Solidification Simulation in Casting
Theory: where solidifies last
Overview
Our aluminium castings get shrinkage cavities in thick sections. What can solidification simulation tell us?
Metal shrinks a few percent as it solidifies. If liquid remains around it, that liquid flows in to fill the shrinkage; but liquid trapped by already-solid surroundings solidifies last with nothing to feed it, leaving a cavity — shrinkage porosity. The main purpose of solidification simulation is to find where solidifies last and whether a feeding path from the riser stays open until the end. Start with a simple formula to estimate solidification time by shape.
Chvorinov's rule
$V/A$ is volume ÷ surface area in contact with the mould, called the modulus. Stored heat scales with volume and loss to the mould with surface area, so this ratio sets solidification time. Different shapes with the same modulus solidify in roughly the same time.
Constant B from properties
Sand conducts poorly, so its heat absorption (the product of mould conductivity, density and specific heat) controls solidification rate. $\rho_m$ is melt density, $L'$ latent heat plus the superheat, $T_m$ the melting point and $T_0$ initial mould temperature. In permanent (metal) moulds the metal–mould interface resistance dominates and this formula doesn't apply.
A 1940 rule still gives the first estimate
In 1940 the Czech engineer Chvorinov measured solidification times of many castings and summarised them as proportional to the square of the volume-to-surface ratio. Before computers, foundry engineers sized and placed risers with this rule and experience. Later, finite-element and finite-difference methods computed temperatures in detail, and from the 1980s dedicated software coupling mould filling and solidification predicted misruns and shrinkage. Even so, modulus calculations are still used to compare design options at the earliest stage.
Worked examples
Example 1: constants by metal
Silica-sand mould (conductivity 0.52 W/(m·K), density 1,600 kg/m³, specific heat 1,170 J/(kg·K)), initial mould temperature 25 °C, 50 K superheat:
| Metal | Constant B |
|---|---|
| Aluminium | 3.9 min/cm² |
| Cast iron | 3.7 min/cm² |
| Steel | 2.9 min/cm² |
Example 2: shape, modulus and solidification time
| Shape | Volume | Modulus | Aluminium | Steel |
|---|---|---|---|---|
| Cube 50 mm | 125 cm³ | 8.3 mm | 2.7 min | 2.0 min |
| Plate 200×200×20 mm | 800 cm³ | 8.3 mm | 2.7 min | 2.0 min |
| Cube 100 mm | 1,000 cm³ | 16.7 mm | 10.7 min | 8.1 min |
| Cylinder D100 × H100 mm | 785 cm³ | 16.7 mm | 10.7 min | 8.1 min |
The plate is over six times heavier than the cube, yet solidifies in the same time.
Yes — a thin, wide plate has lots of surface to shed heat. Conversely, the regions with the largest modulus — thick, with little surface — solidify last. In a plate joined to a thick boss, the boss solidifies later and is where shrinkage tends to form. Computing modulus section by section flags risky spots even before simulation. Doubling the modulus quadruples solidification time, so differences are stark.
Example 3: riser size
The riser must solidify after the casting, so its modulus is about 1.2 times the casting's (about 1.44 times the time). A cylindrical riser with equal diameter and height has a modulus of one-sixth its diameter, so a 100 mm cube (16.7 mm) needs about 120 mm diameter and height, and the plate (8.3 mm) about 60 mm. The riser also needs enough volume to supply the casting's shrinkage; size it to satisfy both.
How to approach the analysis
Procedure
- Compute section moduli, identify last-to-freeze regions and propose riser locations.
- Analyse mould filling for misruns and entrainment.
- Run solidification analysis for temperature history and find isolated liquid pockets (hot spots) from solid-fraction maps.
- Assess shrinkage tendency with criteria such as Niyama and revise risers and chills.
Cautions
- Interface resistance: with metal moulds and chills, the metal–mould gap resistance dominates and grows as solidification shrinkage opens the gap.
- Alloy freezing range: alloys solidify over a range; wide mushy zones spread porosity.
- Latent heat: large time steps can skip it.
“A bigger riser didn't cure the shrinkage”
The riser was enlarged, yet a cavity remains in the same place — usually because a thin section between riser and cavity freezes first, closing the feeding path. However big the riser, it can't feed through a closed path. Use solidification analysis to check over time whether a liquid path stays connected from the riser to the problem area, then thicken the intervening section (padding) or move the riser. The order in which feeding paths close matters as much as riser size.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Judging by riser size alone | Feeding path closes early | Track liquid connectivity over time |
| Using sand constants for metal moulds | Wrong solidification time | Include interface resistance |
| Looking only at total time | Hot spots missed | Section moduli |
| Solidification without filling | Wrong initial temperatures | Couple filling and solidification |
| Ignoring freezing range | Wrong porosity morphology | Use solid-fraction curves |
I'd like to try solidification-time and riser calculations myself.
Try the Chvorinov solidification time tool for solidification time and the riser design tool for riser size. Solidification theory is covered in the Stefan problem, the mushy zone and melting and solidification, and latent-heat handling in latent-heat modelling.
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