A Sharp-Interface Model of the Diffusive Phase Transformation in a Nickel-Based Superalloy
Abstract
:1. Introduction
- Do not artificially thicken the interface in order to reduce mesh resolution to a tractable level (unlike CH-type models)
- Offer a good pathway for further verification of phase transformation models
- Offer low computational cost in the framework of finite elements compared to CH-type models.
2. Free Boundary Problem
3. Constitutive Assumptions in the Bulk
4. Numerical Method
4.1. Balance of Linear Momentum and Approximation of the Displacement Field
- It is only active within the enriched elements; thus, no blending is required.
- The condition number of the system matrix does not significantly increase compared to the condition number of a similar FE problem without any enrichments. This also holds if elements are barely intersected by the interface.
4.2. Computing Input Quantities for the Gibbs–Thomson Equation
4.3. Approximation of the Concentration Field
4.4. Computing the Normal Interface Velocity
4.5. Surface Tracking
4.6. Staggered Solution Scheme
- The old point is on the same side of the interface as the new point.
- The side is determined by the sign of the updated new level set.
5. Numerical Results
5.1. Elastic Matrix
- with ,
- with ,
- with
5.2. Ostwald Ripening
5.3. Ductile Matrix
- with (base symmetry plane).
- and with (x-axis fixed in y-direction).
- and with (y-axis fixed in x-direction).
- The precipitate volume fraction is increased.
- The phase transformation leads to changes in topology.
6. Conclusions and Outlook
- A SI model for phase transformations was extended by a path-dependent non-linear crystal plasticity model.
- The model captures cuboidal equilibrium shapes and Ostwald ripening.
- By solving the diffusion equation explicitly, the transport of solute atoms within the -matrix can be visualized.
- By introducing a crystal plasticity model the precipitate’s shape is qualitatively altered due to the anisotropy of the material’s mechanical response.
- For isolated precipitates, the shape changes do not influence the global mechanical behaviour, as was confirmed by simulations with a fixed interface.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Slip System i | ||
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3 | ||
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7 | ||
8 | ||
9 | ||
10 | ||
11 | ||
12 |
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Munk, L.; Reschka, S.; Maier, H.J.; Wriggers, P.; Löhnert, S. A Sharp-Interface Model of the Diffusive Phase Transformation in a Nickel-Based Superalloy. Metals 2022, 12, 1261. https://doi.org/10.3390/met12081261
Munk L, Reschka S, Maier HJ, Wriggers P, Löhnert S. A Sharp-Interface Model of the Diffusive Phase Transformation in a Nickel-Based Superalloy. Metals. 2022; 12(8):1261. https://doi.org/10.3390/met12081261
Chicago/Turabian StyleMunk, Lukas, Silvia Reschka, Hans Jürgen Maier, Peter Wriggers, and Stefan Löhnert. 2022. "A Sharp-Interface Model of the Diffusive Phase Transformation in a Nickel-Based Superalloy" Metals 12, no. 8: 1261. https://doi.org/10.3390/met12081261