This work focuses on the influence of the rotational and travel speed on the strength of AA 2024 T3 friction stir welded lap joints. Tensile tests were carried out on minispecimens extracted from different welding zones. A central composite design was applied to identify the relative importance of the variable factors’ effects and their interaction on yield/ultimate strength and elongation for both the heat affectedzone (HAZ) and nugget zone. Surface methods and gradient algorithms were used to optimize the yield strength of the joints. Shear and microhardness tests were executed to achieve a more complete mechanical characterization.
The feasibility of replacing the riveting process with friction stir welding (FSW) technology in the assembly of fuselage skinstiffener panels was the objective of several scientific papers in the last decades [
AA 2024 T3 sheets were used as the bottom and the top sheet of the lap joints. The nominal weight percent composition (major alloying additions) of AA 2024 is 4.4% Cu, 1.5% Mg, 0.6% Mn, and the rest is aluminium. Sheets’ thickness is 1.27 mm. The ultimate tensile strength (UTS) of the AA 2024 T3 base metal is 475 MPa. As for the welding process parameters, the inverse of travel speed (TS^{−1}) ranged from 0.155 to 0.533 s/mm and the rotational speed (RS) ranged from 950 to 2222.5 rpm. Plunge depth was fixed to 2.11 mm, tilt angle to zero degree, and travel angle to one degree.
Nine different TS^{−1}RS combinations were used for obtaining 13 welds in this study; five combinations were derived by 2^{2} factorial design with five centre points, and the remaining four combinations were obtained by using the steepest ascent algorithm. One tool configuration equipped with a pin consisting of a threaded frustum of the cone was used; the lower and the upper diameters are 2.77 mm and 5.06 mm, respectively, with a length of 2.03 mm. The shoulder diameter is 12.04 with a concavity of 7°. Two different machines were used to perform FSW lap and overlap joints with single pass. A controlled numerical machine (CNM) was employed to perform the set of runs concerned with the central factorial design featured by high heat generation (hot runs); a vertical milling machine was used to carry out the set of runs concerned with the steepest algorithm featured by low heat generation (cold runs).
Both the top and bottom sheets, 152.40 mm long and 2.54 mm thick, were positioned as shown in Figure
Schematic of friction stir welding.
Minitensile testing was carried out by following design of experiments. Figure
Minitensile specimen drawing.
The mechanical characterization of the lap joints obtained by FSW technology also included shear testing and microhardness measurements. The strength of the lap joints loaded nominally in overlap shear was examined, even though in this case, 150 h elapsed before shear testing was carried out. All the specimens tested were 25.4 mm wide, 127 mm long, and 2.54 mm thick (Figure
Shear specimens drawing.
As for the experiments design, the central composite design (CCD), able to fit the response surface through a quadratic regression model, was used in this study. CCD contains an embedded factorial or fractional factorial design with centre points that are augmented with a group of “star points.” The importance of the centre points is that they allow for a curvature estimation [
Table data for two factorial designs with five centre points.
Runs order  rpm  s/mm 

1  1377.5  0.267 
7  2222.5  0.267 
6  1377.5  0.533 
5  2222.5  0.533 
2  1800.0  0.400 
3  1800.0  0.400 
4  1800.0  0.400 
9  1800.0  0.400 
8  1800.0  0.400 
To avoid systematic errors, the whole set of experiments has been randomized. To perform an ANOVA in every possible case, even in the case of heteroskedasticity of data (i.e., not constant variance), a weighted ANOVA was carried out [
Experimental data of yield strength are shown in Table
Yield strength experimental responses.
rpm  s/mm  Ys1  Ys2  Ys3  Ys4  Std. Ys  Dim  Avg. Ys  WGTS_ADJ 

1377.5  0.267  372  365  353  —  9.609  3  363.333  0.0390 
2222.5  0.267  361  323  356  —  20.648  3  346.667  0.0084 
1377.5  0.533  349  319  368  —  24.705  3  345.333  0.0059 
2222.5  0.533  402  345  249  343  63.373  4  334.750  0.0011 
1800.0  0.400  353  356  326  —  16.523  3  345.000  0.0063 
1800.0  0.400  356  374  320  —  27.495  3  350.000  0.0063 
1800.0  0.400  360  366  348  —  9.165  3  358.000  0.0063 
1800.0  0.400  342  357  397  338  26.938  4  358.500  0.0084 
1800.0  0.400  355  343  392  —  25.541  3  363.333  0.0063 
Results of yield strength analysis of variability.
Regression estimated effects and coefficients for natural log of std. Ys ratio (coded units)  
Term  Effect  Effect  Coef.  SE coef. 


Constant  —  —  3.0796  0.1407  21.89  0.0 
rpm  0.8733  2.395  0.4367  0.2118  2.06  0.094 
s/mm  1.0527  2.865  0.5264  0.2118  2.49  0.055 
rpm ∗ s/mm  0.1084  1.115  0.0542  0.2118  0.26  0.808 





Analysis of variance for natural log of std. Ys  
Source  DF  Seq. SS  Adj. SS  Adj. MS 


Main effects  2  6.319  5.900  2.950  5.981  0.047 
2Way interactions  1  0.032  0.032  0.032  0.070  0.808 
Residual error  5  2.465  2.465  0.493  —  — 
Curvature  1  0.130  0.130  0.130  0.222  0.661 
Pure error  4  2.335  2.335  0.583  —  — 
Total  8  8.816  —  —  —  — 
This analysis shows that only two effects could be considered significant: rpm with a
Results of yield strength weighted analysis of variance.
Estimated effects and coefficients for avg. Ys (coded units)  
Term  Effect  Coef.  SE coef. 



Constant  —  346.718  3.953  87.71  0.0  
rpm  −15.948  −7.974  3.004  −2.65  0.0045  
s/mm  −17.026  −8.513  3.413  −2.49  0.0055  
Ct Pt  —  8.469  4.903  1.73  0.45  






Analysis of variance for avg. Ys (coded units)  
Source  DF  Seq. SS  Adj. SS  Adj. MS 


Main effects  2  3.051  3.709  1.855  6.52  0.040 
Curvature  1  0.849  0.850  0.850  2.98  0.145 
Residual error  5  1.423  1.422  0.285  —  — 
Lack of fit  1  0.031  0.030  0.030  0.09  0.782 
Pure error  4  1.393  1.392  0.348  —  — 
Total  8  5.327  —  —  —  — 


Estimated coefficients for avg. Ys using data in uncoded units  
Term  Coef.  
Constant  406.30  
rpm  −0.019  
s/mm  −64.01  
Ct Pt  8.47 
The analysis shows a curvature
Ultimate strength experimental responses.
rpm  s/mm  Us1  Us2  Us3  Us4  Std. US  Dim  Avg. US  WGTS_ADJ 

1377.5  0.267  502.0  480.0  484.0  —  11.719  3  488.667  0.0324 
2222.5  0.267  431.0  432.5  460.2  —  16.443  3  441.233  0.0081 
1377.5  0.533  444.6  419.5  478.0  —  29.348  3  447.367  0.0026 
2222.5  0.533  435.6  452.0  285.0  392  75.160  4  391.150  0.0008 
1800.0  0.400  491.0  501.4  449.0  —  27.743  3  480.467  0.0046 
1800.0  0.400  496.6  492.5  428.6  —  38.131  3  472.567  0.0046 
1800.0  0.400  456.0  485.7  483.3  —  16.498  3  475.000  0.0046 
1800.0  0.400  475.7  451.8  494.0  —  21.162  3  473.833  0.0046 
1800.0  0.400  472.0  466.8  514.0  —  25.881  3  484.267  0.0046 
Results of ultimate strength analysis of variability.
Regression estimated effects and coefficients for natural log of std. US ratio (coded units)  
Term  Effect  Effect  Coef.  SE coef. 


Constant  —  —  3.2266  0.0909  35.48  0.0 
rpm  0.6428  1.902  0.3214  0.1317  2.44  0.059 
s/mm  1.2221  3.394  0.6111  0.1317  6.64  0.006 
rpm ∗ s/mm  0.3041  1.355  0.1520  0.1317  1.15  0.301 





Analysis of variance for natural log of std. US  
Source  DF  Seq. SS  Adj. SS  Adj. MS 


Main effects  2  6.6109  5.8970  2.9485  15.46  0.007 
2Way interactions  1  0.2540  0.2540  0.2540  1.33  0.301 
Residual error  5  0.9537  0.9537  0.1907  —  — 
Curvature  1  0.0037  0.0037  0.0037  0.02  0.907 
Pure error  4  0.9500  0.9500  0.2375  —  — 
Total  8  7.8187  —  —  —  — 
It can be seen that only two effects could be considered significant: rpm with a
Results of ultimate strength weighted analysis of variance.
Estimated effects and coefficients for avg. US (coded units)  
Term  Effect  Coef.  SE coef. 



Constant  —  442.97  2.973  148.99  0.0  
rpm  −48.23  −24.12  1.860  −12.96  0.0  
s/mm  −43.49  −21.75  2.798  −7.77  0.001  
Ct Pt  —  34.26  3.629  9.44  0.0  






Analysis of variance for avg. US (coded units)  
Source  DF  Seq. SS  Adj. SS  Adj. MS 


Main effects  2  14.7680  23.677  11.838  117.76  0.0 
Curvature  1  8.9605  8.9605  8.9605  89.13  0.0 
Residual error  5  0.5027  0.5027  0.1005  —  — 
Lack of fit  1  0.0464  0.0464  0.0464  0.41  0.558 
Pure error  4  0.4563  0.4563  0.1141  —  — 
Total  8  24.2317  —  —  —  — 


Estimated coefficients for avg. US using data in uncoded units  
Term  Coef.  
Constant  611.11  
rpm  −0.057  
s/mm  −163.52  
Ct Pt  34.26 
The analysis shows a significant curvature
As for the nugget zone, a 2^{2} factorial design with two centre points and three repeated measurements was carried out for the elongation. Experimental data of yield strength are shown in Table
Elongation experimental responses.
rpm  s/mm  El1  El2  El3  Std. El  Dim  Avg. El 

1377.5  0.267  31.5  30.5  32.0  0.764  3  31.333 
2222.5  0.267  9.0  9.0  15.0  3.464  3  11.000 
1377.5  0.533  23.0  30.5  27.5  3.775  3  27.000 
2222.5  0.533  11.5  4.5  9.0  3.547  3  8.333 
1800.0  0.400  33.6  25.0  32.0  4.574  3  30.200 
1800.0  0.400  26.0  28.0  31.0  2.517  3  28.333 
In this case, a simple ANOVA was carried out since the analysis of variability did not show any significant effect. Reliance on this consideration would deem the weights negligible. The ANOVA related to the experimental data of elongation is shown in Table
Results of elongation analysis of variance (nugget zone).
Estimated effects and coefficients for avg. El (coded units)  
Term  Effect  Coef.  SE coef. 



Constant  —  19.417  0.5612  34.60  0.018  
rpm  −19.500  −9.750  0.5612  −17.37  0.037  
s/mm  −3.500  −1.750  0.5612  −3.12  0.198  
rpm ∗ s/mm  0.833  0.417  0.5612  0.74  0.593  
Ct Pt  —  9.850  1.089  9.04  0.070  






Analysis of variance for avg. El (coded units)  
Source  DF  Seq. SS  Adj. SS  Adj. MS 


Main effects  2  179.25  149.80  74.90  195.26  0.051 
2Way interactions  1  0.256  0.211  0.211  0.55  0.593 
Curvature  1  31.37  31.37  31.37  81.80  0.070 
Residual error  1  0.384  0.384  0.384  —  — 
Pure error  1  0.384  0.384  0.84  —  — 
Total  5  211.26  —  —  —  — 


Estimated coefficients for avg. El using data in uncoded units  
Term  Coef.  
Constant  71.56  
rpm  −0.026  
s/mm  −23.51  
rpm ∗ s/mm  0.0074  
Ct Pt  9.85 
The analysis shows a curvature
Regarding the optimization of the response surface related to the yield strength, which is the main mechanical property of interest, an algorithm of steepest ascent to the yield strength response of the nugget zone was proposed. Assuming that
This algorithm can be applied only when the regression model is of the first order and does not include interactions. Runs obtained by implementing the aforementioned algorithm are shown in Table
Yield strength, ultimate strength, and elongation experimental responses performed along the steepest ascent direction (summarized data for nugget and HAZ).
rpm  s/mm  Avg. YS  Avg. US  Avg. El 



1250  0.241  399.25  511.8  28.75 
1150  0.213  395.8  507.9  26.36 
1050  0.184  339.33  453  25.25 
950  0.155  368.67  475.6  25.23 




1250  0.241  370  482.3  19.8 
1150  0.213  368  474.5  20.17 
1050  0.184  386  491  21.4 
950  0.155  405.7  506.25  21.45 
The results are similar to those expected, and this ascertainment guarantees the reliability of the previous analysis. The average of the yield strength has increased from a value of 363.33 MPa (point: 1377.5 rpm; 0.267 s/mm) to values of 399.25 MPa (point: 1250 rpm; 0.241 s/mm) and 395.8 MPa (point: 1150 rpm; 0.213 s/mm). The region where the two last points are set is the optimum region; a new investigation using a central composite design would have been necessary to determine the exact position of the yield strength optimum point. Following the next steps of the steepest path, the yield strength decreases, which suggests that the steepest path is leaving from the optimum region. A similar behaviour is acted also by the ultimate strength, but steepest yield strength of the nugget zone path is even one of the improvement directions of yield and ultimate strength of the heataffected zone. Seemingly, the mechanical properties of the HAZ improve markedly when the process gets colder and colder.
As for the shear testing, the results showed averaged failure loads, since three specimens were tested for each run. In Table
Shear testing results of averaged failure loads.
rpm  s/mm  Shear testing results (N) 

950  0.155  7433.596 
1050  0.184  7531.358 
1150  0.213  10125.16 
1250  0.241  8394.355 
1377.5  0.533  5708.624 
1377.5  0.267  7768.978 
1800  0.25  7001.34 
2222.5  0.533  6682.956 
2222.5  0.267  4074.074 
According to the tensile testing results, the runs corresponding to the first two steepest ascent algorithms show the best performances for yield strength, especially the run (1150 rpm; 0.213 s/mm) which had an averaged failure load of 10125.16 N. Those failures occur always in the nugget zone explaining the correlation between tensile and shear testing.
Vickers microhardness measurements, which were carried out from the centre of the welding along the cross section passing through HAZ, TMAZ, and nugget zone, are shown in Figure
Vickers microhardness measurement results.
The results reveal a switch of the best mechanical behaviour zones, from welds showing better hardness performances in the nugget zone to welds showing better hardness performances in the HAZ. Looking at the welds carried out by setting rpm equal to 1050 and TS^{−1} equal to 0.184 s/mm and the ones obtained with rpm equal to 1150 and TS^{−1} equal to 0.213 s/mm (Figure
Optical investigations included the study of the oxide film; this kind of defect, which is a feature for friction stir welding technology, is commonly called hook defect because of its shape. Hook defects must be taken seriously since they represent crosssection thinning, and for this reason, they may explain shear testing results [
Minimum hook distances measured on advancing (AS) and retreating (RS).
rpm  s/mm  Loaded AS thickness (mm)  Loaded RS thickness (mm) 

950  0.155  0.12  0.12 
1050  0.184  0.11  0.12 
1150  0.213  0.114  0.116 
1250  0.241  0.09  0.12 
1377.5  0.533  0.074  0.12 
1377.5  0.267  0.032  0.12 
2222.5  0.533  0.044  0.12 
2222.5  0.267  0.08  0.12 
This study does not contain statistical evidence for hook’s distance and shear tests correlation; in fact, a linear regression analysis showed a very low coefficient of determination (
As for the grain size number of the nugget zone, the results are shown in Table
ASTM grains size number versus heat index regression.
rpm  s/mm 

HI 

950  0.155  8.54  5.710 
1050  0.184  8.60  8.350 
1150  0.213  8.66  11.664 
1250  0.241  8.72  15.749 
1377.5  0.267  8.78  42.841 
1377.5  0.533  8.84  21.421 
1800  0.25  8.90  54.864 
2222.5  0.267  8.96  55.762 
It can be seen a decrease in grain size for runs featured by high heat generation. A regression analysis between grain size estimates and heat index was carried out as proof. Heat index is considered as a measurement of heat generated during welding, as the higher the index, the higher is the heat generated. It was defined by using the following equation:
The coefficient of determination presented a high value (
In this study, a procedure to optimize the mechanical behaviour of friction stir welded joints was developed. The yield strength was chosen as a factor of interest, and its response was optimized by using a response surface method. This method, which consisted of a central composite design and a subsequent steepest ascent algorithm, provided for optimal yield strength surface. Tensile tests on base metal specimens were conducted with benchmarking measures obtained from processed samples proving the high performance of FSW technology. The best performances, which were evaluated choosing the minimum value between HAZ and nugget zone ratio for both yield and ultimate strength, were found under these welding conditions: rpm = 1250 and TS^{−1} = 0.241 s/mm. Shear testing confirmed the results provided by tensile tests. Hook’s defect was studied, and the grain size of the nugget zone was estimated.
The data used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest.