Abstract
In this study a material model is developed to predict the solidification microstructure of an additive-manufactured, fully dense magnesium (Mg) alloy using uniform droplet spraying (UDS). Specifically, the crystallite size distribution is simulated by a solidification model, consisting of a nucleation/fragmentation and a constrained growth description, calibrated via microstructural data from a single droplet splat. This is enabled by a semi-analytical thermal modeling framework, based on the superposition of moving Green’s and Rosenthal functions for the temperature field generated by a Gaussian source distribution. The model is implemented for layered ellipsoidal deposit sections on planar substrates by multi-pass spraying, and its predictions are validated against measured crystal sizes by image analysis of experimental micrographs of a Mg97ZnY2 alloy, to an error margin of ± 15%. The computationally efficient simulation provides insights to the deposit microstructure, and is intended as a process observer in a closed-loop, adaptive control scheme based on infrared temperature measurements.
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Data availability
The data that support the findings of this study are available on request from the corresponding author YL at leonl@iastate.edu.
Abbreviations
- T :
-
Temperature field
- v :
-
Average volume of a solidified domain
- \(\vec{q}\) :
-
Heat flux
- Δh :
-
Volumetric latent heat of fusion
- \(\varrho\) :
-
Density
- k :
-
Conductivity
- \(\alpha\) :
-
Thermal diffusivity of solidifying material
- c p :
-
Specific heat capacity
- T m :
-
Solidification temperature
- T a :
-
Ambient temperature
- h a :
-
Convective heat transfer coefficient
- ε :
-
Surface emissivity
- σ :
-
Stefan–Boltzmann constant
- T s :
-
Deposit temperature
- ρ :
-
Distance of location from that of droplet impingement
- Q :
-
Enthalpic content of a molten droplet
- ς :
-
Standard deviation radius
- \(\dot{Q}\) :
-
Total thermal power
- F :
-
Piezoelectric UDS droplet ejection frequency
- r, φ :
-
The radial and azimuthal angle variables of integration location
- υ :
-
Moving speed
- s :
-
Domain size
- η i :
-
Source modulation efficiency
- N :
-
Cumulative fraction of droplets falling the molten puddle
- Da j, Db j :
-
Major thickness and width increments
- n :
-
Aspect ratio
- T o :
-
Initial temperature
- Γ :
-
Green’s function
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Acknowledgements
Y. Liao gratefully acknowledges the faculty startup support provided by College of Engineering at the Iowa State University.
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Jaffar, S.M., Kostoglou, N., Fukuda, H. et al. Additive manufacturing of magnesium alloy using uniform droplet spraying: modeling of microstructure evolution. MRS Advances 6, 391–403 (2021). https://doi.org/10.1557/s43580-021-00028-x
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DOI: https://doi.org/10.1557/s43580-021-00028-x