Casting Thermal Analysis
Theory: what controls solidification rate
Overview
I hear the same aluminium alloy has different strength in sand and metal moulds. What differs thermally?
The slowest heat path controlling solidification differs. In sand, low conductivity means the mould absorbs heat slowly, and that sets solidification time. In a metal die the mould conducts well, but a thin gap or coating at the casting–die boundary makes heat transfer across it (the interface coefficient) the limit. A different limiting step changes both solidification time and how it scales with size — and faster solidification gives finer, stronger microstructure. Let's compare with a 20 mm aluminium plate.
Two limits for solidification time
Left: mould absorption controls (sand; Chvorinov's rule from mould properties). Right: interface heat transfer controls (metal die). The former scales with modulus V/A squared, the latter linearly.
Microstructure and validity
Secondary dendrite arm spacing λ₂ scales with roughly the 1/3 power of solidification time. The die formula applies when temperature differences within the casting are small (low Biot number).
The rise of die casting
Die casting — forcing molten metal into steel dies under pressure — began in the 19th century to mass-produce printing type. In the 20th century it spread to aluminium and zinc car parts, and today engine blocks and even large EV body sections are cast in one piece. Solidification in dies takes seconds to tens of seconds, so small differences in die cooling or interface condition strongly affect shrinkage porosity and microstructure. Solidification analysis has become essential for designing die cooling channels and gating.
Worked example: a 20 mm aluminium plate
A plate cooled from both faces (modulus 10 mm); aluminium density 2,700 kg/m³, latent heat 397 kJ/kg, melting point 660 °C (no superheat). Silica sand mould (0.6 W/mK, 1,500 kg/m³, 1,100 J/kgK) at 25 °C; metal die preheated to 300 °C.
| Mould | Solidification time | Relative arm spacing (sand = 1) |
|---|---|---|
| Sand | 226 s | 1.00 |
| Die h = 500 W/m²K | 60 s | 0.64 |
| Die h = 1,500 W/m²K | 20 s | 0.44 |
| Die h = 4,000 W/m²K | 7 s | 0.32 |
The casting's Biot number in the die cases is 0.03 to 0.20, so temperature differences within the plate are small.
Effect of thickness (die h = 1,500 W/m²K)
| Thickness | Sand | Die |
|---|---|---|
| 5 mm | 14 s | 5 s |
| 10 mm | 57 s | 10 s |
| 20 mm | 226 s | 20 s |
| 40 mm | 904 s | 40 s |
Even in a die, solidification time differs over eightfold between an interface coefficient of 500 and 4,000.
In a die, most of the thermal resistance concentrates at the interface. As the casting solidifies and shrinks it pulls away, opening a gap that can cut the coefficient several-fold mid-solidification; coating thickness and injection pressure change it too. So die solidification analyses usually calibrate this value against measured temperatures. In sand the mould itself is slow, so interface conditions hardly matter. Another difference is size dependence: doubling thickness quadruples sand time but only doubles die time. In castings mixing thick and thin sections, this changes the solidification sequence and where shrinkage forms.
Analysis tips
- First identify the mould material and whether mould or interface controls.
- For dies, calibrate the interface coefficient with temperature measurements (it may change during solidification).
- Model latent heat release via the solid fraction–temperature curve.
- Dies heat up over repeated shots; run several cycles to a steady state.
- Predict shrinkage-prone and coarse-structure regions from the solidification-time map.
“Defects only in the morning, same die”
At a die-casting plant, shrinkage defects clustered in parts made just after the morning start. The die wasn't yet warm; while it was cold, thin sections froze first and fast, cutting off feed metal to thick ones. Warming the die with a few scrap shots at start-up and monitoring die temperature before producing parts reduced defects. Die solidification analysis must include the die's thermal history.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Chvorinov for dies | Large time error | Interface-controlled formula |
| Constant interface coefficient | Wrong sequence | Calibrate with data |
| Ignoring die preheat | Start-up defects missed | Include die history |
| Latent heat at one temperature | Alloy errors | Use solidification curve |
| Constant sand properties | Time errors | Temperature dependence |
I'd like to learn related topics.
Try the Chvorinov solidification tool and riser design tool. Related pages include casting solidification, mushy zone and Stefan problem.
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