A Multi-Phase Modeling Framework Suitable for Dynamic Applications
Abstract
:1. Introduction
2. Methods
2.1. Traditional Model Decomposition
2.2. Multi-Phase Description of Shear Modulus and Flow Stress
2.3. Phase-Specific Shear Modulus and Strength Models
2.4. Phase-Specific Accumulated Effective Plastic Strain
2.4.1. Evolution Method
- The approach here is described in terms of volume fractions with k being the phase index, but the same approach holds for quantities that should be weighted by mass. One just uses the mass fractions instead of the volume fractions.
- We assume that volume fractions are available at the beginning and end of the time step, and . That does not amount to utilizing all of the transformation rates among the various phases. In many cases for polycrystalline metals, only two phases are exchanging mass at a given spatial location such that having the volume fractions provides complete information. The algorithm based on volume (or mass) fractions rather than rates can be simpler to implement.
- Cutoffs and thresholds can be important to numerically robust behavior of the implementation. These are particularly important in an Eulerian or Arbitrary Lagrangian–Eulerian (ALE) hydrocodes [19] given the action of the “advection” (or remap) step on the history variables. The monotonicity enforcement mentioned in the following section is similar to the monotonicity enforcement in the fixed-time mesh remap step in a hydrocode, but here the monotonicity is enforced during the time-evolution step. It can be useful to skip the contribution of phases with a tiny volume fraction, less than say .
2.4.2. Evolution Algorithm
2.4.3. Specific Examples
2.5. Multi-Phase Equation of State (EOS) and Kinetics of Transformation
2.5.1. Multi-Phase EOS with Equilibrium Phase Fractions
2.5.2. Multi-Phase EOS with Finite Rate Kinetics
3. Results
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Parameter | Value | Parameter | Value |
---|---|---|---|
0.0597 | p | 2.82 | |
0.0256 | 0.00239 | ||
0.000675 | 0.000313 | ||
0.186 | 0.0355 | ||
0.00000136 | 0.45 | ||
0.45 |
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Phase | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
g/cm | GPa | g/cm | K | * | * | - | * | - | - | |
7.40 | 25.4 | 7.18 | 505.1 | 0 | 600 | 3.2 | 800 | 3.2 | 0.53 | |
7.82 | 26.8 | 7.585 | 595.0 | 0 | 820 | 3.2 | 2300 | 3.2 | 0.7 | |
10.50 | 23.0 | 9.425 | 1900.0 | 2.125 | 8.0 | 8.0 | 0.2 |
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Barton, N.R.; Luscher, D.J.; Battaile, C.; Brown, J.L.; Buechler, M.; Burakovsky, L.; Crockett, S.; Greeff, C.; Mattsson, A.E.; Prime, M.B.; et al. A Multi-Phase Modeling Framework Suitable for Dynamic Applications. Metals 2022, 12, 1844. https://doi.org/10.3390/met12111844
Barton NR, Luscher DJ, Battaile C, Brown JL, Buechler M, Burakovsky L, Crockett S, Greeff C, Mattsson AE, Prime MB, et al. A Multi-Phase Modeling Framework Suitable for Dynamic Applications. Metals. 2022; 12(11):1844. https://doi.org/10.3390/met12111844
Chicago/Turabian StyleBarton, Nathan R., Darby J. Luscher, Corbett Battaile, Justin L. Brown, Miles Buechler, Leonid Burakovsky, Scott Crockett, Carl Greeff, Ann E. Mattsson, Michael B. Prime, and et al. 2022. "A Multi-Phase Modeling Framework Suitable for Dynamic Applications" Metals 12, no. 11: 1844. https://doi.org/10.3390/met12111844