Optimization of low-velocity impact behavior of FML structures at different environmental temperatures using Taguchi method and grey relational analysis

Optimization of low-velocity impact behavior of FML structures at different environmental temperatures using Taguchi method and grey relational analysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Optimization of low-velocity impact behavior of FML structures at different environmental temperatures using Taguchi method and grey relational analysis Mustafa DÜNDAR, İlyas Uygur, Ergün EKİCİ This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4807683/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Carbon fiber-reinforced Aluminum Laminate(CARALL) materials are a relatively new generation of Fibre Metal Laminate(FML) materials that have attracted interest due to their superior properties. This study investigates the low-velocity impact behavior of CARALL structures at different environmental temperatures(-40°C, 23°C and 80°C). Two different groups of CARALL composite structures with varying fiber orientations were produced by hot pressing in a 3/2 arrangement: C1(Al/0°90°/Al/90°0°/Al) and C2(Al/0°0°/Al/0°0°/Al/0°0°/Al). Low-velocity impact tests were conducted at 23J, 33J, and 48J energy levels using a Ø20 mm spherical impactor tip. The area of damage was detected by ultrasonic C-Scan. In addition, analysis of variance(ANOVA) was applied to reveal the influential parameters and their effect levels. After conducting experiments using the Taguchi L 18 test set, it was observed that the C2-coded specimen yielded better results in terms of maximum peak load, maximum displacement, and damage area. While the decrease in temperature increased the damage and maximum peak load, the increase in temperature did not cause a significant change in the maximum peak load. The primary damage mechanisms observed in damage investigations were matrix cracks and delamination between composite layers. Although delamination is present between the Al/CFRP layer, it is not significant. This result highlights the success and importance of the Phospho-Sulphuric Anodizing(PSA) pre-surface treatment applied to the aluminum plates. In all experiments, the most effective parameter was the impact energy. The optimal experimental conditions (23°C temperature and 23J impact energy with the C1-coded sample) were determined using grey relational analysis based on principal component analysis. Gri relation analysis Taguchi method Fiber metal laminates(FML) Carbon fiber-reinforced aluminium laminate (CARALL) Low-velocity impact Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Fiber Metal Laminates (FML) are hybrid structures consisting of thin metal layers and fiber composite structures [ 1 – 3 ]. Fiber Metal Laminate materials are classified as GLARE when glass fiber is used, ARALL when Aramid fiber is used, and CARALL when carbon fiber is used. [ 4 – 6 ]. FMLs combine the mechanical properties of fiber and metal materials, making them ideal for aerospace applications due to their superior properties, such as high specific strength, specific stiffness, and resistance to impact damage [ 7 – 10 ]. This outstanding performance of FMLs has attracted increased attention for aerospace applications, particularly due to their excellent impact resistance [ 11 – 14 ]. Internal damage caused by low-velocity, which is an important cause of damage, reduces the strength of the material and causes the damage to increase with the loads occurring after the damage. [ 15 ]. Therefore, investigating the low-velocity impact behavior of FMLs is crucial [ 16 ]. Carbon fiber-reinforced aluminium laminates (CARALL) are a relatively new type of fiber metal laminate material. Its characteristics include high fatigue strength, low density, and high impact resistance and stiffness. [ 17 , 18 ]. Carbon fiber-reinforced polymer matrix composite (FRP) structures are susceptible to dynamic loads, causing complex damage types. [ 19 – 21 ]. CARALL FML materials are almost inevitably subjected to low-velocity impacts during service life. Examples of low-velocity impacts include the impact of a stone during take-off, the dropping of a tool during service, or the impact of an object while the aircraft is stationary. [ 22 – 24 ]. These and similar events can damage FML structures, reducing their lifetime and load-carrying capacity. Even barely visible impact damage (BVID) may occur after low-velocity impacts and could lead to major accidents [ 10 ]. Therefore, investigating the impact resistance of CARALL materials is important. In the literature, many researchers have investigated the behavior of FML materials under impact loading. Jaroslaw et al. [ 21 ]. investigated the low-velocity impact behavior of carbon fiber and glass fiber-reinforced FML materials, focusing on fiber orientation and damage area at different energy loads. They reported that the initiation and propagation of delamination in glass fiber-reinforced FML performs energy absorption, while carbon fiber-reinforced FML absorbs energy through the perforation. Megeri and Naik [ 25 ] numerically investigated the low-velocity impact behavior of glass fiber-reinforced FML and glass-carbon hybrid FML. Analyzing the Force-Time and Force-Displacement graphs, they found that the glass-carbon hybrid FML showed superior properties. Drozdziel et al. [ 26 ] subjected conventional-thickness carbon fiber-reinforced FML and thin-thickness carbon fiber-reinforced materials to low-velocity impact tests at impact loads ranging from 2.5J to 30J. They observed that thin laminates were not effective in absorbing impact energy. Yao et al. [ 27 ] first investigated the low-velocity impact behavior and residual stress performance of carbon fiber-reinforced FML materials with different composite layers experimentally and numerically. They developed a numerical model in ABAQUS VUMAT to simulate the low-velocity impact and post-impact stress behavior, verifying the numerical model with experimental results. In their study, they concluded that the aluminum layer is dominant in maintaining structural integrity, while the composite layer disperses the impact energy through complex damage modes. Wang et al. [ 28 ] conducted a three-level low-velocity impact test on glass fiber-reinforced GLARE material under two different boundary conditions. They stated that the boundary conditions had a minimal effect on the force-energy responses compared to the test results and almost no effect on the damage behavior when perforation occurred. In aerospace applications, FMLs are exposed to a wide range of operating temperatures, from − 55˚C to 80˚C [ 29 ]. In the literature, Sarasini et al. [ 30 ] investigated the low-velocity impact behavior of two different PP-based thermoplastic fiber metal laminates (TMFLs) reinforced with Al2024-T3 basalt and glass fibers at room temperature and − 40°C. They reported that both TMFLs absorbed more impact energy than monolithic aluminum. Furthermore, basalt hybrid laminates exhibited lower damage in terms of matrix cracking and fibre breakage at low temperatures compared to their glass fibre counterparts. Chow et al. [ 31 ] studied the quasi-static perforation of FMLs at temperatures experimentally and numerically. They conducted quasi-static tests on the FML materials they produced at 30°C, 70°C, and 110°C. They reported that increasing the temperature decreased the structural integrity and damage resistance of all the materials. Cortes and Cantwell [ 32 ] investigated the low and high-velocity impact properties of FMLs based on carbon fiber-reinforced poly-ether-ether-ketone (CF/PEEK) and glass fiber-reinforced poly-ether-imide (GF/PEI) at elevated temperatures. Experimental results showed that the contribution of high-strength Ti alloy did not improve the impact properties of FMLs at elevated temperatures. Statistical methods are commonly used in literature to analyze experimental research. Since engineering problems affect many outcomes simultaneously, multi-parameter optimization methods are often preferred. Kopparthi et al. [ 33 ] used the Taguchi-grey relational analysis method to model mechanical properties and multi-response optimization of E-glass/polyester composite structures. Giammaria et al. [ 34 ] focused on an optimization study on linen/epoxy composite laminates at three different energies (5J, 10J, and 15J) using LS-OPT commercial software. Torabizadeh and Fereidoon [ 35 ] evaluated the effect of the impact element type, core thickness, and top layer arrangement of aluminum foam sandwich panels (AFSP) under impact loads. They also investigated the effective parameters on specific absorbed energy (SAE), maximum displacement (MD), and maximum impact force (MIF) using the Taguchi optimization method. Ardakani et al. [ 36 ] investigated the effect of layout on the impact response of polypropylene/E-glass composite laminates with different orientations (unidirectional, plain weave, and twill weave fiber). They used the Taguchi method to estimate and optimize the absorbed energy. Kumar et al. [ 37 ] ] investigated the ballistic impact behavior of Jute-Rubber-Jute-Epoxy (Sand)-Jute-Rubber-Jute (JRJ-ES-JRJ) hybrid sandwich composite materials subjected to ballistic impact for different core thicknesses, different filler compositions, and different projectile shapes by using Taguchi's design of experiments approach. Chauhan et al. [ 38 ] used Taguchi-based grey relational analysis to optimize cotton grass fiber-reinforced epoxy composites' mechanical and abrasive wear properties. In studies of composite structures, the Taguchi method is often used to evaluate the influence of input parameters on the response and their level of influence. However, research on FMLs in this context is very limited. Therefore, our study investigates the effects of impact energy, fiber orientation, and environmental temperature on the low-velocity impact behavior of FML structures. Additionally, multi-parameter optimization was applied for maximum impact force (MIF), maximum displacement (MD), and damage area (DA) using grey relational analysis. 2. Material Metod 2.1. Materials Al2024-T3 material with a thickness of 0.5 mm, supplied by Amag Rolling GmbH, was used as the metal layer due to its ductility and high strength-to-weight ratio. Carbon fiber was obtained from Dowaksa, and the resin was sourced from Fibermak Composite Company. The properties of all materials are presented in Table 1 . Before FML production, the aluminum plates were pre-treated to enhance the interfacial properties. 2.2. Surface Treatment of Metal Sheets Since the bond between the FRP and the metal layer is crucial for the performance of the FML material, the metallic layer is pre-treated to ensure stronger interfacial bonding. Well-prepared metal surfaces are particularly important for influencing the impact behavior of FML materials. While electrochemical processes are widely used due to their simplicity, phospho-sulphuric anodising (PSA) is notable for its superior interfacial bonding properties [ 39 ]. For these reasons, the PSA process was applied for 20 minutes at 21°C and 22 Volts to all aluminium plates following chemical pre-treatment. Table 1 Type and properties of materials Material Type Material Properties Aluminum 2024-T3 E: 72 GPa ρ = 2.7 g/cm³ Carbon fiber Uni Directional (UD) \(\:{\rho\:}_{A}\) = 300 g/m², Normal thickness= 0.3 mm Epoxy system F-RES 21/ F-HARD 22 ρ = 1.1 g/cm³ CFRP Carbon Fiber Reinforced Polymers \(\:{E}_{1}=\) 95.88 GPa, \(\:{E}_{2}=\) 7.387 GPa 2.2. Production of CARALL FMLs C1-coded specimens with Al/0°90°/Al/90°0°/Al orientation and C2-coded specimens with Al/0°0°/Al/0°0°/Al orientation were prepared based on the fiber orientation. CARALL FML composites, arranged in a 3/2 array and with dimensions of 500x500x2.75 mm, were produced using the hot pressing method at 125°C, 6 bar, for 75 minutes. The study flow chart is presented in Fig. 1 . 2.3. Low-Velocity İmpact Low-velocity impact test specimens were prepared by cutting with a water jet to dimensions of 80x80 mm. The experiments were conducted using the Instron CEAST 9350 impact testing machine, as shown in Fig. 2 a. This machine has a circular span of 40 mm, shown in Fig. 2 b. The schematic representation of the test setup is also shown in Fig. 2 b. The Ceast Visuall Impact software was utilized to obtain test parameters and data. A Ø20 spherical impactor was used in all experiments. The specimens were conditioned to test temperatures of -40°C, 23°C and 80°C in the cooling-heating cabin of the machine and kept in the cabin for 45 min before the experiments started (Fig. 2 a). 2.4. Ultrasonik C-Scan Ultrasonic C-Scan is a non-destructive testing method that allows for examining the image and size of damage in CARALL FML materials after low-velocity impact testing. This system provides an image of the damaged area within the material. Data is collected by moving the measurement probe across the material's surface. The device processes the collected data and generates an image of the damaged area, as shown in Fig. 3 . All scans were conducted using the Olympus Omniscan MX device. 2.5. X-Ray with crack analyses The X-ray machine was used to investigate the damage to the CARALL FML material in detail after a low-velocity impact event, particularly focusing on the cracks in the middle metal layer of the Al layers. The images that were obtained are presented and discussed in detail in the next sections. 3. Optimization methodology Engineering problems often require the simultaneous optimization of multiple responses. Consequently, researchers frequently encounter complex optimization challenges when seeking the optimal combination of parameters. In our study, which investigates the effects of FML on low-velocity impact behavior, single-parameter optimization was conducted using Taguchi S/N ratios to assess the individual effects of control factors. Following this, multi-parameter optimization was performed using grey relational analysis. 3.1. Single‑objective optimization Taguchi's signal-to-noise (S/N) ratio optimization technique, as a mono-optimization method, is an effective and widely applied approach in research [ 40 ]. The Taguchi method simplifies the analysis by evaluating experimental results based on the S/N ratio. This approach first converts the measured results into an S/N ratio to quantify the deviation between the observed values and the desired targets [ 41 ]. Doing so reduces variability in experiments, allowing for the identification of an optimal parameter set and minimizing the influence of uncontrollable factors [ 42 ]. For this study, the Taguchi L 18 (2 1 x3 2 ) orthogonal experimental design was utilized to investigate the effects of control factors (see Table 2 ) on the low-velocity impact behavior of FML. The S/N ratio criteria for maximum displacement and damage area were defined as "lower-better" (Eq. 1), while the S/N ratio criterion for maximum impact force was defined as "higher-better" (Eq. 2). $$\:S/N=-10\:log\left(\frac{1}{n}\sum\:_{i=1}^{n}{yi}^{2}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(1\right)$$ $$\:S/N=-10\:log\left(\frac{1}{n}\sum\:_{i=1}^{n}\frac{1}{{yi}^{2}}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(2\right)$$ Where n represents the number of observations and y denotes the observed data. Table 2 Factors and levels of the experimentation process Parameters Symbol Units Levels 1 2 3 Materials M - C1 C2 - Temperature T (°C) -40 25 80 Impact Energy IE (J) 23 33 48 3.2. Mutiple‑objective optimization Grey relational analysis is a commonly used method for establishing the relationships between data groups. Step 1. The first step of this method is to normalize the experimentally obtained data between 0 and 1 values [ 43 ]. The ‘bigger is better’ approach is normalized for maximum impact force values using Eq. 3. The Maximum displacement and damage area values are normalized using the 'smaller is better' approach, as described in Eq. 4. $$\:{X}_{i}^{*}\left(k\right)=\frac{{X}_{i}^{0}\left(k\right)-min{X}_{i}^{0}\left(k\right)}{max{X}_{i}^{0}\left(k\right)-min{X}_{i}^{0}\left(k\right)}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(3\right)$$ $$\:{X}_{i}^{*}\left(k\right)=\frac{{mak{X}_{i}^{0}\left(k\right)-\:X}_{i}^{0}\left(k\right)}{max{X}_{i}^{0}\left(k\right)-min{X}_{i}^{0}\left(k\right)}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(4\right)$$ Where \(\:{X}_{i}\left(k\right)\) represents the sequence after data preprocessing and \(\:{\:X}_{i}^{0}\left(k\right)\) represents the original sequence, while the maximum and minimum values of the original sequence are represented by \(\:{\:maxX}_{i}^{0}\left(k\right)\) and \(\:{\:maxX}_{i}^{0}\left(k\right)\) , respectively. Step 2 : After data preprocessing, the deviation sequence and the grey relational coefficient (GRC) are calculated. The grey relational coefficient (GRC) is determined using Eq. 5 to characterize the relationship between the desired and actual data. $$\:{\xi\:}_{i}\left(k\right)=\frac{{\varDelta\:}_{min}+\xi\:.{\varDelta\:}_{max}}{{\varDelta\:}_{oi}\left(k\right)+\xi\:.{\varDelta\:}_{max}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:0<\xi\:\le\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(5\right)$$ The descriptive coefficient \(\:\xi\:\) was set to 0.5 to allocate equal weight to each response parameter. Step 3 : After calculating the grey relational coefficients, the grey relational degree (GRG) is determined as the final step. The grey relational degree represents the weighted sum of the grey relational coefficients, indicating the degree of importance. The calculation of GRG is performed using Eq. 6. $$\:{\alpha\:}_{i}=\sum\:_{k=1}^{n}Wk{\xi\:}_{i}\left(k\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(6\right)$$ Here, Wk , represents the weight assigned to each factor. The weights used in the calculation of the grey relational degree (GRG) can be determined based on the researcher’s expertise [ 40 – 42 ]. Generally, when all process parameters are assumed to be equally weighted, the grey relational coefficients are averaged [ 33 , 41 , 43 , 44 ]. However, this approach may compromise the reliability of the results. Therefore, a more rigorous procedure is needed to calculate the weighting factors based on their effects on maximum impact force, maximum displacement, and damage area. The GRG's ranking may vary depending on the method used to determine the weights. This study employed principal component analysis (PCA) to determine the weights, ensuring a standardized protocol. The eigenvalues and contribution ratios of the principal components are presented in Table 3 . Table 3 Eigenvalues and contribution ratios of the principal components Response Eigenvalue Contr. (%) Maximum impact force λ 1 0.3364 33.6 Maximum displacement λ 2 0.35640 35.6 Damage area λ 3 0.30802 30.8 4. Results and discussion 4.1.Taguchi approach– single objective optimization The S/N ratios calculated with the help of the Minitab programme by considering the experimental plan, experimental results obtained and Equations 1 and 2 according to the factor levels specified in Table 2 are presented in Table 4 . Table 4 Experimental results and S/N ratio acquired based on Taguchi L 18 orthogonal array Exp. no. Control parameters Experimental results S/N ratios M T IE MIF MD DA MIF MD DA 1 1 -40 23 11474.144 4.241 819.072 81.194 -12.549 -58.266 2 1 -40 33 12937.012 5.016 924.121 82.237 -14.007 -59.315 3 1 -40 48 12956.466 5.112 1152.407 82.250 -14.172 -61.232 4 1 25 23 11167.657 4.128 716.337 80.959 -12.315 -57.102 5 1 25 33 12524.584 4.440 838.670 81.955 -12.948 -58.472 6 1 25 48 13718.938 4.670 1004.430 82.746 -13.386 -60.038 7 1 80 23 10742.583 4.003 954.651 80.622 -12.048 -59.597 8 1 80 33 12518.747 4.600 1045.490 81.951 -13.255 -60.386 9 1 80 48 13421.420 5.260 1162.266 82.556 -14.420 -61.306 10 2 -40 23 11949.713 4.466 776.774 81.547 -12.998 -57.806 11 2 -40 33 13501.182 4.736 902.222 82.607 -13.508 -59.106 12 2 -40 48 13779.376 4.900 1090.564 82.785 -13.804 -60.753 13 2 25 23 11024.668 4.124 760.960 80.847 -12.306 -57.627 14 2 25 33 12367.005 4.655 929.190 81.845 -13.358 -59.362 15 2 25 48 13929.173 5.054 1035.680 82.879 -14.073 -60.305 16 2 80 23 10546.096 4.074 830.216 80.462 -12.200 -58.384 17 2 80 33 12678.271 4.883 978.857 82.061 -13.774 -59.814 18 2 80 48 15257.892 5.597 1152.739 83.670 -14.959 -61.235 Maximum impact force total mean value (MIF): 12583.052 N Maximum displacement total mean value (MD): 4.664 mm Damage area total mean value (DA): 948.591 mm 2 4.1.1. Taguchi analysis for maximum impact force (Fmax) The main effect graphs of the maximum impact force (Ultimate Load-Peak Load or Fmax) of CARALL FML materials on low-velocity impact tests at different environmental temperatures are presented in Fig. 4 . Analysis of the average maximum impact force values reveals that the most influential factor is impact energy. The average maximum impact force values obtained were 11,150.8 N, 12,754.5 N, and 13,843.9 N for energy loads of 23 J, 33 J, and 48 J, respectively. With the increase in energy load, the maximum peak loads increased by 14.38% from 23 J to 33 J and 8.54% from 33 J to 48 J. This indicates that although the energy loads increase proportionally, the maximum peak loads do not increase proportionally. This can be explained by the damage conditions that occur within the internal structure of the materials after impact. At low-impact energies, the primary damage mechanism is the occurrence of delaminations and matrix cracks, not fiber cracking. Higher impact energies are related to a higher rate of damage [ 45 ]., This leads to a decrease in the stiffness of FML materials as fiber fractures occur, resulting in a loss of their ability to carry load [ 18 ]. Additionally, matrix cracks and fiber fractures are key damage mechanisms in laminates and typically occur under maximum impact force [ 46 , 47 ]. Fiber breakage, delamination, matrix cracks, and fracture of the aluminum layers are the main mechanisms that absorb the energy of the impactor. As the damage to the material increases, its load-carrying capacity decreases. Specimen C2 (0°-0°, fiber direction) exhibited higher peak loads across all energy levels compared to specimen C1 (0°-90°, fiber direction). The average peak load for specimen C2 was 12,781.5 N, whereas for specimen C1 it was 12,384.6 N. Thus, specimen C2 demonstrated 3.2% higher maximum impact force values than specimen C1. This is due to the delamination that frequently occurs in FRP structures with different fiber orientations. The reason for this is matrix cracks. During impact, the initial damage occurs at the interface between the matrix and the fiber. Here, the crack propagates between the two FRP layers and halts when there is a change in layer and fiber orientation. As a result of matrix cracking halting due to the change in fiber orientation, delamination occurs between the two FRP structures [ 48 ]. Delaminations are caused by matrix cracks, shear stress between layers, layer configuration, and plate deformation. Another main cause of delaminations is incompatible flexural stiffness due to fiber orientation. This mismatch is due to the ratio of modulus of elasticity( \(\:{(E}_{1}/{E}_{2})\) in unidirectional (UD) composite structures. The greater the ratio of \(\:{(E}_{1}/{E}_{2})\) , the larger the extent of delamination (e.g., FRPs with 0°-90° fiber orientation) [ 49 ] This has been confirmed by other researchers [ 50 ]. The main effect graph shows that environmental temperature conditions significantly impact the maximum peak load. The maximum peak loads were 12,766.3 N at -40°C, 12,455.3 N at room temperature, and 12,527.5 N at 80°C. The load at -40°C was 2.49% higher than at room temperature. At 80°C, it was 0.57% higher than at room temperature, though this difference was not very significant. The decrease in temperature increased the peak load, potentially due to the rise in thermal stresses in the inner layers, as the mismatch in the coefficient of thermal expansion facilitates the formation and propagation of matrix cracks [ 51 ]. The lower temperature also made the epoxy resin more brittle [ 52 ], increasing the material's brittleness and causing fractures in the carbon fibers, which are already sensitive to brittleness. This increased brittleness at low temperatures helps to absorb and dissipate impact energy, resulting in higher peak loads [ 21 ]. The increase in temperature did not result in a negligible increase in peak load. However, the damage conditions are quite different from each other. When all the results were analysed, it was seen that the most effective parameter was the energy load. 4.1.2. Taguchi analysis for maximum displacement Figure 5 illustrates the main effect graph for the maximum displacement of CARALL FML materials under varying environmental temperatures and energy loads. Analysis of the graph reveals that the energy load is the most influential parameter. The maximum displacements obtained were 4.17267 mm, 4.72167 mm and 5.0988 mm for 23 J, 33 J and 48 J energy loads, respectively. The maximum displacement increased by 13.15% from 23 J to 33 J and 7.98% from 33 J to 48 J. This indicates that specimens reaching the maximum peak load typically exhibit maximum displacement under non-penetration conditions [ 18 , 47 ]. The increased impact energy leads to greater stresses in the impact zone, resulting in more significant displacements due to shear forces between the layers [ 53 ]. Higher impact energies result in more structure damage (Table 5 . c-d). Caprino et al. reported that displacement increases proportionally with the rise in energy load [ 47 ]. When analyzing the main effect graph concerning fiber orientation, it is observed that the C1-coded specimen exhibits less displacement than the C2-coded specimen. The average displacements for specimens C1 and C2 are 4.607 mm and 4.721 mm, respectively. The C2-coded specimen displaces 2.47% more than the C1-coded specimen. However, the damage conditions are independent of these observations. Specimen C2 has fibers oriented in the same direction. Specimens with a 0°-0° fiber orientation have a higher longitudinal modulus, which is an important property for flexural strength. This allows specimen C2 to have more displacement [ 54 ]. However, the damage conditions are unrelated to this. When the main effect graph is analyzed regarding environmental temperatures in CARALL FML materials, the decrease and increase in temperature affected the displacement. When the average values were analyzed, it was observed that the material displaced 4.745 mm at -40°C, 4.511 mm at room temperature, and 4.736 mm at 80°C. At -40°C and 80°C, the displacement increased by 5.18% and 4.98%, respectively. The decrease and increase in temperature increased the displacement by 5%. The decrease in temperature is due to the brittle epoxy contained in the CFRP structure, a component of the CARALL FML material. The decrease in temperature makes the epoxy material even more brittle [ 55 , 56 ]. The fracture of the brittle epoxy makes the carbon fibers, which are sensitive to impact and prone to fracture, even more vulnerable to fracture. The brittleness of carbon fibers is a characteristic feature of this material group [ 48 , 57 ]. This caused more displacement of the material (Table 5 ). The increase in temperature is related to the deterioration of the stiffness and strength of CARALL FML material. The decrease in flexural stiffness with the deterioration of CFRP and cohesive layers reduces the load-carrying capacity of the material. Thus, the material causes more displacement. Chow et al. [ 58 ] Investigated the impact behavior of GLARE FML at different temperatures (30, 50, 70, 90, and 110°C). In the study, it was observed that there was a significant difference in the curves obtained at 30 and 50°C, but the increase in the maximum displacement became more noticeable at 50–70°C and the intensity gradually increased at 90–110°C. They also stated that the critical temperature value is important in FML materials. 4.1.3. Taguchi analysis for damage area Figure 6 presents the main effect graph of the damage area in CARALL FML materials under different environmental temperature conditions and energy loads. The area of damage was investigated by ultrasonic C-Scan method. The damage area is another crucial criterion for evaluating the impact resistance of FML materials. Analysis of the main effect graph reveals that the damage area increases with the rise in impact energy. The measured damage area includes all damage modes, including plastic deformation of the metal, delaminations between composite layers, matrix cracks, etc. [ 21 ]. The average damage areas observed at 23J, 33J, and 48J energy loads were 809.688 mm², 936.425 mm², and 1099.68 mm², respectively. The damage area increased by 15.65% from 23J to 33J and by 17.43% from 33J to 48J. This situation shows that the damage area increases with the energy load, but the increase of the damage area from 33J to 48J increased more. This trend suggests that material degradation intensifies with higher energy loads, leading to the emergence of various damage modes (Table 5 ). These implications for material degradation and the development of severe damage modes underscore the need for proactive measures and the potential impact of our research. It is also seen that the damage propagates over the full impact area as the energy load increases. This indicates that there is a progressive deterioration depending on the energy load and that different forms of damage occur with increasing impact energy. [ 45 ]. The impact energy was observed to be the most significant parameter affecting the increase in damage area. When specimens C1 and C2 are investigated in terms of fibre orientation, the main effective damage mode for specimen C1 is delamination between composite layers. This damage mode is characteristic of materials with different fiber orientations. According to Richardson and Wisheart [ 59 ], laminates with bidirectional fibre orientation are the worst in terms of damage accumulation because they produce strong shear stresses due to cracks and delaminations caused by the stiffness mismatch between the layers. Therefore, laminates with 0°/90° fibre orientation are one of the reasons for the complexity of the damage. Table 5 shows that the initial damage observed in the C1 coded specimens during tests at room temperature and 23J impact energy was between the composite plies, with some small micro-cracks also detected. In contrast, the C2-coded specimens exhibited small delaminations at the Al/CFRP interface. The average damage areas for the C1 and C2 coded specimens were 957.494 mm² and 939.689 mm², respectively. The damage area for the C1-coded specimens was 1.89% larger than that for the C2-coded specimens. Although the difference is relatively small, the two specimen types' matrix crack and delamination conditions are distinct. When analyzing the main effect graph regarding environmental temperatures for CARALL FML materials, both decreasing and increasing temperatures were observed to influence the damage area. In experiments conducted at -40°C, 23°C, and 80°C, the average damage area values were 944.193 mm², 880.878 mm², and 1020.7 mm², respectively. Compared to room temperature, a decrease in temperature resulted in a 7.18% increase in the damage area, while an increase in temperature led to a 15.87% increase. This indicates that temperature is a significant factor affecting the damage area. Lower temperatures and higher energy loads contributed to increased delamination between composite layers (Table 5 c). Additionally, delaminations, matrix cracks, fiber fracture, and other damage modes were observed between the Al/CFRP structure, with metal cracking occurring in all Al layers. This increased brittleness of the structure at lower temperatures, while the rise in temperature further expanded the damage area. This trend suggests a gradual deterioration of the CFRP and cohesive structure with temperature variations [ 58 ]. These findings have practical implications for the design and application of CARALL FML materials, enhancing the relevance of our research. Analysis of the macroscopic images in Table 5 d reveals that fractures in the middle Al layer resulted from combined global bending and local stress [ 54 ]. Cheng et al. [ 60 ] investigated the damage area of FML containing S-Glass (GLARE) at different temperatures (-30°C, 25°C, and 80°C), various FML types, and different energy loads using Ultrasonic C-Scan and X-Ray Computed Tomography (CT) during low-velocity impact. Their study found that temperature changes increased the damage area, with temperature variation being the most influential parameter after impact energy. However, intense delamination was not observed at the Al/CFRP interface. FML materials with high interfacial quality demonstrated higher load-bearing capacity, reduced metal/composite interfacial delamination, and smaller displacement than materials with poor interfacial bonding [ 61 , 62 ]. The literature confirms that the PSA process provides the most effective interfacial bonding [ 39 ]. 4.1.4. Variance analysis (ANOVA) The analysis of variance (ANOVA) technique is commonly employed to assess the contribution of each parameter and identify significant terms in the response [ 63 ]. The F statistic and p-values are used to evaluate the significance of the parameters, with a p-value less than 0.05 indicating a significant effect on the response. The results of the ANOVA, performed at a 95% confidence interval for the low-velocity impact test, are illustrated in Fig. 7 . The analysis reveals that impact energy (IE) is the most influential parameter across all responses. IE accounts for 81% of the contribution to maximum impact force, 75% to maximum displacement, and 76% to the damage area. For maximum impact force, the factors M and T have minimal significant effects, with contribution rates of 2.6% and 1.17%, respectively. The interaction between T and IE contributes significantly, at a rate of 9%. In terms of maximum displacement, the contribution rates for M and T are 1.67% and 6.08%, respectively, with the T*IE interaction contributing 10.2%. For the damaged area, T has a notable effect with a contribution rate of 17.57%. Overall, the ANOVA results indicate that IE has a predominant effect compared to all other factors. 4.1.5. Grey relational analysis (GRA) based multi‑objective optimization The single-parameter optimization section obtained optimal results for maximum impact force, maximum displacement, and damage area individually. However, these individual responses are interrelated. To address this, grey relational analysis was employed to integrate these responses into a single composite measure. Initially, the experimental results presented in Table 4 were normalized using Equations 3 and 4. A critical step in this process was the computation of the grey relational coefficient (GRC) using Eq. 5. This coefficient played a crucial role in the normalization process. The grey relational degree (GRG) was then calculated with Eq. 6, incorporating the weights determined through principal component analysis (see Table 3 ). A GRG value of 1, or close to 1, indicates ideal conditions. The ideal condition was achieved in experiment 4 (M = C2, T = 23°C, IE = 23J), which yielded a GRG of 0.7391 (refer to Table 6 ). Experiment 4 was followed by experiment 13 in terms of high GRG values. Table 7 presents the ideal conditions after single- and multi-parameter optimization of the input parameters for the desired targets of the responses after the low-velocity impact experiments performed under the conditions created according to the Taguchi L 18 experimental Table 6 Normalized results, grey relational coefcient, grey relational grade, and ranking Exp. No Normalization Deviation sequence GRC GRG MIF MD DA MIF MD DA MIF MD DA 1 0.1970 0.8507 0.7696 0.8030 0.1493 0.2304 0.38372 0.7700 0.6846 0.6144 2 0.5074 0.3645 0.5340 0.4926 0.6355 0.4660 0.50374 0.4403 0.5176 0.4858 3 0.5116 0.3043 0.0221 0.4884 0.6957 0.9779 0.50585 0.4182 0.3383 0.4234 4 0.1319 0.9216 1.0000 0.8681 0.0784 0.0000 0.36547 0.8644 1.0000 0.7391 5 0.4199 0.7258 0.7257 0.5801 0.2742 0.2743 0.46292 0.6459 0.6457 0.5848 6 0.6734 0.5816 0.3539 0.3266 0.4184 0.6461 0.60487 0.5444 0.4363 0.5319 7 0.0417 1.0000 0.4656 0.9583 0.0000 0.5344 0.34287 1.0000 0.4834 0.6206 8 0.4187 0.6255 0.2619 0.5813 0.3745 0.7381 0.46239 0.5717 0.4038 0.4837 9 0.6102 0.2114 0.0000 0.3898 0.7886 1.0000 0.56195 0.3880 0.3333 0.4300 10 0.2979 0.7095 0.8645 0.7021 0.2905 0.1355 0.41594 0.6325 0.7867 0.6077 11 0.6272 0.5402 0.5832 0.3728 0.4598 0.4168 0.57285 0.5209 0.5453 0.5463 12 0.6862 0.4373 0.1608 0.3138 0.5627 0.8392 0.61441 0.4705 0.3734 0.4894 13 0.1016 0.9241 0.8999 0.8984 0.0759 0.1001 0.35754 0.8682 0.8332 0.6864 14 0.3865 0.5910 0.5227 0.6135 0.4090 0.4773 0.44902 0.5500 0.5116 0.5047 15 0.7180 0.3407 0.2839 0.2820 0.6593 0.7161 0.63939 0.4313 0.4111 0.4954 16 0.0000 0.9555 0.7446 1.0000 0.0445 0.2554 0.33333 0.9182 0.6619 0.6433 17 0.4525 0.4479 0.4113 0.5475 0.5521 0.5887 0.47734 0.4753 0.4593 0.4714 18 1.0000 0.0000 0.0214 0.0000 1.0000 0.9786 1 0.3333 0.3381 0.5594 Abbreviations : Maximum impact force (MIF), Maximum displacement (MD) and Damage area (DA) Table 7 Optimum parameter levels by Taguchi and GRA Target Response Single‑objective optimization (Taguchi analysis) Mutiple‑objective optimization (GRA) Max. MIF M = C2, T=-40°C, IE = 48J Min. MD M = C1, T = 23°C, IE = 23J M = C2, T = 23°C, IE = 23J Min. DA M = C2, T = 23°C, IE = 23J 5. Conclusions The following results were obtained by investigating the low-velocity impact behavior of CARALL FML structures with different fiber orientations at different environmental temperatures; According to ANOVA results, impact energy was the most effective parameter for maximum impact force, maximum displacement, and damage area, with contribution rates of 81%, 74%, and 76%, respectively. After the grey relational analysis based on principal component analysis, in the set of experiments created after the grey relational analysis based on the principal component analysis, the experimental condition 4 (23°C temperature and 23J impact energy with the sample coded C1) was reached. From the Taguchi main effect graphs, the optimum parameters were determined as follows: C2 specimen at -40°C and 48 J for maximum impact force; C1 specimen at 23°C and 23 J for maximum displacement; and C2 specimen at 23°C and 23 J for minimum damage area. CARALL FML materials were found to be sensitive to the damage caused by changes in temperature. Temperature variation affects the maximum peak load, maximum displacement, and damage area. However, more detailed studies are needed, especially at high temperatures. Temperature change and an increase in impact energy increased the degradation of the material, leading to the expansion of the damage area. In all test conditions, the primary damage mechanism was found to be matrix cracks in CARALL FML materials and delamination between composite layers. This was followed by cracks in the aluminum metal layers, fiber rupture, and, to a lesser extent, delamination between the Al/CFRP structure. The low level of delamination between the Al/CFRP structure is due to the effectiveness of the pre-treatment PSA process applied to Al2024-T3 materials. Impact energy and different temperatures increased the displacement because CARALL increased the distortion in FML materials. Declarations Conflict of interest No potential confict of interest was reported by the author(s) Funding This study is supported by Düzce University Research Fund Project Number: 2020.06.05.1123 and 2021.06.05.1191 Author Contributions Mustafa Dündar is the owner of the research topic and contributed to the experiments, analysis of experimental data and preparation of the manuscript. Ilyas Uygur contributed to the supervision and preparation of the manuscript. Ergün Ekici contributed to the setup of the taguchi experimental set and the analysis of the optimisation. References Wang K, Taheri F (2023) Comparison of the Low-Velocity Impact Responses and Compressive Residual Strengths of GLARE and a 3DFML. 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Supplementary Files Table5Macroscopicexaminationsafterlowvelocityimpact.docx Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 08 Sep, 2024 Reviewers invited by journal 05 Sep, 2024 Editor assigned by journal 29 Jul, 2024 First submitted to journal 26 Jul, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4807683","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":349934133,"identity":"208de53c-3917-4641-8e71-eceec3555c87","order_by":0,"name":"Mustafa DÜNDAR","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxUlEQVRIiWNgGAWjYHACAwYGNgYGfiiPsYFoLZINcC3MRGoxOECsFt0G5m3SBWV2+cbHDx/dzMNgI7vhAP+xD/i0mB1gK5OecS7ZctuZtLTbPAxpxhsOMDPPwK+Fx0yat43ZwOwGjxlQy+FEkBa8DoNqqTcwngHW8p9oLYcNDCTAWg4QoeUwW7E1z7njBhJAv9ycY5BsPPMwszF+LcebN97mKas24G8/fOzGmwo72b7jjY/xakGLBAMMkVEwCkbBKBgF5AAANqhBFTcGtbcAAAAASUVORK5CYII=","orcid":"","institution":"Duzce Universitesi, Institute of Graduate Education, Mechanical Engineering","correspondingAuthor":true,"prefix":"","firstName":"Mustafa","middleName":"","lastName":"DÜNDAR","suffix":""},{"id":349934134,"identity":"aad776f6-e76c-4e69-b561-7c3022e021f2","order_by":1,"name":"İlyas Uygur","email":"","orcid":"","institution":"Duzce University, Faculty of Enginneering, Mechanical Engineering","correspondingAuthor":false,"prefix":"","firstName":"İlyas","middleName":"","lastName":"Uygur","suffix":""},{"id":349934135,"identity":"4cb8e771-ae94-4365-b694-ebe90791d2db","order_by":2,"name":"Ergün EKİCİ","email":"","orcid":"","institution":"Canakkale Onsekiz Mart University, Faculty of Engineering, Industrial Engineering","correspondingAuthor":false,"prefix":"","firstName":"Ergün","middleName":"","lastName":"EKİCİ","suffix":""}],"badges":[],"createdAt":"2024-07-26 11:34:58","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4807683/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4807683/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":67104921,"identity":"e0d39059-5f1d-49bd-a519-505d13c7c553","added_by":"auto","created_at":"2024-10-21 08:39:23","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":307288,"visible":true,"origin":"","legend":"\u003cp\u003eFlow chart\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4807683/v1/40d6cfc696eee5331279dd3d.png"},{"id":67103753,"identity":"74f82432-049c-497d-a405-b220ed47b85e","added_by":"auto","created_at":"2024-10-21 08:31:23","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":776870,"visible":true,"origin":"","legend":"\u003cp\u003ea) Instron Ceast 9350 Impact Test Machine, b) Schematic representation of the impact test setup\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4807683/v1/54613d706a5a7a23441e9072.png"},{"id":67103760,"identity":"d43f24f5-16ed-4e9e-8edf-bea0d8422478","added_by":"auto","created_at":"2024-10-21 08:31:23","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":998902,"visible":true,"origin":"","legend":"\u003cp\u003eDamage area measurement by ultrasonic C-Scan method\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4807683/v1/fc85dd694876c43fbfd812d0.png"},{"id":67105418,"identity":"9fdd21d3-6516-41c6-b2fe-4c2b53942531","added_by":"auto","created_at":"2024-10-21 08:47:23","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":114813,"visible":true,"origin":"","legend":"\u003cp\u003eMean response graph for maximum impact force\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4807683/v1/c262d24d3cc54ed194cf4c72.png"},{"id":67103756,"identity":"e1c6ace6-9846-4213-b325-66f1e4ea5152","added_by":"auto","created_at":"2024-10-21 08:31:23","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":112579,"visible":true,"origin":"","legend":"\u003cp\u003eMean response graph for maximum displacement\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4807683/v1/b1d4844a1c050a52b8f2b2a1.png"},{"id":67106558,"identity":"fe4256b5-7111-4dd0-9e59-d266c69f513a","added_by":"auto","created_at":"2024-10-21 08:55:23","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":107072,"visible":true,"origin":"","legend":"\u003cp\u003eMean response graph for damage area\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4807683/v1/7c54e9466c7111756fb21030.png"},{"id":67105417,"identity":"d75a82b8-3533-4c21-9c6c-f53d5ddbe0b4","added_by":"auto","created_at":"2024-10-21 08:47:23","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":79569,"visible":true,"origin":"","legend":"\u003cp\u003eANOVA results: a) Maximum impact force, b) Maximum displacement and c) Damage area\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4807683/v1/d3a4f48aa6e799bbdd998bd1.png"},{"id":67106747,"identity":"6d15c4f0-5b40-4f5f-b053-c2a223bc606e","added_by":"auto","created_at":"2024-10-21 09:03:26","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3905462,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4807683/v1/0e626c08-abb4-4270-80c9-23baaa8759db.pdf"},{"id":67104958,"identity":"58999118-0fb3-409c-9ad0-d6b7ec3fe72d","added_by":"auto","created_at":"2024-10-21 08:39:23","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1919641,"visible":true,"origin":"","legend":"","description":"","filename":"Table5Macroscopicexaminationsafterlowvelocityimpact.docx","url":"https://assets-eu.researchsquare.com/files/rs-4807683/v1/e9f7e19d5d634b24825ef52c.docx"}],"financialInterests":"","formattedTitle":"Optimization of low-velocity impact behavior of FML structures at different environmental temperatures using Taguchi method and grey relational analysis","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eFiber Metal Laminates (FML) are hybrid structures consisting of thin metal layers and fiber composite structures [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Fiber Metal Laminate materials are classified as GLARE when glass fiber is used, ARALL when Aramid fiber is used, and CARALL when carbon fiber is used. [\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. FMLs combine the mechanical properties of fiber and metal materials, making them ideal for aerospace applications due to their superior properties, such as high specific strength, specific stiffness, and resistance to impact damage [\u003cspan additionalcitationids=\"CR8 CR9\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. This outstanding performance of FMLs has attracted increased attention for aerospace applications, particularly due to their excellent impact resistance [\u003cspan additionalcitationids=\"CR12 CR13\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Internal damage caused by low-velocity, which is an important cause of damage, reduces the strength of the material and causes the damage to increase with the loads occurring after the damage. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Therefore, investigating the low-velocity impact behavior of FMLs is crucial [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Carbon fiber-reinforced aluminium laminates (CARALL) are a relatively new type of fiber metal laminate material. Its characteristics include high fatigue strength, low density, and high impact resistance and stiffness. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Carbon fiber-reinforced polymer matrix composite (FRP) structures are susceptible to dynamic loads, causing complex damage types. [\u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. CARALL FML materials are almost inevitably subjected to low-velocity impacts during service life. Examples of low-velocity impacts include the impact of a stone during take-off, the dropping of a tool during service, or the impact of an object while the aircraft is stationary. [\u003cspan additionalcitationids=\"CR23\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. These and similar events can damage FML structures, reducing their lifetime and load-carrying capacity. Even barely visible impact damage (BVID) may occur after low-velocity impacts and could lead to major accidents [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Therefore, investigating the impact resistance of CARALL materials is important.\u003c/p\u003e \u003cp\u003eIn the literature, many researchers have investigated the behavior of FML materials under impact loading. Jaroslaw et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. investigated the low-velocity impact behavior of carbon fiber and glass fiber-reinforced FML materials, focusing on fiber orientation and damage area at different energy loads. They reported that the initiation and propagation of delamination in glass fiber-reinforced FML performs energy absorption, while carbon fiber-reinforced FML absorbs energy through the perforation. Megeri and Naik [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] numerically investigated the low-velocity impact behavior of glass fiber-reinforced FML and glass-carbon hybrid FML. Analyzing the Force-Time and Force-Displacement graphs, they found that the glass-carbon hybrid FML showed superior properties. Drozdziel et al. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] subjected conventional-thickness carbon fiber-reinforced FML and thin-thickness carbon fiber-reinforced materials to low-velocity impact tests at impact loads ranging from 2.5J to 30J. They observed that thin laminates were not effective in absorbing impact energy. Yao et al. [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] first investigated the low-velocity impact behavior and residual stress performance of carbon fiber-reinforced FML materials with different composite layers experimentally and numerically. They developed a numerical model in ABAQUS VUMAT to simulate the low-velocity impact and post-impact stress behavior, verifying the numerical model with experimental results. In their study, they concluded that the aluminum layer is dominant in maintaining structural integrity, while the composite layer disperses the impact energy through complex damage modes. Wang et al. [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] conducted a three-level low-velocity impact test on glass fiber-reinforced GLARE material under two different boundary conditions. They stated that the boundary conditions had a minimal effect on the force-energy responses compared to the test results and almost no effect on the damage behavior when perforation occurred.\u003c/p\u003e \u003cp\u003eIn aerospace applications, FMLs are exposed to a wide range of operating temperatures, from \u0026minus;\u0026thinsp;55˚C to 80˚C [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. In the literature, Sarasini et al. [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] investigated the low-velocity impact behavior of two different PP-based thermoplastic fiber metal laminates (TMFLs) reinforced with Al2024-T3 basalt and glass fibers at room temperature and \u0026minus;\u0026thinsp;40\u0026deg;C. They reported that both TMFLs absorbed more impact energy than monolithic aluminum. Furthermore, basalt hybrid laminates exhibited lower damage in terms of matrix cracking and fibre breakage at low temperatures compared to their glass fibre counterparts. Chow et al. [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] studied the quasi-static perforation of FMLs at temperatures experimentally and numerically. They conducted quasi-static tests on the FML materials they produced at 30\u0026deg;C, 70\u0026deg;C, and 110\u0026deg;C. They reported that increasing the temperature decreased the structural integrity and damage resistance of all the materials. Cortes and Cantwell [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] investigated the low and high-velocity impact properties of FMLs based on carbon fiber-reinforced poly-ether-ether-ketone (CF/PEEK) and glass fiber-reinforced poly-ether-imide (GF/PEI) at elevated temperatures. Experimental results showed that the contribution of high-strength Ti alloy did not improve the impact properties of FMLs at elevated temperatures.\u003c/p\u003e \u003cp\u003eStatistical methods are commonly used in literature to analyze experimental research. Since engineering problems affect many outcomes simultaneously, multi-parameter optimization methods are often preferred. Kopparthi et al. [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] used the Taguchi-grey relational analysis method to model mechanical properties and multi-response optimization of E-glass/polyester composite structures. Giammaria et al. [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] focused on an optimization study on linen/epoxy composite laminates at three different energies (5J, 10J, and 15J) using LS-OPT commercial software. Torabizadeh and Fereidoon [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] evaluated the effect of the impact element type, core thickness, and top layer arrangement of aluminum foam sandwich panels (AFSP) under impact loads. They also investigated the effective parameters on specific absorbed energy (SAE), maximum displacement (MD), and maximum impact force (MIF) using the Taguchi optimization method. Ardakani et al. [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] investigated the effect of layout on the impact response of polypropylene/E-glass composite laminates with different orientations (unidirectional, plain weave, and twill weave fiber). They used the Taguchi method to estimate and optimize the absorbed energy. Kumar et al. [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e] ] investigated the ballistic impact behavior of Jute-Rubber-Jute-Epoxy (Sand)-Jute-Rubber-Jute (JRJ-ES-JRJ) hybrid sandwich composite materials subjected to ballistic impact for different core thicknesses, different filler compositions, and different projectile shapes by using Taguchi's design of experiments approach. Chauhan et al. [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e] used Taguchi-based grey relational analysis to optimize cotton grass fiber-reinforced epoxy composites' mechanical and abrasive wear properties.\u003c/p\u003e \u003cp\u003eIn studies of composite structures, the Taguchi method is often used to evaluate the influence of input parameters on the response and their level of influence. However, research on FMLs in this context is very limited. Therefore, our study investigates the effects of impact energy, fiber orientation, and environmental temperature on the low-velocity impact behavior of FML structures. Additionally, multi-parameter optimization was applied for maximum impact force (MIF), maximum displacement (MD), and damage area (DA) using grey relational analysis.\u003c/p\u003e"},{"header":"2. Material Metod","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Materials\u003c/h2\u003e \u003cp\u003eAl2024-T3 material with a thickness of 0.5 mm, supplied by Amag Rolling GmbH, was used as the metal layer due to its ductility and high strength-to-weight ratio. Carbon fiber was obtained from Dowaksa, and the resin was sourced from Fibermak Composite Company. The properties of all materials are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Before FML production, the aluminum plates were pre-treated to enhance the interfacial properties.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Surface Treatment of Metal Sheets\u003c/h2\u003e \u003cp\u003eSince the bond between the FRP and the metal layer is crucial for the performance of the FML material, the metallic layer is pre-treated to ensure stronger interfacial bonding. Well-prepared metal surfaces are particularly important for influencing the impact behavior of FML materials. While electrochemical processes are widely used due to their simplicity, phospho-sulphuric anodising (PSA) is notable for its superior interfacial bonding properties [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. For these reasons, the PSA process was applied for 20 minutes at 21\u0026deg;C and 22 Volts to all aluminium plates following chemical pre-treatment.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eType and properties of materials\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eMaterial\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eType\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eMaterial Properties\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAluminum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2024-T3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eE: 72 GPa ρ\u0026thinsp;=\u0026thinsp;2.7 g/cm\u0026sup3;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCarbon fiber\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUni Directional (UD)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\rho\\:}_{A}\\)\u003c/span\u003e\u003c/span\u003e = 300 g/m\u0026sup2;, Normal thickness= 0.3 mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEpoxy system\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eF-RES 21/ F-HARD 22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eρ\u0026thinsp;=\u0026thinsp;1.1 g/cm\u0026sup3;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCFRP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCarbon Fiber Reinforced\u003c/p\u003e \u003cp\u003ePolymers\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{1}=\\)\u003c/span\u003e\u003c/span\u003e 95.88 GPa, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{2}=\\)\u003c/span\u003e\u003c/span\u003e 7.387 GPa\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Production of CARALL FMLs\u003c/h2\u003e \u003cp\u003eC1-coded specimens with Al/0\u0026deg;90\u0026deg;/Al/90\u0026deg;0\u0026deg;/Al orientation and C2-coded specimens with Al/0\u0026deg;0\u0026deg;/Al/0\u0026deg;0\u0026deg;/Al orientation were prepared based on the fiber orientation. CARALL FML composites, arranged in a 3/2 array and with dimensions of 500x500x2.75 mm, were produced using the hot pressing method at 125\u0026deg;C, 6 bar, for 75 minutes. The study flow chart is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Low-Velocity İmpact\u003c/h2\u003e \u003cp\u003eLow-velocity impact test specimens were prepared by cutting with a water jet to dimensions of 80x80 mm. The experiments were conducted using the Instron CEAST 9350 impact testing machine, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea. This machine has a circular span of 40 mm, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb. The schematic representation of the test setup is also shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb. The Ceast Visuall Impact software was utilized to obtain test parameters and data. A \u0026Oslash;20 spherical impactor was used in all experiments. The specimens were conditioned to test temperatures of -40\u0026deg;C, 23\u0026deg;C and 80\u0026deg;C in the cooling-heating cabin of the machine and kept in the cabin for 45 min before the experiments started (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Ultrasonik C-Scan\u003c/h2\u003e \u003cp\u003eUltrasonic C-Scan is a non-destructive testing method that allows for examining the image and size of damage in CARALL FML materials after low-velocity impact testing. This system provides an image of the damaged area within the material. Data is collected by moving the measurement probe across the material's surface. The device processes the collected data and generates an image of the damaged area, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. All scans were conducted using the Olympus Omniscan MX device.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.5. X-Ray with crack analyses\u003c/h2\u003e \u003cp\u003eThe X-ray machine was used to investigate the damage to the CARALL FML material in detail after a low-velocity impact event, particularly focusing on the cracks in the middle metal layer of the Al layers. The images that were obtained are presented and discussed in detail in the next sections.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Optimization methodology","content":"\u003cp\u003eEngineering problems often require the simultaneous optimization of multiple responses. Consequently, researchers frequently encounter complex optimization challenges when seeking the optimal combination of parameters. In our study, which investigates the effects of FML on low-velocity impact behavior, single-parameter optimization was conducted using Taguchi S/N ratios to assess the individual effects of control factors. Following this, multi-parameter optimization was performed using grey relational analysis.\u003c/p\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1. Single‑objective optimization\u003c/h2\u003e\n \u003cp\u003eTaguchi\u0026apos;s signal-to-noise (S/N) ratio optimization technique, as a mono-optimization method, is an effective and widely applied approach in research [\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e]. The Taguchi method simplifies the analysis by evaluating experimental results based on the S/N ratio. This approach first converts the measured results into an S/N ratio to quantify the deviation between the observed values and the desired targets [\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e]. Doing so reduces variability in experiments, allowing for the identification of an optimal parameter set and minimizing the influence of uncontrollable factors [\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e]. For this study, the Taguchi L\u003csub\u003e18\u003c/sub\u003e (2\u003csup\u003e1\u003c/sup\u003ex3\u003csup\u003e2\u003c/sup\u003e) orthogonal experimental design was utilized to investigate the effects of control factors (see Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e) on the low-velocity impact behavior of FML. The S/N ratio criteria for maximum displacement and damage area were defined as \u0026quot;lower-better\u0026quot; (Eq.\u0026nbsp;1), while the S/N ratio criterion for maximum impact force was defined as \u0026quot;higher-better\u0026quot; (Eq.\u0026nbsp;2).\u003c/p\u003e\n \u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e$$\\:S/N=-10\\:log\\left(\\frac{1}{n}\\sum\\:_{i=1}^{n}{yi}^{2}\\right)\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(1\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equb\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e$$\\:S/N=-10\\:log\\left(\\frac{1}{n}\\sum\\:_{i=1}^{n}\\frac{1}{{yi}^{2}}\\right)\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(2\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eWhere n represents the number of observations and y denotes the observed data.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eFactors and levels of the experimentation process\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e\u003cem\u003eParameters\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e\u003cem\u003eSymbol\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e\u003cem\u003eUnits\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cem\u003eLevels\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e2\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e3\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaterials\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eM\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTemperature\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eT\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(\u0026deg;C)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eImpact Energy\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eIE\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(J)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e48\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2. Mutiple‑objective optimization\u003c/h2\u003e\n \u003cp\u003eGrey relational analysis is a commonly used method for establishing the relationships between data groups.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eStep 1.\u003c/strong\u003e The first step of this method is to normalize the experimentally obtained data between 0 and 1 values [\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e]. The \u0026lsquo;bigger is better\u0026rsquo; approach is normalized for maximum impact force values using Eq.\u0026nbsp;3. The Maximum displacement and damage area values are normalized using the \u0026apos;smaller is better\u0026apos; approach, as described in Eq.\u0026nbsp;4.\u003c/p\u003e\n \u003cdiv id=\"Equc\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e$$\\:{X}_{i}^{*}\\left(k\\right)=\\frac{{X}_{i}^{0}\\left(k\\right)-min{X}_{i}^{0}\\left(k\\right)}{max{X}_{i}^{0}\\left(k\\right)-min{X}_{i}^{0}\\left(k\\right)}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(3\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e$$\\:{X}_{i}^{*}\\left(k\\right)=\\frac{{mak{X}_{i}^{0}\\left(k\\right)-\\:X}_{i}^{0}\\left(k\\right)}{max{X}_{i}^{0}\\left(k\\right)-min{X}_{i}^{0}\\left(k\\right)}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(4\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{i}\\left(k\\right)\\)\u003c/span\u003e\u003c/span\u003e represents the sequence after data preprocessing and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:X}_{i}^{0}\\left(k\\right)\\)\u003c/span\u003e\u003c/span\u003e represents the original sequence, while the maximum and minimum values of the original sequence are represented by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:maxX}_{i}^{0}\\left(k\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:maxX}_{i}^{0}\\left(k\\right)\\)\u003c/span\u003e\u003c/span\u003e, respectively.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eStep 2 :\u0026nbsp;\u003c/strong\u003eAfter data preprocessing, the deviation sequence and the grey relational coefficient (GRC) are calculated. The grey relational coefficient (GRC) is determined using Eq. 5 to characterize the relationship between the desired and actual data.\u003c/p\u003e\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e$$\\:{\\xi\\:}_{i}\\left(k\\right)=\\frac{{\\varDelta\\:}_{min}+\\xi\\:.{\\varDelta\\:}_{max}}{{\\varDelta\\:}_{oi}\\left(k\\right)+\\xi\\:.{\\varDelta\\:}_{max}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:0\u0026lt;\\xi\\:\\le\\:1\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(5\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eThe descriptive coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\xi\\:\\)\u003c/span\u003e\u003c/span\u003e was set to 0.5 to allocate equal weight to each response parameter.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eStep 3 :\u0026nbsp;\u003c/strong\u003eAfter calculating the grey relational coefficients, the grey relational degree (GRG) is determined as the final step. The grey relational degree represents the weighted sum of the grey relational coefficients, indicating the degree of importance. The calculation of GRG is performed using Eq. 6.\u003c/p\u003e\n \u003cdiv id=\"Equf\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e$$\\:{\\alpha\\:}_{i}=\\sum\\:_{k=1}^{n}Wk{\\xi\\:}_{i}\\left(k\\right)\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(6\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eHere, \u003cem\u003eWk\u003c/em\u003e, represents the weight assigned to each factor. The weights used in the calculation of the grey relational degree (GRG) can be determined based on the researcher\u0026rsquo;s expertise [\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e]. Generally, when all process parameters are assumed to be equally weighted, the grey relational coefficients are averaged [\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e]. However, this approach may compromise the reliability of the results. Therefore, a more rigorous procedure is needed to calculate the weighting factors based on their effects on maximum impact force, maximum displacement, and damage area. The GRG\u0026apos;s ranking may vary depending on the method used to determine the weights. This study employed principal component analysis (PCA) to determine the weights, ensuring a standardized protocol. The eigenvalues and contribution ratios of the principal components are presented in Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eEigenvalues and contribution ratios of the principal components\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eResponse\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEigenvalue\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eContr. (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMaximum impact force \u0026lambda;\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.3364\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e33.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMaximum displacement \u0026lambda;\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.35640\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e35.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eDamage area \u0026lambda;\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.30802\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Results and discussion","content":"\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003e4.1.Taguchi approach\u0026ndash; single objective optimization\u003c/h2\u003e\n \u003cp\u003eThe S/N ratios calculated with the help of the Minitab programme by considering the experimental plan, experimental results obtained and Equations 1 and 2 according to the factor levels specified in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e are presented in Table \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eExperimental results and S/N ratio acquired based on Taguchi L\u003csub\u003e18\u003c/sub\u003e orthogonal array\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" rowspan=\"2\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003eExp. no.\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\" style=\"width: 10.1257%;\"\u003e\n \u003cp\u003eControl parameters\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\" style=\"width: 15.6583%;\"\u003e\n \u003cp\u003eExperimental results\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\" style=\"width: 13.7793%;\"\u003e\n \u003cp\u003eS/N ratios\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003eM\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003eT\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003eIE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003eMIF\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003eMD\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003eDA\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003eMIF\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003eMD\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003eDA\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e-40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e11474.144\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.241\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e819.072\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e81.194\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-12.549\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-58.266\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e-40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e12937.012\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e5.016\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e924.121\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e82.237\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-14.007\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-59.315\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e-40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e12956.466\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e5.112\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e1152.407\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e82.250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-14.172\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-61.232\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e11167.657\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.128\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e716.337\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e80.959\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-12.315\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-57.102\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e12524.584\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.440\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e838.670\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e81.955\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-12.948\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-58.472\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e13718.938\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.670\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e1004.430\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e82.746\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-13.386\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-60.038\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e10742.583\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.003\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e954.651\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e80.622\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-12.048\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-59.597\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e12518.747\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e1045.490\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e81.951\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-13.255\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-60.386\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e13421.420\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e5.260\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e1162.266\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e82.556\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-14.420\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-61.306\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e-40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e11949.713\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.466\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e776.774\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e81.547\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-12.998\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-57.806\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e-40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e13501.182\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.736\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e902.222\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e82.607\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-13.508\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-59.106\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e-40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e13779.376\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.900\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e1090.564\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e82.785\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-13.804\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-60.753\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e11024.668\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.124\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e760.960\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e80.847\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-12.306\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-57.627\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e12367.005\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.655\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e929.190\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e81.845\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-13.358\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-59.362\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e13929.173\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e5.054\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e1035.680\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e82.879\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-14.073\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-60.305\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e10546.096\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.074\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e830.216\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e80.462\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-12.200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-58.384\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e12678.271\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e4.883\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e978.857\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e82.061\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-13.774\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-59.814\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.3843%;\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 2.9229%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.9668%;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.2361%;\"\u003e\n \u003cp\u003e48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 6.4199%;\"\u003e\n \u003cp\u003e15257.892\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5492%;\"\u003e\n \u003cp\u003e5.597\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.6892%;\"\u003e\n \u003cp\u003e1152.739\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.2799%;\"\u003e\n \u003cp\u003e83.670\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-14.959\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7497%;\"\u003e\n \u003cp\u003e-61.235\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"10\" style=\"width: 44.7306%;\"\u003e\n \u003cp\u003eMaximum impact force total mean value (MIF): 12583.052 N\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"10\" style=\"width: 44.7306%;\"\u003e\n \u003cp\u003eMaximum displacement total mean value (MD): 4.664 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"10\" style=\"width: 44.7306%;\"\u003e\n \u003cp\u003eDamage area total mean value (DA): 948.591 mm\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e\n \u003ch2\u003e4.1.1. Taguchi analysis for maximum impact force (Fmax)\u003c/h2\u003e\n \u003cp\u003eThe main effect graphs of the maximum impact force (Ultimate Load-Peak Load or Fmax) of CARALL FML materials on low-velocity impact tests at different environmental temperatures are presented in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. Analysis of the average maximum impact force values reveals that the most influential factor is impact energy. The average maximum impact force values obtained were 11,150.8 N, 12,754.5 N, and 13,843.9 N for energy loads of 23 J, 33 J, and 48 J, respectively. With the increase in energy load, the maximum peak loads increased by 14.38% from 23 J to 33 J and 8.54% from 33 J to 48 J. This indicates that although the energy loads increase proportionally, the maximum peak loads do not increase proportionally. This can be explained by the damage conditions that occur within the internal structure of the materials after impact. At low-impact energies, the primary damage mechanism is the occurrence of delaminations and matrix cracks, not fiber cracking. Higher impact energies are related to a higher rate of damage [\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e]., This leads to a decrease in the stiffness of FML materials as fiber fractures occur, resulting in a loss of their ability to carry load [\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e]. Additionally, matrix cracks and fiber fractures are key damage mechanisms in laminates and typically occur under maximum impact force [\u003cspan class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e]. Fiber breakage, delamination, matrix cracks, and fracture of the aluminum layers are the main mechanisms that absorb the energy of the impactor. As the damage to the material increases, its load-carrying capacity decreases. Specimen C2 (0\u0026deg;-0\u0026deg;, fiber direction) exhibited higher peak loads across all energy levels compared to specimen C1 (0\u0026deg;-90\u0026deg;, fiber direction). The average peak load for specimen C2 was 12,781.5 N, whereas for specimen C1 it was 12,384.6 N. Thus, specimen C2 demonstrated 3.2% higher maximum impact force values than specimen C1. This is due to the delamination that frequently occurs in FRP structures with different fiber orientations. The reason for this is matrix cracks. During impact, the initial damage occurs at the interface between the matrix and the fiber. Here, the crack propagates between the two FRP layers and halts when there is a change in layer and fiber orientation. As a result of matrix cracking halting due to the change in fiber orientation, delamination occurs between the two FRP structures [\u003cspan class=\"CitationRef\"\u003e48\u003c/span\u003e]. Delaminations are caused by matrix cracks, shear stress between layers, layer configuration, and plate deformation. Another main cause of delaminations is incompatible flexural stiffness due to fiber orientation. This mismatch is due to the ratio of modulus of elasticity(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{(E}_{1}/{E}_{2})\\)\u003c/span\u003e\u003c/span\u003e in unidirectional (UD) composite structures. The greater the ratio of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{(E}_{1}/{E}_{2})\\)\u003c/span\u003e\u003c/span\u003e, the larger the extent of delamination (e.g., FRPs with 0\u0026deg;-90\u0026deg; fiber orientation) [\u003cspan class=\"CitationRef\"\u003e49\u003c/span\u003e] This has been confirmed by other researchers [\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eThe main effect graph shows that environmental temperature conditions significantly impact the maximum peak load. The maximum peak loads were 12,766.3 N at -40\u0026deg;C, 12,455.3 N at room temperature, and 12,527.5 N at 80\u0026deg;C. The load at -40\u0026deg;C was 2.49% higher than at room temperature. At 80\u0026deg;C, it was 0.57% higher than at room temperature, though this difference was not very significant. The decrease in temperature increased the peak load, potentially due to the rise in thermal stresses in the inner layers, as the mismatch in the coefficient of thermal expansion facilitates the formation and propagation of matrix cracks [\u003cspan class=\"CitationRef\"\u003e51\u003c/span\u003e]. The lower temperature also made the epoxy resin more brittle [\u003cspan class=\"CitationRef\"\u003e52\u003c/span\u003e], increasing the material\u0026apos;s brittleness and causing fractures in the carbon fibers, which are already sensitive to brittleness. This increased brittleness at low temperatures helps to absorb and dissipate impact energy, resulting in higher peak loads [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e]. The increase in temperature did not result in a negligible increase in peak load. However, the damage conditions are quite different from each other. When all the results were analysed, it was seen that the most effective parameter was the energy load.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e\n \u003ch2\u003e4.1.2. Taguchi analysis for maximum displacement\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the main effect graph for the maximum displacement of CARALL FML materials under varying environmental temperatures and energy loads. Analysis of the graph reveals that the energy load is the most influential parameter. The maximum displacements obtained were 4.17267 mm, 4.72167 mm and 5.0988 mm for 23 J, 33 J and 48 J energy loads, respectively. The maximum displacement increased by 13.15% from 23 J to 33 J and 7.98% from 33 J to 48 J. This indicates that specimens reaching the maximum peak load typically exhibit maximum displacement under non-penetration conditions [\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e]. The increased impact energy leads to greater stresses in the impact zone, resulting in more significant displacements due to shear forces between the layers [\u003cspan class=\"CitationRef\"\u003e53\u003c/span\u003e]. Higher impact energies result in more structure damage (Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e. c-d). Caprino et al. reported that displacement increases proportionally with the rise in energy load [\u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eWhen analyzing the main effect graph concerning fiber orientation, it is observed that the C1-coded specimen exhibits less displacement than the C2-coded specimen. The average displacements for specimens C1 and C2 are 4.607 mm and 4.721 mm, respectively. The C2-coded specimen displaces 2.47% more than the C1-coded specimen. However, the damage conditions are independent of these observations. Specimen C2 has fibers oriented in the same direction. Specimens with a 0\u0026deg;-0\u0026deg; fiber orientation have a higher longitudinal modulus, which is an important property for flexural strength. This allows specimen C2 to have more displacement [\u003cspan class=\"CitationRef\"\u003e54\u003c/span\u003e]. However, the damage conditions are unrelated to this.\u003c/p\u003e\n \u003cp\u003eWhen the main effect graph is analyzed regarding environmental temperatures in CARALL FML materials, the decrease and increase in temperature affected the displacement. When the average values were analyzed, it was observed that the material displaced 4.745 mm at -40\u0026deg;C, 4.511 mm at room temperature, and 4.736 mm at 80\u0026deg;C. At -40\u0026deg;C and 80\u0026deg;C, the displacement increased by 5.18% and 4.98%, respectively. The decrease and increase in temperature increased the displacement by 5%. The decrease in temperature is due to the brittle epoxy contained in the CFRP structure, a component of the CARALL FML material. The decrease in temperature makes the epoxy material even more brittle [\u003cspan class=\"CitationRef\"\u003e55\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e]. The fracture of the brittle epoxy makes the carbon fibers, which are sensitive to impact and prone to fracture, even more vulnerable to fracture. The brittleness of carbon fibers is a characteristic feature of this material group [\u003cspan class=\"CitationRef\"\u003e48\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e57\u003c/span\u003e]. This caused more displacement of the material (Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e). The increase in temperature is related to the deterioration of the stiffness and strength of CARALL FML material. The decrease in flexural stiffness with the deterioration of CFRP and cohesive layers reduces the load-carrying capacity of the material. Thus, the material causes more displacement. Chow et al. [\u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e] Investigated the impact behavior of GLARE FML at different temperatures (30, 50, 70, 90, and 110\u0026deg;C). In the study, it was observed that there was a significant difference in the curves obtained at 30 and 50\u0026deg;C, but the increase in the maximum displacement became more noticeable at 50\u0026ndash;70\u0026deg;C and the intensity gradually increased at 90\u0026ndash;110\u0026deg;C. They also stated that the critical temperature value is important in FML materials.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e\n \u003ch2\u003e4.1.3. Taguchi analysis for damage area\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e presents the main effect graph of the damage area in CARALL FML materials under different environmental temperature conditions and energy loads. The area of damage was investigated by ultrasonic C-Scan method. The damage area is another crucial criterion for evaluating the impact resistance of FML materials. Analysis of the main effect graph reveals that the damage area increases with the rise in impact energy. The measured damage area includes all damage modes, including plastic deformation of the metal, delaminations between composite layers, matrix cracks, etc. [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e]. The average damage areas observed at 23J, 33J, and 48J energy loads were 809.688 mm\u0026sup2;, 936.425 mm\u0026sup2;, and 1099.68 mm\u0026sup2;, respectively. The damage area increased by 15.65% from 23J to 33J and by 17.43% from 33J to 48J. This situation shows that the damage area increases with the energy load, but the increase of the damage area from 33J to 48J increased more. This trend suggests that material degradation intensifies with higher energy loads, leading to the emergence of various damage modes (Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e). These implications for material degradation and the development of severe damage modes underscore the need for proactive measures and the potential impact of our research. It is also seen that the damage propagates over the full impact area as the energy load increases. This indicates that there is a progressive deterioration depending on the energy load and that different forms of damage occur with increasing impact energy. [\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eThe impact energy was observed to be the most significant parameter affecting the increase in damage area. When specimens C1 and C2 are investigated in terms of fibre orientation, the main effective damage mode for specimen C1 is delamination between composite layers. This damage mode is characteristic of materials with different fiber orientations. According to Richardson and Wisheart [\u003cspan class=\"CitationRef\"\u003e59\u003c/span\u003e], laminates with bidirectional fibre orientation are the worst in terms of damage accumulation because they produce strong shear stresses due to cracks and delaminations caused by the stiffness mismatch between the layers. Therefore, laminates with 0\u0026deg;/90\u0026deg; fibre orientation are one of the reasons for the complexity of the damage. Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e shows that the initial damage observed in the C1 coded specimens during tests at room temperature and 23J impact energy was between the composite plies, with some small micro-cracks also detected. In contrast, the C2-coded specimens exhibited small delaminations at the Al/CFRP interface. The average damage areas for the C1 and C2 coded specimens were 957.494 mm\u0026sup2; and 939.689 mm\u0026sup2;, respectively. The damage area for the C1-coded specimens was 1.89% larger than that for the C2-coded specimens. Although the difference is relatively small, the two specimen types\u0026apos; matrix crack and delamination conditions are distinct.\u003c/p\u003e\n \u003cp\u003eWhen analyzing the main effect graph regarding environmental temperatures for CARALL FML materials, both decreasing and increasing temperatures were observed to influence the damage area. In experiments conducted at -40\u0026deg;C, 23\u0026deg;C, and 80\u0026deg;C, the average damage area values were 944.193 mm\u0026sup2;, 880.878 mm\u0026sup2;, and 1020.7 mm\u0026sup2;, respectively. Compared to room temperature, a decrease in temperature resulted in a 7.18% increase in the damage area, while an increase in temperature led to a 15.87% increase. This indicates that temperature is a significant factor affecting the damage area. Lower temperatures and higher energy loads contributed to increased delamination between composite layers (Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec). Additionally, delaminations, matrix cracks, fiber fracture, and other damage modes were observed between the Al/CFRP structure, with metal cracking occurring in all Al layers. This increased brittleness of the structure at lower temperatures, while the rise in temperature further expanded the damage area. This trend suggests a gradual deterioration of the CFRP and cohesive structure with temperature variations [\u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e]. These findings have practical implications for the design and application of CARALL FML materials, enhancing the relevance of our research.\u003c/p\u003e\n \u003cp\u003eAnalysis of the macroscopic images in Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ed reveals that fractures in the middle Al layer resulted from combined global bending and local stress [\u003cspan class=\"CitationRef\"\u003e54\u003c/span\u003e]. Cheng et al. [\u003cspan class=\"CitationRef\"\u003e60\u003c/span\u003e] investigated the damage area of FML containing S-Glass (GLARE) at different temperatures (-30\u0026deg;C, 25\u0026deg;C, and 80\u0026deg;C), various FML types, and different energy loads using Ultrasonic C-Scan and X-Ray Computed Tomography (CT) during low-velocity impact. Their study found that temperature changes increased the damage area, with temperature variation being the most influential parameter after impact energy. However, intense delamination was not observed at the Al/CFRP interface. FML materials with high interfacial quality demonstrated higher load-bearing capacity, reduced metal/composite interfacial delamination, and smaller displacement than materials with poor interfacial bonding [\u003cspan class=\"CitationRef\"\u003e61\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e62\u003c/span\u003e]. The literature confirms that the PSA process provides the most effective interfacial bonding [\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e].\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e\n \u003ch2\u003e4.1.4. Variance analysis (ANOVA)\u003c/h2\u003e\n \u003cp\u003eThe analysis of variance (ANOVA) technique is commonly employed to assess the contribution of each parameter and identify significant terms in the response [\u003cspan class=\"CitationRef\"\u003e63\u003c/span\u003e]. The F statistic and p-values are used to evaluate the significance of the parameters, with a p-value less than 0.05 indicating a significant effect on the response. The results of the ANOVA, performed at a 95% confidence interval for the low-velocity impact test, are illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e. The analysis reveals that impact energy (IE) is the most influential parameter across all responses. IE accounts for 81% of the contribution to maximum impact force, 75% to maximum displacement, and 76% to the damage area. For maximum impact force, the factors M and T have minimal significant effects, with contribution rates of 2.6% and 1.17%, respectively. The interaction between T and IE contributes significantly, at a rate of 9%. In terms of maximum displacement, the contribution rates for M and T are 1.67% and 6.08%, respectively, with the T*IE interaction contributing 10.2%. For the damaged area, T has a notable effect with a contribution rate of 17.57%. Overall, the ANOVA results indicate that IE has a predominant effect compared to all other factors.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e\n \u003ch2\u003e4.1.5. Grey relational analysis (GRA) based multi‑objective optimization\u003c/h2\u003e\n \u003cp\u003eThe single-parameter optimization section obtained optimal results for maximum impact force, maximum displacement, and damage area individually. However, these individual responses are interrelated. To address this, grey relational analysis was employed to integrate these responses into a single composite measure. Initially, the experimental results presented in Table \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e were normalized using Equations 3 and 4. A critical step in this process was the computation of the grey relational coefficient (GRC) using Eq. 5. This coefficient played a crucial role in the normalization process. The grey relational degree (GRG) was then calculated with Eq. 6, incorporating the weights determined through principal component analysis (see Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). A GRG value of 1, or close to 1, indicates ideal conditions. The ideal condition was achieved in experiment 4 (M\u0026thinsp;=\u0026thinsp;C2, T\u0026thinsp;=\u0026thinsp;23\u0026deg;C, IE\u0026thinsp;=\u0026thinsp;23J), which yielded a GRG of 0.7391 (refer to Table \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e). Experiment 4 was followed by experiment 13 in terms of high GRG values.\u003c/p\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e presents the ideal conditions after single- and multi-parameter optimization of the input parameters for the desired targets of the responses after the low-velocity impact experiments performed under the conditions created according to the Taguchi L\u003csub\u003e18\u003c/sub\u003e experimental\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab6\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eNormalized results, grey relational coefcient, grey relational grade, and ranking\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" rowspan=\"2\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003eExp.\u003c/p\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\" style=\"width: 16.5521%;\"\u003e\n \u003cp\u003eNormalization\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\" style=\"width: 16.5521%;\"\u003e\n \u003cp\u003eDeviation sequence\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\" style=\"width: 21.2381%;\"\u003e\n \u003cp\u003eGRC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" rowspan=\"2\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003eGRG\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003eMIF\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003eMD\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003eDA\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003eMIF\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003eMD\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003eDA\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003eMIF\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003eMD\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003eDA\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.1970\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.8507\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.7696\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.8030\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.1493\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.2304\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e0.38372\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.7700\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6846\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6144\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5074\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.3645\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5340\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4926\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6355\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4660\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e0.50374\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4403\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5176\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4858\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5116\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.3043\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.0221\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4884\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6957\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.9779\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e0.50585\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4182\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.3383\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4234\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.1319\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.9216\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e1.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n 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align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.7258\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.7257\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5801\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.2742\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.2743\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e0.46292\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6459\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6457\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5848\u003c/p\u003e\n \u003c/td\u003e\n 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align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5344\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e0.34287\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e1.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4834\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6206\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4187\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6255\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n 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align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6102\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.2114\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.3898\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.7886\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e1.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e0.56195\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.3880\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.3333\u003c/p\u003e\n \u003c/td\u003e\n 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align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4598\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4168\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e0.57285\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5209\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5453\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5463\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6862\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n 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align=\"left\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.1016\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.9241\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.8999\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.8984\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.0759\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.1001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e0.35754\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.8682\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.8332\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6864\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.3865\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5910\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5227\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6135\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4090\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4773\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e0.44902\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5116\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5047\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.7180\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.3407\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.2839\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.2820\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6593\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.7161\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e0.63939\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4313\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4111\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4954\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.9555\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.7446\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e1.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.0445\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.2554\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e0.33333\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.9182\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6619\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.6433\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4525\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4479\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4113\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5475\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5521\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5887\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e0.47734\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4753\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4593\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.4714\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.0813%;\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e1.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.0214\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e1.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.9786\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 10.2033%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.3333\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.3381\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.5174%;\"\u003e\n \u003cp\u003e0.5594\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"11\" style=\"width: 64.7724%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eAbbreviations\u003c/strong\u003e: \u003cem\u003eMaximum impact force (MIF), Maximum displacement (MD) and Damage area (DA)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab7\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eOptimum parameter levels by Taguchi and GRA\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTarget\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eResponse\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eSingle‑objective optimization\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e(Taguchi analysis)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e\u003cem\u003eMutiple‑objective optimization\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e(GRA)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMax.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMIF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM\u0026thinsp;=\u0026thinsp;C2, T=-40\u0026deg;C, IE\u0026thinsp;=\u0026thinsp;48J\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMin.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM\u0026thinsp;=\u0026thinsp;C1, T\u0026thinsp;=\u0026thinsp;23\u0026deg;C, IE\u0026thinsp;=\u0026thinsp;23J\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eM\u0026thinsp;=\u0026thinsp;C2, T\u0026thinsp;=\u0026thinsp;23\u0026deg;C, IE\u0026thinsp;=\u0026thinsp;23J\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMin.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM\u0026thinsp;=\u0026thinsp;C2, T\u0026thinsp;=\u0026thinsp;23\u0026deg;C, IE\u0026thinsp;=\u0026thinsp;23J\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThe following results were obtained by investigating the low-velocity impact behavior of CARALL FML structures with different fiber orientations at different environmental temperatures;\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eAccording to ANOVA results, impact energy was the most effective parameter for maximum impact force, maximum displacement, and damage area, with contribution rates of 81%, 74%, and 76%, respectively.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eAfter the grey relational analysis based on principal component analysis, in the set of experiments created after the grey relational analysis based on the principal component analysis, the experimental condition 4 (23\u0026deg;C temperature and 23J impact energy with the sample coded C1) was reached.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eFrom the Taguchi main effect graphs, the optimum parameters were determined as follows: C2 specimen at -40\u0026deg;C and 48 J for maximum impact force; C1 specimen at 23\u0026deg;C and 23 J for maximum displacement; and C2 specimen at 23\u0026deg;C and 23 J for minimum damage area.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eCARALL FML materials were found to be sensitive to the damage caused by changes in temperature.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTemperature variation affects the maximum peak load, maximum displacement, and damage area. However, more detailed studies are needed, especially at high temperatures.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTemperature change and an increase in impact energy increased the degradation of the material, leading to the expansion of the damage area.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eIn all test conditions, the primary damage mechanism was found to be matrix cracks in CARALL FML materials and delamination between composite layers. This was followed by cracks in the aluminum metal layers, fiber rupture, and, to a lesser extent, delamination between the Al/CFRP structure. The low level of delamination between the Al/CFRP structure is due to the effectiveness of the pre-treatment PSA process applied to Al2024-T3 materials.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eImpact energy and different temperatures increased the displacement because CARALL increased the distortion in FML materials.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eNo potential confict of interest was reported by the author(s)\u003c/p\u003e\n\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eThis study is supported by D\u0026uuml;zce University Research Fund Project Number: 2020.06.05.1123 and 2021.06.05.1191\u003c/p\u003e\n\u003ch2\u003eAuthor Contributions\u003c/h2\u003e\n\u003cp\u003eMustafa D\u0026uuml;ndar is the owner of the research topic and contributed to the experiments, analysis of experimental data and preparation of the manuscript. Ilyas Uygur contributed to the supervision and preparation of the manuscript. Erg\u0026uuml;n Ekici contributed to the setup of the taguchi experimental set and the analysis of the optimisation.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eWang K, Taheri F (2023) Comparison of the Low-Velocity Impact Responses and Compressive Residual Strengths of GLARE and a 3DFML. Polymers (Basel) 15:. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/polym15071723\u003c/span\u003e\u003cspan address=\"10.3390/polym15071723\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTsartsaris N, Meo M, Dolce F et al (2011) Low-velocity impact behavior of fiber metal laminates. 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J Brazilian Soc Mech Sci Eng 40:400. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s40430-018-1318-y\u003c/span\u003e\u003cspan address=\"10.1007/s40430-018-1318-y\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Table","content":"\u003cp\u003eTable 5 is available in the Supplementary Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-the-brazilian-society-of-mechanical-sciences-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmse","sideBox":"Learn more about [Journal of the Brazilian Society of Mechanical Sciences and Engineering](http://link.springer.com/journal/40430)","snPcode":"40430","submissionUrl":"https://www.editorialmanager.com/bmse/default2.aspx","title":"Journal of the Brazilian Society of Mechanical Sciences and Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Gri relation analysis, Taguchi method, Fiber metal laminates(FML), Carbon fiber-reinforced aluminium laminate (CARALL), Low-velocity impact","lastPublishedDoi":"10.21203/rs.3.rs-4807683/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4807683/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCarbon fiber-reinforced Aluminum Laminate(CARALL) materials are a relatively new generation of Fibre Metal Laminate(FML) materials that have attracted interest due to their superior properties. This study investigates the low-velocity impact behavior of CARALL structures at different environmental temperatures(-40\u0026deg;C, 23\u0026deg;C and 80\u0026deg;C). Two different groups of CARALL composite structures with varying fiber orientations were produced by hot pressing in a 3/2 arrangement: C1(Al/0\u0026deg;90\u0026deg;/Al/90\u0026deg;0\u0026deg;/Al) and C2(Al/0\u0026deg;0\u0026deg;/Al/0\u0026deg;0\u0026deg;/Al/0\u0026deg;0\u0026deg;/Al). Low-velocity impact tests were conducted at 23J, 33J, and 48J energy levels using a \u0026Oslash;20 mm spherical impactor tip. The area of damage was detected by ultrasonic C-Scan. In addition, analysis of variance(ANOVA) was applied to reveal the influential parameters and their effect levels. After conducting experiments using the Taguchi L\u003csub\u003e18\u003c/sub\u003e test set, it was observed that the C2-coded specimen yielded better results in terms of maximum peak load, maximum displacement, and damage area. While the decrease in temperature increased the damage and maximum peak load, the increase in temperature did not cause a significant change in the maximum peak load. The primary damage mechanisms observed in damage investigations were matrix cracks and delamination between composite layers. Although delamination is present between the Al/CFRP layer, it is not significant. This result highlights the success and importance of the Phospho-Sulphuric Anodizing(PSA) pre-surface treatment applied to the aluminum plates. In all experiments, the most effective parameter was the impact energy. The optimal experimental conditions (23\u0026deg;C temperature and 23J impact energy with the C1-coded sample) were determined using grey relational analysis based on principal component analysis.\u003c/p\u003e","manuscriptTitle":"Optimization of low-velocity impact behavior of FML structures at different environmental temperatures using Taguchi method and grey relational analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-21 08:31:18","doi":"10.21203/rs.3.rs-4807683/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2024-09-08T05:20:03+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-09-05T09:54:55+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-29T14:48:07+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of the Brazilian Society of Mechanical Sciences and Engineering","date":"2024-07-26T07:34:13+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-the-brazilian-society-of-mechanical-sciences-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmse","sideBox":"Learn more about [Journal of the Brazilian Society of Mechanical Sciences and Engineering](http://link.springer.com/journal/40430)","snPcode":"40430","submissionUrl":"https://www.editorialmanager.com/bmse/default2.aspx","title":"Journal of the Brazilian Society of Mechanical Sciences and Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"815c9a7a-503c-4ea5-a2e0-38c7472d3004","owner":[],"postedDate":"October 21st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-10-21T08:31:18+00:00","versionOfRecord":[],"versionCreatedAt":"2024-10-21 08:31:18","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4807683","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4807683","identity":"rs-4807683","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}