Modeling and optimization of tool parameters in friction stir lap joining of aluminum using RSM and NSGA II

Figures & data

Table 1. Chemical composition of the 5083 aluminum plates (wt%).

Si	Fe	Cu	Mn	Mg	Zn	Ti
0.1	0.31	0.04	0.61	4.27	0.02	0.026

Figure 1. (a) The experimental setup, (b) a specially designed fixture, (c) a representation of different components of the force measurement fixture.

Figure 2. Schematic presentation of welding setup.

Table 2. Input parameters and their changes range in the FSW.

Variable	Symbol	Unit	−1	0	1
Shoulder diameter (mm)	SD	mm	16	18	20
Pin diameter (mm)	PD	mm	4.5	6	7.5
Pin Height (mm)	PH	mm	2.5	3.5	4.5

Figure 3. Dimensions of the prepared specimens for the tensile shear test.

Table 3. The layout of the FSW trials.

	Shoulder diameter (mm)	Pin diameter (mm)	Pin height (mm)	Temperature (C)	Force (N)	Failure load (kN)
1	20	7.5	2.5	396	7505	1.51
2	16	6	3.5	325	4720	3.3
3	16	7.5	4.5	359	6920	2.3
4	20	7.5	4.5	431	11240	2.8
5	20	4.5	4.5	387	6120	3.3
6	18	7.5	3.5	372	7120	2.9
7	18	6	3.5	346	5510	4.7
8	18	4.5	3.5	333	3840	3.5
9	18	6	3.5	353	5430	4.6
10	18	6	2.5	338	4050	2.7
11	20	6	3.5	392	7670	4
12	16	4.5	2.5	323	4380	1.7
13	18	6	3.5	357	5480	4.4
14	20	4.5	2.5	390	7112	1.9
15	16	4.5	4.5	319	3731	2.7
16	18	6	4.5	368	6070	5.1
17	16	7.5	2.5	327	4617	1.2

Table 4. ANOVA of the regression model for the temperature.

Source	Sum of	df	Mean	F-value	p-Value
Model	17931.33	9	1992.37	209.9277	1.13E-07
A–A	11356.9	1	11356.9	1196.629	4.38E-09
B–B	3960.1	1	3960.1	417.2592	1.69E-07
C–C	2433.6	1	2433.6	256.4182	9E-07
AB	18	1	18	1.896585	0.210885
AC	12.5	1	12.5	1.317073	0.288823
BC	8	1	8	0.842926	0.3891
A²	90.43649	1	90.43649	9.528914	0.017644
B²	0.096864	1	0.096864	0.010206	0.922363
C²	0.257242	1	0.257242	0.027104	0.873885
Residual	66.43521	7	9.490744
Lack of fit	4.435211	5	0.887042	0.028614	0.998848
Pure error	62	2	31
Cor total	17997.76	16

Table 5. ANOVA of the regression model for the force.

Source	Sum of	df	Mean	F-value	p-Value
Model	66715372	9	7412819	443.2051	8.34E-09
A–A	20073222	1	20073222	1200.158	4.33E-09
B–B	29282054	1	29282054	1750.745	1.16E-09
C–C	12791610	1	12791610	764.7977	2.08E-08
AB	1278401	1	1278401	76.4343	5.15E-05
AC	605000	1	605000	36.17235	0.000535
BC	970224.5	1	970224.5	58.00876	0.000125
A²	1477617	1	1477617	88.34526	3.21E-05
B²	2045.944	1	2045.944	0.122325	0.736813
C²	412473.1	1	412473.1	24.66136	0.001626
Residual	117078.4	7	16725.48
Lack of fit	113811.7	5	22762.34	13.93613	0.068301
Pure error	3266.667	2	1633.333
Cor total	66832450	16

Table 6. ANOVA of the regression model for the failure load.

Source	Sum of	df	Mean	F-value	p-Value
Model	21.81012	9	2.423346	23.05256	0.000214
A–A	0.68121	1	0.68121	6.480145	0.038348
B–B	0.52441	1	0.52441	4.988554	0.060656
C–C	5.31441	1	5.31441	50.55438	0.000192
AB	0.010512	1	0.010512	0.100002	0.761048
AC	0.010512	1	0.010512	0.100002	0.761048
BC	0.001512	1	0.001512	0.014388	0.907893
A²	1.316266	1	1.316266	12.52124	0.009488
B²	3.548946	1	3.548946	33.76005	0.000657
C²	0.544757	1	0.544757	5.182108	0.056936
Residual	0.735859	7	0.105123
Lack of fit	0.689192	5	0.137838	5.907359	0.151084
Pure error	0.046667	2	0.023333
Cor total	22.54598	16

Figure 4. Normal probability diagram.

Figure 5. Response surface and contour plots of temperature against pin diameter, pin height, and shoulder diameter.

Figure 6. The perturbation plot for the response temperature.

Figure 7. The axial force history.

Figure 8. Response surface and contour plots of force against pin diameter, pin height, and shoulder diameter.

Figure 9. Response surface and contour plots of temperature against pin diameter, pin height, and shoulder diameter.

Figure 10. Macrostructure and defects of joints with different tool parameters.

Figure 11. Optimization result (Pareto front).