Multi-objective optimization and evolution of dissimilar welding process between Cr-Mo steel and austenitic stainless steel for power plant application

In this study, response surface methodology (RSM) was employed to optimize the welding parameters’ effects on mechanical properties of dissimilar welds between Cr-Mo steel grade (P11) and austenitic stainless steel (AISI 316LN). To determine the best welding parameters, variance analysis (ANOVA), desirability function, and perturbation analysis were used to create regression models and identify the significant parameters influencing tensile strength and hardness gaps in the weld joints. The results indicated that welding speed is the most significant parameter affecting both the austenitic hardness gap and tensile strength, while gas flow has the most significant impact on the hardness gap of Cr-Mo steel. Furthermore, welding speed positively influences the mechanical properties of dissimilar weld, whereas welding current has a slight negative effect on tensile strength. The optimum welding parameters were found to be 130 A for welding current, 70 mm min−1 for welding speed, and 13 l min−1 for welding gas flow, resulting in hardness gap values of 18.10 HV (Stainless steel side), 27.38 HV (Cr-Mo steel side), and a tensile strength of 453.90 MPa. The optimum parameter effect is concentrated at the weld interfaces between the fusion zone and the heat-affected zone. This effect led to limitations in grain coarsening, a reduction in the martensite and delta ferrite phase percentages, a slight increase in the bainite ratio, and a decrease in carbide precipitations. As a result, a homogenization of strain distribution in the optimum weld was achieved, leading to ductile fracture in Cr-Mo steel.


Introduction
Cr-Mo steels and austenitic stainless steels (ASS) are of great importance in power plants tubes due to their unique characteristics and benefits.These alloys are used in pipe manufacturing, silos, and injection tanks for power generation systems, due to their resistance to extreme mechanical stresses, corrosion and thermal deformation [1][2][3].As industrial technologies advance, as well as the development of steam pumping pipeline networks and water supply pipeline systems to cool nuclear power plant reactors, it became necessary to combine pipes that not have the same chemical composition by a dissimilar welded joint to benefit from the common advantages of steels like 316LN ASS and Cr-Mo P11 steel.The joining method between these materials is heavily relies on welding processes to ensure permanent links between welded components, caused by thermal welding cycles that induce complete fusion and recrystallization of microstructures in one dissimilar weld joint [4][5][6][7].
Despite significant improvements in dissimilar weld joints aimed at achieving a final weld joint free from imperfections that could compromise its microstructural integrity or affect its functionality, such as cracks or voids, it has also been observed that dissimilar welding of Cr-Mo/ASS weld joints poses a dual challenge.This involves the formation of fragile microstructures in both the heat-affected zone (HAZ) and fusion zone (FZ), leading to a deterioration in the mechanical properties of the welded materials, particularly in terms of hardness and tensile strength of Cr-Mo/ASS dissimilar weld joints [7,8].These mechanical degradations are strongly The reseaches mentioned above are based only on RSM analyses of welding parameters for one material and they also lacked effective mechanical factors analyses like hardness and tensile strenght.This study deals the optimization dissimilar welding parameters of Cr-Mo P11 and AISI 316LN SS Steels with the application of RSM method under the effect of varying welding parameters of current, speed and gas flow rate.Where hardness gap and maximum tensile strength were introduced for improving mechanical properties of dissimilar welds.

Materials
The base materials used in this work were 4 mm thick plates of austenitic stainless steel AISI 316LN and Cr-Mo P11 steel.The compositions of base materials and filler metal were evaluated with using a Foundry Master Xpert spectrometer (OES) (table 1).

Welding process
Automatic welding device was used to conduct a tungsten arc welding process (TIG) [10,24].The welding process involved joining plates of 4 mm thickness at a 60°angle using a V chamfer and a E2209 filler metal diameter of 1.5mm [25,26].TIG welding parameters, were changed across vary values of current, argon flow and welding speed.

Mechanical tests and characterizations
Mechanical properties of weld joints were evaluated through hardness and tensile tests.Hardness measurements were performed using Hv Hardness TESTER a 0.2 Kg load (Hv0.2).Tensile test was conducted using a SATEC INSTRON tensile testing machine at a strain rate of 0.1/s according to ASTM E8M [27] requirements.
For deeper analyses of local tensile stresses, specimens were tested by high-resolution camera by using special matte white and black paints and image processing GOM software.The black dots of the speckle were uniformly distributed on the white.The diameter of the black dots was adapted to the pixels of CCD camera, in that it was deposited about four black dots in 1 mm 2 of white surface.ZEISS Gemini SEM 300 Scanning electron microscope was used for metallurgical characterization and fractography examination.

RSM tools
In this study, the methodology (RSM) is employed to model and optimize welding process functioning using saved results of specified experiment combinations as per RSM matrix.and output parameters data as a starting point; these optimization will make it possible to analyze all welding experiments even that they are not included in RSM matrix combination, among the main goals pursued in this work are: Adoption of two of the most important mechanical properties required to determine the quality and reliability of a weld joints, are hardness and tensile strength; Determine the optimal execution conditions for a dissimilar welding process; Deduce an interval of welding parameters in which the operating criteria are satisfied; Establish a relationship by response surface equations between the input parameters and the desired output response.
Analyze a dissimilar welding process by RSM tools.
Here, RSM analysis is adopted for three factors with 3 levels, which gives 27 appointed sets of RSM matrix.The mechanical properties of tensile strength and hardness of TIG welding experiments were analyzed by analysis of variance (ANOVA) to determine interaction effects of the welding process parameters on tensile strength and hardness.
RSM methodology goes through define the independent input variables and the desired output parameters.In our case, the input variables are current, welding speed and gas flow.While, the output parameters concerned are hardness and tensile strength, which represent the desired welding parameters to create the design of the experimental plan.This plan serves to establish mathematical models of responses by regression equation that links the desired response Y and the input parameters of the process according to the following formula [14-16]: Where Y is the desired machinability aspect and j is the response function.The approximation of Y is proposed by using a non-linear (quadratic) mathematical model.In the present work, RSM method is based on mathematical model that is given by [18,19]: Where, the coefficients: a , 0 b , i b , ij b ii respectively represent the free coefficient of equation, linear, interactive and quadratic terms for the regression model.Generally, they are must be calculated from the results of experiments.
With, X i represents the level assigned to factor i., X j represents the level assigned to factor j.
To analyze previous mathematical equations, variance analysis (ANOVA) is carried out.It serves to determine effectiveness of the models developed and the contribution of each welding parameter in mechanical properties.And then creating graphs of response surfaces that accurately represent interactions effects of process parameters on desired response.Finally reaching the optimization of operating welding parameters and the confirmation of predicted performance characteristics by using desirability function.
In this study, outputs properties were as hardness and tensile strength.To evaluate these mechanical properties, each experiment takes five measurements; arithmetic average of the measurements was set as final value of mechanical property of hardness or tensile strength of weld joint.
The high and low welding parameters levels as reported in table 2 are chosen and selected within the intervals recommended by our previous experiences (Current (70/130), Speed (50/90) and Gas flow (5/14)), provided the welds are free of defect or cracks.
Table 3 represents RSM design combinations of welding parameters (according to RSM matrix) with their experimental results for Hardness gaps and tensile strength, where, three welding parameters at three measurements levels lead to 27 experiences.
The figure 1 illustrates that the hardness value for the fusion zone falls within the range of values for the heataffected zone and the base material.This is in agreement with previous researches [16,17].Consequently, the hardness gaps (ΔH316LN, ΔHP11) between the highest and lowest levels were selected to achieve optimal welding parameters and to ensure the reliability of the welded structure.
According to the RSM matrice, the histogram of figure contains data from 27 experiments (table 3).Each experiment included hardness values for HAZ-316LN, HAZ-P11 and FZ-E2209 represented by three columns.In all experiments, the hardness values of the base materials (316LN, P11 steel) unaffected by microstructural  Vickers's hardness scale was employed for measuring the hardness along the weld joint with 200 g load and 20 s dwelling time.Five readings were taken in each zoneand the average was recorded in figure 1 to be used in RSM analyses.
It is observed on in every welding experiment that hardness reaches a maximum value in the heat affected zone (figure 1).As a result, the hardness peaks across P11/316LN dissimilar weld joint can cause fragile structure, and later a brittle fracture of weld joints.Thus, this work aims to minimize HAZ hardness gaps both in P11 and 316LN steel side, and to maximize tensile strength.For optimizing welding parameters, three criteria were chosen, which are: • ΔH 316LN: Hardness gap between BM of 316LN SS and HAZ of 316LN steel; • ΔH P11: Hardness gap between BM of Cr-Mo P11 and the HAZ of P11 steel; • σ max : Tensile strength of dissimilar weld joint.

RSM analyses 3.1.1. Regression equations
The relationship between input parameters (Current, Welding speed, Gas flow) and performance measurements (outputs) is modeled by polynomial regression.The regression equations obtained for the response factors of ΔH P11, ΔH316LN and σ max using quadratic regressions for hardness and linear regression for tensile strength.The final models of mechanical properties as mentioned in equation (2) appear as follows:  To gain compendium into how the independent variables interact with the responses and how to deduce predictions for mechanical properties, a variance analysis (ANOVA) was conducted based on the proposed regression models [28].The purpose of this analysis was to examine the impact of three input parameters on the overall variance of output response that based on hardness gaps (ΔH316LN, ΔH P11) and the tensile strength (σ) described in tables 4-6, respectively.
The ANOVA tables was used to present the findings.It includes the degrees of freedom (DF), sum of squares (SC), mean squares (MS), F values (F), and probability (P).The final column of the table illustrates the contribution percentage (Cont.%) of each factor and different products to the total variation.To determine the statistical significance of each coefficient, the P values and F values were examined.A low P value (0.05) indicates statistical significance for the corresponding response, assuming an alpha value of 0.05 (or a 95% confidence level).This implies that the generated models are considered statistically reliable.It confirms that the terms in the model have a substantial impact on the response.Additionally, higher F values for each coefficient suggest a greater significance of that particular term within the model [18].
In figure 2, a residual analysis is presented for three dependent variables of ΔH 316LN, ΔH P11, and σ max .This analysis serves as a means to assess the reliability of the mathematical model used and its compatibility with experimental values of the majority of welding parameters values, as evidenced by the points positioning that fall around the straight line of residual analysis.This alignment suggests a strong agreement between the model and the experimental data with minimal bias found in the predicted results.The consistency of points around the resulting model of quadratic models of ΔH 316LN and ΔH P11 indicates high level of convergence between experimental and predicted results, that are very identical in the case of linear model of tensile strength.Consequently, RSM models of mechanical properties of weld joints are considered reliable [17][18][19].
The normal probability analysis derived from the models provide predictive function for output responses.The analysis are associated with positive and negative signals for residual values.The positive signal denotes that the model underestimates predicted response compared to the real response, while a negative signal indicates that the model overestimates the response.In ΔH316LN and ΔHP11 analysis (figure 2), the symmetrical distribution of negative and positive values relative to the zero column gives more reliability to the models.

Perturbation plotting
The figure 3 illustrates the main effects of the input factors (A: current, B: Welding speed, C: Gas flow) on the perturbation plots for three response parameters: ΔH P11, ΔH316LN and σ max .These graphs confirm the findings of the ANOVA results presented in tables 4-6, where, x axis represents the low and high levels of the input welding parameter, while y axis represents the mean value of the response factor at a specific level.By examining these plots, we gain findings into welding parameter effect on mechanical properties.Where, it observed that welding speed has a positive effect on the mechanical properties.This means that as welding speed increases, there is a significant decrease in ΔH P11, ΔH316LN and increase in σ max , and thus more homogeneity and reliability of mechanical properties.On the other hand, Gas flow has adverse effect on ΔH P11 only, and current has an adverse effect on the tensile strength only.We conclude that the perturbation plots provide visual confirmation that welding speed has a positive effect on the mechanical properties, while, current and Gas flow exhibit a limited effect on mechanical properties.

Response surface analysis
After fitting models using BBD design [20,21], response surfaces were generated using Design-Expert software, which are visual representations of 3d curves.They provide insights into the effects of welding parameters as well as their interactions on the response parameters of ΔH P11, ΔH 316LN and σmax.These response surfaces help in understanding how variation in welding parameters levels influence of the response factors.By examining response surfaces, it is possible to analyze how welding parameters influence mechanical properties.Furthermore, these output properties can be effectively compared with each other when when changing welding parameters values.
The illustrations of figure 4 depict how various welding parameters impact the resulting changes in ΔH 316LN, ΔH P11, and σmax at a specific gas flow level.It demonstrates that the welding speed notably influences the hardness of the P11 side more than that of the 316LN side.This difference is expressed by a hardness gap exceeding 40 HV in the P11 steel side.
In addition, it shows that tensile strength is more responsive to variations in current and speed compared to hardness of dissimilar joints.This is particularly evident in the higher bending rates observed in the tensile strength curve due to parameter changes, in contrast to the ΔH 316LN and ΔH P11 curves.

Desirability function of dissimilar weld joint
It is employed a desirability function of RSM method to assess the three input welding parameters associated with the mechanical properties.It undertakes a survey on interaction effects of the process parameters on the mechanical properties [28], the optimal welding conditions for hardness gaps and tensile strength of dissimilar joints of Cr-Mo P11/316LN SS steels.It serves visualizing and mapping the contours of optimal combinations parameters to achieve the most desirable outcome.Where, the desirability value is represented on the y-axis, while the corresponding parameter values are displayed on the x-axis.
Desirability contours are graphical representations used to visualize the variation in desirability values across different levels of multiple process parameters [22,23].The contour plots is consisted of undulating lines, each representing a specific level of desirability, with regions of higher desirability being indicated by denser color (from light green to dark red) with closer contour lines.The x and y axes of the plot represent two welding parameters, alternate between welding current and welding speed and gas flow.Desirability contours provide valuable insights into the interaction surfaces between welding parameters and their effects on achieving desirable mechanical outcomes.By examining the contours, we can identify combinations space of welding parameters that result in the highest overall desirability for hardness gaps and tensile strength.These contours gives optimal region where the desired mechanical properties can be performed at defined spaces, where the optimal areas of welding parameters combinations (current, speed; gas flow) are in (126.52 to 130A), (62.64 to 70 mm min −1 ) and (8.71 to 14 l min −1 ) respectively (figure 5).The bar graph of desirability is a graphical representation of the overall desirability scores for each mechanical property.Each property is represented by a bar, and the height of the bar corresponds to its overall desirability score [28,29].
By looking at the bar graph (figure 6), you can quickly compare the desirability of different mechanical properties.It is observed that ΔHP11 has the highest bar (i.e., the highest overall desirability) this mean that it is most desirable factor based on the welding parameter levels.thus, ΔHP11 represent best factor by considered its high desirability value compared to ΔH316LN an σ max across all relevant input welding levels of current,  welding speed and gas flow.This result is particularly very useful in making decision when it is obligated to focus on just one parameter (that has high desirability) rather than another when varying welding parameters.
The ramp plot of desirability for the current study reveals how hardness gaps and tensile strength, vary as the welding parameters change, helping to identify the regions with the highest desirability values that correspond to the most favorable combination of mechanical properties (figure 7).It showcases how the desirability of hardness gaps and tensile strength evolve.Hence, it locates the peak region on ramp plot, where the desirability is at its highest, indicating the optimal welding conditions for achieving the best compromise between hardness gaps and tensile strength in the dissimilar joints of Cr-Mo P11/316LN SS steels.By studying the ramp plot of desirability, it found that the most suitable welding parameter values to achieve the desired mechanical properties for dissimilar weld joints is 130 A, 70 mm min −1 and 13 l min −1 , giving these properties as follows: 18.10 Hv (ΔH 316LN) , 27.38 Hv (ΔH P11) and 453.90 MPa.

Evolution of OP and SOP parameters 3.2.1. Effect of parameters on metallurgical behavior of dissimilar welds
A comparison of optimum and suboptimum parameters predicted by RSM methodology provides deep analyses into the metallurgical and mechanical behavior between the best-performing welding conditions and those that fall short of the optimal outcome.In RSM analysis of this study, 'optimum parameter' refer to combination values of welding parameters of current, speed and gas flow variables (130 A, 70 mm min −1 , 13 l min −1 ) that result in the highest desirable response of mechanical properties.On the other hand, 'suboptimal parameters' represent tripartite set of input parameters that yield mechanical responses that have low desirability values which amounts to 70A, 50 mm min −1 , 5 l min −1 , on lowest desirability value (figure 5).The comparison of optimal and suboptimal parameters obtained through RSM helps in understanding the sensitivity of the process to mechanical and metallurgical evolutions of welding parameters and provides valuable information for linking RSM variable by microstructural and tensile strain behavior, and assessing their success in achieving reliable microstructure for welds.
Figure 8 exhibits optical micrographs showcasing (a) weld description (Cross-section), (b) dissimilar weld interface between P11 and AISI 316LN (divided into three sections: the fusion zone (FZ) and the connection zones (316LN -FZ, P11-FZ), heat affected zones and base materials), (c) Cr-Mo P11 base material microstructure, (d) SS 316LN base material microstructure.The microstructure of the received P11 material consists of polygonal ferrite α (white color) and pearlite P (black color) (figure 8(c)).It comprises approximately 85% ferrite with varying grain sizes ranging from 9 to 12 μm.The microstructure of 316LN steel is primarily composed of γ austenitic grains with twins that resulted from prior thermomechanical treatment, with an average austenite grain diameter of approximately 25 μm.
Cross-section of dissimilar joint (figure 8(b)) is analyzed by taking best and bad welding combinations (current, speed and gas flow) which correspond to optimal and suboptimal weld.
During the TIG welding process, fusion zone (FZ) and the heat affected zones (HAZ) undergo a metallurgical transformations due to welding thermal cycle.Within HAZ 316LN, the OP parameter is characterized by dampen the austenitic grain coarsening compared to the SOP parameter, thus reducing the mass fraction of the precipitated phases (such as sigma phase (σ) and delta (δ),).
In HAZ-P11 side, the use of the OP parameter leads to a reduction in martensite phase rate (α') and carbide precipitations with slightly increase of bainite ratio, this will be accompanied by improvement in mechanical properties of weld joints compared to OP parameter.
Figures 9(a), (c) show the microstructural overlap between the FZ and austenitic HAZ of OP and SOP welds, respectively.It captures a ferrite solidification mode in fusion zone, during which a minor quantity of secondaryphase ferrite and sigma phase (σ) form in HAZ.In HAZ, the resultant microstructure closely resembles 316LN BM microstructure, except for coarsening of austenite grains particularly in a SOP parameter case where this coarsening of grain size reaches a 38 μm.Also, an intermittent presence of ferrite particles along austenite boundaries, that reveals the occurrence of ferrite stringers within HAZ region.Where, δ stringers have grown  and raised near the diffusion line.This growth of δ stringers is attributed to fast cooling rate of austenite grain induced by ferritic transformation to austenite (α → γ + δ) during the thermal welding cycle, consequently retaining a heightened proportion of ferrite represented by δ stringers [16,30].Furthermore, It is observed that suboptimal parameter gives thick branches of δ phase in FZ and HAZ with dendritic morphology in the most FZ, while an OP parameter weld results in thin branches of δ phase with vermicular morphology of austenite in FZ (figures 9(a), (c)).
To comprehensively assess the influence of OP and SOP parameters on the metallurgical characteristics of dissimilar welds between 316LN and P11, an examination of the distribution of key chemical elements in the studied materials was conducted.This analysis encompassed heat affected zones, fusion zone and the weld interfaces.The concentrations of Fe, C, Mn, Mo, Cr, and Ni elements were determined along a concentration line spanning from the heat affected zone (HAZ) in the 316LN region to the HAZ in the P11 region.This assessment was carried out using Energy Dispersive x-ray (EDX) analysis conducted along scanning electron Micrographs (SEM) as illustrated in figure 10.
At the beginning of the heat affected zones (HAZ's) (figure 10), the concentration lines depicting the main chemical elements (Fe, C, Mn, Mo, Cr, and Ni) in the studied materials reveal that the percentages of these elements align with the rates specified in the chemical composition of the studied materials (refer to table 1).This observation indicates a consistency between the actual chemical composition based on table 1 and the anticipated distribution of elements in the examined HAZ's regions by EDX analyses.In the case of OP weld, a decrease in carbon content is evident in HAZ-P11 (approximately 10% of Carbone) compared to SOP weld (approximately 15% Carbone) as illustrated in figures 10(b) and (d) respectively.Additionally, there is an observed increase in the iron content rate, with an average of 89% in HAZ-P11 of OP weld, in contrast to 81% in SOP weld.This indicates a reduction in phases rich in carbon and metallic precipitates when comparing OP weld to SOP weld.This finding aligns with references that discuss the diffusion of alloying elements between dissimilar welding interfaces of a low carbone steel and austenitic stainless seel [30,31].The consequence of this phenomenon is a diminished hardness and an augmented metallurgical and mechanical homogeneity in OP parameters in contrast to SOP parameters.On the other hand, SOP parameters induce slight fluctuations in C, Cr, and Ni rates in HAZ-316LN (figure 10(c)) compared to OP parameters (figure 10(a)).This can be explained by a higher rate of intermetallic precipitates formed with SOP parameters compared to those of OP parameters (refer to figure 9(a)), such as σ phase precipitates (refer to figure 9(c)), resulting in decreased mechanical properties.Additionally, in the fusion zones (FZ's) of SOP parameters (figure 10(c)), the slight reduction in Fe rate from an average of 71% Fe in OP weld to 65% in SOP weld indicates a higher percentage of the δ intermetallic phase compared to OP parameters (figure 10(a)) [7,31].This causes a decrease in the mechanical behavior within the FZ zone of SOP weld and thus underscores the positive effect of OP parameters on the FZ side.

Effect of parameters on fracture behavior of dissimilar welds
For precise measurement of stain contours and fracture process zone in σ max of OP and SOP parameters, it was employed DIC image techniques that is one of the recent method to analyze the mechanical behavior of materials [32,33].It is showed also that tensile local strain are distributed more homogeneously across OP weld compared to those of SOP weld.At OP parameter, the fracture occurred in in P11-BM, while SOP parameter caused a fracture at HAZ-P11/FZ interface (figure 11(b)).
To comprehend the impact of optimal welding parameters on weld joint fracture mechanisms, a fractographic analysis is performed using a scanning electron microscope (SEM).This analysis aims to investigate and delineate the fracture surface characteristics under tensile loading, examining both the ductility and brittleness of the fractures at a microscopic scale.
Figure 12 shows that OP weld has a ductile fracture aspect (figure 12(a)) whereas SOP weld gives brittle fracture with rivers pattern aspect (figure 12(b)).OP fracture presents isolated spherical cupules with thin wells in fractured surfaces.Hence, the high amount cupules area signs the good tenacity of OP weld joint.Instead, SOP fracture is characterized by a smooth surface with the presence of ribs in and around ferrite grains; this is due to slight increase of carbide precipitation rate with high rate of martensite phase in HAZ-FZ interface compared to OP parameter.

Conclusion
This study demonstrates the effective application of response surface methodology in the evaluation, modelling and optimization of TIG dissimilar welding between 316LN stainless steel and Cr-Mo P11 steels, with the aim of achieving dependable welds for power plant applications while considering into account two crucial mechanical properties: hardness and tensile strength.The precise assessment of TIG welding parameters is achieved through experimental investigations utilizing the RSM methodology design.Multiple of RSM analyses are employed to optimize TIG dissimilar welding, ensuring the attainment of desired outcomes by establishing correlations between three input parameters and mechanical variables output, through ANOVA, perturbation plotting and desirability function.Mathematical ANOVA models were established to estimate the maximum tensile strength and hardness gaps for automatic dissimilar welding of 316LN SS and Cr-Mo P11 steels by integrating welding current, welding speed and gas flow (at a 95% confidence level).Where, these predictive models are highly dependable, serving as a crucial tool in automated welding by getting reliable predictions of mechanical properties within the scope of experiments.As indicated by perturbation plotting and response surface analysis, increased welding speed correlates positively with mechanical properties.It concluded that higher welding speed leads to a significant reduction in ΔH P11 and ΔH316LN, coupled with an increase in σmax.This implies that elevating welding speed within the experimental range enhances the mechanical properties of the welds, whereas welding current has a slight negative effect on tensile strength.It is also found that welding speed is the main significant parameter affecting on both austenitic hardness gap and tensile strength, while gas flow has the most significant effect on hardness gap of Cr-Mo steel.It is found that the optimum parameter has the following input parameters values 130 A current, 70 mm min −1 weld speed and 13 l min −1 gas flow, it is correspond to optimal weld that having the mechanical properties of 18.10 Hv (ΔH 316LN), 27.38 Hv (ΔH P11) and 453.90 MPa tensile strength.Furthermore, the optimum parameter derived from desirability function showed significant metallurgical evolutions when compared to a suboptimum parameter.It results in thin branches of δ phase with vermicular morphology in fusion zone.And also made a great impact on heat affected zones interface, it leads to a reduction in martensite and ferrite delta phases, slightly increase of bainite ratio, decrease of carbide precipitations, limited grain coarsening, and all of this contributed to improved weld properties and more homogenous of strain distributions across weld joints, which caused a ductile fracture in P11 base material.This work contributes, on one hand, to the inclusion of RSM optimization design in the optimization of dissimilar welding by considering hardness gaps and tensile strength.On the other hand, it permits direct access to the most important metallurgical and mechanical evolution within the experimental range by comparing the behaviors of optimum and suboptimum parameters using metallography and DIC digital image correlation in specific regions of weld joints.

Figure 3 .
Figure 3. Effects of welding parameters on the perturbation plots of ΔH 316LN, ΔH P11 and σ max .

Figure 5 .
Figure 5. Contour plots for global desirability of Current-Welding speed, Gaz flow-Current and Gaz flow-Welding speed.

Figure 10 .
Figure 10.SEM image of : (a), (b) EDX line spectrum of element concentrations in OP weld joint (c), (d) EDX line spectrum of element concentrations in SOP weld joint.

Figure 11
Figure 11 gives representation of local strain fields in OP and SOP welds from DIC images (figures 11(a), (b)) and stress-strain curve (figure 11(d)) of tensile test specimen (figure 11(c)).It indicates that high deformation is located around fracture contours, when the tensile test reaches its maximum tensile strength, which corresponds to high local strain (red colors) compared to the rest of tested surface specimen.Then, fracture contours continue to propagate by necking mode until a complete fracture occurs [34], forming fractured surfaces as shown in the figure 11, where P11 side withstands much greater deformations than 316LN side (figures 11(a), (b)).It is showed also that tensile local strain are distributed more homogeneously across OP weld compared to those of SOP weld.At OP parameter, the fracture occurred in in P11-BM, while SOP parameter caused a fracture at HAZ-P11/FZ interface (figure11(b)).To comprehend the impact of optimal welding parameters on weld joint fracture mechanisms, a fractographic analysis is performed using a scanning electron microscope (SEM).This analysis aims to investigate and delineate the fracture surface characteristics under tensile loading, examining both the ductility and brittleness of the fractures at a microscopic scale.Figure12shows that OP weld has a ductile fracture aspect (figure12(a)) whereas SOP weld gives brittle fracture with rivers pattern aspect (figure12(b)).OP fracture presents isolated spherical cupules with thin wells in fractured surfaces.Hence, the high amount cupules area signs the good tenacity of OP weld joint.Instead, SOP fracture is characterized by a smooth surface with the presence of ribs in and around ferrite grains; this is due to slight increase of carbide precipitation rate with high rate of martensite phase in HAZ-FZ interface compared to OP parameter.

Figure 11 .
Figure 11.Representation of local strain fields in OP and SOP welds with accompanying tensile curves.

Table 2 .
Assignment of the levels to the factors.

Table 3 .
RSM design combinations and experimental results.

Table 6 .
Analysis of variance of tensile strength σ max .