Analysis and Optimization of Laser Beam Welding Parameters for Aluminium Composite (Al-Zn-Cu Alloy) by Grey Relational Optimization

Abstract

Aluminium and its composites are widely used in production to enhance the strength of lightweight objects. In this study, an AA7075/SiC composite was fabricated using a stir casting route. Multi-objective optimization and finite element analysis were performed with various process parameters on a manufactured aluminium composite (AA7075 + SiC) undergoing a laser beam welding process. Four welding parameters, i.e., pulse frequency, power, welding speed (transverse), and wire size were taken for laser welding as per the L-9 orthogonal array for experimental study. Tensile strength, deflection, temperature distribution, Rockwell hardness (fusion zone), and Rockwell hardness (heat affected zone) were taken as output parameters after welding. The standard deviation objective weighting–grey relational optimization method optimized the process parameter. ANSYS APDL 23 software was utilized to simulate the entire laser welding method with a cylindrical heat source to predict the temperature distribution in the butt-welded plates. This software uses finite element analysis and gives a deviation of only 5.85% for temperature distribution with experimental results. This study helps to understand the effect of various parameters on the welding strength of the aluminium composite.

1. Introduction

Aluminium composite sheets are widely used in the aerospace and automotive industries due to their lightweight strength, excellent resistance to corrosion, high fatigue durability, resistance to creep, and superior formability compared to traditional aluminium [1]. Aluminium composites help to reduce the weight of automobile vehicles and aeroplanes without affecting their performance, and they also improve fuel efficiency due to their low weight and high stiffness [2]. AA 7XXX series aluminium alloys can also be used for considerable mass reduction in producing super lightweight cars [3,4,5]. Aluminium alloys are joined using conventional TIG welding, but it is impossible to remove welding defects like cracks, hot tears, and porosity [6]. Laser welding is a non-contact fusion welding method in which a laser beam is directed into the cavity between two metal pieces to be welded, producing heat that melts the material from the metal piece and fills the cavity as it strikes the metal pieces [7]. The types of laser welding machines used depend on the method of laser production. Commonly used lasers are helium–neon and Nd:YAG lasers [8]. Laser welding produces a small heat-affected zone and reduces welding defects compared to conventional welding. The laser welding of thin sheets (less than 3 mm) of aluminium alloy and the yield of high-strength welded joints through the laser welding process have been validated by researchers [9]. Laser pulse welding has a minimal heat-affected zone and is less prone to thermal distortion, which reduces welding defects [10]. The weakest sections of aluminium composite material weldments are the weld bead and the heat-affected zone because welding deformation readily creates cracks due to the generation of intergranular fractures under residual tensile stress and stress concentration [11]. Accordingly, the parametric study of laser welding is essential for improving the properties of the weld. Finite element analysis (FEA) can be used for thermal analysis (temperature distribution) and for the prediction of residual stress during the welding process [12]. The temperature distribution and weld bead profile can be predicted using ANSYS [13,14], ABAQUS [15], SYSWELD [16], and simufact welding [17]. Among finite element techniques, ANSYS APDL is one of the most efficient tools. In the past, experienced technicians determined welding parameters through trial and error, a process that was both time-consuming and costly, to ensure that each new welded product met the required joint specifications. To mitigate these challenges, various researchers have employed single-quality characteristic analyses. However, the single-objective approach only simplifies the complexity of the real problem. The Nd:YAG laser welding process includes various parameters, such as pulse frequency, power, welding speed (transverse), and wire size. Each of these factors can affect the quality and properties of the weld.

Determining the optimal design of Nd:YAG laser welding process parameters is challenging when using single-objective optimization methods like ANOVA, response surface optimization [18], and the Taguchi method [19], as multiple quality characteristics are required to assess overall quality. Therefore, to enhance welding quality under optimal process conditions, it is essential to explore a multi-objective optimization approach. In these situations, links between quality attributes in the process may be subsequently established using grey relational analysis (GRA) [20,21]. The optimization of laser welding process parameters has been widely studied. However, to the best of our knowledge, no systematic research has combined the GRA-based Taguchi method with the standard deviation objective weighting technique for the multi-objective optimization of the Nd:YAG laser welding process. To address the multi-criteria optimization problem regarding Nd:YAG laser welding process parameters for the AA7075 + SiC composite, this study explored the application of the standard deviation objective weighting method, an objective weighting technique, in combination with the grey relational analysis (GRA)-based Taguchi method. A composite with improved mechanical qualities, including greater hardness, wear resistance, and perhaps longer fatigue life, is produced when SiC is added to the AA7075 matrix. Because of these enhancements, the composite is more suited for uses where traditional AA7075 would not be as effective, especially in the high-stress or high-wear settings seen in the automotive industry. During Nd:YAG laser welding, this method aids in improving mechanical properties such as tensile strength, deformation, and hardness (both in the weld zone and the heat-affected zone) with uniform quality. This study predicts the temperature distribution for the Nd:YAG laser welding process by simulating the AA7075 + SiC aluminium composite sheet butt joint using ANSYS APDL 19.0, with the results validated against experimental findings.

2. Experimental Methods

2.1. Materials

The 7075 series of aluminium alloys were selected as the matrix metal for this study due to their widespread use in various industrial sectors, including automotive, aerospace, marine, construction, and outdoor applications, as well as their suitability for aging heat treatment [22]. To make the material harder for use in high-strength structural applications, it can be aged (heat treated) [23]. Despite being lightweight structural materials with particular strength, AA7075 alloys have limited uses due to their poor weldability [24,25]. Ola et al. [24] examined the impact of laser welding process parameters on AA7075 alloys and came to the conclusion that adjusting the process parameters might improve AA7075’s weldability. The basic material for this project was an AA7075 + 3 weight percent SiC aluminium composite plate, which was created using the stir casting method. Aluminium AA7075 exhibits outstanding mechanical strength, corrosion resistance, fatigue strength, high creep resistance, and excellent formability [26,27]. The chemical composition of the matrix material was analysed using energy dispersive spectroscopy (EDS) on a scanning electron microscope (SEM), as shown in

Table 1. Chemical Composition of AA7075 Alloy [28].

Element	Cu	Mg	Al	Si	Ca	Mn	Fe	Zn
Weight %	2.1	3.81	86.18	0.75	0.06	0.82	0.76	5.52

. Zinc’s interaction with magnesium produces strengthening precipitates, which contribute significantly to the strength of 7xxx series alloys. While zinc enhances mechanical qualities such as tensile strength and hardness, it can also cause corrosion resistance and weldability issues, particularly when employed at greater concentrations.

2.2. Material Synthesis

The AA7075 alloy ingot, a 1.5 kg bar obtained from Ripon Metal Pvt. Ltd. in Ahmedabad, India, was cleaned and then positioned in a top-loaded, bottom-pouring stir casting furnace (Figure 1) for melting at a temperature of 750 °C. Many authors have reported using the stir casting technique: This approach is simple to use and inexpensive for preparing composites [29,30]. Consequently, stir casting is currently being utilized in research to develop hybrid composites. To minimize temperature variations between the melt and the reinforcement particles, 25 μm SiC particles were preheated in a separate furnace at 450 °C during the addition process. After the AA7075 alloy was melted, the temperature was raised from 750 °C to 900 °C. The molten metal was stirred at 350–450 rpm with a graphite impeller to form a vortex. Preheated reinforcing particles were then added to the melt. At the same time, the melt was mechanically agitated at 750–780 rpm until the reinforcing mixture was completely blended. To achieve better dispersion, stirring continued for an additional five minutes after the reinforcement was introduced. After the melt was thoroughly mixed, it was poured into the graphite-coated cast iron die for reheating, as shown in Figure 2a. Following solidification, the cast melt was extracted from the die, as illustrated in Figure 2b.

2.3. Design of Experiment

This study focused on four process parameters for the laser welding process: pulse frequency, laser power, welding speed, and wire size. The levels of these parameters are detailed in

Table 2. Process parameters and their levels.

Parameters	Level 1	Level 2	Level 3
Pulse frequency (Hz)	170	172	174
Laser power (kW)	3.04	3.23	3.42
Welding speed (transverse) (m/min)	4	5	6
Wire size (mm)	1	1.5	2

, leading to a total of 81 possible combinations (3 × 3 × 3 × 3). However, by employing Taguchi’s L-9 orthogonal array, the number of combinations was reduced to nine, while still maintaining the same level of confidence as if all combinations had been tested individually [31]. The Taguchi orthogonal array was generated using the design of experiments (DOE) method in Minitab 19 software, as illustrated in

Table 3. Design of experiment according to L-9 orthogonal array.

S.No.	Pulse Frequency (Hz)	Laser Power (KW)	Welding (Transverse) (m/min)	Wire Size (mm)	Heat Input (J/mm)
1	170	3.04	4	1	45.6
2	170	3.23	5	1.5	38.76
3	170	3.42	6	2	34.2
4	172	3.04	5	2	36.48
5	172	3.23	6	1	32.3
6	172	3.42	4	1.5	51.3
7	174	3.04	6	1.5	30.4
8	174	3.23	4	2	48.45
9	174	3.42	5	1	41.04

.

2.4. Experimental Details

The welding process was performed using a laser welding machine equipped with a 400 W pulsed Nd:YAG laser (Dhanlaxmi, average power 400 W, maximum power 6 kW, maximum wavelength 1064 nm, maximum frequency 500 Hz, with a pulse range of 0.3–20 ms), as depicted in Figure 3. This machine is available at Mascot Technocrats Ltd., Moraiya, Ahmedabad, Gujarat, India. A long rectangular aluminium AA7075 + SiC composite sheet was cut using wire EDM into 18 pieces per dimension, as provided in

Table 4. Dimensions of selected plates.

Length (mm)	90
Width (mm)	100
Thickness (mm)	6
Numbers of plates	18

. For laser welding, a manual mode was set in the power source, and the welding constraints—laser power, frequency, and welding speed—were initially specified in the laser welding machine. In the welding process, ER4043 filler wire with different diameters was used according to the design of the experiment. The chemical compositions as per supplier knowledge of the filler material are presented in

Table 5. Chemical composition of filler wire.

Composition	Al	Si	Fe	Cu	Mn	Mg	Zn	Cr	Ti
ER4043	Bal.	5.6	0.8	0.3	0.05	0.05	0.10	0.05	0.02

. After setting the welding parameters based on the L-9 Taguchi orthogonal array experimental design, the distance between the workpiece and lens was set at 90 mm on the welding machine. Prior to welding, we polished the two sheet pieces using silicon carbide sandpaper (P600) and subsequently cleaned the sample surface with acetone to remove any oxide film [32]. Argon, a shielding gas, was employed during the laser welding process. This gas envelops the welding area, displacing environmental oxygen, which in turn minimizes the likelihood of oxide formation during welding. The shielding gas creates a protective environment, which successfully prevents the formation of new oxides when the material undergoes heating [33]. Welding was initiated using the pedal switch. Temperature measurements during the laser welding process were conducted using an infrared (IR) thermometer. We carefully selected three crucial time nodes at which temperature readings were taken. These time nodes were designated as T₁ = 0.3 s, T₂ = 4 s, and T₃ = 14 s, corresponding to specific points during the welding process at which an average temperature was taken. As seen in Figure 4, the welded sample, which had dimensions of 150 mm in length, 12 mm in gauge width, 50 mm in gauge length, and 12 mm in fillet radius, was machined using a wire EDM machine in accordance with the ASTM E8M standard for tensile testing [34]. A tensile test was performed at room temperature with a strain rate of 0.01/S using the UTE/C-400 universal testing equipment. Using a Rockwell hardness machine (FIE manufacture model IRB-250), Rockwell hardness tests were performed on all the welded samples. The welded sample’s surface was indented at the heat-affected zone and fusion zone using an indenter fitted with a 1/16 diamond ball and a 100 kgf force for the hardness test. Rockwell hardness values were taken at three locations, and average values were reported to ensure accuracy in both regions.

3. Standard Deviation Objective Weighting Method

Each criterion’s weight ($w_j$) was assessed using the standard deviation objective weighting approach [35,36]. The performance-defining criteria (PDC) were determined for each response based on its weight. The first step is to build an initial decision matrix that includes nine experiments and five process parameters. Equation (1) is then used to normalize the decision matrix following the computation of the best and worst values for each process parameter:

$$X_{ij}^{+}={\displaystyle \frac{X_{ij}-X_j^{worst}}{X_j^{best}-X_j^{worst}}}$$

(1)

where $X_{ij}^{+}$ denotes the i^th design’s normalized value on the j^th answer using the standard deviation coefficient and correlation (Minitab 19 software). The evaluation of information production was then performed using correlation and standard deviation coefficients. Equation (2) was then used to determine the weight (${\mathsf{\xi }}_j$) of each criterion. The performance-defining criteria (PDC) for each response were determined based on the weight of the responses, as indicated in

Table 6. Performance-defining Criteria (PDC).

SN	Performance-Defining Criteria (PDC)			Impact on PDC
	Response	Weight $(\mathsf{\xi })$	Designation
1	Tensile strength (MPa)	0.192996	PDC-3	Higher the better
2	Deflection (mm)	0.159433	PDC-4	Higher the better
3	Temperature (°C)	0.157066	PDC-5	Higher the better
4	Rockwell Hardness (Fusion zone) HRB	0.267041	PDC-1	Higher the better
5	Rockwell Hardness (HAZ) HRB	0.223464	PDC-2	Higher the better

:

$${\xi }_j={\displaystyle \frac{c_j}{{{\displaystyle \sum }}_{k=1}^m{c}_j}}$$

(2)

where, ${\mathsf{\xi }}_j$ ≥ 0 and ${\displaystyle {\displaystyle \sum }_{k=1}^m}{c}_j=1$.

4. Hybrid Gray Relational Methodology

S/N ratio

There are three different SN (signal to noise) ratios based on characteristics: nominally better, higher better, and lower better. For tensile strength, deflection, temperature distribution, and Rockwell hardness (fusion zone) and Rockwell hardness (heat-affected zone), the greater the better in this study. The following list contains the phrases that reflect these approaches:

$$\mathrm{SN}\mathrm{ratio}\mathrm{for}“\mathrm{larger}\mathrm{is}\mathrm{better}”:S{N}_L=-10log({\displaystyle \frac{1}{n}}{{\displaystyle \sum }}_{i=1}^n{\displaystyle \frac{1}{y^{i^2}}})$$

(3)

$${\mathrm{SN}}_{\mathrm{s}}\mathrm{ratio}\mathrm{for}“\mathrm{smaller}\mathrm{is}\mathrm{better}”:S{N}_s=-10log{{\displaystyle \sum }}_{i=1}^n{y}^{i^2}$$

(4)

SN_n ratio for “nominal is better”:

$$S{N}_n=10log10(Squareofmean/\mathrm{v}ariance)$$

(5)

Normalization of S/N ratio

For the “larger is better” characteristics of tensile strength, deflection, temperature distribution, Rockwell hardness (fusion zone), and Rockwell hardness (heat affected zone):

$$y_i^{*}(m)={\displaystyle \frac{y_i\left(m\right)-\min y_i\left(m\right)}{\max y_i\left(m\right)-\min y_i\left(m\right)}}$$

(6)

For “smaller is better”:

$$y_i^{*}(m){\displaystyle \frac{\max y_i\left(m\right)-y_i\left(m\right)}{\max y_i\left(m\right)-\min y_i\left(m\right)}}$$

(7)

For “nominal is better”:

$$y_i^{*}(m)={\displaystyle \frac{1-/y_i\left(m\right)-y_{0}b(m)/}{\max y_i\left(m\right)-y_{0}b(m)}}$$

(8)

The data preparation and comparability arrangements are denoted by y∗(m) and y_i(m). Tensile strength, deflection, temperature distribution, Rockwell hardness (fusion zone), and Rockwell hardness (heat-affected zone) are measured using m = 1, m = 2, m = 3, m = 4, and m = 5. For experiments 1 through 9, i = 1, 2, 3, 9.

Deviation sequence

One way to depict the deviation sequence is as [37]:

$${\Delta }_{0i}\left(k\right)=\left|y_0^{*}\left(m\right)-y_k^{*}\left(m\right) \right|$$

(9)

Grey relational coefficient (GRC)

The relationship between the ideal and the actual normalized experimental value is represented by the grey relational coefficient (GRC) [38]:

$$GRC={\mathsf{\xi }}_i\left(k\right)={\displaystyle \frac{{\Delta }_{\min }+\mathsf{\xi }{\Delta }_{\max }}{{\Delta }_{0\mathrm{i}}\left(\mathrm{k}\right)+\mathsf{\xi }{\Delta }_{\max }}}$$

(10)

Grey relational grade

The average of the GRCs for each performance attribute is used to calculate it. Grey relational grades are used to calculate several performance metrics overall [39]:

$${\gamma }_i={\displaystyle \frac{1}{n}}{\displaystyle \sum }_{k=1}^n{\xi }_i\left(k\right)$$

(11)

5. Optimization Using GRA Method

According to the L-9 orthogonal array, the investigations were carried out at ambient temperature [39]. Utilizing the load–displacement data displayed in Figure 5, tensile strength was computed. The deflection, temperature distribution, and Rockwell hardness for both the fusion zone and heat-affected zone across all nine experimental sets are illustrated in Figure 5, Figure 6, Figure 7 and Figure 8 and summarized in

Table 7. Experimental results.

	Process Parameter				Response
S. No.	Pulse Frequency (Hz)	Laser Power (kW)	Welding Speed (Transverse) (m/min)	Wire Size (mm)	Tensile Strength (MPa)	Deflection (mm)	Temperature (°C)	Rockwell Hardness (Fusion Zone) HRB	Rockwell Hardness (HAZ) HRB
1	170	3.04	4	1	50.67	8.1044	308.924	35	59
2	170	3.23	5	1.5	53.75	8.5565	307.754	70	54
3	170	3.42	6	2	48.63	7.7863	305.084	63	73
4	172	3.04	5	2	60.42	8.0451	310.584	57	74
5	172	3.23	6	1	52.63	8.4744	314.504	49	75
6	172	3.42	4	1.5	50.57	8.9821	315.664	34	76
7	174	3.04	6	1.5	58.83	9.3119	321.164	71	76.5
8	174	3.23	4	2	55.73	9.9791	316.914	70	77
9	174	3.42	5	1	53.17	8.7070	318.304	60	78

. It is noteworthy that all the tested specimens exhibited failure at the heat-affected zone, as depicted in Figure 9. This outcome is a typical occurrence for aluminium alloys since the welding process tends to diminish the mechanical properties of the metal by vaporizing alloying elements. The strongest weld was achieved in sample 4, with a tensile strength of 60.42 MPa. This result was obtained with a pulse frequency of 172 Hz, a laser power of 3.04 kW, a welding speed of 5 m/min, and a wire size of 2 mm. The weakest weld was seen in sample 3, which had a tensile strength of 48.63 MPa. The following welding settings were used: pulse frequency of 170 Hz, laser power of 3.42 kW, speed of 6 m/min, and wire size of 2 mm. The weld with the highest strength exhibited an 18.1% reduction in the mechanical properties of the base alloy AA7075. This outcome is favourable considering that aluminium alloys often experience losses ranging from 20% to 40% during welding [40]. The highest average temperature was achieved in sample 7, with a temperature of 321.16 °C. With a wire size of 1.5 mm, a laser power of 3.04 kW, a welding speed of 6 m/min, and a pulse frequency of 174 Hz, this outcome was achieved. Conversely, sample 3 had the lowest temperature, measuring 305.08 °C, when the following welding parameters were used: 2 mm wire size, 3.42 kW laser power, 170 Hz pulse frequency, and 6 m/min welding speed. The peak temperature developed during welding does not depend on the heat input, but the other parameters also do not follow any of the particular trends that have been reported by earlier researchers [11,24]. When the peak temperature is higher, the participant metals melt in excess, resulting in the creation of undesired compounds at the interface, which accounts for sample 7’s high hardness.

Table 8. Signal-to-noise ratio of response.

	Process Parameter				S/N Ratio of Response
S.No.	Pulse Frequency (Hz)	Laser Power (kW)	Welding Speed (Transverse) (m/min)	Wire Size (mm)	S/N Ratio Tensile Strength	S/N Ratio Deflection (mm)	S/N Ratio Temperature	S/N Ratio Rockwell Hardness (Fusion Zone)	S/N Ratio Rockwell Hardness (HAZ)
1	170	3.04	4	1	34.095	18.174	49.797	30.88	35.42
2	170	3.23	5	1.5	34.607	18.646	49.764	36.90	34.65
3	170	3.42	6	2	33.738	17.827	49.684	35.99	37.27
4	172	3.04	5	2	35.624	18.110	49.843	35.12	37.38
5	172	3.23	6	1	34.425	18.562	49.952	33.80	37.50
6	172	3.42	4	1.5	34.078	19.068	49.984	30.63	37.61
7	174	3.04	6	1.5	35.392	19.381	50.134	37.02	37.67
8	174	3.23	4	2	34.922	19.982	50.019	36.90	37.73
9	174	3.42	5	1	34.513	18.797	50.057	35.56	37.84

shows the S/N ratio, which was computed using Equation (3) for tensile strength, deflection, temperature, Rockwell hardness (fusion zone), and Rockwell hardness (heat-affected zone) (larger is better).

Table 9. Normalized signal-to-noise ratio of response.

	Process Parameter				Normalized S/N Ratio of Response
S. No.	Pulse Frequency (Hz)	Laser Power (kW)	Welding Speed (Transverse) (m/min)	Wire Size (mm)	Nor. S/N Tensile Strength	Nor. S/N Deflection	Nor. S/N Temperature	Nor. Rockwell Hardness (Fusion Zone)	Nor. Rockwell Hardness (HAZ)
1	170	3.04	4	1	0.1893	0.1610	0.2511	0.0391	0.2413
2	170	3.23	5	1.5	0.4607	0.3800	0.1778	0.9812	0.0000
3	170	3.42	6	2	0.0000	0.0000	0.0000	0.8388	0.8213
4	172	3.04	5	2	1.0000	0.1313	0.3533	0.7026	0.8558
5	172	3.23	6	1	0.3643	0.3410	0.2422	0.4960	0.8934
6	172	3.42	4	1.5	0.1803	0.5758	0.6667	0.0000	0.9279
7	174	3.04	6	1.5	0.8769	0.7211	1.0000	1.0000	0.9467
8	174	3.23	4	2	0.6277	1.0000	0.7444	0.9812	0.9655
9	174	3.42	5	1	0.4109	0.4501	0.8289	0.7715	1.0000

shows the normalized S/N ratios obtained from Equation (6) for tensile strength, deflection, temperature, Rockwell hardness (fusion zone), and Rockwell hardness (heat-affected zone).

Table 10. The deviation sequences for all experiments.

Exp. No.	∆0i (1)	∆0i (2)	∆0i (3)	∆0i (4)	∆0i (5)
1	0.8107	0.839	0.7489	0.9609	0.7587
2	0.5393	0.62	0.8222	0.0188	1
3	1	1	1	0.1612	0.1787
4	0	0.8687	0.6467	0.2974	0.1442
5	0.6357	0.659	0.7578	0.504	0.1066
6	0.8197	0.4242	0.3333	1	0.0721
7	0.1231	0.2789	0	0	0.0533
8	0.3723	0	0.2556	0.0188	0.0345
9	0.5891	0.5499	0.1711	0.2285	0
$\mathsf{\xi }$	0.192995883	0.15943312	0.157065993	0.267040871	0.223464133

shows the deviation sequence estimated using Equation (9) for all experimental trials.

The grey relational coefficient (GRC) was computed using Equation (10). The weight of each response ($\mathsf{\xi })$ is collected from Table 6 and assessed using the standard deviation objective weighting approach, as indicated in

Table 11. Grey relational coefficient for the response.

Exp. No.	GRC Tensile Strength	GRC Deflection	GRC Temperature	GRC Rockwell Hardness (Fusion Zone)	GRC Rockwell Hardness (HAZ)
1	0.192283208	0.159686664	0.173370657	0.217474649	0.227540562
2	0.263571911	0.204562275	0.160387913	0.93429666	0.1826487
3	0.16177414	0.137509544	0.135745061	0.623591826	0.555677016
4	1	0.155073898	0.195420693	0.473157538	0.607793178
5	0.232880684	0.194818886	0.279720523	0.346377522	0.677067188
6	0.190571778	0.273206331	0.320281829	0.210759477	0.756058909
7	0.610731877	0.363737286	1	1	0.807441935
8	0.341457382	1	0.380653879	0.93429666	0.866318379
9	0.246774675	0.224769878	0.478601314	0.538907253	1

.

The grey relational grade (GRG) and ranking were obtained with Equation (11) and are displayed in

Table 12. The calculated grey relational grade and its order.

Exp. No.	Pulse Frequency (Hz)	Laser Power (KW)	Welding Speed (Transverse) m/min	Wire Size (mm)	GRG	Rank
1	170	3.04	4	1	0.083965	9
2	170	3.23	5	1.5	0.089244	8
3	170	3.42	6	2	0.14349	7
4	172	3.04	5	2	0.321559	1
5	172	3.23	6	1	0.18199	6
6	172	3.42	4	1.5	0.189326	5
7	174	3.04	6	1.5	0.283635	2
8	174	3.23	4	2	0.241555	4
9	174	3.42	5	1	0.249355	3

.

The mean grey relational coefficient (GRC) for pulse frequency at levels 1, 2, and 3 was determined by averaging the GRC values for experiments 1–3, 4–6, and 7–9, respectively. The GRA grade responses are displayed in

Table 13. Responses for the GRA grade.

Sr. No	Laser Welding Process Parameters	Grey Relational Grade			Main Effect (Max-Min)	Rank	Mean
		Level 1	Level 2	Level 3
1	A (pulse frequency)	0.105566	0.230958	0.258182	0.152615	1	0.19823544
2	B (Laser power)	0.22972	0.17093	0.194057	0.05879	2	0.19823544
3	C (welding speed)	0.185642	0.220053	0.203038	0.034411	4	0.202911
4	D (wire size)	0.17177	0.187402	0.218125	0.046355	3	0.19243222

. The significance of each factor for the grey relational grade is determined by the ranking of the process parameters, with pulse frequency being the most important, followed by laser power, wire size, and welding speed. That is to say, pulse frequency is the most dominant parameter in the whole process of laser welding performance. Figure 10 shows the main effects plot of GRG from Minitab 19: Optimal process parameters are A3B1C2D3, and pulse frequency is 174 Hz, laser power is 3.04 kW, welding speed is 5 m/min, and wire size is 2.0 mm.

6. Numerical Study

ANSYS APDL 19.0 was used for the numerical analysis on two chosen plates with a butt-welding joint arrangement. The governing equation for each element in the finite element formulation is as follows [41]:

$$\left[C\left(T\right)\right]\left\{\stackrel{⌵}{T}\right\}+\left[K\left(T\right)\right]\left\{T\right\}=\left\{Q\left(T\right)\right\}$$

(12)

This study requires the integration of the heat conduction equation over time. The system of equations is solved using the Crank–Nicholson/Euler theta integration technique [42]. This element type can handle three-dimensional thermal conduction. The heat input from the laser power is represented by heat flux, which is evaluated per unit surface area qqq as a function of the temperature gradient [43]

$$q=-k\delta T$$

(13)

where k is the thermal conductivity and ∇T indicates the temperature gradient.

The heat equation used for convection is represented below:

$$q=h_{c}AdT$$

(14)

where $\mathrm{q}$ represents the heat transfer per unit time, ${\mathrm{h}}_{\mathrm{c}}$ is the convective heat transfer coefficient, A is the heat transfer area of the surface, and $\mathrm{dT}$ is the temperature difference between the surface and the bulk field. A thermal analysis along with a Gaussian heat distribution model was employed to determine the temperature distribution for the laser welding model [41].

$$q\left(r\right)={\displaystyle \frac{2P}{\mathsf{\pi }{\mathsf{\sigma }}^2}}{e}^{{\displaystyle \frac{-2r^2}{{\mathsf{\sigma }}^2}}}$$

(15)

where $P$ = laser power, $\mathsf{\sigma }$ = radial distance (0.0045m), $r$ = beam radius (0.004 m).

To obtain the global temperature, a non-linear transient thermal analysis was performed. The dimensions of the plate were the same as the experimental dimension shown in Figure 11; the elements taken were tetrahedrons. During meshing, element size two, shown in Figure 12, had element number 41075. The material properties of AA7075 + SiC are Young’s modulus of elasticity 77.7 GPa, Poisson’s ratio 0.35, thermal conductivity of 130 W/mk, and density of 2810 kg/m³. Numerical simulations are done for nine cases of different heat fluxes calculated using Equation (15) with a cylindrical heat source. The simulated temperature (K) distribution for experiment 1 is shown in Figure 13.

The validation of the simulated temperature distribution against experimental results is shown in Figure 13. Figure 14 reveals that the maximum error is 9.59 percent (sample 5), occurring in just one instance. However, the average error is 5.85 percent, which falls within the acceptable range of 4% to 12% [7]. This suggests that the simulated environment developed for laser welding can be utilized to assess the temperature distribution for other materials.

7. Conclusions

The AA7075/SiC composite was successfully fabricated using a top-loaded, bottom-pouring stir casting furnace. Nd:YAG laser welding was effectively conducted based on an orthogonal array design of experiments on the fabricated composites. The following are the key findings from the current study:

• This study successfully employed the standard deviation objective weighting method along with the grey relational optimization method to enhance multiple responses, including tensile strength, deflection, temperature distribution, Rockwell hardness in the fusion zone, and Rockwell hardness in the heat-affected area. The optimal combination of parameters identified was A3B1C2D3.
• A pulse frequency of 174 Hz, laser power of 3.04 kW, welding (transverse) speed of 5 m/min, and wire size of 2 mm are the ideal process parameters found for the laser welding procedure.
• The pulse frequency plays a significant role in laser welding, followed by wire size, laser power, and welding (transverse) speed.
• The weight fractions for tensile strength, deflection, temperature distribution, hardness (fusion zone), and hardness (HAZ) were effectively determined using the standard deviation objective weighting technique; they were 0.1930, 0.1594, 0.0.1570, 0.2670, and 0.2235, respectively.
• As the experimental measurements are costly, FEA was employed for attaining approximate outcomes. ANSYS APDL 19.0 was used for numerical analysis on two chosen plates with a butt-welding joint arrangement to predict the temperature distribution. The numerical results were compared with the experimental results, and it was noted that the average error was only 5.85%.