Figure 2 shows the 9 welds corresponding to each of the experiments carried out according to what is indicated in Table 4. These welds have been polished with different grain sizes as indicated in the reference [17].
3.1 Macrographs of the nine experiments performed
To measure the grain size, the Grani software is used. It allows the "G" index to be calculated with precision according to the standards ASTM E112 [3] and NF ISO 643 [4]. A complete set of measurements is performed for the 9 experiments using the Grani software.
On the macrograph, the grain size is measured in the thermally affected area, that is, in the HAZ. For each experiment, the G-index of the grain and the number of grains is measured. The Grani software uses the Hilliard method [23, 24] to determine these values. Figure 3 shows the measurements made in each experiment. A red circle marks the area where the grain's G-index and the number of grains have been measured.
Table 6
Grain size values obtained in the HAZ
Experiment Nº
|
Grain G index
|
Number of grains
|
1
|
4
|
16
|
2
|
4
|
16
|
3
|
3.2
|
12
|
4
|
5.1
|
23
|
5
|
5.2
|
24
|
6
|
4
|
16
|
7
|
2
|
8
|
8
|
3.6
|
14
|
9
|
4.4
|
18
|
Figure 4 represents the relationship between the G index of the ASTM standard and the number of grains identified by the Grani programme. Therefore, the grain size is evaluated and not the letter number since the relationship is the same.
To evaluate the effect of each of the variables on the number of grains, the following multivariate linear regression equation is obtained:
\(Number of grain=20.3 -0.0011\bullet P,W -0.22\bullet Vs,mm/s +0.81\bullet Sp,mm\) (eq. 2)
Table 7
Analysis of Variance. ANOVA
Source
|
DF
|
Adj SS
|
Adj MS
|
F-Value
|
P-Value
|
Regression
|
3
|
1.845
|
0.6149
|
0.02
|
0.997
|
P, W
|
1
|
0.065
|
0.0651
|
0.00
|
0.969
|
Vs, mm/s
|
1
|
0.167
|
0.1667
|
0.00
|
0.951
|
Sp, mm
|
1
|
1.613
|
1.6129
|
0.04
|
0.848
|
Error
|
5
|
198.155
|
39.6311
|
|
|
Total
|
8
|
200.000
|
|
|
|
In the analysis of variance in Table 7 the influence of each of the variables on grain size is determined. The three P-values shown are large, that is, they have no significant influence on the number of grains of the aluminium weld. Therefore, these three variables do not affect the number of grains in the weld.
In accordance with the above, the effect of the three main variables on the number of grains is not further analysed because they have not influenced the number of grains.
3.2 Size of the HAZ in each experiment performed
The size of the HAZ of each weld is measured using a profile meter. Figure 5 shows the test tubes carried out in each experiment on which the size of the HAZ is measured using the profile meter.
Figure 6 shows the micrograph of the HAZ made at each of the joints.
In each of the experiments carried out, the size of the HAZ is measured, being reflected in red on each of the experiments. The HAZ values obtained are as follows:
Table 8
HAZ size for each experiment
Experiment Nº
|
Size of HAZ (mm)
|
1
|
0.64
|
2
|
0.65
|
3
|
0.76
|
4
|
0.89
|
5
|
1.17
|
6
|
0.84
|
7
|
1.27
|
8
|
0.92
|
9
|
0.85
|
To evaluate the effect of each of the variables on the size of the HAZ, the multivariate linear regression equation is obtained:
\(Size of HAZ=-1.30+0.001831\bullet P,W -0.0778\bullet Vs,mm/s +0.1495\bullet Sp,mm\) (eq. 3)
The adjustment of equation 3 has an R2 (adjusted) = 51.87%, which is a long way from 95%.
Figure 7. Representation of each of the variables with respect to the size of the HAZ
Table 9
Analysis of Variance. ANOVA
Source
|
DF
|
Adj SS
|
Adj MS
|
F-Value
|
P-Value
|
Regression
|
3
|
0.25504
|
0.08501
|
3.87
|
0.089
|
P, W
|
1
|
0.17923
|
0.17923
|
8.17
|
0.035
|
Vs, mm/s
|
1
|
0.02042
|
0.02042
|
0.93
|
0.379
|
Sp, mm
|
1
|
0.05540
|
0.05540
|
2.52
|
0.173
|
Error
|
5
|
0.10971
|
0.02194
|
|
|
Total
|
8
|
0.36476
|
|
|
|
In the analysis of variance Table 9 the influence of each of the variables on grain size is determined. The three P-values shown are small, that is, they have a significant influence on the size of the HAZ of the aluminium weld. Therefore, these three variables significantly affect the HAZ size of the weld.
The variable that has the most influence is power, P; it is followed by the edge separation, Sp, and finally the welding speed, Vs. The following graph shows the effect of each of the variables on the size of the HAZ.
From Figure 8 the specific weight of each of the variables is obtained: P (53%); Sp (29%); Vs (18%) on the size of the HAZ.
3.3 Dilution obtained in each of the experiments performed
Figure 9 shows area of dilution in the weld bead (area marked in red). From equation 1 the dilution ratio is determined by dividing the total molten base by the total base metal.
Figure 9 shows the dilution values (%), weld bead area, and molten base metal area. The area of the weld bead was determined in reference [17] by measuring it with a profile meter.
Table 10
For each experiment, dilution values, total molten metal sizes, and molten base metal sizes
Experiment Nº
|
Weld bead area
|
Molten base metal area
|
Dilution (%)
|
1
|
1.86E-05
|
9.72E-06
|
52%
|
2
|
1.25E-05
|
4.65E-06
|
21%
|
3
|
1.16E-05
|
3.82E-06
|
12%
|
4
|
1.91E-05
|
9.16E-06
|
37%
|
5
|
1.92E-05
|
1.00E-05
|
46%
|
6
|
1.57E-05
|
7.31E-06
|
47%
|
7
|
2.29E-05
|
1.22E-05
|
43%
|
8
|
1.99E-05
|
1.06E-05
|
53%
|
9
|
1.24E-05
|
6.11E-06
|
33%
|
3.3.1 Determination of the molten base metal area. Degree of dilution
The area of the molten base metal is determined from the CAD representation of the weld joint using the profile gauge and the initial geometry of the tubular profile before it is welded. The bead is superimposed on the tube geometry and the molten base metal found in the weld metal is obtained. Figure 10 represents the weld bead and base metal. Edge separation, Sp, is considered in determining the degree of dilution.
To evaluate the effect of each of the variables on the dilution of the base metal with the weld metal, the multivariate linear regression equation is obtained:
\(Dilution=0.207+0.000834\bullet P,W -0.0889\bullet Vs,\frac{mm}{s}-0.1616\bullet Sp,mm\) (eq. 4)
The fit of equation 4 has an R2 (adjusted) = 70.09%, which is acceptable.
Figure 11 represents the trend of each of the welding variables against dilution in the weld bead. As the power increases, the dilution in the weld bead increases, and as both Vs and Sp decrease, the dilution in the weld bead decreases.
In the analysis of variance in Table 11 the influence of each of the variables on the degree of dilution is determined. The three P-values shown are small, that is, they have a significant influence on the degree of dilution in the weld bead. Therefore, these three variables significantly affect the degree of dilution in the weld bead.
Table 11
Analysis of Variance. ANOVA
Source
|
DF
|
Seq SS
|
Seq MS
|
F-Value
|
P-Value
|
Regression
|
3
|
0.12859
|
0.042862
|
7.25
|
0.029
|
P, W
|
1
|
0.03719
|
0.037188
|
6.29
|
0.054
|
Vs, mm/s
|
1
|
0.02667
|
0.026667
|
4.51
|
0.087
|
Sp, mm
|
1
|
0.06473
|
0.064731
|
10.95
|
0.021
|
Error
|
5
|
0.02957
|
0.005914
|
|
|
Total
|
8
|
0.15816
|
|
|
|
In Figure 12, the influence of each of the variables on the degree of dilution is presented. The variable that has the most influence is the edge separation, Sp, followed by the power, P; and finally, the welding speed, Vs.
From Figure 12, the specific weight of each of the variables (P (32%); Sp (42%); Vs (27%)) on the dilution of the base metal in the weld bead is obtained.