AM Microstructure Simulation
Theory: G and R set the microstructure
Overview
Does AM microstructure simulation compute every individual grain?
There are three levels, chosen by purpose. Simplest is a part-scale thermal analysis giving thermal gradient G and solidification rate R at the solidification front, mapped onto the alloy's solidification map to predict where grains are columnar or equiaxed and how fine they are; it is light and suits design comparisons. Next is cellular automata (CA), computing grain nucleation and growth as changes in cell state to show grain shape and orientation over a few mm. Finest is the phase-field method, resolving dendrite arms and solute segregation but limited to tens to hundreds of µm. All start from the temperature field, so getting G and R right from thermal analysis is the foundation.
Cooling rate, solidification rate and cell spacing
Ṫ is cooling rate, v scan speed, θ the angle between the front normal and the scan direction, and λ the cell (primary dendrite) spacing. Larger G×R means finer structure; larger G/R favours planar or cellular fronts, smaller G/R equiaxed grains.
From welding research to additive manufacturing
A moving melt pool that solidifies behind the beam makes laser additive manufacturing much like laser welding. Relations between cooling rate and cell spacing worked out in 1980s research on laser welding of stainless steels are still used to predict AM microstructure. The big difference is that in AM the same spot is reheated many times by later layers, so the structure formed first can be tempered or transformed.
Worked examples
Cell spacing is calculated from the stated empirical relation, not a direct prediction of grain size or strength. The 1 K/s casting entry is an extrapolation, not a validated measurement. Grain morphology also depends on nucleation and alloy composition, not G/R alone.
Example 1: cooling rate and cell spacing by process (316L)
| Process | G (typical) | R (typical) | Cooling rate | Cell spacing |
|---|---|---|---|---|
| LPBF | 10⁶ K/m | 1 m/s | 10⁶ K/s | 0.84 µm |
| DED | 10⁵ K/m | 0.01 m/s | 10³ K/s | 8.2 µm |
| Sand casting | — | — | ≈ 1 K/s | 80 µm |
G and R are order-of-magnitude values. For the same 316L, LPBF structure is about 100 times finer than cast, one reason for LPBF material's high yield strength.
Example 2: G/R within the melt pool (1 m/s scan)
| Location | Front angle θ | Solidification rate R | G (typical) | G/R |
|---|---|---|---|---|
| Pool bottom | 89° | 0.017 m/s | 10⁷ K/m | 5.7×10⁸ K·s/m² |
| Middle | 45° | 0.71 m/s | 3×10⁶ K/m | 4.2×10⁶ K·s/m² |
| Top (trailing edge) | 0° | 1.0 m/s | 10⁶ K/m | 1.0×10⁶ K·s/m² |
Solidification rate depends on front orientation and is only a small fraction of scan speed at the pool bottom. G/R falls about 570-fold from bottom to top, so the bottom tends to cellular/columnar growth and the top toward equiaxed grains.
If the top favours equiaxed grains, why do finished cross-sections show mostly long columnar grains along the build direction?
Because the next layer remelts the top. In LPBF the melt pool is often two to three times as deep as the layer (tens of µm), so the equiaxed layer formed at the top is mostly remelted by the next pass. What remains is the lower part of each pool — where high G/R grew columnar grains — and it seeds the next layer, continuing upward in the same orientation (epitaxial growth). Predicting the structure therefore requires computing remelting over several layers, not one. To promote equiaxed grains, conditions giving shallower, wider pools or alloys with added nucleating particles are used, and simulation helps find those conditions.
Practical workflow
- Calibrate the heat source in a melt-pool-scale thermal analysis against cross-section micrographs of pool shape.
- Extract G and R at the solidification front and map cooling rate and G/R.
- Predict morphology and fineness from a solidification map or correlations; compare with micrographs.
- If grain shape and orientation are needed, use cellular automata including multilayer remelting.
- Estimate strength anisotropy from the structure and use it to choose part orientation and process settings.
“The melt-pool shape is where everything starts”
When microstructure prediction goes wrong, the cause is usually not the microstructure model but the thermal analysis before it. Laser absorptivity changes greatly between powder, solid and liquid, and a pool twice as deep changes G and R at the bottom and how much is remelted. Building and sectioning single tracks, measuring pool width and depth, and fitting the heat source first makes subsequent microstructure prediction far more stable.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Uncalibrated heat source | Wrong G and R | Fit to single-track sections |
| Computing one layer only | Columnar grains missed | Include multilayer remelting |
| Taking R as scan speed | Bottom solidification rate overestimated | Correct for front orientation |
| Constant absorptivity | Wrong pool depth | State-dependent absorptivity |
| Ignoring reheating transformations | Wrong hardness and phases | Evaluate transformations from thermal history |
I'd like to learn related topics.
Frequently asked questions
What determines AM microstructure?
Mainly two quantities at the solidification front: thermal gradient G and solidification rate R (front speed). The product G×R is the cooling rate and sets fineness; the ratio G/R sets morphology (planar, cellular, columnar dendritic or equiaxed). The basic approach is to compute G and R from thermal analysis and place them on a solidification map.
How fine is LPBF microstructure?
In laser powder bed fusion cooling rates reach about 10⁶ K/s, and an empirical correlation gives 316L stainless cell spacing near 0.84 µm. Directed energy deposition at about 10³ K/s gives about 8 µm and sand casting (about 1 K/s) about 80 µm — a 100-fold difference for the same alloy.
Why are columnar grains common in AM?
At the melt-pool bottom R is small and G/R large, so grains continue epitaxially from the layer below and grow upward as columns. With a 1 m/s scan, G/R is about 5.7×10⁸ K·s/m² at the bottom and 1×10⁶ at the top, a 570-fold difference. Columnar grains along the build direction cause anisotropic strength.
References and scope of verification
Numbers are educational reference calculations under the stated assumptions. Sources document theory and setup, not proof that these numerical values were reproduced in each package. Engineering decisions require validation for the actual conditions.
Related Topics
Experience the theory firsthand with the interactive simulator for this field
All Simulators