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

doi:10.21203/rs.3.rs-4807683/v1

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 L₁₈ 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

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.

2.1. 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. 2a. This machine has a circular span of 40 mm, shown in Fig. 2b. The schematic representation of the test setup is also shown in Fig. 2b. 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. 2a).

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.

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 L₁₈ (2¹x3²) 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
Parameters	Symbol	Units	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 λ₁	0.3364	33.6
Maximum displacement λ₂	0.35640	35.6
Damage area λ₃	0.30802	30.8

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 L₁₈ orthogonal array
Exp. no.	Control parameters			Experimental results			S/N ratios
Exp. no.	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 mm²

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 5c). 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 5d 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 L₁₈ experimental

Table 6

Normalized results, grey relational coefcient, grey relational grade, and ranking
Exp. No	Normalization			Deviation sequence			GRC			GRG
Exp. No	MIF	MD	DA	MIF	MD	DA	MIF	MD	DA	GRG
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

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.

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.

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Table 5 is available in the Supplementary Files section.

Table5Macroscopicexaminationsafterlowvelocityimpact.docx

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

Status:

Version 1

Abstract

Figures

1. Introduction

2. Material Metod