Modeling of glass fiber reinforced composites for optimal mechanical properties using teaching learning based optimization and artificial neural networks
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Abstract
The present work is aimed at determining mechanical properties of chopped strand glass fiber reinforced composite laminates manufactured based on the design of experiments by resin transfer molding at various injection pressures with 4, 5 and 6 layers. Response surface methodology was implemented to the experimental data for evaluating the effect of number of layers and resin injection pressure on mechanical properties and void content. Teaching learning based optimization (TLBO) has been proposed to predict optimal (maximum) mechanical properties of composite by optimizing the number of layers and injection pressure. Artificial neural network (ANN) with feed forward back propagation algorithm was also used to predict the responses and compare with experimental and TLBO results. It was found that the predicted values of responses from TLBO and ANN are good in agreement with experimental results.
Keywords
Artificial neural network (ANN) Teaching learning based optimization (TLBO) Glass fiber reinforced plastic (GFRP) Resin transfer molding (RTM) Mechanical properties1 Background
Now-a-days, composite materials have been gaining demand in aerospace, automobile and marine industries due to their high strength, corrosion resistance, rigidity and less weight over metallic components. Resin transfer molding (RTM) is a potential and feasible manufacturing method which can produce composite parts from low to moderate sizes due to its reliable experimental set up and low tooling cost [1, 2, 3]. Additionally, it allows higher fiber volume fraction and attracts automotive industry [4] due to its low manufacturing cost. These industries demand composites with excellent mechanical properties. In the field of optimization of fiber reinforced composites, response surface methodology (RSM), Taguchi, grey relation analysis, teaching learning-based optimization (TLBO), genetic algorithm, artificial neural network (ANN) are used for optimization and modeling. RSM was used reliably and exactly to model surface roughness, thrust force and delamination in drilling of carbon/epoxy composites and predict their values [5]. RSM was implemented for metals to make a relationship between cutting parameters, surface roughness and work piece vibration [6]. RSM was used to determine the machining performance under the influence of various parameters of machining. The expressions emerging out of RSM are useful for optimization in other algorithms such as TLBO [7]. RSM was implemented through ellistic teaching learning-based optimization (ETLBO) with cutting speed, feed, depth of cut and fiber orientation as the input parameters for determining surface roughness of glass fiber reinforced plastic (GFRP) composite turned on a lathe. The TLBO is a powerful and best method for optimizing process parameters of machining operations in manufacturing industries [8]. This method was employed to optimize spindle speed, depth of cut, feed rate and fiber orientation angle for maximum metal removal rate, minimum surface roughness and cutting force [9].
Furthermore, a biological motivated paradigm of ANN emerged out as an accurate modeling tool for optimum design of metallic as well as composite structures and predicting mechanical properties [10]. A well trained ANN is a useful tool for systematic parametric studies and characterization of failure mechanisms of composites. It was used by several researchers due to reduction in time and cost of required experimental measurements [11, 12, 13, 14]. ANN can be used to simulate the relationship between process parameters and performance of composite material by process optimization for its design and prediction of mechanical properties before fabrication/testing [15]. ANN was employed through resilient back propagation to predict the performance of glass fiber composite suffered from cyclic loads with static and cyclic properties as one input layer and fatigue life as output layer [16]. ANN was used to study mechanical properties of carbon/epoxy and glass/epoxy laminates produced in different volume fractions. The composites with fiber orientation angle of 0°/90°/± 45° would give better performance [17].
A multilayer feed forward ANN with back propagation was implemented to expect the nonlinear behavior of composite laminate subjected to cyclic loads and establish accurate relationship between input parameters and the number of cycles to failure. This has been the most popular and commonly used tool due to its acceptable generating capabilities [18]. A back propagation neural network was used in ANN architecture for short fiber/polyamide laminates fabricated by injection process. The material compositions and mechanical properties were considered as inputs for different outputs [11, 19].
To the authors’ knowledge, researchers focused on RSM for optimizing the process variables and maximizing responses without constraints in the field of composites because this tool does not allow constraints. Therefore, the efforts must be continued to implement a multi objective optimization tool allowing constraints for optimizing the process variables to produce quality FRP composites. TLBO is such a tool for optimizing process parameters to maximize the responses. In the present work, TLBO has been used considering both the number of layers and injection pressure as process variables in the fabrication of composites for maximizing their mechanical properties (tensile, flexural and impact strengths) keeping Reynolds number and void content as constraints. Further, ANN was employed to predict the responses for the given input variables and RSM was used to know the interaction effect of input variables on the responses.
2 Materials and methodology
The raw materials used in the composite laminates manufactured for the present investigations are E-glass chopped strand fiber mat of 450 gsm (Code: M6450-104) with fiber length 50 mm, diameter 9 µm and polyester resin (viscosity: 450 ± 50 Cp). Cobalt napthanate and methyl ethyl ketone peroxide were respectively used as accelerator and catalyst in the proportions of 1:1.25. A customized RTM was used to prepare three different composites which consisted of 4, 5 and 6 layers (L) [20]. Each of the three different composites was manufactured at five different pressures (P) of 0.196, 0.245, 0.294, 0.343 and 0.392 MPa by injecting polyester resin from the center of mold. The laminates had 5 mm thickness. The calculated fiber volume fractions of the three composites used are 32.13%, 40.94% and 53.2% for 4, 5 and 6 layers respectively [21].
Experimental results of 15 GFRP composite specimens
L | P (MPa) | R_{e} | V_{c} (%) | σ_{t} (MPa) | σ_{f} (MPa) | σ_{i} (kJ/m^{2}) |
---|---|---|---|---|---|---|
4 | 0.196 | 82.73 | 1.83 | 71.9 | 75.81 | 331.4 |
4 | 0.245 | 186.14 | 1.75 | 104.16 | 87.36 | 351.58 |
4 | 0.294 | 330.93 | 1.85 | 103.95 | 76.18 | 312.59 |
4 | 0.343 | 517.08 | 1.87 | 83.5 | 69.72 | 258.38 |
4 | 0.392 | 744.59 | 2.05 | 81.41 | 64.73 | 251.98 |
5 | 0.196 | 37.36 | 1.63 | 86.62 | 84.77 | 400.6 |
5 | 0.245 | 103.78 | 1.6 | 112.48 | 95.86 | 433.54 |
5 | 0.294 | 149.44 | 1.54 | 126.81 | 114.23 | 435.94 |
5 | 0.343 | 330.24 | 1.68 | 119.5 | 118.73 | 392.5 |
5 | 0.392 | 415.12 | 1.71 | 113.3 | 74.26 | 345.75 |
6 | 0.196 | 14.2 | 1.5 | 136.84 | 111 | 430.05 |
6 | 0.245 | 56.81 | 1.52 | 143.58 | 120.73 | 447.58 |
6 | 0.294 | 127.83 | 1.56 | 144.07 | 126.41 | 467.16 |
6 | 0.343 | 227.2 | 1.46 | 153.06 | 151.23 | 468.19 |
6 | 0.392 | 355.1 | 1.58 | 136.7 | 88.9 | 387.09 |
In phase-2, interaction effect of input parameters on responses was studied using RSM. In phase-3, optimal input parameters were determined for optimal mechanical properties of composites using TLBO algorithm. Phase 4 was described with ANN modeling and prediction of responses. The responses obtained from TLBO and ANN were compared with experimental results.
2.1 Response surface methodology
2.2 Teaching learning based optimization
Step 1 The population, design variables and termination criteria (Z′) are initialized. The best solution was selected based on non-dominance rank, crowding distance assignment (X _{j, k best, i}) and mean of each design variable was calculated.
- Step 2 Modified values of variables were obtained based on the best solution.$$\begin{aligned} & Difference \, \_ \, Mean_{j, \, k, \, i} = \, r_{i} \left( {X_{j, \, k \, best, \, I} - \, T_{F} M_{j, \, i} } \right) \\ & X_{j, \, k, \, i}^{'} = \, X_{j, \, k, \, i} + \, Difference \, \_ \, Mean_{j, \, k, \, i} \\ \end{aligned}$$
Step 3 Modified solutions were combined with the initial solutions.
Step 4 Ranking was given based on non-dominated sorting. Crowding distance was calculated after normalizing objective function to accomplish the teacher phase.
- Step 5 The two solutions X′_{total − P, i} and X′_{total − Q,j} were selected randomly.$$\begin{aligned} X''_{j, \, P, \, i} & = X'_{j, \, P, \, i} + r_{i} \left( {X'_{j, \, P, \, i} - X'_{j, \, Q, \, i} } \right) \\ & \quad {\text{if}}\,X'_{total \, - \, P, \, I} \,{\text{is}}\,{\text{better}}\,{\text{than}}\,X'_{total \, - \, Q, \, i} \quad {\text{otherwise}} \\ X''_{j, \, P, \, i} & = X'_{j, \, P, \, i} + \, r_{i} \left( {X^{'}_{j, \, Q, \, i} {-} \, X \, '_{j, \, P, \, i} } \right). \\ \end{aligned}$$
Step 6 The new solutions of step 5 were combined with the solutions obtained after teacher phase (Step 4). The ranking was given based on non-dominated sorting and then crowding distance was calculated.
Step 7 When the termination criterion is satisfied, the non-dominated set of solutions is reported.
2.3 Artificial neural networks
A feed forward multilayer perceptron architecture (2-8-3) was used in this work for modeling of mechanical properties. This architecture consisted of two neurons in input, three neurons in output and eight neurons in hidden layers. The network was trained by adapting weights to the connections between neurons in each layer.
In the present work, RSM was used to analyze the experimental results for identifying the significance of process parameters on responses. TLBO method was adopted to optimize the process parameters for maximization of responses. In addition to these, ANN was employed to validate the results of TLBO.
3 Results and discussion
3.1 Analysis of variance
Analysis of variance for five responses (Reynolds number, void content, tensile, flexural and impact strengths)
Source | df | ANOVA for R_{e} | ANOVA for V_{c} | ANOVA for σ_{t} | ANOVA for σ_{f} | ANOVA for σ_{i} | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
F value | p value | F value | p value | F value | p value | F value | p value | F value | p value | ||
Model | 5 | 12.95 | 0.001 | 20.04 | 0.000 | 21.94 | 0.000 | 6.12 | 0.010 | 40.00 | 0.000 |
Linear | 2 | 22.79 | 0.000 | 47.25 | 0.000 | 47.54 | 0.000 | 10.81 | 0.004 | 83.88 | 0.000 |
P | 1 | 4.75 | 0.057 | 84.35 | 0.011 | 1.97 | 0.194 | 0.30 | 0.594 | 22.08 | 0.001 |
L | 1 | 40.83 | 0.000 | 10.16 | 0.000 | 93.10 | 0.000 | 21.32 | 0.001 | 145.6 | 0.000 |
Square | 2 | 6.42 | 0.019 | 2.42 | 0.144 | 7.27 | 0.013 | 4.37 | 0.047 | 13.48 | 0.002 |
P * P | 1 | 0.57 | 0.469 | 2.54 | 0.145 | 13.79 | 0.005 | 8.67 | 0.016 | 17.24 | 0.002 |
L * L | 1 | 12.26 | 0.007 | 2.31 | 0.163 | 0.75 | 0.410 | 0.08 | 0.784 | 9.73 | 0.012 |
2FI | 1 | 6.35 | 0.033 | 0.85 | 0.380 | 0.08 | 0.790 | 0.24 | 0.637 | 5.27 | 0.047 |
P * L | 1 | 6.35 | 0.033 | 0.85 | 0.380 | 0.08 | 0.790 | 0.24 | 0.637 | 5.27 | 0.047 |
Error | 9 | ||||||||||
Total | 14 |
From the experimental results, void volume fractions of 1.75%, 1.54%, and 1.46% were noticed to be minimum at pressures 0.245, 0.294, 0.343 MPa for 4, 5 and 6 layered composites respectively. These pressures were considered as optimal injection pressures in the present study as the composites exhibited better mechanical properties due to better impregnation of fiber with resin caused by low percent of void content.
The response surfaces in Fig. 3c–e describe the variations in tensile, flexural and impact strengths respectively with respect to both resin injection pressure and number of layers. They also represent maximum strengths gained by the composites. For 4, 5 and 6 layered composites, the maximum tensile strengths were noticed as 104.16, 126.81 and 153.06 MPa at the respective injection pressures of 0.245, 0.294 and 0.343 MPa respectively. Increase in injection pressure beyond the optimal value led to reduction in tensile strength of the composite as reported by Patel et al. [33] for glass fiber/polyester composite. At the same injection pressures, the respective composites had maximum flexural strengths of 87.36, 120.73 and 151.23 MPa. Flexural strength also decreased beyond the optimal pressure due to increase of void content present in the composite as noticed by Karbhari et al. [34]. The composites also had maximum impact strengths of 351.58, 435.94 and 468.19 kJ/m^{2}. Although all the three types of composites exhibited maximum mechanical properties, of them 6 layered composites manufactured at injection pressure 0.343 MPa gave maximum tensile, flexural and impact strengths due to less content of voids present in it.
Estimated regression coefficients, t values and p values
V_{c} | σ_{t} | |||||
---|---|---|---|---|---|---|
Term | Coef | t value | p value | Coef | t value | p value |
C_{0} | 1.342 | 1.98 | 0.079 | 121.86 | 25.41 | 0 |
C_{1} | − 2.518 | − 6.39 | 0 | 26.93 | 9.65 | 0 |
C_{2} | 0.992 | 2.18 | 0.057 | 4.53 | 1.41 | 0.194 |
C_{11} | 2.39 | 3.5 | 0.007 | 4.18 | 0.86 | 0.41 |
C_{22} | 0.581 | 0.76 | 0.469 | − 20.23 | − 3.71 | 0.005 |
C_{12} | − 1.404 | − 2.52 | 0.033 | 1.08 | 0.27 | 0.79 |
σ_{f} | σ_{i} | |||||
---|---|---|---|---|---|---|
Term | Coef | t value | p value | Coef | t value | p value |
C_{0} | 110.82 | 14.34 | 0 | 424.97 | 43 | 0 |
C_{1} | 22.45 | 4.99 | 0.001 | 69.41 | 12.07 | 0 |
C_{2} | − 3.44 | − 0.66 | 0.524 | − 31.21 | − 4.7 | 0.001 |
C_{11} | − 0.36 | − 0.05 | 0.964 | − 31.07 | − 3.12 | 0.012 |
C_{22} | − 26.51 | − 3.02 | 0.014 | − 46.6 | − 4.15 | 0.002 |
C_{12} | 2.61 | 0.41 | 0.691 | 18.67 | 2.3 | 0.047 |
3.2 Teaching learning based optimization
Objective functions Minimize R_{e} = 88 − 108L + 2373P and V_{c} = 2.364 − 0.1830L + 0.748P.
Maximize σ_{t} = − 33.7 + 26.93L + 46.2P, σ_{f} = − 4.6 + 22.45 L − 35.1P and σ_{i} = 120.0 + 69.4 L − 293P.
Constraints Reynolds number 1 ≤ R_{e} ≤ 300 and void content 0 ≤ V_{c} ≤ 1.46.
Parameter bounds 4 ≤ L ≤ 6 and 0.196 ≤ P ≤ 0.392 MPa.
Initial population
S. no. | L | P | R_{e} | V_{c} | σ_{t} (MPa) | σ_{f} (MPa) | σ_{i} (kJ/m^{2}) | \(Z_{{R_{e} }}\) | \(Z_{{V_{c} }}\) | Z^{’} | Rank |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 4 | 0.196 | 82.73 | 1.83 | 71.9 | 75.81 | 312.59 | 0 | 0.37 | 0.6271186 | 10 |
2 | 4 | 0.245 | 186.14 | 1.75 | 104.16 | 87.36 | 351.58 | 0 | 0.29 | 0.4915254 | 9 |
3 | 4 | 0.294 | 330.93 | 1.85 | 103.95 | 76.18 | 331.4 | 30.93 | 0.39 | 0.7305867 | 12 |
4 | 4 | 0.343 | 517.08 | 1.87 | 83.5 | 69.72 | 258.38 | 217.08 | 0.41 | 1.1831853 | 13 |
5 | 4 | 0.392 | 744.59 | 2.05 | 81.41 | 64.73 | 251.98 | 444.59 | 0.59 | 2 | 14 |
6 | 5 | 0.196 | 37.36 | 1.63 | 86.62 | 84.77 | 400.6 | 0 | 0.17 | 0.2881356 | 6 |
7 | 5 | 0.245 | 103.78 | 1.6 | 112.48 | 95.86 | 433.54 | 0 | 0.14 | 0.23728814 | 5 |
8 | 5 | 0.294 | 149.44 | 1.54 | 126.81 | 114.23 | 435.94 | 0 | 0.08 | 0.13559322 | 3 |
9 | 5 | 0.343 | 330.24 | 1.68 | 119.5 | 118.73 | 392.5 | 30.24 | 0.22 | 0.4408991 | 8 |
10 | 5 | 0.392 | 415.12 | 1.71 | 113.3 | 74.26 | 345.75 | 115.12 | 0.25 | 0.682664 | 11 |
11 | 6 | 0.196 | 14.2 | 1.4 | 136.84 | 111 | 430.05 | 0 | 0 | 0 | 1 |
12 | 6 | 0.245 | 56.81 | 1.52 | 143.58 | 120.73 | 447.58 | 0 | 0.06 | 0.10169492 | 2 |
13 | 6 | 0.294 | 127.83 | 1.56 | 144.07 | 126.41 | 467.16 | 0 | 0.1 | 0.16949153 | 4 |
14 | 6 | 0.343 | 227.2 | 1.46 | 153.06 | 151.23 | 468.19 | 0 | 0 | 0 | 1 |
15 | 6 | 0.392 | 355.1 | 1.58 | 136.7 | 88.9 | 387.09 | 55.1 | 0.12 | 0.3273242 | 7 |
Mean | 5 | 0.294 |
Updated input parameters, responses, constraints and violations (teacher phase)
L | P | R_{e} | V_{c} | σ_{t} (MPa) | σ_{f} (MPa) | σ_{i} (kJ/m^{2}) | \(Z_{{R_{e} }}\) | \(Z_{{V_{c} }}\) | Z′ |
---|---|---|---|---|---|---|---|---|---|
5 | 0.245 | 129.385 | 1.63226 | 112.269 | 99.0505 | 395.215 | 0 | 0.17226 | 0.610384 |
5 | 0.294 | 245.662 | 1.668912 | 114.5328 | 97.3306 | 380.858 | 0 | 0.208912 | 0.740256 |
5 | 0.343 | 361.939 | 1.705564 | 116.7966 | 95.6107 | 366.501 | 61.939 | 0.245564 | 1.21769 |
5 | 0.392 | 478.216 | 1.742216 | 119.0604 | 93.8908 | 352.144 | 178.216 | 0.282216 | 2.000034 |
5 | 0.392^{a} | 478.21 | 1.742216 | 119.06 | 93.89 | 352.144 | 178.21 | 0.282216 | 2 |
6 | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 |
6 | 0.294 | 137.662 | 1.485912 | 141.4628 | 119.7806 | 450.258 | 0 | 0.025912 | 0.091816 |
6 | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 |
6 | 0.392 | 370.216 | 1.559216 | 145.9904 | 116.3408 | 421.544 | 70.216 | 0.099216 | 0.745568 |
6 | 0.392^{a} | 370.216 | 1.559216 | 145.9904 | 116.3408 | 421.544 | 70.216 | 0.099216 | 0.745568 |
6^{a} | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 |
6^{a} | 0.294 | 137.662 | 1.485912 | 141.4628 | 119.7806 | 450.258 | 0 | 0.025912 | 0.091816 |
6^{a} | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 |
6^{a} | 0.392 | 370.216 | 1.559216 | 145.9904 | 116.3408 | 421.544 | 70.216 | 0.099216 | 0.745568 |
6^{a} | 0.392^{a} | 370.216 | 1.559216 | 145.9904 | 116.3408 | 421.544 | 70.216 | 0.099216 | 0.745568 |
Combined population (teacher phase)
L | P | R_{e} | V_{c} | σ_{t} (MPa) | σ_{f} (MPa) | σ_{i} (kJ/m^{2}) | \(Z_{{R_{e} }}\) | \(Z_{{V_{c} }}\) | Z′ | Rank |
---|---|---|---|---|---|---|---|---|---|---|
4 | 0.196 | 82.73 | 1.83 | 71.9 | 75.81 | 312.59 | 0 | 0.37 | 0.627119 | 12 |
4 | 0.245 | 186.14 | 1.75 | 104.16 | 87.36 | 351.58 | 0 | 0.29 | 0.491525 | 10 |
4 | 0.294 | 330.93 | 1.85 | 103.95 | 76.18 | 331.4 | 30.93 | 0.39 | 0.730587 | 14 |
4 | 0.343 | 517.08 | 1.87 | 83.5 | 69.72 | 258.38 | 217.08 | 0.41 | 1.183185 | 17 |
4 | 0.392 | 744.59 | 2.05 | 81.41 | 64.73 | 251.98 | 444.59 | 0.59 | 2 | 19 |
5 | 0.196 | 37.36 | 1.63 | 86.62 | 84.77 | 400.6 | 0 | 0.17 | 0.288136 | 7 |
5 | 0.245 | 103.78 | 1.6 | 112.48 | 95.86 | 433.54 | 0 | 0.14 | 0.2372881 | 6 |
5 | 0.294 | 149.44 | 1.54 | 126.81 | 114.23 | 435.94 | 0 | 0.08 | 0.1355932 | 3 |
5 | 0.343 | 330.24 | 1.68 | 119.5 | 118.73 | 392.5 | 30.24 | 0.22 | 0.440899 | 9 |
5 | 0.392 | 415.12 | 1.71 | 113.3 | 74.26 | 345.75 | 115.12 | 0.25 | 0.682664 | 13 |
6 | 0.196 | 14.2 | 1.4 | 136.84 | 111 | 430.05 | 0 | 0 | 0 | 1 |
6 | 0.245 | 56.81 | 1.52 | 143.58 | 120.73 | 447.58 | 0 | 0.06 | 0.1016949 | 2 |
6 | 0.294 | 127.83 | 1.56 | 144.07 | 126.41 | 467.16 | 0 | 0.1 | 0.1694915 | 4 |
6 | 0.343 | 227.2 | 1.46 | 153.06 | 151.23 | 468.19 | 0 | 0 | 0 | 1 |
6 | 0.392 | 355.1 | 1.58 | 136.7 | 88.9 | 387.09 | 55.1 | 0.12 | 0.327324 | 8 |
5 | 0.245 | 129.385 | 1.63226 | 112.269 | 99.0505 | 395.215 | 0 | 0.17226 | 0.610384 | 11 |
5 | 0.294 | 245.662 | 1.668912 | 114.5328 | 97.3306 | 380.858 | 0 | 0.208912 | 0.740256 | 15 |
5 | 0.343 | 361.939 | 1.705564 | 116.7966 | 95.6107 | 366.501 | 61.939 | 0.245564 | 1.217678 | 18 |
5 | 0.392 | 478.216 | 1.742216 | 119.0604 | 93.8908 | 352.144 | 178.216 | 0.282216 | 2 | 19 |
5 | 0.392^{a} | 478.216 | 1.742216 | 119.06 | 93.89 | 352.144 | 178.216 | 0.282216 | 2 | 19 |
6 | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 1 |
6 | 0.294 | 137.662 | 1.485912 | 141.4628 | 119.7806 | 450.258 | 0 | 0.025912 | 0.091816 | 2 |
6 | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 5 |
6 | 0.392 | 370.216 | 1.559216 | 145.9904 | 116.3408 | 421.544 | 70.216 | 0.099216 | 0.745554 | 16 |
6 | 0.392^{a} | 370.216 | 1.559216 | 145.9904 | 116.3408 | 421.544 | 70.216 | 0.099216 | 0.745554 | 16 |
6^{a} | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 1 |
6^{a} | 0.294 | 137.662 | 1.485912 | 141.4628 | 119.7806 | 450.258 | 0 | 0.025912 | 0.091816 | 2 |
6^{a} | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 5 |
6^{a} | 0.392 | 370.216 | 1.559216 | 145.9904 | 116.3408 | 421.544 | 70.216 | 0.099216 | 0.745554 | 16 |
6^{a} | 0.392^{a} | 370.216 | 1.559216 | 145.9904 | 116.3408 | 421.544 | 70.216 | 0.099216 | 0.745554 | 16 |
Candidate solution based on the non-dominance rank (teacher phase)
S. no. | L | P | R_{e} | V_{c} | σ_{t} (MPa) | σ_{f} (MPa) | σ_{i} (kJ/m^{2}) | \(Z_{{R_{e} }}\) | \(Z_{{V_{c} }}\) | Z′ | Rank |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 6 | 0.196 | 14.2 | 1.4 | 136.84 | 111 | 430.05 | 0 | 0 | 0 | 1 |
2 | 6 | 0.343 | 227.2 | 1.46 | 153.06 | 151.23 | 468.19 | 0 | 0 | 0 | 1 |
3 | 6 | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 1 |
4 | 6^{a} | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 1 |
5 | 6 | 0.245 | 56.81 | 1.52 | 143.58 | 120.73 | 447.58 | 0 | 0.06 | 0.1016949 | 2 |
6 | 6 | 0.294 | 137.662 | 1.485912 | 141.4628 | 119.7806 | 450.258 | 0 | 0.025912 | 0.091816 | 2 |
7 | 6^{a} | 0.294 | 137.662 | 1.485912 | 141.4628 | 119.7806 | 450.258 | 0 | 0.025912 | 0.091816 | 2 |
8 | 5 | 0.294 | 149.44 | 1.54 | 126.81 | 114.23 | 435.94 | 0 | 0.08 | 0.1355932 | 3 |
9 | 6 | 0.294 | 127.83 | 1.56 | 144.07 | 126.41 | 467.16 | 0 | 0.1 | 0.1694915 | 4 |
10 | 6 | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 5 |
11 | 6^{a} | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 5 |
12 | 5 | 0.245 | 103.78 | 1.6 | 112.48 | 95.86 | 433.54 | 0 | 0.14 | 0.2372881 | 6 |
13 | 5 | 0.196 | 37.36 | 1.63 | 86.62 | 84.77 | 400.6 | 0 | 0.17 | 0.288136 | 7 |
14 | 6 | 0.392 | 355.1 | 1.58 | 136.7 | 88.9 | 387.09 | 55.1 | 0.12 | 0.327324 | 8 |
15 | 5 | 0.343 | 330.24 | 1.68 | 119.5 | 118.73 | 392.5 | 30.24 | 0.22 | 0.440899 | 9 |
New values of L, P, σ_{t}, σ_{f}, σ_{i}, R_{e}, V_{c} and violations (learner phase)
S. no. | L | P | R_{e} | V_{c} | σ_{t} (MPa) | σ_{f} (MPa) | σ_{i} (kJ/m^{2}) | \(Z_{{R_{e} }}\) | \(Z_{{V_{c} }}\) | Z′ | Interaction |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 6^{a} | 0.196^{a} | 14.2 | 1.4 | 136.84 | 111 | 430.05 | 0 | 0 | 0 | 1 and 15 |
2 | 6 | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 2 and 14 |
3 | 6^{a} | 0.294 | 137.662 | 1.485912 | 141.4628 | 119.7806 | 450.258 | 0 | 0.025912 | 0.091816 | 3 and 13 |
4 | 6^{a} | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 4 and 12 |
5 | 6^{a} | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 5 and 11 |
6 | 6 | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 6 and 10 |
7 | 6^{a} | 0.294 | − 94.892 | 1.412608 | 136.9352 | 123.2204 | 478.972 | 0 | 0 | 0 | 7 and 9 |
8 | 6 | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 8 and 1 |
9 | 6 | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 9 and 2 |
10 | 6 | 0.392^{a} | 370.216 | 1.559216 | 145.9904 | 116.3408 | 421.544 | 70.216 | 0.099216 | 0.745554 | 10 and 3 |
11 | 6^{a} | 0.392^{a} | 370.216 | 1.559216 | 145.9904 | 116.3408 | 421.544 | 70.216 | 0.099216 | 0.745554 | 11 and 4 |
12 | 6 | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 12 and 5 |
13 | 6 | 0.294 | 137.662 | 1.485912 | 141.4628 | 119.7806 | 450.258 | 0 | 0.025912 | 0.091816 | 13 and 6 |
14 | 6^{a} | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 14 and 7 |
15 | 5 | 0.343 | 478.216 | 1.742216 | 119.0604 | 93.8908 | 421.544 | 178.216 | 0.282216 | 2 | 15 and 8 |
Combined population (learner phase)
S. no. | L | P | R_{e} | V_{c} | σ_{t} (MPa) | σ_{f} (MPa) | σ_{i} (kJ/m^{2}) | \(Z_{{R_{e} }}\) | \(Z_{{V_{c} }}\) | Z′ | Rank |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 6 | 0.196 | 14.2 | 1.4 | 136.84 | 111 | 430.05 | 0 | 0 | 0 | 1 |
2 | 6 | 0.343 | 227.2 | 1.46 | 153.06 | 151.23 | 468.19 | 0 | 0 | 0 | 1 |
3 | 6 | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 1 |
4 | 6^{a} | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 1 |
19 | 6^{a} | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 1 |
22 | 6^{a} | 0.294 | − 94.892 | 1.412608 | 139.9352 | 123.2204 | 478.972 | 0 | 0 | 0 | 1 |
23 | 6 | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 1 |
27 | 6 | 0.245 | 21.385 | 1.44926 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 1 |
6 | 6 | 0.294 | 137.662 | 1.485912 | 141.4628 | 119.7806 | 450.258 | 0 | 0.025912 | 0.091816 | 2 |
7 | 6^{a} | 0.294 | 137.662 | 1.485912 | 141.4628 | 119.7806 | 450.258 | 0 | 0.025912 | 0.091816 | 2 |
18 | 6^{a} | 0.294 | 137.662 | 1.485912 | 141.4628 | 119.7806 | 450.258 | 0 | 0.025912 | 0.091816 | 2 |
28 | 6 | 0.294 | 137.662 | 1.485912 | 141.4628 | 119.7806 | 450.258 | 0 | 0.025912 | 0.091816 | 2 |
5 | 6 | 0.245 | 56.81 | 1.52 | 143.58 | 120.73 | 447.58 | 0 | 0.06 | 0.101695 | 3 |
8 | 5 | 0.294 | 149.44 | 1.54 | 126.81 | 114.23 | 435.94 | 0 | 0.08 | 0.135593 | 4 |
9 | 6 | 0.294 | 127.83 | 1.56 | 144.07 | 126.41 | 467.16 | 0 | 0.1 | 0.169492 | 5 |
10 | 6 | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 6 |
11 | 6^{a} | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 6 |
16 | 6^{a} | 0.196^{a} | 94.892 | 1.412608 | 136.9352 | 123.2204 | 478.972 | 0 | 0.062564 | 0.221688 | 6 |
17 | 6 | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 6 |
20 | 6^{a} | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 6 |
21 | 6 | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 6 |
24 | 6 | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 6 |
29 | 6^{a} | 0.343 | 253.939 | 1.522564 | 143.7266 | 118.0607 | 435.901 | 0 | 0.062564 | 0.221688 | 6 |
12 | 5 | 0.245 | 103.78 | 1.6 | 112.48 | 95.86 | 433.54 | 0 | 0.14 | 0.237288 | 7 |
13 | 5 | 0.196 | 37.36 | 1.63 | 86.62 | 84.77 | 400.6 | 0 | 0.17 | 0.288136 | 8 |
14 | 6 | 0.392 | 355.1 | 1.58 | 136.7 | 88.9 | 387.09 | 55.1 | 0.12 | 0.327324 | 9 |
15 | 5 | 0.343 | 330.24 | 1.68 | 119.5 | 118.73 | 392.5 | 30.24 | 0.22 | 0.440899 | 10 |
25 | 6 | 0.392^{a} | 370.216 | 1.559216 | 145.9904 | 116.3408 | 421.544 | 70.216 | 0.099216 | 0.745554 | 11 |
26 | 6^{a} | 0.392^{a} | 370.216 | 1.559216 | 145.9904 | 116.3408 | 421.544 | 70.216 | 0.099216 | 0.745554 | 11 |
30 | 5 | 0.343 | 478.216 | 1.742216 | 119.0604 | 93.8908 | 421.544 | 178.216 | 0.282216 | 2 | 12 |
Crowding distance (CD) for objective function
Step 1 All rank 1 solutions were collected.
Step 2 The first objective function of tensile strength was considered and arranged in the ascending order irrespective of the remaining objective functions.
Step 3 The maximum and minimum values of the objective function from the entire population were observed.
- Step 4 For the best and worst solutions of objective function, crowding distance was assigned to be infinity (∞). The crowding distance \(CD_{22 }^{1}\) was calculated with the following expression.\(CD_{22}^{1}\) represents crowding distance for the first objective function of 22nd sample. Where \(\left( {\sigma_{t} } \right)_{1}\) and \(\left( {\sigma_{t} } \right)_{3}\) represent tensile strengths of 1st and 3rd samples respectively. \(\left( {\sigma_{t} } \right)_{max}\) and \(\left( {\sigma_{t} } \right)_{min}\) represent maximum and minimum tensile strengths respectively.$$\begin{aligned} CD_{22}^{1} & = 0 + \frac{{\left( {\sigma_{t} } \right)_{3} - \left( {\sigma_{t} } \right)_{1} }}{{\left( {\sigma_{t} } \right)_{max} - \left( {\sigma_{t} } \right)_{min} }} \\ CD_{22}^{1} & = 0 + \frac{139.19 - 136.84}{153.06 - 136.84} = 0.145436 \\ \end{aligned}$$
- Step 5 For the second objective function, steps 4 and 5 were followed and \(CD_{22}^{2}\) was determined as follows.\(CD_{22}^{2}\) represents crowding distance for the second objective function of 22nd sample. Where \(\left( {\sigma_{f} } \right)_{1}\) and \(\left( {\sigma_{f} } \right)_{3}\) represent flexural strength of samples 1 and 3 respectively. \(\left( {\sigma_{f} } \right)_{max}\) and \(\left( {\sigma_{f} } \right)_{min}\) represent maximum and minimum flexural strengths respectively.$$\begin{aligned} CD_{22}^{2} & = CD_{22}^{1} + \frac{{\left( {\sigma_{f} } \right)_{3} - \left( {\sigma_{f} } \right)_{1} }}{{\left( {\sigma_{f} } \right)_{max} - \left( {\sigma_{f} } \right)_{min} }} \\ CD_{22}^{2} & = 0.145436 + \frac{121.50 - 111}{151.23 - 111} = 0.884426 \\ \end{aligned}$$
Step 6 The procedure was repeated for remaining objective functions.
Crowding distance for tensile strength
S. no. | L | P | σ_{t} (MPa) | CD − σ_{t} |
---|---|---|---|---|
1 | 6 | 0.196 | 136.84 | ∞ |
22 | 6^{a} | 0.294 | 136.9352 | 0.145438 |
3 | 6 | 0.245 | 139.199 | 0.139568 |
4 | 6^{a} | 0.245 | 139.199 | 0 |
19 | 6^{a} | 0.245 | 139.199 | 0 |
23 | 6 | 0.245 | 139.199 | 0 |
27 | 6 | 0.245 | 139.199 | 0.854562 |
2 | 6 | 0.343 | 153.06 | ∞ |
Total crowding distances for three responses
S. no. | CD − σ_{t} | CD − σ_{f} | CD − σ_{i} | CD − Total |
---|---|---|---|---|
1 | ∞ | ∞ | ∞ | ∞ |
2 | ∞ | ∞ | ∞ | ∞ |
22 | 0.145438 | 0.884426 | ∞ | ∞ |
27 | 0.854562 | 0.897314 | 0.970392 | 2.722268 |
3 | 0.139568 | 0.40058 | 1.107142 | 1.64729 |
4 | 0 | 0 | 0 | 0 |
19 | 0 | 0 | 0 | 0 |
23 | 0 | 0 | 0 | 0 |
Final solutions based on the ranks and crowding distances
S. no. | L | P | σ_{t} (MPa) | σ_{f} (MPa) | σ_{i} (kJ/m^{2}) | \(Z_{{R_{e} }}\) | \(Z_{{V_{c} }}\) | Z′ | Rank |
---|---|---|---|---|---|---|---|---|---|
2 | 6 | 0.343 | 153.06 | 151.23 | 468.19 | 0 | 0 | 0 | 1 |
22 | 6^{a} | 0.294 | 139.9352 | 123.2204 | 478.972 | 0 | 0 | 0 | 1 |
27 | 6 | 0.245 | 139.199 | 121.5005 | 464.615 | 0 | 0 | 0 | 1 |
1 | 6 | 0.196 | 136.84 | 111 | 430.05 | 0 | 0 | 0 | 1 |
3.3 Prediction of responses using ANN
Validation of optimization results with experiments
S.No | L | P | σ_{t} (MPa) | σ_{f} (MPa) | σ_{i} (kJ/m^{2}) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
TLBO | EXP | ANN | TLBO | EXP | ANN | TLBO | EXP | ANN | |||
2 | 6 | 0.343 | 153.06 | 153.06 | 152.65 | 151.23 | 151.23 | 150.93 | 468.19 | 468.19 | 466.28 |
22 | 6 | 0.294 | 139.93 | 144.07 | 151.71 | 123.22 | 126.41 | 148.94 | 478.97 | 467.16 | 464.19 |
27 | 6 | 0.245 | 139.19 | 143.58 | 136.84 | 121.50 | 120.73 | 111.04 | 464.61 | 447.58 | 431.67 |
4 Conclusion
The experiments reveal that mechanical properties of the composite are affected by resin injection pressure, number of layers and void content. However, the maximum tensile, flexural and impact strengths were obtained at optimal injection pressures of 0.245, 0.294, 0.343 MPa for 4, 5 and 6 layered composites respectively with minimum void content and Reynolds number less than 300.
Based on ANOVA, number of layers and resin injection pressure during the fabrication of composite were proved to be significant on Reynolds number, void content, tensile, flexural and impact strengths.
TLBO and ANN models were developed for manufacturing GFRP composites by RTM with number of layers and injection pressure as variables. Both models have given maximum mechanical properties for 4, 5 and 6 layered composites at their respective optimal injection pressures.
However, the maximum mechanical properties from TLBO and ANN models were obtained for 6 layered composites at an optimal injection pressure of 0.343 MPa with minimum void content and Reynolds number of resin flow less than 300 as observed from experiments.
Finally, mechanical properties obtained from the models of TLBO and ANN are good in agreement with experimental results.
Notes
Compliance with ethical standards
Conflict of interest
Authors declare that they have no conflict of interest.
References
- 1.Friedrich K, Almajid AA (2013) Manufacturing aspects of advanced polymer composites for automotive applications. Appl Compos Mater 20:107–128CrossRefGoogle Scholar
- 2.Deleglise M, Le GP, Binetruy C, Krawczak P, Claude B (2011) Modeling of high-speed RTM injection with highly reactive resin with on-line mixing. Compos A 42:1390–1397CrossRefGoogle Scholar
- 3.Luo J, Liang Z, Zhang C, Wang B (2001) Optimum tooling design for resin transfer molding with virtual manufacturing and artificial intelligence. Compos A 32:877–888CrossRefGoogle Scholar
- 4.Kendall KN, Rudd CD, Owen MJ, Middleton V (1992) Characterization of the resin transfer molding process. Compos Manuf 4:235–249CrossRefGoogle Scholar
- 5.Shahrajabian H, Farahnakian M (2013) Modeling and multi-constrained optimization in drilling. Int J Pr Eng Man 14(10):1829–1837CrossRefGoogle Scholar
- 6.Rao KV, Murthy PBGSN (2016) Modeling and optimization of tool vibration and surface roughness in boring of steel using RSM, ANN and SVM. J Intell Manuf. https://doi.org/10.1007/s10845-016-1197-y CrossRefGoogle Scholar
- 7.Mehrvar A, Basti A, Jamali A (2016) Optimization of electrochemical machining process parameters: combining response surface methodology and differential evolution algorithm. Proc I Mech Part E J Intell Manuf. https://doi.org/10.1177/0954408916656387 CrossRefGoogle Scholar
- 8.Ramesh R, Lakhan R, Arun P, Santosh C, Nagaraju D (2016) Parametric optimization for turning of GFRP composites using ellistic teaching learning-based optimization (ETLBO). Int J Adv Prod Mech Eng 2(3):25–30Google Scholar
- 9.Abhishek K (2015) Experimental investigations on machining of CFRP composites: study of parametric influence and machining performance optimization. PhD Thesis, NIT-Rourkela, IndiaGoogle Scholar
- 10.Kadi EH (2006) Modeling the mechanical behavior of fiber-reinforced polymeric composite materials using artificial neural networks—a review. Compos Struct 73:1–26CrossRefGoogle Scholar
- 11.Zhang Z, Friedrich K, Velten K (2002) Prediction on tribological properties of short fiber composites using artificial neural networks. Wear 252:668–675CrossRefGoogle Scholar
- 12.Fazilat H, Ghatarb M, Mazinani ZA, Asadi S, Shiri ME, Kalaee MR (2012) Predicting the mechanical properties of glass fiber reinforced polymers via artificial neural network and adaptive neuro-fuzzy inference system. Comput Mater Sci 58:31–37CrossRefGoogle Scholar
- 13.Zhu J, Shi Y, Feng X, Wang H, Lu X (2009) Prediction on tribological properties of carbon fiber and TiO_{2} synergistic reinforced polytetrafluoroethylene composites with artificial neural networks. Mater Des 30:1042–1049CrossRefGoogle Scholar
- 14.Bar HN, Bhat MR, Murthy CRL (2004) Identification of failure modes in GFRP using PVDF sensors: an approach. Compos Struct 65:231–237CrossRefGoogle Scholar
- 15.Zhang Z, Friedrich K (2003) Artificial neural networks applied to polymer composites: a review. Compos Sci Technol 63:2029–2044CrossRefGoogle Scholar
- 16.Assadi AM, Kadi EIH, Deiab IM (2010) Predicting the fatigue life of different composite materials using artificial neural networks. Appl Compos Mater 17:1–14CrossRefGoogle Scholar
- 17.Bezerra EM, Ancelotti AC, Pardini LC, Rocco JAFF, Iha K, Ribeiro CHC (2007) Artificial neural networks applied to epoxy composites reinforced with carbon and E-glass fibers: analysis of the shear mechanical properties. Mater Sci Eng A 464:177–185CrossRefGoogle Scholar
- 18.Assaf AY, Kadi EIH (2001) Fatigue life prediction of unidirectional glass fiber/epoxy composite laminae using neural networks. Compos Struct 53:65–71CrossRefGoogle Scholar
- 19.Jiang Z, Gyurova L, Zhang Z, Friedrich K, Schlarb AK (2008) Neural network-based prediction on mechanical and wear properties of short fibers reinforced polyamide composites. Mater Des 29:628–637CrossRefGoogle Scholar
- 20.Bickerton S, Sozer EM, Graham PJ, Advani SG (2000) Fabric structure and mold curvature effects on preform permeability and mold filling in the RTM process part I experiments. Compos Part A Appl Sci 31:423–438CrossRefGoogle Scholar
- 21.Dong C (2014) Experimental investigations on the fiber preform deformation due to mold closure for composites processing. Int J Adv 71:585Google Scholar
- 22.Jenarthanan MP, Ramesh KS, Jeyapaul R (2015) Modeling of machining force in end milling of GFRP composites using MRA and ANN. Aust J Mech Eng. https://doi.org/10.1080/14484846.2015.1093227 CrossRefGoogle Scholar
- 23.Baker MJ (2011) CFD simulation of flow through packed beds using the finite volume technique. PhD Thesis, University of Exeter, ExeterGoogle Scholar
- 24.Myers RH, Montgomery DC (2002) Response surface methodology: process and product optimization using designed experiments, 2nd edn. Wiley, LondonzbMATHGoogle Scholar
- 25.Montgomery DC (2001) Design and analysis of experiments, 5th edn. Wiley, New YorkGoogle Scholar
- 26.Tzeng CJ, Yang YK, Lin YH, Tsai CH (2012) A study of optimization of injection molding process parameters for SGF and PTFE reinforced PC composites using neural network and response surface methodology. Int J Adv Manuf Technol 63:691–704CrossRefGoogle Scholar
- 27.Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, ChichesterzbMATHGoogle Scholar
- 28.Rao RV (2016) Teaching learning-based optimization algorithm. Springer, Cham, pp 9–39CrossRefGoogle Scholar
- 29.Hosseini S, Barker K, Ramirez MJE (2016) A review of definitions and measures of system resilience. Relia Eng Sys Saf 45:47–61CrossRefGoogle Scholar
- 30.Kishan M, Chilukuri KM, Sanjay R (1997) Elements of artificial neural networks. The MIT Press, CambridgezbMATHGoogle Scholar
- 31.Jean SL, Edu R (2008) Porosity reduction using optimized flow velocity in resin transfer molding. Compos Part A Appl Sci Manf 39:1859–1868CrossRefGoogle Scholar
- 32.Chang LL, Kung HW (2000) Resin transfer molding (RTM) process of a high-performance epoxy resin II: effects of process variables on the physical, static and dynamic mechanical behavior. Polym Eng Sci 4:935–943Google Scholar
- 33.Patel N, Rohatgi V, Lee LJ (1993) Influence of processing and material variables on resin fiber interface in liquid composite molding. Polym Compos 14(2):161–172CrossRefGoogle Scholar
- 34.Karbhari VM, Slotee SG, Steen Kamer DA, Wilkins DJ (1992) Effect of material process and equipment variables on the performance of resin transfer moulded parts. J Compos Manuf 3:143CrossRefGoogle Scholar
- 35.Mousavi SM, Niaei A, Salari D, Panahi PN, Samandari M (2013) Modelling and optimization of Mn/activate carbon for no reduction: comparision of RSM and ANN techniques. Environ Technol 34(11):1377–1384CrossRefGoogle Scholar
- 36.Rao KV (2018) A novel approach for minimization of tool vibration and surface roughness in orthogonal turn milling of silicon bronze alloy. Silica. https://doi.org/10.1007/s12633-018-9953-6 CrossRefGoogle Scholar