Laser Weld Aspect Optimization of Thin AISI 316 SS Using RSM in Relation with Welding Parameters and Sulfur Content
Abstract
:1. Introduction
2. Materials and Methods
2.1. Material
2.2. Welding Procedure
2.3. Mathematical Modeling for 316 HS Cast
2.4. Mathematical Modeling for 316 LS Cast
3. Results and Discussions
3.1. Analysis and Discussions of 316 HS Cast
3.1.1. Modeling of Weld Depth of Penetration (Yd)
3.1.2. Modeling of Weld Aspect Ratio (Yr)
3.1.3. Modeling of Weld Bead Area (Ya)
3.2. Analysis and Discussions of 316 LS Cast
3.2.1. Modeling of Weld Depth of Penetration (Yd)
3.2.2. Modeling of Weld Aspect Ratio (Yr)
3.2.3. Modeling of Weld Bead Area (Ya)
3.3. Surface Surfactant Element and the Laser Weld Morphology
4. Conclusions
- -
- The developed regression equations from the response surface methodology has been used successfully to model geometries of the laser welds of thin plates of 316 stainless steel. The predicted values of geometric weld morphology were close to the actual experimental results.
- -
- For cast 316 HS, the main input factors influencing the depth weld (Yd) is the focal point with contribution up to 19.32%. The aspect ratio (Yr) is influenced by the focal point with a proportion of 70.6% of the data variance. For the weld bead area (Ya), the major contributor is the interaction of the two factors Xf and Xp. This interaction effect contributes to about 24.25% of the data variance.
- -
- Regarding cast 316 LS, the main input factors affecting the depth weld (Yd) is the combination effect of focus point and power input energy with contribution up to 10.65%. The shield gas Xg has a highest contribution up to 25.75% influencing the aspect ratio (Yr). The combination effect of shield gas Xg and power Xp affect the size area of weld bead (Ya) up to 13.91%.
- -
- The role of the shield gas in protecting the weld pool is related to the level of energy supplied. Thus, at high energy level, either helium or mixture gas (70% He + 30% Ar) produces weld beads larger than those produced under the shield gas mixture (40% He + 60% Ar). This is ascribed to the fact that helium is characterized by a high ionization potential, which performs a better protection of the weld pool by expelling the plasma ensuring less loss heat transfer.
- -
- The surface-active elements fully play their role only in the case where the chosen welding parameters would result in partially penetrated weld. To quantify these results, the statistical study shows that 71% of the partially penetrated weld confirms the role of the surface-active elements of sulfur for the 316 HS cast. However, in the case of fully penetrated welds, the contribution of surfactant elements in determining the shape of the weld bead for the 316 HS cast is diminished or completely hidden. The aerodynamic currents of the shield gas is the more important factor when the level of energy is high, resulting in fully penetrated welds, such that only 50% welds where sulfur as surfactant contributes significantly in imposing the inverse Marangoni convection.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Elements | C | Mn | Si | P | S | Cr | Ni | Fe | γ (N/m) at Melting Temperature (1400 °C) [26] | d γ/dT (N/m K) [26] |
---|---|---|---|---|---|---|---|---|---|---|
316 HS SS | 0.06 | 0.82 | 0.47 | 0.028 | 0.006 | 17.55 | 11.83 | Balance | 1.60 | +10−4 |
316 LS SS | 0.05 | 0.84 | 0.54 | 0.024 | 0.001 | 17.58 | 11.74 | Balance | 1.88 | −10−4 |
Exp. Number | Input Laser Welding Parameters | Linear Energy (J/cm) | |||
---|---|---|---|---|---|
Focal (mm) | Speed (mm/min) | Power (w) | Shield Gas Gaz Proportion | ||
Xf | Xs | Xp | Xg | ||
1 | 2 | 1500 | 3000 | 1:(70% He + 30% Ar) | 120 |
2 | 2 | 3000 | 3000 | 1:(70% He + 30% Ar) | 60 |
3 | 2 | 3000 | 5000 | 1:(70% He + 30% Ar) | 100 |
4 | 2 | 4500 | 5000 | 1:(70% He + 30% Ar) | 67 |
5 | 12 | 1500 | 3000 | 1:(70% He + 30% Ar) | 120 |
6 | 12 | 3000 | 3000 | 1:(70% He + 30% Ar) | 60 |
7 | 12 | 3000 | 5000 | 1:(70% He + 30% Ar) | 100 |
8 | 12 | 4500 | 5000 | 1:(70% He + 30% Ar) | 67 |
9 | 7 | 1500 | 3000 | 1:(70% He + 30% Ar) | 120 |
10 | 7 | 3000 | 3000 | 1:(70% He + 30% Ar) | 60 |
11 | 7 | 3000 | 5000 | 1:(70% He + 30% Ar) | 100 |
12 | 7 | 4500 | 5000 | 1:(70% He + 30% Ar) | 67 |
13 | 2 | 1500 | 3000 | 2:(100% He) | 120 |
14 | 2 | 3000 | 3000 | 2:(100% He) | 60 |
15 | 2 | 3000 | 5000 | 2:(100% He) | 100 |
16 | 2 | 4500 | 5000 | 2:(100% He) | 67 |
17 | 12 | 1500 | 3000 | 2:(100% He) | 120 |
18 | 12 | 3000 | 3000 | 2:(100% He) | 60 |
19 | 12 | 3000 | 5000 | 2:(100% He) | 100 |
20 | 12 | 4500 | 5000 | 2:(100% He) | 67 |
21 | 2 | 1500 | 300 | 3:(40% He + 60% Ar) | 120 |
22 | 2 | 3000 | 3000 | 3:(40% He + 60% Ar) | 60 |
23 | 2 | 3000 | 5000 | 3:(40% He + 60% Ar) | 100 |
24 | 2 | 4500 | 5000 | 3:(40% He + 60% Ar) | 67 |
25 | 12 | 1500 | 3000 | 3:(40% He + 60% Ar) | 120 |
26 | 12 | 3000 | 3000 | 3:(40% He + 60% Ar) | 60 |
27 | 12 | 4500 | 5000 | 3:(40% He + 60% Ar) | 100 |
Laser Welding Gas | Molecular Weight (g/mol) | Thermal Conductivity at 1 Bar, 15 °C (W/m K) | Ionization Energy (ev) | Dissociation Energy (ev) | Density Relative to Air |
---|---|---|---|---|---|
Helium | 4 | 0.15363 | 24.6 | 0 | 0.14 |
Argon | 40 | 0.01732 | 15.8 | 0 | 1.38 |
Exp. Number | Input Welding Parameters | Experimental Values | |||||
---|---|---|---|---|---|---|---|
Focal (mm) | Speed (mm/min) | Power (w) | Shield Gas | Weld Depth Penetration (mm) | Aspect Ratio | Area (mm2) | |
Xf | Xs | Xp | Xg | Yd | Yr | Ya | |
1 | 2 | 1500 | 3000 | 1 | 2 | 3.42 | 74 |
2 | 2 | 3000 | 3000 | 1 | 2 | 1.73 | 45 |
3 | 2 | 3000 | 5000 | 1 | 2 | 1.42 | 63 |
4 | 2 | 4500 | 5000 | 1 | 2 | 1.63 | 55 |
5 | 12 | 1500 | 3000 | 1 | 0.6 | 0.42 | 15.5 |
6 | 12 | 3000 | 3000 | 1 | 0.35 | 0.27 | 7 |
7 | 12 | 3000 | 5000 | 1 | 0.62 | 0.74 | 34 |
8 | 12 | 4500 | 5000 | 1 | 0.44 | 0.33 | 11 |
9 | 7 | 1500 | 3000 | 1 | 2 | 1.58 | 86 |
10 | 7 | 3000 | 3000 | 1 | 1.15 | 0.98 | 25 |
11 | 7 | 3000 | 5000 | 1 | 2 | 1.19 | 79 |
12 | 7 | 4500 | 5000 | 1 | 1.09 | 0.65 | 32 |
13 | 2 | 1500 | 3000 | 2 | 2 | 2.9 | 78.5 |
14 | 2 | 3000 | 3000 | 2 | 2 | 2.43 | 49 |
15 | 2 | 3000 | 5000 | 2 | 2 | 2.24 | 51 |
16 | 2 | 4500 | 5000 | 2 | 2 | 2.86 | 42 |
17 | 12 | 1500 | 3000 | 2 | 0.44 | 0.25 | 14 |
18 | 12 | 3000 | 3000 | 2 | 0.38 | 0.26 | 10 |
19 | 12 | 3000 | 5000 | 2 | 1.12 | 0.7 | 36 |
20 | 12 | 4500 | 5000 | 2 | 0.72 | 0.52 | 16 |
21 | 2 | 1500 | 3000 | 3 | 1.98 | 3.31 | 70 |
22 | 2 | 3000 | 3000 | 3 | 0.65 | 2 | 40 |
23 | 2 | 3000 | 5000 | 3 | 0.49 | 0.25 | 9 |
24 | 2 | 4500 | 5000 | 3 | 0.91 | 2.3 | 47 |
25 | 12 | 1500 | 3000 | 3 | 0.8 | 0.71 | 12 |
26 | 12 | 3000 | 3000 | 3 | 0.48 | 0.41 | 8 |
27 | 12 | 4500 | 5000 | 3 | 0.44 | 1 | 10 |
Exp. Number | Xf | Xs | Xp | Xg | Yd | Transformed Value of Actual Yd | Predicted Value | Residual |
---|---|---|---|---|---|---|---|---|
1 | 2 | 1500 | 3000 | 0.7 | 2 | 0.7071 | 0.8059 | −0.0988 |
2 | 2 | 3000 | 3000 | 0.7 | 2 | 0.7071 | 0.7224 | −0.0153 |
3 | 2 | 3000 | 5000 | 0.7 | 2 | 0.7071 | 0.7575 | −0.0503 |
4 | 2 | 4500 | 5000 | 0.7 | 2 | 0.7071 | 1.05 | −0.3425 |
5 | 12 | 1500 | 3000 | 0.7 | 0.6 | 1.29 | 1.21 | 0.0785 |
6 | 12 | 3000 | 3000 | 0.7 | 0.35 | 1.69 | 1.62 | 0.0727 |
7 | 12 | 3000 | 5000 | 0.7 | 0.62 | 1.27 | 1.199 | −0.0710 |
8 | 12 | 4500 | 5000 | 0.7 | 0.44 | 1.51 | 1.4 | 0.1109 |
9 | 7 | 1500 | 3000 | 0.7 | 2 | 0.7071 | 0.7192 | −0.0121 |
10 | 7 | 3000 | 3000 | 0.7 | 1.15 | 0.9325 | 0.9739 | −0.0414 |
11 | 7 | 3000 | 5000 | 0.7 | 2 | 0.7071 | 0.6784 | 0.0287 |
12 | 7 | 4500 | 5000 | 0.7 | 1.09 | 0.9578 | 0.9331 | 0.0247 |
13 | 2 | 1500 | 3000 | 1 | 2 | 0.7071 | 0.7463 | −0.0392 |
14 | 2 | 3000 | 3000 | 1 | 2 | 0.7071 | 0.6579 | 0.0492 |
15 | 2 | 3000 | 5000 | 1 | 2 | 0.7071 | 0.6929 | 0.0142 |
16 | 2 | 4500 | 5000 | 1 | 2 | 0.7071 | 0.6045 | 0.1026 |
17 | 12 | 1500 | 3000 | 1 | 0.44 | 1.51 | 1.43 | 0.0821 |
18 | 12 | 3000 | 3000 | 1 | 0.38 | 1.62 | 1.64 | −0.0156 |
19 | 12 | 3000 | 5000 | 1 | 1.12 | 0.9449 | 1.01 | −0.0668 |
20 | 12 | 4500 | 5000 | 1 | 0.72 | 1.18 | 1.22 | −0.0456 |
21 | 2 | 1500 | 3000 | 0.6 | 1.98 | 0.7107 | 0.8258 | −0.1151 |
22 | 2 | 3000 | 3000 | 0.6 | 0.65 | 1.24 | 0.9944 | 0.246 |
23 | 2 | 3000 | 5000 | 0.6 | 0.49 | 1.43 | 1.03 | 0.3992 |
24 | 2 | 4500 | 5000 | 0.6 | 0.91 | 1.05 | 1.2 | −0.1497 |
25 | 12 | 1500 | 3000 | 0.6 | 0.8 | 1.12 | 1.14 | −0.0235 |
26 | 12 | 3000 | 3000 | 0.6 | 0.48 | 1.44 | 1.61 | −0.1675 |
27 | 12 | 4500 | 5000 | 0.6 | 0.44 | 1.51 | 1.45 | 0.0534 |
Source | Sum of Squares | DF | Mean Square | F-Value | p-Value | Contribution (%) |
---|---|---|---|---|---|---|
Model | 2.64 | 9 | 0.2935 | 10.43 | <0.0001 | 11.80 |
Xf | 0.4807 | 1 | 0.4807 | 17.09 | 0.0007 | 19.32 |
Xs | 0.3025 | 1 | 0.3025 | 10.75 | 0.0044 | 12.16 |
Xp | 0.3153 | 1 | 0.3153 | 11.21 | 0.0038 | 12.67 |
Xg | 0.0086 | 1 | 0.0086 | 0.3046 | 0.5882 | 0.35 |
Xf Xs | 0.1862 | 1 | 0.1862 | 6.62 | 0.0198 | 7.48 |
Xf Xp | 0.3439 | 1 | 0.3439 | 12.23 | 0.0028 | 13.82 |
Xf Xg | 0.134 | 1 | 0.134 | 4.76 | 0.0434 | 5.39 |
Xs Xg | 0.1489 | 1 | 0.1489 | 5.29 | 0.0343 | 5.98 |
Xf ² | 0.2743 | 1 | 0.2743 | 9.75 | 0.0062 | 11.03 |
Residual | 0.4783 | 17 | 0.0281 | |||
Cor Total | 3.12 | 26 |
Exp. Number | Xf | Xs | Xp | Xg | Yr | Predicted Value | Residual | |
---|---|---|---|---|---|---|---|---|
1 | 2 | 1500 | 3000 | 0.7 | 3.42 | 1.85 | 1.59 | 0.2602 |
2 | 2 | 300 | 3000 | 0.7 | 1.73 | 1.32 | 1.59 | −0.2738 |
3 | 2 | 300 | 5000 | 0.7 | 1.42 | 1.19 | 1.19 | −0.0025 |
4 | 2 | 4500 | 5000 | 0.7 | 1.63 | 1.28 | 1.19 | 0.0826 |
5 | 12 | 1500 | 3000 | 0.7 | 0.42 | 0.6481 | 0.6605 | −0.0125 |
6 | 12 | 3000 | 3000 | 0.7 | 0.27 | 0.5196 | 0.6605 | −0.1409 |
7 | 12 | 3000 | 5000 | 0.7 | 0.74 | 0.8602 | 0.7804 | 0.0798 |
8 | 12 | 4500 | 5000 | 0.7 | 0.33 | 0.5745 | 0.7804 | −0.206 |
9 | 7 | 1500 | 3000 | 0.7 | 1.58 | 1.26 | 1.12 | 0.1322 |
10 | 7 | 3000 | 3000 | 0.7 | 0.98 | 0.9899 | 1.12 | −0.1349 |
11 | 7 | 3000 | 5000 | 0.7 | 1.19 | 1.09 | 0.9873 | 0.1036 |
12 | 7 | 4500 | 5000 | 0.7 | 0.65 | 0.8062 | 0.9873 | −0.1811 |
13 | 2 | 1500 | 3000 | 1 | 2.9 | 1.7 | 1.68 | 0.0208 |
14 | 2 | 3000 | 3000 | 1 | 2.43 | 1.56 | 1.68 | −0.1232 |
15 | 2 | 3000 | 5000 | 1 | 2.24 | 1.5 | 1.55 | −0.0493 |
16 | 2 | 4500 | 5000 | 1 | 2.86 | 1.69 | 1.55 | 0.1451 |
17 | 12 | 1500 | 3000 | 1 | 0.25 | 0.5 | 0.4325 | 0.0675 |
18 | 12 | 3000 | 3000 | 1 | 0.26 | 0.5099 | 0.4325 | 0.0774 |
19 | 12 | 3000 | 5000 | 1 | 0.7 | 0.8367 | 0.8113 | 0.0253 |
20 | 12 | 4500 | 5000 | 1 | 0.52 | 0.7211 | 0.8113 | −0.0902 |
21 | 2 | 1500 | 3000 | 0.6 | 3.31 | 1.82 | 1.56 | 0.2612 |
22 | 2 | 3000 | 3000 | 0.6 | 2 | 1.41 | 1.56 | −0.1439 |
23 | 2 | 3000 | 5000 | 0.6 | 0.25 | 0.5 | 1.08 | −0.5769 |
24 | 2 | 4500 | 5000 | 0.6 | 2.3 | 1.52 | 1.08 | 0.4397 |
25 | 12 | 1500 | 3000 | 0.6 | 0.71 | 0.8426 | 0.7365 | 0.1061 |
26 | 12 | 3000 | 3000 | 0.6 | 0.41 | 0.6403 | 0.7365 | −0.0962 |
27 | 12 | 4500 | 5000 | 0.6 | 1 | 1 | 0.7701 | 0.2299 |
Source | Sum of Squares | DF | Mean Square | F-Value | p-Value | Contribution (%) |
---|---|---|---|---|---|---|
Model | 4.03 | 6 | 0.6714 | 12.86 | <0.0001 | 14.02 |
Xf | 3.38 | 1 | 3.38 | 64.69 | <0.0001 | 70.60 |
Xp | 0.0167 | 1 | 0.0167 | 0.3202 | 0.5778 | 0.35 |
Xg | 0.0288 | 1 | 0.0288 | 0.5523 | 0.466 | 0.60 |
Xf Xp | 0.3763 | 1 | 0.3763 | 7.21 | 0.0142 | 7.86 |
Xf Xg | 0.1882 | 1 | 0.1882 | 3.6 | 0.0722 | 3.93 |
Xp Xg | 0.1259 | 1 | 0.1259 | 2.41 | 0.1361 | 2.63 |
Residual | 1.04 | 20 | 0.0522 | |||
Cor Total | 5.07 | 26 |
Exp. Number | Xf | Xs | Xp | Xg | Ya | Predicted Value | Residual | |
---|---|---|---|---|---|---|---|---|
1 | 2 | 1500 | 3000 | 0.7 | 74 | 0.0135 | 0.0236 | −0.0101 |
2 | 2 | 300 | 3000 | 0.7 | 45 | 0.0222 | 0.0052 | 0.017 |
3 | 2 | 300 | 5000 | 0.7 | 63 | 0.0159 | 0.0323 | −0.0164 |
4 | 2 | 4500 | 5000 | 0.7 | 55 | 0.0182 | 0.0323 | −0.0141 |
5 | 12 | 1500 | 3000 | 0.7 | 15.5 | 0.0645 | 0.0706 | −0.0061 |
6 | 12 | 3000 | 3000 | 0.7 | 7 | 0.1429 | 0.1316 | 0.0112 |
7 | 12 | 3000 | 5000 | 0.7 | 34 | 0.0294 | 0.0455 | −0.0161 |
8 | 12 | 4500 | 5000 | 0.7 | 11 | 0.0909 | 0.0835 | 0.0074 |
9 | 7 | 1500 | 3000 | 0.7 | 86 | 0.0116 | 0.0128 | −0.0011 |
10 | 7 | 3000 | 3000 | 0.7 | 25 | 0.04 | 0.0444 | −0.0044 |
11 | 7 | 3000 | 5000 | 0.7 | 79 | 0.0127 | 0.0149 | −0.0022 |
12 | 7 | 4500 | 5000 | 0.7 | 32 | 0.0313 | 0.0235 | 0.0077 |
13 | 2 | 1500 | 3000 | 1 | 78.5 | 0.0127 | 0.0068 | 0.0059 |
14 | 2 | 3000 | 3000 | 1 | 49 | 0.0204 | 0.0091 | 0.0113 |
15 | 2 | 3000 | 5000 | 1 | 51 | 0.0196 | 0.0362 | −0.0166 |
16 | 2 | 4500 | 5000 | 1 | 42 | 0.0238 | 0.0155 | 0.0083 |
17 | 12 | 1500 | 3000 | 1 | 14 | 0.0714 | 0.0538 | 0.0176 |
18 | 12 | 3000 | 3000 | 1 | 10 | 0.1 | 0.1148 | −0.0148 |
19 | 12 | 3000 | 5000 | 1 | 36 | 0.0278 | 0.0287 | −0.0009 |
20 | 12 | 4500 | 5000 | 1 | 16 | 0.0625 | 0.0667 | −0.0042 |
21 | 2 | 1500 | 3000 | 0.6 | 70 | 0.0143 | 0.0292 | −0.0149 |
22 | 2 | 3000 | 3000 | 0.6 | 40 | 0.025 | 0.0315 | −0.0065 |
23 | 2 | 3000 | 5000 | 0.6 | 9 | 0.1111 | 0.0586 | 0.0525 |
24 | 2 | 4500 | 5000 | 0.6 | 47 | 0.0213 | 0.0379 | −0.0166 |
25 | 12 | 1500 | 3000 | 0.6 | 12 | 0.0833 | 0.0762 | 0.0071 |
26 | 12 | 3000 | 3000 | 0.6 | 8 | 0.125 | 0.1372 | −0.0122 |
27 | 12 | 4500 | 5000 | 0.6 | 10 | 0.1 | 0.0891 | 0.0109 |
Source | Sum of Squares | DF | Mean Square | F-Value | p-Value | Contribution (%) |
---|---|---|---|---|---|---|
Model | 0.0356 | 8 | 0.0044 | 13.12 | <0.0001 | 11.00 |
Xf | 0.0024 | 1 | 0.0024 | 7 | 0.0165 | 6.00 |
Xs | 0.0072 | 1 | 0.0072 | 21.3 | 0.0002 | 18.00 |
Xp | 0.0029 | 1 | 0.0029 | 8.61 | 0.0089 | 7.25 |
Xg | 0.002 | 1 | 0.002 | 5.93 | 0.0255 | 5.00 |
Xf Xs | 0.0062 | 1 | 0.0062 | 18.39 | 0.0004 | 15.50 |
Xf Xp | 0.0097 | 1 | 0.0097 | 28.75 | <0.0001 | 24.25 |
Xf² | 0.0038 | 1 | 0.0038 | 11.24 | 0.0035 | 9.50 |
Xs² | 0.0014 | 1 | 0.0014 | 4.03 | 0.0601 | 3.50 |
Residual | 0.0061 | 18 | 0.0003 | |||
Cor Total | 0.0417 | 26 |
Exp. Number | Input Welding Parameters | Experimental Values | |||||
---|---|---|---|---|---|---|---|
Focal (mm) | Speed (mm/min) | Power (w) | Shield Gas | Weld Depth of Penetration (mm) | Aspect Ratio | Weld Area (mm2) | |
Xf | Xs | Xp | Xg | Yd | Yr | Ya | |
1 | 2 | 1500 | 3000 | 1 | 2 | 2.52 | 67 |
2 | 2 | 3000 | 3000 | 1 | 2 | 2 | 55.5 |
3 | 2 | 3000 | 5000 | 1 | 2 | 2 | 48 |
4 | 2 | 4500 | 5000 | 1 | 2 | 2.31 | 46.5 |
5 | 12 | 1500 | 3000 | 1 | 0.39 | 0.2 | 12.5 |
6 | 12 | 3000 | 3000 | 1 | 0.29 | 0.18 | 8 |
7 | 12 | 3000 | 5000 | 1 | 0.48 | 0.23 | 17 |
8 | 12 | 4500 | 5000 | 1 | 0.61 | 0.43 | 15 |
9 | 7 | 1500 | 3000 | 1 | 2 | 1.89 | 98.5 |
10 | 7 | 3000 | 3000 | 1 | 0.93 | 0.76 | 24 |
11 | 7 | 3000 | 5000 | 1 | 2 | 2.5 | 68.5 |
12 | 7 | 4500 | 5000 | 1 | 1.08 | 0.58 | 39 |
13 | 2 | 1500 | 3000 | 2 | 2 | 2.9 | 73 |
14 | 2 | 3000 | 3000 | 2 | 2 | 2 | 47 |
15 | 2 | 3000 | 5000 | 2 | 2 | 2.4 | 50 |
16 | 2 | 4500 | 5000 | 2 | 2 | 2.53 | 47 |
17 | 12 | 1500 | 3000 | 2 | 0.74 | 0.51 | 18.5 |
18 | 12 | 3000 | 3000 | 2 | 0.28 | 0.18 | 8 |
19 | 12 | 3000 | 5000 | 2 | 1.04 | 0.62 | 28 |
20 | 12 | 4500 | 5000 | 2 | 0.53 | 0.38 | 13 |
21 | 2 | 1500 | 3000 | 3 | 0.63 | 0.34 | 11 |
22 | 2 | 3000 | 3000 | 3 | 2 | 1.7 | 50 |
23 | 2 | 3000 | 5000 | 3 | 0.18 | 0.08 | 4 |
24 | 2 | 4500 | 5000 | 3 | 0.61 | 0.27 | 8.6 |
25 | 12 | 1500 | 3000 | 3 | 0.77 | 0.57 | 17.9 |
26 | 12 | 3000 | 3000 | 3 | 0.5 | 1.09 | 9 |
27 | 12 | 4500 | 5000 | 3 | 0.6 | 0.49 | 12 |
Exp. Number | Xf | Xs | Xp | Xg | Yd | Predicted Value | Residual | |
---|---|---|---|---|---|---|---|---|
1 | 2 | 1500 | 3000 | 1 | 2 | 0.6931 | 0.5773 | 0.1159 |
2 | 2 | 3000 | 3000 | 1 | 2 | 0.6931 | 0.7046 | −0.0114 |
3 | 2 | 3000 | 5000 | 1 | 2 | 0.6931 | 0.6899 | 0.0033 |
4 | 2 | 4500 | 5000 | 1 | 2 | 0.6931 | 0.8009 | −0.1077 |
5 | 12 | 1500 | 3000 | 1 | 0.39 | −0.9416 | −0.9215 | −0.0202 |
6 | 12 | 3000 | 3000 | 1 | 0.29 | −1.24 | −1.18 | −0.0596 |
7 | 12 | 3000 | 5000 | 1 | 0.48 | −0.734 | −0.625 | −0.109 |
8 | 12 | 4500 | 5000 | 1 | 0.61 | −0.4943 | −0.6831 | 0.1888 |
9 | 7 | 1500 | 3000 | 1 | 2 | 0.6931 | 0.7285 | −0.0354 |
10 | 7 | 3000 | 3000 | 1 | 0.93 | −0.0725 | −0.0371 | 0.0354 |
11 | 7 | 3000 | 5000 | 1 | 2 | 0.6931 | 0.6578 | 0.0354 |
12 | 7 | 4500 | 5000 | 1 | 1.08 | 0.077 | 0.1124 | −0.0354 |
13 | 2 | 1500 | 3000 | 2 | 2 | 0.6931 | 0.7689 | −0.0758 |
14 | 2 | 3000 | 3000 | 2 | 2 | 0.6931 | 0.6435 | 0.0497 |
15 | 2 | 3000 | 5000 | 2 | 2 | 0.6931 | 0.6435 | 0.0497 |
16 | 2 | 4500 | 5000 | 2 | 2 | 0.6931 | 0.7167 | −0.0236 |
17 | 12 | 1500 | 3000 | 2 | 0.74 | −0.3011 | −0.352 | 0.0509 |
18 | 12 | 3000 | 3000 | 2 | 0.28 | −1.27 | −1.24 | −0.0309 |
19 | 12 | 3000 | 5000 | 2 | 1.04 | 0.0392 | 0.0578 | −0.0186 |
20 | 12 | 4500 | 5000 | 2 | 0.53 | −0.6349 | −0.6335 | −0.0014 |
21 | 2 | 1500 | 3000 | 3 | 0.63 | −0.462 | −0.3503 | −0.1117 |
22 | 2 | 3000 | 3000 | 3 | 2 | 0.6931 | 0.6598 | 0.0334 |
23 | 2 | 3000 | 5000 | 3 | 0.18 | −1.71 | −1.75 | 0.0334 |
24 | 2 | 4500 | 5000 | 3 | 0.61 | −0.4943 | −0.5393 | 0.045 |
25 | 12 | 1500 | 3000 | 3 | 0.77 | −0.2614 | −0.3582 | 0.0968 |
26 | 12 | 3000 | 3000 | 3 | 0.5 | −0.6931 | −0.6561 | −0.037 |
27 | 12 | 4500 | 5000 | 3 | 0.6 | −0.5108 | −0.451 | −0.0598 |
Source | Sum of Squares | DF | Mean Square | F-Value | p-Value | Contribution (%) |
---|---|---|---|---|---|---|
Model | 14.54 | 19 | 0.7654 | 41.91 | <0.0001 | 3.81 |
Xf | 1.95 | 1 | 1.95 | 106.56 | <0.0001 | 9.70 |
Xs | 1.27 | 1 | 1.27 | 69.5 | <0.0001 | 6.32 |
Xp | 0.9667 | 1 | 0.9667 | 52.94 | 0.0002 | 4.81 |
Xg | 1.57 | 1 | 1.57 | 85.77 | <0.0001 | 7.81 |
XfXs | 1.36 | 1 | 1.36 | 74.29 | <0.0001 | 6.77 |
XfXp | 2.14 | 1 | 2.14 | 117.3 | <0.0001 | 10.65 |
XfXg | 1.11 | 1 | 1.11 | 60.73 | 0.0001 | 5.52 |
XsXp | 1.26 | 1 | 1.26 | 68.74 | <0.0001 | 6.27 |
XsXg | 0.6937 | 1 | 0.6937 | 37.98 | 0.0005 | 3.45 |
XpXg | 1.26 | 1 | 1.26 | 68.85 | <0.0001 | 6.27 |
Xf² | 1.24 | 1 | 1.24 | 68.16 | <0.0001 | 6.17 |
Xs² | 1.39 | 1 | 1.39 | 76.02 | <0.0001 | 6.91 |
Xg² | 0.0739 | 1 | 0.0739 | 4.04 | 0.0842 | 0.37 |
XfXsXg | 0.0719 | 1 | 0.0719 | 3.93 | 0.0877 | 0.36 |
XfXpXg | 0.2165 | 1 | 0.2165 | 11.86 | 0.0108 | 1.08 |
Xf²Xs | 0.8362 | 1 | 0.8362 | 45.79 | 0.0003 | 4.16 |
Xf²Xp | 0.6394 | 1 | 0.6394 | 35.02 | 0.0006 | 3.18 |
XfXg² | 1.19 | 1 | 1.19 | 65.29 | <0.0001 | 5.92 |
XsXg² | 0.0986 | 1 | 0.0986 | 5.4 | 0.0531 | 0.49 |
Residual | 0.1278 | 7 | 0.0183 | |||
Cor Total | 14.67 | 26 |
Exp. Number | Xf | Xs | Xp | Xg | Yr | Predicted Value | Residual | |
---|---|---|---|---|---|---|---|---|
1 | 2 | 1500 | 3000 | 1 | 2.52 | 1.59 | 1.56 | 0.0285 |
2 | 2 | 3000 | 3000 | 1 | 2 | 1.41 | 1.41 | 0.0047 |
3 | 2 | 3000 | 5000 | 1 | 2 | 1.41 | 1.4 | 0.0095 |
4 | 2 | 4500 | 5000 | 1 | 2.31 | 1.52 | 1.56 | −0.0427 |
5 | 12 | 1500 | 3000 | 1 | 0.2 | 0.4472 | 0.4132 | 0.034 |
6 | 12 | 3000 | 3000 | 1 | 0.18 | 0.4243 | 0.4915 | −0.0672 |
7 | 12 | 3000 | 5000 | 1 | 0.23 | 0.4796 | 0.5771 | −0.0976 |
8 | 12 | 4500 | 5000 | 1 | 0.43 | 0.6557 | 0.525 | 0.1307 |
9 | 7 | 1500 | 3000 | 1 | 1.89 | 1.37 | 1.42 | −0.0465 |
10 | 7 | 3000 | 3000 | 1 | 0.76 | 0.8718 | 0.8253 | 0.0465 |
7 | 3000 | 5000 | 1 | 2.5 | 1.58 | 1.53 | 0.0465 | |
12 | 7 | 4500 | 5000 | 1 | 0.58 | 0.7616 | 0.8081 | −0.0465 |
13 | 2 | 1500 | 3000 | 2 | 2.9 | 1.7 | 1.7 | −0.0001 |
14 | 2 | 3000 | 3000 | 2 | 2 | 1.41 | 1.46 | −0.0476 |
15 | 2 | 3000 | 5000 | 2 | 2.4 | 1.55 | 1.55 | 0.0009 |
16 | 2 | 4500 | 5000 | 2 | 2.53 | 1.59 | 1.54 | 0.0468 |
17 | 12 | 1500 | 3000 | 2 | 0.51 | 0.7141 | 0.7202 | −0.0061 |
18 | 12 | 3000 | 3000 | 2 | 0.18 | 0.4243 | 0.3705 | 0.0537 |
19 | 12 | 3000 | 5000 | 2 | 0.62 | 0.7874 | 0.7822 | 0.0052 |
20 | 12 | 4500 | 5000 | 2 | 0.38 | 0.6164 | 0.6693 | −0.0529 |
21 | 2 | 1500 | 3000 | 3 | 0.34 | 0.5831 | 0.6658 | −0.0827 |
22 | 2 | 3000 | 3000 | 3 | 1.7 | 1.3 | 1.21 | 0.0972 |
23 | 2 | 3000 | 5000 | 3 | 0.08 | 0.2828 | 0.2645 | 0.0183 |
24 | 2 | 4500 | 5000 | 3 | 0.27 | 0.5196 | 0.5525 | −0.0328 |
25 | 12 | 1500 | 3000 | 3 | 0.57 | 0.755 | 0.6906 | 0.0644 |
26 | 12 | 3000 | 3000 | 3 | 1.09 | 1.04 | 1.12 | −0.0789 |
27 | 12 | 4500 | 5000 | 3 | 0.49 | 0.7 | 0.6855 | 0.0145 |
Source | Sum of Squares | DF | Mean Square | F-Value | p-Value | Contribution (%) |
---|---|---|---|---|---|---|
Model | 5.53 | 18 | 0.3072 | 29.91 | <0.0001 | 4.59 |
Xf | 1.72 | 1 | 1.72 | 167.64 | <0.0001 | 25.73 |
Xs | 0.5878 | 1 | 0.5878 | 57.22 | <0.0001 | 8.79 |
Xp | 0.4856 | 1 | 0.4856 | 47.27 | 0.0001 | 7.26 |
Xg | 0.2437 | 1 | 0.2437 | 23.72 | 0.0012 | 3.64 |
Xf Xs | 0.0175 | 1 | 0.0175 | 1.71 | 0.2279 | 0.26 |
Xf Xp | 0.0565 | 1 | 0.0565 | 5.5 | 0.047 | 0.85 |
Xf Xg | 0.8492 | 1 | 0.8492 | 82.67 | <0.0001 | 12.70 |
Xs Xp | 0.0001 | 1 | 0.0001 | 0.0109 | 0.9193 | 0.00 |
Xs Xg | 0.2414 | 1 | 0.2414 | 23.5 | 0.0013 | 3.61 |
Xp Xg | 0.1785 | 1 | 0.1785 | 17.38 | 0.0031 | 2.67 |
Xf² | 0.2701 | 1 | 0.2701 | 26.29 | 0.0009 | 4.04 |
Xg² | 0.2763 | 1 | 0.2763 | 26.9 | 0.0008 | 4.13 |
Xs Xp Xg | 0.0604 | 1 | 0.0604 | 5.88 | 0.0415 | 0.90 |
Xf² Xs | 0.4127 | 1 | 0.4127 | 40.17 | 0.0002 | 6.17 |
Xf²Xp | 0.2018 | 1 | 0.2018 | 19.65 | 0.0022 | 3.02 |
Xf Xg² | 0.6501 | 1 | 0.6501 | 63.28 | <0.0001 | 9.72 |
XsXg² | 0.0343 | 1 | 0.0343 | 3.34 | 0.1049 | 0.51 |
XpXg² | 0.0826 | 1 | 0.0826 | 8.04 | 0.022 | 1.24 |
Residual | 0.0822 | 8 | 0.0103 | |||
Cor Total | 5.61 | 26 |
Run Order | Xf | Xs | Xp | Xg | Ya | Predicted Value | Residual | |
---|---|---|---|---|---|---|---|---|
1 | 2 | 1500 | 3000 | 1 | 67 | 0.1222 | 0.1416 | −0.0195 |
2 | 2 | 3000 | 3000 | 1 | 55.5 | 0.1342 | 0.122 | 0.0122 |
3 | 2 | 3000 | 5000 | 1 | 48 | 0.1443 | 0.1478 | −0.0035 |
4 | 2 | 4500 | 5000 | 1 | 46.5 | 0.1466 | 0.1359 | 0.0107 |
5 | 12 | 1500 | 3000 | 1 | 12.5 | 0.2828 | 0.2822 | 0.0007 |
6 | 12 | 3000 | 3000 | 1 | 8 | 0.3536 | 0.3497 | 0.0039 |
7 | 12 | 3000 | 5000 | 1 | 17 | 0.2425 | 0.2333 | 0.0092 |
8 | 12 | 4500 | 5000 | 1 | 15 | 0.2582 | 0.272 | −0.0138 |
9 | 7 | 1500 | 3000 | 1 | 98.5 | 0.1008 | 0.1096 | −0.0088 |
10 | 7 | 3000 | 3000 | 1 | 24 | 0.2041 | 0.1953 | 0.0088 |
11 | 7 | 3000 | 5000 | 1 | 68.5 | 0.1208 | 0.112 | 0.0088 |
12 | 7 | 4500 | 5000 | 1 | 39 | 0.1601 | 0.1689 | −0.0088 |
13 | 2 | 1500 | 3000 | 2 | 73 | 0.117 | 0.1141 | 0.0029 |
14 | 2 | 3000 | 3000 | 2 | 47 | 0.1459 | 0.147 | −0.0011 |
15 | 2 | 3000 | 5000 | 2 | 50 | 0.1414 | 0.1425 | −0.0011 |
16 | 2 | 4500 | 5000 | 2 | 47 | 0.1459 | 0.1466 | −0.0007 |
17 | 12 | 1500 | 3000 | 2 | 18.5 | 0.2325 | 0.2353 | −0.0028 |
18 | 12 | 3000 | 3000 | 2 | 8 | 0.3536 | 0.3519 | 0.0016 |
19 | 12 | 3000 | 5000 | 2 | 28 | 0.189 | 0.1887 | 0.0003 |
20 | 12 | 4500 | 5000 | 2 | 13 | 0.2774 | 0.2765 | 0.0008 |
21 | 2 | 1500 | 3000 | 3 | 11 | 0.3015 | 0.2886 | 0.0129 |
22 | 2 | 3000 | 3000 | 3 | 50 | 0.1414 | 0.1489 | −0.0075 |
23 | 2 | 3000 | 5000 | 3 | 4 | 0.5 | 0.5075 | −0.0075 |
24 | 2 | 4500 | 5000 | 3 | 8.6 | 0.341 | 0.339 | 0.002 |
25 | 12 | 1500 | 3000 | 3 | 17.9 | 0.2364 | 0.2438 | −0.0074 |
26 | 12 | 3000 | 3000 | 3 | 9 | 0.3333 | 0.3293 | 0.004 |
27 | 12 | 4500 | 5000 | 3 | 12 | 0.2887 | 0.2853 | 0.0034 |
Source | Sum of Squares | DF | Mean Square | F-Value | p-Value | Contribution (%) |
---|---|---|---|---|---|---|
Model | 0.2515 | 19 | 0.0132 | 56.3 | <0.0001 | 3.61 |
Xf | 0.017 | 1 | 0.017 | 72.23 | <0.0001 | 4.65 |
Xs | 0.0184 | 1 | 0.0184 | 78.19 | <0.0001 | 5.04 |
Xp | 0.0156 | 1 | 0.0156 | 66.42 | <0.0001 | 4.27 |
Xg | 0.0366 | 1 | 0.0366 | 155.46 | <0.0001 | 10.02 |
Xf Xs | 0.0302 | 1 | 0.0302 | 128.26 | <0.0001 | 8.27 |
Xf Xp | 0.0508 | 1 | 0.0508 | 216.23 | <0.0001 | 13.91 |
Xf Xg | 0.0266 | 1 | 0.0266 | 113.25 | <0.0001 | 7.28 |
Xs Xp | 0.0229 | 1 | 0.0229 | 97.43 | <0.0001 | 6.27 |
Xs Xg | 0.0096 | 1 | 0.0096 | 41 | 0.0004 | 2.63 |
Xp Xg | 0.0196 | 1 | 0.0196 | 83.56 | <0.0001 | 5.37 |
Xf² | 0.0197 | 1 | 0.0197 | 83.64 | <0.0001 | 5.39 |
Xs² | 0.026 | 1 | 0.026 | 110.37 | <0.0001 | 7.12 |
Xg² | 0.0068 | 1 | 0.0068 | 28.76 | 0.001 | 1.86 |
Xf Xs Xg | 0.0049 | 1 | 0.0049 | 20.7 | 0.0026 | 1.34 |
Xf Xp Xg | 0.0098 | 1 | 0.0098 | 41.7 | 0.0003 | 2.68 |
Xf² Xs | 0.0093 | 1 | 0.0093 | 39.53 | 0.0004 | 2.55 |
Xf²Xp | 0.0096 | 1 | 0.0096 | 40.71 | 0.0004 | 2.63 |
Xf Xg² | 0.0168 | 1 | 0.0168 | 71.37 | <0.0001 | 4.60 |
XsXg² | 0.0018 | 1 | 0.0018 | 7.8 | 0.0268 | 0.49 |
Residual | 0.0016 | 7 | 0.0002 | |||
Cor Total | 0.2532 | 26 |
Exp. Number | Cast 316 HS | Cast 316 LS | Occurrence of Inverse Marangoni Convection for 316 HS Cast and Occurrence of Conventional Marangoni Convection for 316 LS Cast | ||||
---|---|---|---|---|---|---|---|
Inverse Marangoni Convection | Marangoni Convection | ||||||
Weld Depth (D) (mm) | Weld Width (W) (mm) | Full Penetration Weld (F.P)/ Partial Penetration Weld (P.P) | Weld Depth (D) (mm) | Weld Width (W) (mm) | Full Penetration Weld (F.P)/ Partial Penetration Weld (P.P) | ||
1 | 2 | 0.58 | F.P | 2 | 0.79 | F.P | Yes |
2 | 2 | 1.15 | F.P | 2 | 1 | F.P | No |
3 | 2 | 1.40 | F.P | 2 | 1 | F.P | No |
4 | 2 | 1.22 | F.P | 2 | 0.86 | F.P | No |
5 | 0.6 | 1.43 | P.P | 0.39 | 1.95 | P.P | Yes |
6 | 0.35 | 0.27 | P.P | 0.29 | 1.61 | P.P | Yes |
7 | 0.62 | 0.84 | P.P | 0.48 | 2.1 | P.P | Yes |
8 | 0.44 | 1.33 | P.P | 0.61 | 1.42 | P.P | No |
9 | 2 | 1.27 | F.P | 2 | 1.06 | F.P | No |
10 | 1.15 | 1.17 | P.P | 0.93 | 1.22 | P.P | Yes |
11 | 2 | 0.69 | F.P | 2 | 0.8 | F.P | Yes |
12 | 1.09 | 0.65 | P.P | 1.08 | 1.86 | P.P | Yes |
13 | 2 | 1.68 | F.P | 2 | 0.69 | F.P | No |
14 | 2 | 0.82 | F.P | 2 | 1 | F.P | Yes |
15 | 2 | 0.89 | F.P | 2 | 2.4 | F.P | Yes |
16 | 2 | 0.70 | F.P | 2 | 0.83 | F.P | Yes |
17 | 0.44 | 1.76 | P.P | 0.74 | 1.45 | P.P | No |
18 | 0.38 | 1.46 | P.P | 0.28 | 1.55 | P.P | Yes |
19 | 1.12 | 1.6 | P.P | 1.04 | 1.67 | P.P | Yes |
20 | 0.72 | 1.38 | P.P | 0.53 | 1.39 | P.P | Yes |
21 | 1.98 | 0.59 | P.P | 0.63 | 1.85 | P.P | Yes |
22 | 0.65 | 0.33 | P.P | 1.8 | 1.71 | P.P | No |
23 | 0.49 | 1.96 | P.P | 0.18 | 2.25 | P.P | Yes |
24 | 0.91 | 0.39 | P.P | 0.61 | 2.26 | P.P | Yes |
25 | 0.8 | 1.12 | P.P | 0.77 | 1.35 | P.P | Yes |
26 | 0.48 | 1.17 | P.P | 0.5 | 0.46 | P.P | No |
27 | 0.44 | 0.44 | P.P | 0.6 | 1.22 | P.P | No |
Types of Weld Bead | Times Getting Partial Penetration Weld(PP) or Full Penetration Weld (FP) Weld Bead for Both Casts Out of 27 Tests | Occurrence of Inverse Marangoni Convection for 316 HS Cast and Occurrence of Conventional Marangoni Convection for 316 LS Cast For the Same Welding Parameters | Non Predominance of Conventional Marangoni Convection for 316 LS and/or Non Predominance of Inverse Marangoni Convection for 316 HS | Percentages Occurrences of Inverse Marangoni and Conventional Marangoni Convection % |
---|---|---|---|---|
Partial Penetration weld(PP) | 17 | 12 | 5 | 71 |
Full Penetration weld(FP) | 10 | 5 | 5 | 50 |
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Touileb, K.; Attia, E.; Djoudjou, R.; Benselama, A.; Ibrahim, A.; Boubaker, S.; Ponnore, J.; Ahmed, M.M.Z. Laser Weld Aspect Optimization of Thin AISI 316 SS Using RSM in Relation with Welding Parameters and Sulfur Content. Metals 2023, 13, 1202. https://doi.org/10.3390/met13071202
Touileb K, Attia E, Djoudjou R, Benselama A, Ibrahim A, Boubaker S, Ponnore J, Ahmed MMZ. Laser Weld Aspect Optimization of Thin AISI 316 SS Using RSM in Relation with Welding Parameters and Sulfur Content. Metals. 2023; 13(7):1202. https://doi.org/10.3390/met13071202
Chicago/Turabian StyleTouileb, Kamel, Elawady Attia, Rachid Djoudjou, Abdallah Benselama, Albaijan Ibrahim, Sahbi Boubaker, Jose Ponnore, and Mohamed M. Z. Ahmed. 2023. "Laser Weld Aspect Optimization of Thin AISI 316 SS Using RSM in Relation with Welding Parameters and Sulfur Content" Metals 13, no. 7: 1202. https://doi.org/10.3390/met13071202