.3 49.14 4 442.6 52.92 5 299.5 49.73 6 295 49.4 7 346 50.78 8 369 51.34 9 420 52.46 10 371 51.39 11 307 49.74 12 362.5 51.19 13 318.5 49.90 14 349 50.86 15 297 49.45 16 277.5 48.87 17 335.5 50.51 18 235 47.42 19 402.6 52.10 20 387.5 51.76 21 306.5 45.87 22 149.5 43.49 23 357.5 51.07 24 377.5 51.54 25 477.5 53.58 TABLE 4 ANOVA for tensile load value, without interaction, [F.sub.0,05,4,12 =3,26'] Sum of Source dF squares Mean square F-value P value C (%) A 4 293004 73251 0.80 0.367 6.62 B 4 1447822 361955 3.96 (*) 0.003 (*) 32.71 C 4 1588652 397163 4.34 (*) 0.010 (*) 35.89 Error 12 1097301 91442 Total 24 4426778 (*) Significant at 95% confidence level. TABLE 5 ANOVA for flexural stress value, without interaction, [F.sub.0,05,4,12 =3,26.] Sum of Source dF squares Mean square F-value P value C (%) A 4 12361 3090 1.18 0.367 6.92 B 4 78612 19653 7.53 (*) 0.003 (*) 44.02 C 4 56284 14071 5.39 (*) 0.010 (*) 31.52 Error 12 31335 2611 Total 24 178591 (*) Significant at 95% confidence level. TABLE 6 Confirmation table for optimum tensile performance. Parameter Optimal parameters [A.sub.4][B.sub.4][C.sub.2] Experimental Predicted Tensile load (N) 3862.33 3878.10 Error % 0.41% TABLE 7 Confirmation table for optimum flexural performance. Parameter Optimal parameters [A.sub.2][B.sub.4][C.sub.4] Experimental Predicted Flexural strength (MPa) 498.70 501.93 Error % 0.65%
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|Author:||Seretis, Georgios V.; Kouzilos, Georgios N.; Manolakos, Dimitrios E.; Provatidis, Christopher G.|
|Publication:||SAE International Journal of Materials and Manufacturing|
|Date:||Sep 1, 2018|
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