Optimization and effects of machining parameters on delamination in drilling of pure and Al2O3/SiO2-added GFRP composites

The present study concentrates on optimization and the effect of machining parameters on delamination that occurs during drilling operation of pure glass fiber-reinforced polymer (GFRP) composites and added GFRP composites which were developed for resistance to erosion wear. Contribution of drilling parameters to delamination was investigated by using Taguchi method and analysis of variance (ANOVA). Relationship between machining parameters and delamination was modelled by using response surface methodology. Correlations were established between the machining parameters by quadratic regression using response surface methodology (RSM). Delamination factors in the hole entrance and exit were obtained in drilling of pure glass fiber epoxy, and SiO2- and Al2O3-added GFRP materials using the experimental plan. Delamination factors at the hole exits were found bigger than delamination factors at the hole entrances. The smallest delamination values were obtained in GFRP/epoxy composite compared to Al2O3/SiO2-added GFRP composites at the hole exit. In the investigation of machinability of composites, considering the material as a variable, it has been determined that the material has a greater effect on delamination than the cutting parameters. A new machinability index defined and the material having the best machinability of the three materials was Al2O3-added GFRP composite at the entrance. Good machinability was obtained in drilling of pure GFRP/epoxy composite at the hole exit. It has been found that the effect of feed rate on delamination is greater than the cutting speed and the cutting speed has a low effect. Optimization of the multi-objective function created for maximizing the material removal rate, minimizing the delamination, was performed, and the optimum drilling parameters were obtained. As a result of the experimental study, it was found that the amount of delamination increased although the low mechanical property-added GFRP composites with the high resistance to erosion wear in accordance with pure epoxy GFRP composites due to the lack of a strong bond between the epoxy and the fibers in Al2O3 and SiO2. It was observed that the delamination amounts of pure epoxy GFRP, Al2O3-added GFRP, and SiO2-added GFRP composites increased respectively, while the compressive and tensile strengths of these three materials decreased.


Introduction
Fiber-reinforced polymer composite materials offer superior properties such as high strength-to-weight ratio, stiffness-toweight ratio, and good corrosion resistance, and therefore, they are preferred for high-performance applications in several industries such as in the aerospace, automotive, defense, and sport goods industries.
Due to this increase in the use of FRPCs (fiber-reinforced polymer composites), studies on the machining of FRPCs have become increasingly important. Matrix material in composite materials holds the fibers together and a layered structure is obtained. Unlike conventional chip removal processes, machining of composites requires a special approach. The layered structure of composites, heat sensitivity, and abrasive effects of reinforcements lead to studying machinability of composites in particular [1,2]. The quality of the drilled hole is influenced adversely by matrix grid cratering, thermal damage, spalling, surface delamination, and material debasement or fiber pull-out. Defects such as fiber pull-out, matrix cratering, thermal damage, and delamination effecting quality of hole occur by drilling.
Khashaba et al. studied on the machinability of GFRP composites and investigated the effect of cutting parameters on thrust force and delamination. They concluded that an increase of the cutting speed and feed rate lead an increasing of delamination and as feed rate increases, thrust force and delamination increase. It was shown that a high feed rate of drilling causes a crack around the exit edge of the hole. The next phase of this study is the investigation of the effect of tool wear on thrust force. Results were indicated that an increasing of tool wear at high cutting speed and feed rate causes a rising of thrust force [3,4]. Delamination is a critical damage mode under impact loading in fiber-reinforced composites. It may lead directly to through-thickness failure owing to interlaminar stresses caused by out-of-plane loading, or discontinuities owing to cracks, ply drops, or free edges. Impact loading causes multiple delamination, which can propagate in conjunction with sublaminate buckling, greatly reducing the residual compressive strength. Delamination is a major problem associated with drilling of fiberreinforced composite materials that, in addition to reducing the structural integrity of the material, also results in poor assembly tolerance and has the potential for long-term performance deterioration [5]. Direct and interactive effect of process variables influences machining performance in terms of quality of the drilled hole. Therefore, an optimal parameter setting is indeed required. Abhishek et al. aims at evaluating an appropriate drilling parameter setting toward optimization of thrust, torque, entry, and exist delamination factor during drilling of CFRP (epoxy) composites. An integrated multi-response optimization philosophy combining principal component analysis (PCA), fuzzy inference system (FIS), and Taguchi method have been proposed [6]. In a study conducted by Davim et al., a statistical approach was handled to identify the most appropriate cutting parameters to realize drilling operations on carbon fiber-reinforced thermoset materials. They put forward an approach through Taguchi's experimental analysis along with the multi-purpose optimization [7]. In another study carried out by Mohan et al., the Taguchi technique and response surface methodology were applied on GFRP composites. The major objective of this study is to find out the factors affecting delamination and optimizing the processing parameters for minimum delamination [8]. M. F. Ameur et al. defined the cutting conditions that allow the drilling of carbon fiber-reinforced epoxy (CFRE) composite materials taking into consideration the quality of the drilled holes (the exit delamination factor and the cylindricity error) and the optimum combination of drilling parameters [9]. They used grey relational analysis to improve the quality of the drilled holes. The experiment design was accomplished by application of the statistical analysis of variance (ANOVA). Their results show that the tool materials and the feed rate, which has a strong influence on the exit delamination factor, mainly influence the thrust force. Rajamurugan et al. modelled that the effect of drilling parameters on delamination of GFRP composites by using response surface methodology. Thus, delamination became predictable according to selected cutting parameters [10]. They analyzed delamination in drilling glass fiberreinforced polyester composites. An attempt was made to develop empirical relationships between the drilling parameters. Sardinas et al. [11] used a micro-genetic algorithm and Krishnamoorthy et al. [12] a fuzzy grey method both with the aim of optimizing the drilling process conditions. Gaitonde et al. analyzed the effects of cutting speed, feed rate, and the point angle on the delamination factor by generating response surface methodology (RSM) plots models [13]. S. Prakash et al. presented the systematic experimental investigation, analysis, and optimization of delamination factor in drilling of medium-density fiberboards (MDF). They developed an empirical model for predicting the delamination factor at entry and exit of the holes in drilling of MDF boards. Desirability function-based approach was employed for the optimization drilling parameters for minimizing the delamination factor at entry and exit in drilling of MDF boards [14]. In a study conducted by Davim et al., a statistical approach was handled to identify the most appropriate cutting parameters to realize drilling operations on carbon fiber-reinforced thermoset materials. They put forward an approach through Taguchi's experimental analysis along with the multi-purpose optimization [15,16]. Marques et al. performed delamination analysis of carbon fiber-reinforced laminates and evaluation of a special step drill [17]. Campos Rubio et al. investigated delamination in high-speed drilling of carbon fiber-reinforced plastic (CFRP) [18]. Abrao et al. studied on the effect of cutting tool geometry on thrust force and delamination of drilling of glass fiber-reinforced plastic composites [19]. Palanikumar used Taguchi and response surface methodologies for minimizing the surface roughness in machining glass fiber-reinforced (GFRP) plastics with a polycrystalline diamond (PCD) tool. The cutting parameters used are cutting speed, feed, and depth of cut. The effect of cutting parameters on surface roughness was evaluated and the optimum cutting condition for minimizing the surface roughness is determined [20]. Sait et al. presented a new approach for optimizing the machining parameters on turning glass fiber-reinforced plastic (GFRP) pipes. Optimization of machining parameters was done by an analysis called desirability function analysis, which is a useful tool for optimizing multi-response problems [21]. Işık et al. presented a new comprehensive approach to select cutting parameters for damage factor in drilling of glass fiber-reinforced polymer (GFRP) composite material. The influence of drilling on surface quality of woven GFRP plastic composite material was investigated experimentally. Damage factor was investigated based on hole entrance and exit. Analysis of variance (ANOVA) test was applied to the experimental results [22]. Kilickap investigated the influence of the cutting parameters, such as cutting speed and feed rate, and point angle on delamination produced when drilling a GFRP composite.
The damages generated associated with drilling GFRP composites were observed, both at the entrance and at the exit during the drilling. He obtained the optimum cutting parameters minimizing delamination at drilling of GFRP composites [23]. Ghasemi et al. studied the effects of some the cutting parameters, such as feed rate, drilling rotation speed, and drill point angle on delamination area produced during drilling of glass-epoxy composites using full factorial technique and ANOVA. The results indicated that the drill thrust force was minimum at feed rate of 25 mm/ min, rotational speed of 2000 rpm, and drill point angle of 90° [24]. Liu et al. carried out drilling experiments of glass fiber-reinforced plastic (GFRP) composites and finite element simulations. Three candlestick drills with different drill tip geometries and one twist drill were compared in terms of thrust force, peel-up delamination, and push down delamination [25]. Tian et al. investigated the coupling effect between the clearance angles of outer cutting edges, the spindle speed, and the feed speed when drilling the GFRP materials with candlestick drills. It was found that the reason for the coupling effect of the machining and tool parameters was that the change of these parameters would have different effect on the pushing, cutting, and physical properties of the materials at the same time [26].
In this study, the investigation of the effects of cutting parameters on delamination at hole entry and exit in the drilling of the Al 2 O 3 -and SiO 2 -reinforced glass fiber composites developed for resistance to erosion wear with the pure GFRP/epoxy and the determination of optimum cutting conditions for these composites was aimed. In order to achieve this objective, empirical models have been developed to estimate the delamination factors at the entrance and exit of the holes when drilling pure and Al 2 O 3 /SiO 2doped GFRP composites. In the drilling of composites, Khun-Tucker conditions are used in optimization drilling parameters to minimize the delamination factors at entry and exit. The major objective of this study is to find out the factors affecting delamination and optimizing the machining parameters for minimum delamination. In order to provide delamination minimization and material removal rate maximization, the cutting parameters are optimized with the multi-purpose optimization method, thus enabling the cutting conditions to be applied in the real environment.

Equipment
The samples used in the experiment consisted of pure glass fiber epoxy, SiO 2 /Al 2 O 3 -added reinforced composite GFRP materials. Sample materials were 4 mm thick and had the dimensions of 65 × 165 mm. The mechanical properties of the samples are provided in Table 1 and experiment setup is given in Fig. 1. During the experiments, Mazak Variaxis 500-5X machining center was used as milling machine to perform the experiments. In the drilling operations, K10 carbide drill with 118° point angle and 6 mm diameter was used as cutting tool.
Delamination is a damage phenomenon. The damage (delamination) surrounding the holes was measured using a tool maker's microscope with 30 × magnification and 1-μm resolution. In order to calculate delamination factor at entrance and exit of holes on workpiece, the relation is given as: where D max is maximum diameter of the delamination zone and D is the diameter of hole. The scheme of delamination is indicated in Fig. 2.
Drilling-induced delamination occurs at the entry and exit planes of the workpiece as illustrated schematically in Fig. 2 a. Peel-up occurs as the drill enters the laminate. After the cutting edge of the drill makes contact with the laminate, the cutting force acting in the peripheral direction is the driving force for delamination. It generates a peeling force in the axial direction through the slope of the drill flute that results in separating the laminas from each other forming a delamination zone at the top surface of the laminate [5]. Push-out delamination occurs before the drill completely drills the sheet and exits from it as shown in Fig. 2 b [5]. The drill point exerts compressive force on the uncut plies below causing them to bend elastically. As the drill approaches the exit, the resistance to bending is decreased due to the reduction in the number of uncut layers.

Material properties
Glass fiber-reinforced epoxy composite materials in pure form were selected as the main test sample, and new composite test samples were created by adding SiO 2 and Al 2 O 3 fillers separately, with an average particle diameter of 150 μm and 15% of the resin, into this pure structure. In the new formation, it is aimed to reduce the resin cost and increase the erosion resistance with mechanical property change.
Bagci et al. determined the solid particle erosive wear rates of the %15 Al 2 O 3 -added GFRP test specimens that are at lower level than those of pure GFRP/EP test specimens. Al 2 O 3 filler has helped in improving the wear resistance of the test specimens. Materials with addition of Al 2 O 3 filler material at various amounts exhibited lower wear as compared to neat materials with no added filler material. That means the filler material has increased the erosive wear resistance [27].
Bagci et al. investigated that 15%SiO 2 -added GFRP has had a reducing effects on erosion wear. It increased the GF/EP composite material 's wear resistance. The added  SiO 2 has formed powerful bond with epoxy resin. The bond between epoxy and the filler material has been effective over a wide zone. SiO 2 filler materials were used in order to lower expenses and increase material strength. It was also found that by adding SiO 2 into the matrix, the resulting new composite shows a decrease in erosion rate at about 10-15% lower than material and thereby being the best effect to the erosive wear. SiO 2 -added specimens have exhibited resistance against the abrasive particles and hence only slight deformation was encountered on the specimen surfaces [28]. As a result, abrasives encountered with the resistance of the additives as a result of the abrasive particles hitting the test samples in the silicon oxide-and aluminum oxide-doped GFRP samples created for the purpose of resistance to erosion wear, caused a crushing effect on the surfaces. Crushes on this surface prevented further breakage of the fibers by preventing matrix separation and caused some improvement in the wear properties of the test specimens. Composites with Al 2 O 3 -and SiO 2 -added to the matrix created better erosion resistance compared to the pure GFRP structure, and an improvement in erosion resistance occurred.

Delamination modelling
To model the process, implementation of experimental tests is required to find the relationship between responses and independent variables. An important step in response surface modelling is to define an appropriate approximation for the actual relationship between the response and the set of independent variables. A response surface is an analytical function such as a polynomial that relates the behavior of response variable to several independent variables. After the machining parameters and the response function are identified, the relations between the response and independent variables are modelled [29]. In mathematical model, the relation between cutting parameters and delamination factor is stated as follows: In the above equation, F d indicates delamination factor, v indicates cutting speed, and f indicates feed rate. In order to estimate the model coefficients, it is taken logarithms of both sides of the equation.
In this equation, while C i is a constant coefficient, ρ 1 and ρ 2 are the coefficients of the parameters. Equation (2) is stated in first order polynomial model as follows: When the same mathematical model is stated into second order, it is as follows: In this equation, Y I is the estimated response depending on first-and second-order equations, while y is real response. The coded variables of cutting speed and feed are x 1 and x 2 , experimental error is ε, and the estimated values of related The modelling is accomplished through mathematical and statistical methods to search for the delamination factor as the dependent variable. The cutting parameters were identified at three different levels and these are provided in Table 2.
In this current study, 12 tests based on rotatable centered composite design, three levels for any variable, were conducted. Table 2 shows the levels of variables.
Experimental plan and levels given in Table 3 were used to create second-order RSM model for three different composite materials. Specimens were drilled according to the defined plan and delamination factors were recorded. Relationships of coded variables and real parameters are given as follows: Second-order mathematical models were obtained for three different materials by means of RSM modelling using the experiment plan data given in Table 2. Coded variables were used in equations. Second-order mathematical models of delamination factors at hole entrance for pure GFRP/epoxy, Al 2 O 3 -added GFRP/ epoxy, and SiO 2 -added GFRP/epoxy were given with Eqs. (5), (6), and (7) respectively. Also, second-order mathematical models of delamination factors at hole exit for pure GFRP/epoxy, Al 2 O 3 -added GFRP/epoxy, and SiO 2 -added GFRP/epoxy were given with Eqs. (8), (9), and (10) respectively.
For GFRP/epoxy at the hole entrance: For %15 SiO 2 -added GFRP/epoxy at the hole entrance: The mathematical models derived from second-degree RSM are stated with Eqs. (5), (6), and (7). When the secondorder mathematical models obtained for delamination factor are examined, it is seen that the values of delamination factors for pure GFRP/epoxy composites are lower than for Al 2 O 3 -and SiO 2 -added GFRP composites. The linear effects of feed rate are bigger than cutting speed for three composite materials. The quadratic effects of cutting speed and feed rate are important for three of the materials.
For GFRP/epoxy at the hole exit: For %15 Al 2 O 3 -added GFRP/epoxy at the hole exit: For %15 SiO 2 -added GFRP/epoxy at the hole exit: When the mathematical models derived from seconddegree RSM stated with the Eqs. (8), (9), and (10) for delamination factors at hole exit are examined, it is seen that the values of delamination factors for pure GFRP/ epoxy composites are lower than for Al 2 O 3 and SiO 2 GFRP/epoxy composites. The linear effect of the cutting speed is smaller than the linear effect of the feed rate, but the linear effect of the cutting speed on the delamination factor at the hole exit is greater than the effect on the delamination factor at the hole entrance. The quadratic effects of cutting speed and feed rate are important for three of the materials. But linear effect of cutting speed is very smaller than the quadratic effects of cutting speed for SiO 2 -added GFRP at the hole exit.
As an example, it is seen the surface response, projection of contour plot, and optimum cutting speed and feed rate real values acquired from the delamination equation for GFRP/epoxy at the hole entrance obtained with RSM modelling in Fig. 3. It is obtained the minimum

Taguchi analysis
Taguchi method is an experimental technique developed by Dr. Genichi Taguchi to identify the most appropriate processing parameter intervals. The number of experiments will increase depending on the number of processing parameters. In order to solve this problem, Taguchi method reaches the result by combining three methods: orthogonal experimental design, signal-noise (S/N) ratio, and variance analysis (ANOVA). Orthogonal experimental design is used to create a special design by scanning all parameter space with minimum number of experiments. The results obtained from the planned experiments according to orthogonal experimental design are analyzed by transporting them into S/N ratio. The S/N ratio is used to measure performance characteristics of required values. The S/N ratio is identified depending on three major performance characteristics such as "(S/N) SB , the smallerthe better;" "(S/N) LB , the larger-the better;" and "(S/N) NB , nominal-the best." ANOVA is used to find out the statistical significance degree of processing parameters on performance characteristics. Apart from these there significant tools, one final verification test is conducted to check the reliability of the optimum results obtained through Taguchi method. The above-mentioned three major performance characteristics are stated with Eqs. (11), (12), and (13) [9]. Here, y i indicates the result measured in experiments, ӯ indicates the average of measured results from experiments, ŋ indicates the number of experiments, and s 2 indicates the variance of y.

Taguchi experimental design and selection of parameters
In the Taguchi analysis, the average value of experimental response and its corresponding signal to noise ratio (S/N) of each run can be calculated to analyze the effects of the machining parameters. However, S/N ratio was chosen for the Taguchi analysis because S/N ratio represents both the average and variation of the experimental results. In the current analysis, L9 orthogonal array was used. The data   obtained from experiment plan designed through Taguchi method is shown for at the entrance in Table 4 and for at the exit in Table 5.

Variance analysis for GFRP/epoxy
Within the scope of Taguchi method, the variance analysis for GFRP/epoxy at hole entrance is given in Table 6 and also the response table is given in Table 7.
The peel-up delamination factor obtained for various speed and feed combinations during the drilling of pure GFRP are presented in Fig. 4. The delamination at lower speeds were much lower than those obtained at higher speed. From the ANOVA calculations, it can be inferred that the peel-up delamination is influenced by cutting speed or feed in the selected range (Table 6).
In drilling GFRP/epoxy materials, at the hole entrance, the drilling parameters are feed rate of 0,05 mm/rev and cutting speed of 70 m/min that is obtained according to "the smaller-the better" rule for a minimum of delamination. Feed rate displays the highest effect on delamination factors. The contribution of feed rate is 74.87% and the effect of cutting speed is 13.27%.  Within the scope of Taguchi method, the variance analysis for GFRP/epoxy at the hole exit is provided in Table 8 and the response table is given in Table 9.
The push-out delamination factor obtained for various speed and feed combinations during the drilling of GFRP are presented in Fig. 5. It can be observed that the push-out delamination factor increases with an increase in feed rate and cutting speed. This could be because of smaller thickness of the GFRP laminates.
In the experiments, the delamination factor increased with an increase in cutting speed and feed rate. As feed rate is increased, the thrust force also increases. At high speed, the delamination may be initiated at lower forces because the heating of matrix resulting in lesser stiffness. Therefore, delamination factor increases less from low speed to high speeds.
In the drilling of GFRP/epoxy materials, according to the "smaller-better" rule, optimum drilling parameters were obtained as the feed rate of 0.05 mm/rev and cutting speed of 70 m/min for minimum delamination at the hole exit. Feed rate shows the highest influence on delamination factors. The contribution of feed rate is 91.72% and the effect of cutting speed is 4.13%.

Variance analysis forAl 2 O 3 -added material
Variance analysis for delamination factor at the hole entrance of Al 2 O 3 -added GFRP/epoxy composite material is given in Table 10 and the response table is provided in Table 11.   The peel-up delamination factor obtained for various speed and feed combinations during the drilling of Al 2 O 3 -added GFRP are presented in Fig. 6. The delamination at lower speeds were much lower than those obtained at higher speed. Al 2 O 3 -added GFRP composites showed similar properties to pure GFRP composites in terms of the effect of speed and feed on deformation.
In the drilling of Al 2 O 3 -added composite materials, feed of 0.05 mm/rev and cutting speed of 90 m/min were obtained as minimum drilling parameters for delamination according to "the smaller-the better" rule. Feed rate displays the highest effect on delamination. The effect of feed is 65.878% and the effect of cutting speed is 15.21%.
Variance analysis for delamination factor at the hole exit of Al 2 O 3 -added GFRP/epoxy composite material is given in Table 12 and response table is provided in Table 13.
The push-out delamination factor obtained for various speed and feed combinations during the drilling of Al 2 O 3 -added GFRP are presented in Fig. 7. The push-out delamination factor increases with an increase in feed rate and cutting speed. Delamination factor increases less from low speed to high speeds.
In drilling Al 2 O 3 -added composite materials, feed of 0.05 mm/rev and cutting speed of 50 m/min are obtained as minimum drilling parameters for delamination factor according to "the smaller-the better" rule. Feed rate displays the highest effect on delamination factor. The effect of feed is 81.423% and the effect of cutting speed is 16.889%.

Variance analysis forSiO 2 -added composite material
The peel-up delamination factor obtained for various speed and feed combinations during the drilling of SiO 2 -added GFRP are presented in Fig. 8. Delamination factor increases with an increase in feed rate and cutting speed.
Variance analysis for delamination factor at the hole entrance of SiO 2 -added GFRP/epoxy composite material is    given in Table 14 and response table is provided in Table 15.
In drilling SiO 2 -added materials, feed of 0.05 mm/rev and cutting speed of 50 m/min are obtained as minimum values for delamination factor according to "the smaller-the better" rule. Feed rate displays the biggest effect on delamination factor. The effect of feed is 76.66% and the effect of cutting speed is 19.03%.
The push-out delamination factor obtained for various speed and feed combinations during the drilling of SiO 2 -added GFRP are presented in Fig. 9. The push-out delamination factor increases with an increase in feed rate and cutting speed. The delamination is not influenced by speed in the selected range. The delamination factors are bigger than those Pure GFRP and Al 2 O 3 -added GFRP composites for various speed and feed combinations at the hole exit.
Variance analysis for delamination factor at the hole exit of SiO 2 -added GFRP/epoxy composite material is given in Table 16 and the response tables is provided in Table 17. In drilling SiO 2 -added materials, feed rate of 0.05 mm/rev and cutting speed of 50 m/min were obtained as minimum values for delamination factor at the hole exit according to "the smaller-the better" rule. Feed rate displays the biggest effect on delamination factor. The effect of feed is 93.31% and the effect of cutting speed is 1.05%.

Application of Taguchi approach by taking composite material as a variable
If we take material as the third parameter, orthogonal array in Taguchi method turns into the state in Table 18. Table 19, on the other hand, displays average loss function and S/N ratios. In the application of Taguchi method, for material is taken as a variable, for delamination factor at hole entrance, variance analysis for the three composite materials is given in Table 20 and the response table is in Table 21.
To determine the percentage contribution and optimum combination of drilling parameters more accurately, ANOVA was used. The results of ANOVA of the raw data or mean of delamination factor and the results of ANOVA of S/N ratios are given in Tables 19 and 20. The percentage contributions all the drilling parameters and materials are quantified under the last column of both the tables. Both of the tables suggest that the influence of material on delamination factor is very much larger than the influence of feed rate and cutting speed.
It is clear from Table 20 that delamination factor is minimum at first level of cutting speed, first level of feed rate,  and at second level of material. The S/N ratio analysis from Table 20 also shows the same results that delamination factor is minimum at first levels of cutting speed, feed rate, and second level material. To accordance with that, the minimum delamination factor was obtained for the smallest cutting speed and feed rate in the drilling of Al 2 O 3 -added GFRP composite.
In the application of Taguchi method for delamination factor at hole exit, when material is taken as a variable, orthogonal array in Taguchi method turns into the state in Table 18. Table 22 displays average loss function and S/N ratios, variance analysis for the three materials is given in Table 23, and the response table is in Table 24.
It is clear from Table 24 that delamination factor is minimum at first level of cutting speed, first level of feed rate, and at first level of material. The S/N ratio analysis from Table 24 also shows the similar results. To accordance with that, the minimum delamination factor was obtained for the smallest cutting speed and feed rate in drilling of pure GFRP/epoxy composite. When the percentage of contribution is examined in Table 23, it is seen that the effects of material, feed rate, and cutting speed on the delamination factor are 23.62%, 57.93% and 7.39%, respectively.
In the investigation of the change of delamination factor for the values of three levels of cutting speed and feed rate of three different composite materials in the drilling, it was found that the effect of the material on the delamination  Fig. 9 The effect of cutting speed and feed on push-out delamination factor  factor at the hole exit is larger than effect of cutting speed and less than feed rate. The best result of minimum delamination was obtained at pure GFRP/epoxy composite material in according to the rule is "the smallest is better." The minimum value of delamination factor was obtained at 0.05 mm/rev feed and 50 m/min speed values.
Due to the effect of delamination on the quality of the drilled surface, delamination is an indicator of the machinability of the material. For this reason, the material obtained the minimum delamination is a material that has better machinability from the three examined materials. Good machinability was obtained in drilling of pure GFRP/epoxy composite. Machinability gradually decreases from pure GRFP/epoxy composite toward Al 2 O 3 -added composite and SiO 2 -added composite materials.

Machinability index
A machinability index established in function of delamination factor. L9 orthogonal array that has nine rows corresponding to the number of tests (8 degrees of freedom) with two columns at three levels was chosen for determining machinability index.
The plan of experiments is made of nine tests (array rows) in which the first column was assigned to the cutting velocity (v) and the second column to the feed rate (f).The experimental plan and the chosen cutting parameters are given in Table 2.
In order to analyze the machinability of these materials, delamination factor (Fd) from experimental data have been obtained. These are given in Tables 4 and 5 for delamination factor at hole entrance and exit respectively. A machinability index (MI) is constructed as in Eq. (14).
Machinability indexes calculated with the delamination values obtained by using feed rate and cutting speed values according to L9 orthogonal index used in Taguchi analysis are given in Table 25. It can be evidenced that at the hole entrance, the Al 2 O 3 -added Epoxy/GFRP composite provides a better MI (average MI = 0.865) in comparison to Epoxy/GFRP (average MI = 0.792) and SiO 2 -added Epoxy/GFRP (average MI = 0.778). The material having the best machinability of the three materials was Al 2 O 3 -added GFRP composite at the entrance.
It can be evidenced that at the hole exit the Epoxy/ GFRP composite provides a better MI (average MI = 0.767) in comparison to Al 2 O 3 -added Epoxy/GFRP (average MI = 0.653) and SiO2-added Epoxy/GFRP (average MI = 0.678). Good machinability was obtained in drilling of pure GFRP/epoxy composite at the hole exit.

Optimization of delamination factor
Modified objective function and Kuhn-Tucker conditions Generalized mathematic model for delamination factor is taken as follows: For only one objective function and constraints, the formulation of optimization problem is as follows: Subject to: The derivatives of the modified objective function are as follows: The optimum values for delamination factor of Epoxy/ CFRP plate, SiO 2 -added GFRP/epoxy, and Al 2 O 3 -added GFRP/epoxy plate are given in Table 26 in the constraint region.
The optimum values for delamination factors of Epoxy/GFRP plate, SiO 2 -added GFRP/epoxy plate and Al 2 O 3 -added GFRP/epoxy plate are given in Table 26. For pure epoxy GFRP composite, the optimum parameters are x 1 = 1(v = 90 m/min) and x 2 = − 1(f = 0.05 mm/rev). For both of other materials, the optimum parameters was obtained as x 1 = − 1(v = 50 m/min) and x 2 = − 1(f = 0.05 mm/rev). The results of optimization were shown that the smallest value of feed rate decreases delamination factor, but the effect of cutting speed to delamination factor is less.

Multi-optimization for maximizing the material removal rate and minimizing delamination factor
In machining operation, maximizing the material removal rate and minimizing the surface quality are important criteria. The objectives set for the optimization is maximization of material removal rate and minimization of surface quality. First step in optimization is the formulation of objective function. Multi-objective function consists of the sum of each objective function using different weight coefficients for each criteria. Weighting factor assigns such that their sum was always equal to one. The weighting factor assigns to each parameter based on relative importance.
In the multi-objective optimization problem, two different and mutually conflicting objectives are selected to be optimized. The first objective function is material removal rate. The second objective function is the delamination factor, which describes the hole quality of the produced hole. First objective function must be maximized while the second one must be minimized. In order to homogenize all objectives, the material removal rate must be multiplied by − 1. After this change, in the problem there are only minimization objectives in the problem.
Multi-objective function for maximizing the metal removal rate and minimizing delamination and constraints are given as follows respectively: MOF is multi-objective function; ϕ and θ are weighting factors for material removal rate. where Y represents objective function for delamination factor. Y is any one of Y dfen1 , Y dfen2 , Y dfen3 . Also for the hole exit, the objective function for delamination factor is taken any one of Y dfex1 , Y dfex2 , Y dfex3 .

Constraints
There are the allowed ranges for the cutting parameters given by the validity range of the experimental models: or constraints are given for the coded variables as follows: where d is the diameter of hole, f is the feed rate, and v is the cutting speed.
Material removal rate is inversely proportional to the machining time.
where d is drill diameter, and in this work it was taken as 6 mm. So the statement of material removal is as following. The material removal rate with the coded variables are given as follows: Multi-objective optimization Multi-objective function for maximizing the metal removal rate and minimizing thrust force and constraints are given as follows respectively: or constraints are given for the coded variables as follows: Modified objective functions and Kuhn-Tucker conditions For multi-objective function and constraints, the formulation of problem is as following: or optimization model is as following: Subject to:  The derivatives of the modified objective function are as following: The optimum values for multi-objective functions created from material removal rate and delamination factor for GFRP/epoxy plate, SiO 2 -added GFRP/epoxy plate and Al 2 O 3-added GFRP/epoxy plate are given in Table 27. It can be seen that x 1 has the biggest value for three materials and x 2 have the smallest values for three composite materials. While weighting factor for material removal factor increases, x 1 and x 2 have the biggest values for Y dfex1 + M.

Data analysis on delamination at the entrance hole and exit hole for three composite materials
When the effects of the cutting parameters of the three materials on the delamination were examined, it was observed that the delamination increased gradually towards pure epoxy, Al 2 O 3 -doped, and SiO 2 -added GFRP respectively. This situation can be explained so that the bonding of powder Al 2 O 3 and SiO 2 additives added to pure epoxy with glass fiber is weaker than the bonding of pure epoxy to glass fibers. Therefore, it is easier to separate the fibers. The reason of this is that the mechanical properties of Al 2 O 3 -and SiO 2 -added GFRP composites are lower than Pure Epoxy GFRP.
It was observed that the delamination factor increased as the cutting speed and feed rate increased for the three materials at the hole entrance while the increase of delamination factor was lower with the increase of feed rate at 70 m/ min speed for pure and Al 2 O 3 -added GFRP. The effect on delamination factor of cutting speed is low at high feed rates at pure epoxy GFRP and at Al 2 O 3 -added GFRP as the effect on delamination is less at low feed rates at 70 m/min speed. Also, it was observed that delamination increased as cutting speeds and feed rates increased at SiO 2 -added GFRP. Low cutting speeds and feed rates give low delamination, while high feed and cutting speeds give higher delamination values.
The delamination factor increased with the increase in cutting speed at low feed rates, the effect of cutting speed on delamination was less with the increase in cutting speed at the high feed at pure epoxy GFRP, and the deformation factor increased as the cutting speed increase at Al 2 O 3 -and SiO 2 -added GFRP composites.
In our experimental study, the hole quality obtained as a result of delamination in drilling Al 2 O 3 -and SiO 2 -added glass fiber-reinforced epoxy composites with a twist drill bit determined worse than pure epoxy composites. Although Al 2 O 3 -and SiO 2 -added GFRP composites have high resistance to erosion wear, their mechanical properties are lower than pure epoxy composites as seen in Table 1. This shows that the bond of doped material, fiber, and epoxy is not strong and therefore the amount of delamination is high.

Conclusions
In the drilling of the pure GFRP/epoxy, Al 2 O 3 -and SiO 2 -added GFRP composites which were developed for resistance to erosion wear, the optimization and the effects of the cutting parameters on delamination, and machinability of the three composites were investigated. The following results were the following. The minimum delamination factor obtained at the smallest feed rate for three of the materials and feed rate shown the biggest effect to delamination factor. The effect of cutting speed to delamination factor is less and the cutting speeds for the minimum delamination were obtained 70 m/ min for GFRP/epoxy and 50 m/min for the other composite materials.
The contribution of feed rate is the biggest and the contribution of cutting speed is the smallest for the delamination formation of pure GFRP/epoxy according to added GFRP composites. The minimum delamination factor was obtained for the smallest cutting speed and feed rate in drilling of Al 2 O 3 -added GFRP composite.
The minimum delamination factor was obtained for the smallest cutting speed and feed rate for delamination at the hole exit in the drilling of pure GFRP/epoxy composite. It was found that the effect of the material is higher than feed rate and cutting speed on the delamination factor for delamination at the hole entrance. For delamination at the hole exit, it was found that the effect of the material is smaller than the feed rate and bigger than the cutting speed on the delamination factor. It was observed that the delamination factors at the hole exit were greater than the delamination factors at the hole entrance. It was seen that the delamination factor increased as the cutting speed and feed rate increased at the hole exit for all three materials.
The doped GFRP epoxy composite materials with high resistance to erosion wear have lower mechanical properties, lower machionability, and with higher delamination than pure epoxy GFRP materials since the bond between filler, fibers, and epoxy in doped composite materials is not strong.
According to the machinability index, it was seen that pure epoxy composite material has better machinability than the other composite materials at the exit. Al 2 O 3 -and SiO 2 -added GFRPs have been equivalent machinability. The reason for this deterioration of machining performance may be the abrasive effects of additives such as SiO 2 and Al 2 O 3 .
The optimum of delamination factor was obtained for the smallest cutting speed and feed rate for the three composites. To maximize MRR and minimize deformation factor, a multi-optimization function was created; the weighing factors MRR and deformation factor are taken as equal, optimum machining parameters were found that the cutting speed had the biggest value, and feed rate had the smallest value for the three composites.

Data availability
The authors confirm that the data and material supporting the findings of this work are available within the article.

Declarations
Ethics approval The article follows the guidelines of the Committee on Publication Ethics (COPE) and involves no studies on human or animal subjects.
Consent to participate All authors participated for the publication.
Consent to publish All authors give consent for publication.

Competing interests
The authors declare no competing interests.