Thermomechanical Simulations of Residual Stresses and Distortion in Electron Beam Melting with Experimental Validation for Ti-6Al-4V
Abstract
:1. Introduction
2. Materials and Methods
2.1. Finite Element Modeling
2.1.1. Material Properties
2.1.2. Initial and Boundary Conditions
2.1.3. Electron Beam Modeling
2.2. Contact
- ○
- The deformation effect will be transferred from one layer to another layer through the tied nodes.
- ○
- Heat degree of freedom will be transferred from one layer to another through the tied nodes.
2.3. FE Mesh
2.4. Powder Addition in a Layer by Layer Fashion
2.5. Fabrication of the Thin-Walled EBM Parts
3. Results and Discussion
3.1. Temperature Field
3.1.1. Temperature Gradient
3.1.2. Model Validation
3.2. Residual Stresses
3.2.1. Instantaneous Stress
3.2.2. Model Results Versus Reported Results
3.3. Thermal Distortion
3.4. Experimental Validation
3.5. Microstructure Evolution
4. The Effects of Different Electron Beam Parameters
4.1. The Effect of Scan Speed on the EBM Process
4.2. The Effect of Current on the EBM Process
4.3. The Effect of Voltage on the EBM Process
5. Conclusions
- ○
- The FEA can predict the thermomechanical behavior of products fabricated by the electron beam melting process or similar processes with localized heat sources such as laser sintering, laser cladding, and welding.
- ○
- During the deposition of layers with EBM, high residual stresses resulted after final cooling, i.e., the stresses in the deposited layers increased with cooling due to thermal contraction. It is highly recommended to validate the FE residual stress results by conducting the experimental observations and measurements as well.
- ○
- The distortion in the EBM produced parts was experimentally measured. The experimental results showed that the overall distortion was independent of the part height produced. The simulated pattern of the distortion in the results from the FE model was found to be in close agreement with the experimental data.
- ○
- The maximum predicted temperatures and the temperature profiles were found to be in close agreement with the reported experimental and simulated results.
- ○
- An increase in scan speed leads to a decrease in temperature.
- ○
- An increase in scan speed leads to an increase in the residual stresses within the part produced by EBM.
- ○
- An increase in current leads to a rise in temperature of the electron beam melting process.
- ○
- A decrease in current leads to a reduction in the residual stresses within the part produced by EBM.
- ○
- An increase in voltage leads to a rise in the temperature of the electron beam melting process.
- ○
- An increase in voltage leads to lower residual stresses within the part produced by EBM.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Temperature (K) | Density (kg/m3) | Heat Capacity (J/(kg K)) | Thermal Conductivity (W/(m K)) | Thermal Expansion Coefficient (m/(m K)) | Yield Strength (MPa) | Young’s Modulus (GPa) | Poisson’s Ratio |
---|---|---|---|---|---|---|---|
273 | 0.0079 | 462 | 0.0146 | 265 | 198.5 | 0.294 | |
373 | 0.00788 | 496 | 0.0151 | 218 | 193 | 0.295 | |
473 | 0.00783 | 512 | 0.0161 | 186 | 185 | 0.301 | |
573 | 0.00779 | 525 | 0.0179 | 170 | 176 | 0.31 | |
673 | 0.00775 | 540 | 0.018 | 155 | 167 | 0.318 | |
873 | 0.00766 | 577 | 0.0208 | 149 | 159 | 0.326 | |
1073 | 0.00756 | 604 | 0.0239 | 91 | 151 | 0.333 | |
1473 | 0.00737 | 676 | 0.0322 | 25 | 60 | 0.339 | |
1573 | 0.00732 | 692 | 0.0337 | 21 | 20 | 0.342 | |
1773 | 0.00732 | 935 | 0.12 | 10 | 10 | 0.388 |
Temperature (K) | Density (kg/m3) | Heat Capacity (J/(kg K)) | Thermal Conductivity (W/(m K)) Solid | Thermal Conductivity (W/(m K)) Powder [21] | Thermal Expansion Coefficient (m/(m K)) | Yield Strength (MPa) | Young’s Modulus (GPa) | Poisson’s Ratio |
---|---|---|---|---|---|---|---|---|
293 | 4420 | 546 | 7 | 0.2 | 850 | 102 | 0.345 | |
400 | 4402 | 567 | 7.8 | - | 720 | 101 | 0.35 | |
500 | 4391 | 591 | 8.9 | - | 680 | 95 | 0.355 | |
600 | 4376 | 611 | 10.5 | - | 630 | 91 | 0.36 | |
700 | 4361 | 636 | 11.7 | - | 590 | 85 | 0.365 | |
800 | 4345 | 656 | 13 | - | 540 | 80 | 0.37 | |
900 | 4331 | 679 | 14.5 | - | 490 | 75 | 0.375 | |
1000 | 4319 | 699 | 16.2 | - | 450 | 70 | 0.385 | |
1100 | 4303 | 719 | 18.4 | - | 400 | 65 | 0.395 | |
1200 | 4289 | 733 | 20.1 | - | 360 | 60 | 0.405 | |
1300 | 4278 | 647 | 19.7 | - | 315 | 35 | 0.43 | |
1400 | 4264 | 664 | 21.7 | - | 268 | 20 | 0.43 | |
1950 | 4189 | 790 | 72 | 28.3 | 20 | 10 | 0.43 |
Layer | Phase | Step | Description | Time (s) | Total Time (s) |
---|---|---|---|---|---|
Complete model | Preheating | Initial | Preheating phase for the whole model at 1003k | 0 | 0 |
L1 | Melting | 1 | Electron beam scanning along X-Z direction | 0.0265 | 0.0265 |
Cooling | 2 | Transformation of material from powder to solid-state then cooling phase | 3 | 3.0265 | |
L2 | Melting | 3 | Activation of layer-2 and scanning of electron beam along X-Z direction | 0.0265 | 3.0795 |
Cooling | 4 | Transformation of material from powder to solid-state then cooling phase | 3 | 6.0795 | |
L3 | Melting | 5 | Activation of layer-3 and scanning of electron beam along X-Z direction | 0.0265 | 6.106 |
Cooling | 6 | Transformation of material from powder to solid-state then cooling phase | 3 | 9.106 | |
L4 | Melting | 7 | Activation of layer-4 and scanning of electron beam along X-Z direction | 0.0265 | 9.1325 |
Cooling | 8 | Transformation of material from powder to solid-state then cooling phase | 3 | 12.1325 | |
L5 | Melting | 9 | Activation of the next layer and scanning of electron beam along X-Z direction | 0.0265 | 12.159 |
Cooling | 10 | Transformation of material from powder to solid-state then cooling phase | 1100 | 112.16 | |
Total time | 1112.16 |
Parameters | Values |
---|---|
Electron beam diameter, Φ (mm) | 0.3 |
Scan speed, v (mm/s) | 400 |
Acceleration voltage, U (kV) | 60 |
Beam current, Ib (mA) | 0.002 |
Powder layer thickness, tlayer (mm) | 0.05 |
Beam penetration depth, dP (mm) | 0.05 |
Preheat temperature, Tpreheat (k) | 1003 |
Parameter | Level-1 | Level-2 | Level-3 |
---|---|---|---|
Speed (mm/s) | 300 | 400 | 500 |
Current (mA) | 0.002 | 0.002 | 0.002 |
Voltage (kV) | 60 | 60 | 60 |
Parameter | Level-1 | Level-2 | Level-3 |
---|---|---|---|
Speed (mm/s) | 400 | 400 | 400 |
Current (mA) | 0.001 | 0.002 | 0.003 |
Voltage (kV) | 60 | 60 | 60 |
Parameter | Level-1 | Level-2 | Level-3 |
---|---|---|---|
Speed (mm/s) | 400 | 400 | 400 |
Current (mA) | 0.002 | 0.002 | 0.002 |
Voltage (kV) | 50 | 60 | 70 k |
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M. Abdullah, F.; Anwar, S.; Al-Ahmari, A. Thermomechanical Simulations of Residual Stresses and Distortion in Electron Beam Melting with Experimental Validation for Ti-6Al-4V. Metals 2020, 10, 1151. https://doi.org/10.3390/met10091151
M. Abdullah F, Anwar S, Al-Ahmari A. Thermomechanical Simulations of Residual Stresses and Distortion in Electron Beam Melting with Experimental Validation for Ti-6Al-4V. Metals. 2020; 10(9):1151. https://doi.org/10.3390/met10091151
Chicago/Turabian StyleM. Abdullah, Fawaz, Saqib Anwar, and Abdulrahman Al-Ahmari. 2020. "Thermomechanical Simulations of Residual Stresses and Distortion in Electron Beam Melting with Experimental Validation for Ti-6Al-4V" Metals 10, no. 9: 1151. https://doi.org/10.3390/met10091151