Diffraction-Based Residual Stress Characterization in Laser Additive Manufacturing of Metals
Abstract
:1. Introduction
2. Laser-Based AM Processes
2.1. LPBF (Laser Powder Bed Fusion)
2.2. LMD (Laser Metal Deposition)
3. Definition of Residual Stress
- Type I stresses (σI) equilibrate over large distances (comparable to the size of the part). This type of RS can be caused e.g., by temperature gradients, machining, and other treatments at the component scale. They depend on the material and its history, as well as on the component geometry.
- Type II or intergranular stresses (σII) vary over the grain scale and balance over a few grains. They strongly depend on the microstructure, and on the materials history, but weakly on the part geometry. Type II stress is very common in composites and crystallographically anisotropic materials
- Type III stresses (σIII) vary over the atomic scale. Typically, this type is caused by defects of the crystal lattice (e.g., dislocations). They are balanced within each grain and depend on both the microstructure and the materials history.
4. Residual Stress with Respect to Laser-Based AM
4.1. Origin of Residual Stress
4.2. Distribition of Residual Stress
5. Determination of Residual Stresses with Diffraction-Based Methods
5.1. General Aspects of Diffraction-Based Methods
5.2. X-ray Diffraction
5.2.1. The Monochromatic Case for Surface Analysis
5.2.2. The Energy Dispersive Case
5.3. Neutron Diffraction
5.3.1. The Monochromatic Method
5.3.2. The Time-of-Flight Method
6. Peculiarities of Diffraction-Based Methods in the Case of AM
6.1. Strain-Free Lattice Spacing ()
6.1.1. Use of Raw Powder
6.1.2. Use of Mechanical Filings
6.1.3. Use of Macroscopically Relaxed Samples (Cubes/Combs/Arrays)
6.1.4. Stress and Moment Balance
6.2. Principal Stress Directions
6.3. Diffraction-Elastic Constants (DECs)
6.3.1. The Anisotropy of Single Crystals
6.3.2. Grain Interaction Models for the Calculation of DECs
6.3.3. Experimental Determination of Diffraction Elastic Constants
6.4. Choice of the Appropriate Lattice Planes
- Insensitivity to intergranular stress accumulation (material dependent)
- Crystal symmetry
- Texture of the material
7. Summary & Outlook
- First, one must evaluate if the assumption of a biaxial stress state can be justified (e.g., surface measurements with method) or a triaxial stress state must be considered. In the latter case, neutron diffraction should be preferred to other techniques and precise knowledge about the strain-free lattice spacing () is required. To obtain such a reference, measurements on mechanically relaxed samples are recommended. The stress balance method is recommended as a validation method. If the requirements for the correct application of stress balance conditions (no spatial variation of composition with large number of points) are known to be fulfilled, the stress balance method can be used to obtain a global . Still, the strategy to determine needs to be tailored for each case.
- Secondly, the principal stress directions should be known in advance if one wants to determine the maximum stress values. For conventional processes such as forging or rolling these are often known (they coincide with the main geometrical sample axes). In the case of AM, the complexity of the process conditions hinders the prior knowledge of the principal stress directions. Although research indicates the principal directions to be determined by the scanning strategy (i.e., the main stress axes follow the scanning vector) it is recommended to run experimental checks. Ideally the full stress tensor should be characterized.
- Thirdly, the microstructure and texture of the sample should be well characterized. Texture is one of the driving factors for the determination of the diffraction elastic constants (DECs). Furthermore, the DECs are material-dependent, dictated by the single crystal properties. Therefore, choosing the appropriate modeling scheme for the calculation of DECs from single crystal elastic constants is challenging. At best the DECs should be experimentally determined. If that is not possible, it is indispensable to take the microstructure and the texture into account in the selection of the grain-interaction model.
- Lastly, an appropriate lattice plane must be chosen in the case of a monochromatic measurement technique (Laboratory XRD or steady state Neutron sources), as stresses are derived from one single lattice plane. Such plane should be insensitive to accumulation of intergranular strain and possess a high multiplicity, to represent the macroscopic behavior of the sample.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Method | Advantages | Disadvantages | References |
---|---|---|---|
Cubes/ matchsticks |
|
| [79,82,103,109,110,112] |
Comb/arrays |
| Same as Cubes/matchsticks and:
| [31,46,80,81,91,111] |
Stress balance |
|
| [80,81,86,103,107,113] |
Feedstock powder |
|
| [82,103,107] |
Powder filings |
|
| [82,107] |
Sin2ψ |
|
| [38,82] |
Material | Crystal Structure | C11 | C12 | C44 | C33 | C13 | Ref. | AZ | AL [∙10−2] |
---|---|---|---|---|---|---|---|---|---|
Aluminium | FCC | 108.2 | 61.3 | 28.5 | - | - | [124] | 1.2 | 2.04 |
107.9 | 60.4 | 28.6 | - | - | [125] | 1.2 | 1.85 | ||
106.8 | 60.7 | 28.2 | - | - | [126] | 1.2 | 2.18 | ||
112.4 | 66.3 | 27.7 | - | - | [127] | 1.2 | 1.81 | ||
108.2 | 62.2 | 28.4 | - | - | [128] | 1.2 | 2.38 | ||
105.6 | 63.9 | 28.5 | - | - | [129] | 1.4 | 5.22 | ||
107.3 | 60.9 | 28.3 | - | - | [130] | 1.2 | 2.12 | ||
Average | 108.1 | 62.2 | 28.3 | - | - | - | 1.2 | 2.35 | |
Ti6Al4V | HCP | 150 | 83 | 42 | 137 | 53 | [123] | - | 5.67 |
Inconel 625 | FCC | 243.3 | 156.7 | 117.8 | - | - | [131] | 2.7 | 51.88 |
Inconel 718 | FCC | 240.9 | 140.5 | 105.7 | - | - | [132] | 2.1 | 29.17 |
259.6 | 179 | 109.6 | - | - | [133] | 2.7 | 51.85 | ||
231.2 | 145.1 | 117.2 | - | - | [134] | 2.7 | 51.95 | ||
Average | 243.9 | 154.9 | 110.8 | - | - | - | 2.5 | 43.36 | |
316L | FCC | 191.2 | 117.9 | 138.6 | - | - | [135] | 3.8 | 89.33 |
215.9 | 144.6 | 128.9 | - | - | [136] | 3.6 | 83.72 | ||
198 | 125 | 122 | - | - | [137] | 3.3 | 71.38 | ||
Average | 204.4 | 131.8 | 128.8 | - | - | - | 3.6 | 81.41 |
Material | Process | Condition | E200 | E311 | E420 | E220 | E331 | E111 | Ref. | |
---|---|---|---|---|---|---|---|---|---|---|
AlSi10Mg | LPBF | As built tension | 66 | 68 | - | 71 | - | 73 | [153] | |
IN625 | LMD | As built compression | 123 | 156 | 169 | 210 | 219 | 278 | [131] | |
IN718 | LPBF | FHT * tension | 194 | 196 | 231 | - | 230 | - | [39] | |
IN718 | LPBF | DA ** tension | 152 | 173 | 173 | 199 | 227 | 197 | [39] | |
316L | LPBF | As built tension | 139 | 180 | - | 219 | - | 246 | [154] | |
Ti6Al4V | LPBF | |||||||||
As built tension | 110 | 106 | 117 | - | 107 | 117 | [155] | |||
HT-730 tension | 106 | 116 | 126 | 134 | 128 | 125 | ||||
HT-900 tension | 111 | 114 | 113 | 132 | 118 | 127 | ||||
As built tension | 108 | 110 | 115 | 115 | 116 | 120 | 125 | [156] | ||
As built compression | - | 115 | - | 117 | 123 | 125 | 126 |
Origin of DECs | References |
---|---|
Not given | [75,76,85,88,109,113,159,160,161,162,163] |
unknown origin | [10,103,110,164] |
Experimental values (conventional) | [81,86,165,166] |
Reuss Model | [38,107,167] |
Eshelby–Kröner Model | [13,26,74,79,82,83,96,108,112,168,169,170] |
Voigt-Reuss-Hill | [171] |
Experimental values (AM) | [31,115] |
Material | AM | Conventional | Conclusion |
---|---|---|---|
Inconel 718 (fcc) |
|
| |
316L (fcc) |
|
| |
304 (fcc) | |||
AlSiMg10 (fcc) |
| - |
|
Ti6Al4V (hcp) |
| Unidirectionally rolled plate (UD) (loading along rolling direction (RD)) [181]:
|
|
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Schröder, J.; Evans, A.; Mishurova, T.; Ulbricht, A.; Sprengel, M.; Serrano-Munoz, I.; Fritsch, T.; Kromm, A.; Kannengießer, T.; Bruno, G. Diffraction-Based Residual Stress Characterization in Laser Additive Manufacturing of Metals. Metals 2021, 11, 1830. https://doi.org/10.3390/met11111830
Schröder J, Evans A, Mishurova T, Ulbricht A, Sprengel M, Serrano-Munoz I, Fritsch T, Kromm A, Kannengießer T, Bruno G. Diffraction-Based Residual Stress Characterization in Laser Additive Manufacturing of Metals. Metals. 2021; 11(11):1830. https://doi.org/10.3390/met11111830
Chicago/Turabian StyleSchröder, Jakob, Alexander Evans, Tatiana Mishurova, Alexander Ulbricht, Maximilian Sprengel, Itziar Serrano-Munoz, Tobias Fritsch, Arne Kromm, Thomas Kannengießer, and Giovanni Bruno. 2021. "Diffraction-Based Residual Stress Characterization in Laser Additive Manufacturing of Metals" Metals 11, no. 11: 1830. https://doi.org/10.3390/met11111830