Predictive Models for the Ultimate Tensile and Yield Stresses Occurring in Joints of Untreated Friction Stir Welded 2017 AA ( ENAW-AlCu 4 MgSi ) Plates

Friction Stir Welding (FSW) processes have been applied in numerous industrial fields and broadly embraced by the research community. In this paper, given three FSW process parameters, namely, the tool rotation speed N (rpm), the tool traverse feed F(mm/min) and the tool pin/shoulder diameters ratio (r%), we purpose to ascertain their impact on joints Ultimate Tensile Stress (UTS) and joints Yield Stress (YS). The FSW has been executed using 6 mm thick rolled plate in 2017AA. For the design of experiments strategy, we conducted a face centered central composite strategy through which 18 trials have been executed. Then, we utilized the RSM technique to formulate the predictive models which are relevant to the (UTS) and (YS) outputs. Accordingly, the study has pointed out the prevalence of the tool rotation speed and the tool diameters ratio factors; however, the tool traverse feed (F) was found trivial and statistically insignificant. Likewise, the sensitivity analysis regarding factors N, F and r% on both (UTS) and (YS) has exhibited the dominance of the tool diameters ratio (r%), indistinctively.


Introduction
The Friction Stir Welding (FSW) is a derivative of the conventional friction welding process that is traced back to the early 1960s.The process was patented at the TWI in 1991 [1] and has been applied heavily in many Industrial fields.Many research works have shown the superiority of the FSW on conventional fusion welding.And, the process has concerned polymers [2] and ferrous and non ferrous alloys.Furthermore, the FSW has coped with similar, dissimilar [3] and metal matrix composites [4].
In FSW, a rotating tool with a central pin is driven in the interface of two plates/sheets to be welded.The tool is then fed in the joint line prior retracting to a rest/reference position.The material softens by means of the heat which is generated by the tool/part friction movement and the pin malaxation effect.Because the heat is mainly produced under the tool's shoulder, a local plastic deformation zone occurred so that the welded interface is stirred and homogenously formed.Finally, the tool is pulled away and the weldment converts into a solid state during the cooling phase [5].
During the FSW process, the material stirring power, the non-isothermal treatment and the material flow determine, at a large extent, the mechanical and metal properties of the joint weld zones (i.e., the weld nugget, the thermo-mechanical affected zone and the heat affected zone).The joint macrostructure, the residual stress and the fracture surface tests are important qualitative properties which are inspected in FSW joints.But also, other quantitative properties are required to control the joints quality such that the yield stress (YS) and the Ultimate Tensile Stress (UTS) [6,7].In numerous works, both the quantitative and qualitative properties of FSW joints have been correlated with the process parameters, for instance, the rotation speed and welding feed rate [8,9], the tool axial load [10,11], the tool geometry [12,13] and the weld interface orientation [14].One challenge; however, is how FSW parameters could be determined so that high quality joints are produced cost-effectively.Statistical techniques, among other solutions, have brought substantial contribution in this regard.The statistical techniques may be viewed as four main classes, 1) factorial design and analysis of variance (ANOVA) [15,16], 2) response surface method RSM [17][18][19], 3) Taguchi method [20,21], and 4) artificial neural network & Genetic method [22,23].
For the FSW in the 2017AA (ENAW-AlCu4MgSi), a few studies have been carried out [24,25].This study has considered such an alloy.In a recent work [26], we have coped with the two process responses joints Tensile Elongation (E%) and joints Hardening Capacity (Hc), and at present, we shall report on the two quantitative properties (UTS, YS).Table 1 enlists the nominal mechanical characteristics of the aluminum 2017 AA.
The remaining text is structured as follows.Section 2 lies out the study framework, the design of experiments (DoE) strategy as well as the true stress-strain curves of the tested coupons as benchmarked against the BM.Section 3 discusses and lies out the ANOVA(s) and RSM models being fit to the process responses (UTS) and (YS).Finally, Section 4 will cope with the sensitivity analysis study of the operating factors N, F and r%.

Experiment Setup
The experiment FSW runs have been executed on a 7.5 kw powered universal mill (Momac model), rating up to 1700 r/min in rotation speed and up to 1080 mm/min in tool feed.A series of 6 mm thick plates in 2017AA were cut into (250 × 90) mm rectangular shapes.And, for each run, a pair of plates (set) disposed in butt configuration are welded along their length edge.The welding tool is manufactured in a high steel alloy (35 Rockwell-C Hardness).Figure 1 displayed the experiment setting as well as the tool geometry.

Design of Experiment Strategy
The variation assessment and response predictive models regarding (UTS) and (YS) are assessed using the RSM  technique.The experiment has been undertaken in a sequential strategy.First, a 2 3 plan is put forward to fit first-order models for (UTS) and (YS).Then, owing to the model Lack of Fit (LoF), we augmented the design with six axial runs and four center points to fit higher order models, thereby, a face-centered composite design For the levels setting of N, F and r%, we performed some preliminary trials to better assign lower, intermediate and higher levels of factors.Mainly, we took into account the macroscopic observation of joints texture and the surface defects (e.g., surface irregularities, excessive flash, lack of penetration, surface-open tunnels, etc.).Accordingly, for the DoE coding, the actual units of the −1 and +1 levels are set at 653 rpm and 1280 rpm for the rotation speed (N), 67 mm/min and 109 mm/min for the tool traverse feed and, 33% and 44% for the tool diameters ratio (r%).The intermediate setting of N, F and r% has been maintained at 910 rpm, 86 mm/min and 39%, respectively (Table 2).Table 3 depicts the maintained constant factors throughout the experiment time.
So far, the design encoding, ANOVA tables and sensitivity analysis will be assisted by Minitab ® software.Table 4 shows the study DoE layout as expressed in natural coding units.

Specimens True Stress-Strain
The tensile specimens (ASME E8M-04) have been cut longitudinally in the butt FSWed plates as shown in Figure 2. Figure 3 is a photography of the tensile specimens after fracture.Insofar, these are split into 8 factorial runs, F i = 1,8 (Figure 3(a)), 4 center point runs, C i = 1.4 (Figure 3(b)) and 6 axial runs, A i = 1.6 (Figure 3(c)).Each specimen has been undergone a tensile test at room temperature and at a crosshead speed of 0.1 mm/min.Among the 18 runs, nine of the tension loaded specimens have failed midway of the gauge length and six failed in the vicinity of the grip region.After specimens have been undergone tensile tests, true-stress curves generated for each, have similar pattern compared with the BM plot.Pin small cone diameter/(mm) 4 Tool inclination/(˚) 3 Infeed/(mm) 0.94

Empirical Model for the Ultimate Tensile Stress (UTS)
In this section, we shall lie out the descriptive model which can convey variation in the (UTS) response, reliably.Allowing for a threshold of 95% C.I., the candidate/potential regression model(s) should satisfy the best trade-off among the model statistics, i.e., the LoF, R 2 , R 2 -pred, R 2 -adj and S (see Table 5).
According to Table 5, it is indicated that both variation in (UTS) and (YS) are satisfactorily described by means of second order models.For (UTS), the variation in factors N, F and r% explain 93.62% to 99.48% of the model in T b When screening different models as enlisted Table 5, the LoF and R 2 values advise interchangeably more than one candidate model, however, we kept on the highlighted models which exhibit better pure error standard deviation and, above all, higher model predictability (R 2 (pred)).
Considering the (UTS) full quadratic model shown able 5(a), the visual checking of the residual plots regarding the normality, independency, structureless and independence on factor setting does not question the model adequacy.Nevertheless, at 95% of C.I., the residual distribution is not normal (p-value 0.024) (Figure 4).Also, the ANOVA (see Appendix A) suggests the square terms, F 2 and r% 2 , as fitted in the regression model are insignificant (p-value 0.750 and 0.825, resp).Interestingly, the regression p-values of the interactions (p = 0.000) and the squared terms (p = 0.024) are found statistically significant at 5%, suggesting presence of curvature in the (UTS) surface contour plot.variability.However, the variability in (YS) is explained  The reduced model of (UTS) as expressed in natural/ ac -sets are highlighte tive variables is given below: )  The F × r% interaction plot indicates that maximum (UTS) is met when F is set middle and r% low.low, respectively. When considering the N × F interaction plot, maximum (UTS) is achi  And, finally, for the N × r% interaction plot, maximum (UTS) is attained when N and r% are set lo Accordingly, the best setting which maximizes (UTS) is when N and r% are set low and F being set middle or w.The inspection of the surface contour plot shown in Figure 6 indicates that maximum (UTS) is about 283 ean (UTS).We noticed the following points:  According to the main effect plot, maximum

Empirical Model for the Yield Stress (YS)
Likewise th model to describe variation in the (YS) dataset.Allowi for a threshold of 95% C.I., the candidate/potential r gression model(s) should satisfy the best trade-off among the model statistics, i.e., the LoF, R 2 , R 2 -pred, R 2 -adj and S. In Table 5(b), it is indicated that the full quadratic model (N, F, r%, N × F, F × r%, N × r%, N 2 , F 2 , r% 2 ) is not considered fit (LoF 0.03 < 0.05).For the residuals, the 4-plots graph do not question the model adequacy as it is shown in Figure 7.The ANOVA given in Appendix B, pointed out the regression p-values of the interactions (p = 0.192) and the squared terms (p = 0.03 < 0.05) suggesting presence of curvature in the response surface which mainly originates from the squared terms.When considering the factors effects, the ANOVA shows that only N (p = 0.000), r% (p = 0.000) and roughly r 2 (p = 0.094) are found statistically significant at 5% of Type I error.
A reduced model of (YS) is then obtained by getting rid of insignificant terms (main + interactions).Following is ng.
  3 YS 342.98 14.69 10 13.05 r% 14.77 10 r% From Equation (2), it is shown that the (YS) re is independent of factor (F). Yet, it is advised to kee at low level as the main effects plot suggests (Figure 8).A to the rned the odels (Equa-sponse p it lso, owing to the negative coefficient of terms N and r% in Equation ( 2), lower are N and r% higher is the process response (YS).This is further corroborated by the main effect plot shown in Figure 8.The surface contour plot which is displayed in Figure 8 shows that maximum yield stress (YS) is met when both the rotation speed (N) and tool diameters ratio (r%) are set low and the extra factor F being maintained low.Graphically, maximum yield stress is obtained at about 63.5 MPa.

Discussion: Sensitivity Analysis
ty Analysis o The calculation of the partial derivatives (direct method) , ficients of the regression model of (UTS) with respect to factors N F, and r% is calculated to ascertain the normalized coe- In Table 6, the N,F,r%  , are calculated by averaging over all combinatio ors levels.From the histograms shown in Figure 9, we highlight the fo points. ol trav wing for the factors N and r%, the histograms in y the tool rotation speed (N).

ns of fact llowing
In average, the to erse feed factor (F) is insensitive to the process response (UTS) despite of the N, F and r% setting levels. .The sensitivities of N and r% on (UTS) do not vary with the traverse Copyright © 2013 SciRes.OJMetal

Concluding Remarks
The paper has investigated the influence of three FSW parameters on two process responses, namely, the joint Ultra Tensile Stress (UTS) and the joint Yield Stress (YS) produced in the aluminum 2017AA.

0)
1) The predictive models of (UTS) and (YS) are found fit using quadratic RSM models; 2) The ANOVAs and summary of fit tables (Appendixes A and B) have uncovered the traverse feed (F found irrelevant to the variation in (UTS) and (YS) because of the very small coefficient put in play in the regression Equations ( 1) and (2).
3) In average, the sensitivity analysis of factors N, F and r% on the responses (UTS) and (YS) has emphasi the influence of the tool diameters ratio factor (r%).The sensitivity of the tool rotation speed (N) on (UTS) came seconded in terms of prevalence.Likewise, the FSW process sensitivity was robust vis-à-vis the tool traverse feed factor (F).
The paper findings have s wn that the tool geometry can be highly effective at t ariation of the (UTS) and ) was zed ho he v (YS) and can have significantly beneficial impacts on the quality engineering of the friction stir welded 2017AA.Besides, a shift of the factors variation space should be thought of so that a trade-off between joint macroscopic observations and the optimal parameters for FSW could be reached.

Figure 3 .
Figure 3. Specimens and zones of fracture after tensile tests.

Figure 4 .
Figure 4. Four-plots for the UTS full quadratic model.

1 Figure 5
Figure5shows the main and interaction plots for the m (UTS) is

Figure 5 .
Figure 5. Main effects and interaction plots of response (UTS).

Figure 6 .
Figure 6.Surface contour plot of the process response (UTS).r all combination of factors spaces (N versus r%, versus F and F versus r%) given the extra factor main-

Figure 7 .
Figure 7. Four-plots for the full quadratic model of YS.

Figure 8
Figure 8. Response (YS): Main effects plot and Sur contour plot.face

 Allo Figures 9 (
a)-(c), indicate that, in average, the tool diameters ratio (r%) is the major sensitive factor on (UTS).It is seconded b The maximum sensitivity of r% on (UTS) is met when (N) is set high   r% 4.31   

Figure 9 . 1 
Figure 9. Sensitivity analysis for the process response (UTS): (a) when varying the tool rotation speed (N), (b) when varying the traverse feed (F), and (c) when varying the tool diameters ratio (r%).

Figure 10 .
Figure 10.Sensitivity analysis for the process response (YS), (a) when varying the tool rotation speed (N), and (b) when varying the tool diameters ratio (r%).

Table 4 . FCCD layout for the FSW process experiment.
y 84.48% to 95.75% of the variability in N, F and r%.