1 Introduction

Due to their high strength and low Ni content, SDSS has considerable intensive advantage over different SS. When chloride attack is a major concern, design engineers often choose DSS over austenitic stainless steels for enclosing and constructing assemblies because of the material’s great resistance to pitting corrosion. Maintaining a microstructure with a minimal number of secondary phases, for instance austenite (γ) and delta-ferrite (δ), is what gives DSS its beneficial properties. The ideal microstructure of DSS could be damaged by any thermal treatment above 300ºC, including fusion welding [1,2,3]. Weld metal composition and cooling rate are significant factors in determining the composition of the DSS metal after welding. It is ferrite that is more stable at higher cooling speeds and aid in increasing the likelihood of nitride precipitation, but these effects are highly dependent on heat input, pre-heating, and inter-pass temperatures throughout welding operations [4, 5]. Welding times are lengthened due to the slow cooling rates which raise the prospect of spinodal breakdown of Cr-rich-ferrite (αı), apparently 475ºC precipitation and weakening of intermetallic, include Sigma (σ) and Chi (χ) [6]. Thus, in order to attain moderate cooling rates, conventional multi-pass fusion welding requires heat input to be within strict upper and lower limits and inter-pass temperatures to be kept reasonably low (180-200oC) [1, 7]. Additional time and effort are required in typical multi-pass welding methods for controlling such low-tolerance welding parameters.

If the solidified microstructure can be managed, single-pass welding of DSS would allow for greater welding efficiency and uniformity in metallurgical and mechanical quality. Laser beam welding, Plasma arc welding (PAW), hybrid Laser arc welding and electron beam welding keyhole style can be accustomed to create single-pass weldments of DSS. Since These welding procedures can only be used on connections with a negligible or non-existent gap, it is impossible to incorporate an adequate quantity of filler metal (comprised of too much Ni) into the weld metal to ensure that the resulting alloy has a sufficient amount of γ in δ matrix. Autogenous or partly-autogenous keyhole welding, despite its modest heat inputs [8, 9], can cause an excess of ferrite to develop in the DSS welds, corrosion and toughness are both compromised as a result of this [10, 11]. To get a weld metal microstructure with the right phase balance and no secondary phases, post-weld procedures like solutionizing are typically necessary after PAW, LBW, HLAW, and EBW of DSS [12]. I.Alvarez-Armas et al. [13]. studied the development of cracking in low and high cycle fatigue tests on a duplex stainless steel that had been embrittled. Microcracks cause the ferrite phase to begin during low-cycle fatigue, and this can happen either along the slip planes with the highest Schmid factor (SF) inside the grains or at the a/a grain boundary. Roman Kolmorgen and Horst Biermann [14] investigated the thermo-mechanical fatigue (TMF) characteristics of duplex stainless steel X2CrNiMoN22-5-3. Primary and secondary hardening are clearly visible in the cyclic stress response curves of the duplex steel, Whereas the former agrees with the cyclic hardening regime of the single-phase austenitic steel, the latter agrees with the ferritic steel.Guocai Chai et al. [15] analyzed in-grain and across-grain/phase boundary crack propagation behaviour. Dislocation slip in the grains is responsible for most crack branching, while phase boundaries are responsible for crack deflection. U. Krupp et al. [16] examined the initiation of fatigue cracks and their interactions with initial microstructural barriers using ultrasonic fatigue testing of miniature specimens in conjunction with (i) in-situ observation, (ii) electron backscatter diffraction, (iii) synchrotron computer tomography, and (iv) high-energy X-ray diffraction. Chin-Hyung Lee et al. [17] established a method for calculating the amount by which steel butt welds undergo relaxation after being subjected to cyclic external loading.

Sung-Wook Kang et al. [18] compared the fatigue strength to the S-N curves provided for a series of butt weld specimens welded in both the horizontal (2G) and vertical (3G) positions. The angular distortion of 2G and 3G specimens, as well as their respective effects on fatigue strength, are studied. U. Krupp et al. [19] studied the development of cracks with ultrasonic fatigue testing, electron microscopy, and synchrotron diffraction. It was discovered that the first microstructural barrier has a crucial role in determining Very High Cycle (VHCF) life. Jinwoo Cho and Chin-Hyung Lee [20] Reduction of residual stress under cyclic loading was studied in a girth welded duplex stainless-steel pipe. It is found that residual tensions in and around the girth weld are greatly reduced even after the first few loading cycles, with the degree of stress relaxation depending on the intensity of the cyclic loading. I. S. Cortes-Cervantes et al. [21] carried out gas metal arc welded (GMAW) on plates of AL6XN stainless steel with a higher austenitic content and involving little electromagnetic interaction. Under continuous stress amplitude and uniaxial load, the fatigue behaviour of the welded joints was assessed. Timo Bjork et al. [22] tested the durability of duplex and super-duplex steels against fatigue using a variety of techniques, including practical tests and theoretical analyses that make use of effective notch stress-based procedures like the 4R approach. Eyasin Arafat et al. [23] The influence of friction stir processing (FSP) on the formation of fatigue cracks in super duplex stainless steel was studied (SDSS) SAF 2507. The resistance to fatigue crack development (FCG) and the fatigue life of FSP specimens are found to be greater than those of the base material. Andrew Sales et al. [24] reported fatigue test results and fracture surface fractography of WAAM-processed SDSS, which demonstrated a substantial anisotropy of fatigue characteristics and fatigue crack initiations arising from interior defects rather than surface faults. Andrew Sales et al. [25] modified the interpass temperatures to enhance the fatigue characteristics of the SDSS produced by WAAM. According to their findings, the interpass temperature can play a pivotal role in ensuring that structural components manufactured using the WAAM process have isotropic mechanical characteristics and long fatigue lives. Janardhan Gorti et al. [26] tested the effect of pre-straining HSLA steel sheets on the tensile and fatigue performance of resistance spot- welded joints. Here, super duplex stainless steel (UNS S32750) of 0.33 mm thick sheets were selected. They are welded together using MPAW. In the present work Fatigue test was carried out at a constant frequency of 10Hz. One may try at other frequencies based on the thickness of the material. The purpose of this paper is to investigate the relationship between fatigue life and welding parameters.

2 Materials and methodology

UNS S32750 SDSS sheets measuring 240 × 100 × 0.33 milli meters are autogenously joined with a square butt joint. The chemical composition and tensile characteristics of UNS S32750 SDSS are listed in Tables 1 and 2. In an effort to avoid the absorption of atmospheric oxygen and nitrogen during and immediately following welding, high purity argon gas (99.99%) is utilized as a shielding gas and as a trailing gas. Welding was carried out using the parameters specified in Table 3. Quality of the weld features of the MPAW process are affected by a wide variety of process parameters, including but not limited to peak current, base current, pulse rate and pulse width.

Table 1 UNS S32750 chemical composition (weight%)
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Table 2 UNS S32750 mechanical properties
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From the works reported by Sasidhar et al. [27] and Siva Prasad et al. [28] and observed that the peak current, back current, pulse rate and pulse width are the most important factors influencing weld quality. The input parameters are selected based on the works reported by earlier researchers on PAW of thin sheets. The values of the chosen input parameters are arrived based on trial experiments conducted by varying each parameter separately, by keeping other parameters constant. Table 4 displays the selected values for input parameters.

Table 3 Welding setup conditions
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Table 4 Welding parameters and bounds
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3 Experimentation

Testing for high cycle fatigue is conducted in a tension-tension configuration. Applying a sinusoidal load between 0.6 and 6 kilonewtons while maintaining a stress ratio of 0.1. Experimental setup is shown in Fig. 1a, b; Table 5 displays the results of an analysis of the fatigue life of the weld joints for each of the samples taken. Figure 1c shows wire cut fatigue specimens prepared in accordance with ASTM E647- 04 standards. Each welded sample was processed by electro-discharge machining in the weld transverse direction. Using a 100 KN Fatigue testing machine with computer-controlled servo hydraulic, fatigue tests were conducted (INSTRON, Model No: 8801).

Fig. 1
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(a) Fatigue testing machine, (b) Hydraulic grippers, (c) Fatigue specimen as per ASTM E6474-04

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When engineering buildings or components that will be subjected to repeated loading and unloading cycles, it is essential to predict the fatigue life of the materials used. The S-N (stress-life) curve method is one of the most used empirical formulas and conventional approaches to fatigue life estimation. One way to visualize the results of fatigue tests is via the S-N curve, which shows the relationship between the applied stress (S) and the number of cycles until failure (N). A logarithmic scale is usually used to plot the curve. A common way to represent the S-N curve is:

Table 5 displays the experimental results of fatigue tests that were used to derive the constants A and B.

Table 5 Experimental and predicted responses
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4 Statistical analysis – empirical relationships

Process parameter optimization using response surface methods and empirical relationship establishment were both aided by the design expert software.

4.1 Main effect plot

Main effect plot is drawn for fatigue life at a frequency of 10 Hz as shown in Fig. 2. A higher peak current result in a longer fatigue life. This is because the high current causes a great deal of heat, causing the base metal to properly fuse. Base current extends fatigue life by keeping the peak current steady during pulse welding. Overheating and inadequately fusing the weld joint lead to incorrect fusion of the base metal, reducing its fatigue life. Weld joint strength is reduced because of poor fusing caused by a wider pulse width. Therefore, the pulse width has a negative effect on fatigue strength. In addition, a larger time gap between pulses might cause the weld joint to cool more quickly, leading to coarser grains and a shorter fatigue life.

Fig. 2
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Main effects on fatigue life

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4.2 Mathematical modelling

In RSM, a number of statistical and numerical methods are used to determine the optimal response based on the given range of values for the dependent and independent variables. Response Y from the response surface model is provided as the solution of a second-order polynomial equation with four factors, as shown in Eq. 1.

$$Y={b_o}+\sum {{b_i}{X_i}} +\sum {{b_i}_{j}} {X_i}^{2}+\sum {\sum {{b_i}_{j}} } {X_i}{X_j}+ \in$$
(1)

In the equation, the output function Y stands in for the set of parameters xi to xj. where bo, bi and bj are the coefficients of the polynomial and ∈ represents noise. The current research uses RSM for optimization purposes in order to increase fatigue life. The fatigue life is the output that can be optimized in MPAW, and it is a function of the peak current (Ip), base current (Ib), pulse rate (G), and pulse width (D). Equation 2 provides a mathematical connection to the aforementioned statement:

$${\text{Fatigue life}},{\text{ }}{{\text{F}}_{\text{L}}}=f\left( {{{\text{I}}_{\text{p}}},{\text{ }}{{\text{I}}_{\text{b}}},{\text{ G}},{\text{ D}}} \right)$$
(2)

The empirical relation is constructed using MINTAB software to predict the response is given below in Eq. (3):

$$\eqalign{{{\rm{F}}_{\rm{L}}} & = {\rm{ }}249922.7\, + \,1911.2{\rm{ }}\left( {{{\rm{I}}_{\rm{p}}}} \right) \cr & \, + \,1452{\rm{ }}\left( {{{\rm{I}}_{\rm{b}}}} \right) - \,973.5{\rm{ }}\left( {\rm{G}} \right) \cr & - \,211.7{\rm{ }}\left( {\rm{D}} \right)\, + \,679.2\,{\rm{ }}{\left( {{\rm{Ip}}} \right)^2} \cr & + {\rm{ }}165.3\,{\rm{ }}{\left( {\rm{G}} \right)^2} - 2605\,{\rm{ }}({{\rm{I}}_{\rm{p}}} \times {\rm{G}}) \cr \, & + \,559.5\,{\rm{ }}({{\rm{I}}_{\rm{p}}} \times {\rm{D}})\, + \,10.543\,{\rm{ }}({{\rm{I}}_{\rm{b}}} \times {\rm{G}}) \cr & - \,12.155\,{\rm{ }}({{\rm{I}}_{\rm{b}}} \times {\rm{D}}) \cr}$$
(3)

4.3 Analysis of variance (ANOVA)

Statistical analysis of variance (ANOVA) is used to measure the precision of the models. Based on this method, a value is considered to be acceptable at the confidence limit if its estimated Fratio value is lesser than the standard Fratio value (F-table value 2.56) at 95% confidence level. Table 6 displays the outcomes of an analysis of variance performed on Fatigue Life. Based on the results in Table 6, it can be seen that the computational models produced are satisfactory at the 95% confidence level. Coefficient of determination ‘R2’ for the above developed models is determined to be around 0.98. P values under 0.05 indicate that the model term is statistically significant. The relationship between experimental factors and responses is strongly indicated by a lack-of-fit.

Table 6 Fatigue life (cycles) values using ANOVA
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The scatter plot is generated to see the difference between the expected and experimental values. Predicted values are computed by substituting the weld input parameters in the empirical mathematical equation developed by considering only the significant coefficients. If the experimental and predicted values are same, then we obtain a proportionality curve from the centre of the axis. However due to error present in the developed empirical model, the experimental and predicted values will vary slightly from proportionality curve. If error can be positive or negative. Hence, we can scatter points on the curve. The high appropriateness of the model is demonstrated by the small scatter between the anticipated and observed values. The results are scatter at 10% deviation. The average value is reported in Fig. 3.

Fig. 3
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Predicted values versus experimental values of fatigue life

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4.4 Optimization of process parameters: contour plots

The fatigue life of weld joint contours, as illustrated in Fig. 4(a) to 4(f), provides valuable insights into the influence of welding parameters. Contour graphs are essential in this analysis, helping to determine the most influential welding parameters on fatigue life. Each figure represents a different set of parameters, and the contours visually represent how these parameters affect the output. Circular contours suggest that both parameters exert an identical level of control on the output, indicating a balanced influence. Conversely, elliptical contours reveal an asymmetry in influence, with the parameter closer to the primary axis having a more significant impact on the output response. When contours are elliptical, one parameter is more dominant in shaping the fatigue life. The elongation of the ellipse along a particular axis indicates the direction of higher influence. This information aids in understanding the sensitivity of the fatigue life to different welding parameters. In cases where contours diverge, the impact on the output response is minimal. Diverging contours suggest that changes in these parameters within the analyzed range have a limited effect on the fatigue life. This insight is crucial for optimizing welding processes, as it helps identify the parameters that require more precise control to enhance fatigue life.

Fig. 4
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Fatigue life responses and contours (a) Comparison of peak and base current, (b) Peak current vs. pulse rate, (c) Pulse width vs. peak current (d) Pulse rate against base current, (e) Base current versus pulse width and (f) Rate of pulse versus pulse width

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4.5 Optimization of process parameters: surface plots

In the pursuit of optimizing welding parameters for the fatigue life of a weld joint, the analysis involves plotting surfaces and assessing their curvature. Figure 5(a) to 5(f) display surface plots representing the fatigue life of the weld joint under different parameter combinations. These plots are instrumental in identifying optimal values that contribute to prolonged fatigue life. The surfaces’ curvature is a key factor in this analysis. The apex of the curve surface denotes the highest value, representing the most favorable condition for fatigue life. Conversely, the nadir of the curve surface signifies the least value, representing conditions leading to the shortest fatigue life. Understanding the curvature of these surfaces aids in pinpointing the critical points that significantly influence the weld joint’s fatigue performance. The primary goal in this context is to extend the time until a weld joint experiences fatigue failure. Surface plots act as visual aids, approximating the relationship between two variables and revealing trends that impact fatigue life. By examining the surfaces, researchers and engineers can identify trends, patterns, and relationships that contribute to the fatigue behavior of the weld joint. The MINITAB surface response optimizer is employed to determine the ideal combination of welding parameters. This tool uses statistical algorithms to navigate the surface plots and identify the optimal set of parameter values that maximize fatigue life. The optimizer streamlines the process of finding the optimal combination, enabling efficient and effective decision-making in welding parameter selection.

Fig. 5
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Fatigue life surface plot responses (a) Comparison of peak and base current, (b) Peak current vs. pulse rate, (c) Pulse width vs. peak current (d) Pulse rate against base current, (e) Base current versus pulse width and (f) Rate of pulse versus pulse width

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Maximum fatigue life is attained at a Ip of 22 Amps and a Ib of 12 Amps, as shown in Fig. 5 (a). It can be shown in Fig. 5 (b) that a Ip of 22 Amps and a pulse rate of 20 pulses/sec yield the longest fatigue life. Maximum fatigue life was achieved at Ip of 22 Amps and pulse width of 70%, as shown in Fig. 5 (c). Maximum fatigue life, as shown in Fig. 5 (d), is achieved with a Ib of 12 Amps and a pulse rate of 60 pulses/sec. Figure 5 (e) shows that the optimal conditions for maximizing fatigue life are a Ib of 12 Amps and a pulse width of 60%. Maximum fatigue life was achieved at a pulse rate of 20 pulses/sec and a pulse width of 70%, as shown in fig 0.5 (f).

The optimal set of solution was selected for the following conditions as shown in Table 7; Fig. 6. The set shows the best possible Fatigue life achieved using the Response Surface technique. Fatigue Life of 38,040 is achieved at 22 A peak current, 12 A base current, 20 Pulses/Second pulse rate, and a pulse width of 30%.

Table 7 Optimal solution set from RSM
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Fig. 6
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Optimal values for fatigue life response

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5 Metallurgical features of optimized joint

Scanning electron microscopy (SEM) pictures are taken to investigate fatigue specimen failure. Dimples at the failure zone, as seen in Fig. 7a, is indicative of ductile fracture. Because austenite is still the predominant phase in both the weld and the base metal, ductile failure is expected. The soft austenitic phase causes significant plastic deformation at the joints. Micro voids and greater volume fractions on dimples can be visible in some spots on the weld zone fractography image. Weld penetration is affected by the peak current. Inadequate peak current range results in insufficient penetration, while exceeding the current limit negatively impacts weld quality through material loss. Geometrical properties of the weld are affected by the flow rate of the pulses and the pulse width. It is possible to dilute the weld metal more effectively through a rise in pulse rate, which is related to the plasma jet.

Fig. 7
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(a) SEM picture shows dimples at the failure zone, (b) EDS element analysis data

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Figure 7b presents the results of element analysis and the distribution of weldment phases. The analysis reveals valuable insights into the behavior of chromium in the weldment and its impact on phase formation. Chromium has a natural tendency to form carbides, but this tendency is alleviated by its dispersion in the fusion zone. This dispersion leads to the formation of ferrite phases, which are crucial for the mechanical properties of the welded structure. One notable effect observed in the weld is the acceleration of constitutional supercooling due to nitrogen (N). This phenomenon gives rise to equiaxed dendrites in the weld. Equiaxed dendrites are formed when the rate of constitutional supercooling is increased, resulting in a distinct microstructure in the weld zone. The data further indicate that chromium carbide precipitation is inhibited by the presence of nitrogen, as demonstrated by the analysis [29, 30]. This inhibition is significant for the overall integrity of the weld, as chromium carbide precipitation can lead to detrimental effects on the material’s properties. Examining the results of Energy Dispersive X-ray Spectroscopy (EDS) analysis, it is evident that the weldment contains lower levels of chromium (Cr) at 1.3% and nickel (Ni) at 0.4% compared to the base metal. The variations in the concentrations of these elements can be attributed to the welding process, which induces the development of oxides followed by depletion. The welding-induced oxides contribute to the altered composition of the weldment compared to the base metal.

6 Conclusions

The following findings are derived from the experiments.

  • UNS S32750 SDSS sheets is butt welded using MPAW at various permutations according to the Taguchi Design Matrix, and observed that fatigue life increases with increase in frequency.

  • Fatigue life increases with peak current and base current. This is due to High temperatures cause the metal to expand, forming larger beads on both sides of the base metal.

  • There is no much effect of pulse width and pulse rate on fatigue life of the welded sheet. Nevertheless, fatigue life may decrease with raise in pulse width, due to large time interval between the pulses, leading to faster cooling of weld joint and coarse grain formation.

  • From Response optimizer, the optimal combination for maximum fatigue life of 38,040 cycles is at Peak current 22 Amps, Back Current 12 Amps, Pulse Rate 20 pulses/sec, Pulse Width 30% which is better than experimental value of 35,787 cycles. The deviation from the predicted value is within the range of less than 6%.