$t_s$: solidification time [min]; $B$: mold constant [min/cm²]; $M$: modulus [cm]; $n\approx2$. Modulus is volume divided by cooling area, and the shell grows as $\delta(t)\propto\sqrt{t}$ (parabolic law).
The riser must solidify after the casting. A modulus ratio of $1.2$ gives about $1.44\times$ the solidification time at $n=2$, feeding molten metal until the casting freezes and preventing shrinkage porosity. A sphere has $M=r/3$ and a cube $M=a/6$.
What is Chvorinov’s rule
Chvorinov’s rule is an empirical relation stating that the solidification time $t_s$ scales with a power of the modulus $M=V/A$ (volume divided by cooling area): $t_s=B\,M^n$ ($n\approx2$), where $B$ is a mold constant bundling alloy, mold, and superheat.
Intuitively, a chunkier casting (larger modulus) holds more heat inside, cools slowly, and freezes later. A thin, spread-out shape has a small modulus and solidifies quickly.
This tool draws, in real time, a casting cross-section growing a solid shell inward from the mold wall while the liquid core shrinks and the centre freezes last. The shell thickness grows as the square root of time (parabolic law).
Physical model and key equations
Solidification time: $t_s=B(V/A)^n=B\,M^n$. Modulus: $M=V/A$. For a sphere $V=\tfrac{4}{3}\pi r^3$, $A=4\pi r^2$, so $M=r/3$. For a cube $M=a/6$. For a thin plate (cooled both faces) $M\approx t/2$ ($t$ = plate thickness).
Shell growth follows the parabolic law $\delta(t)=\delta_{max}\sqrt{t/t_s}$. Full solidification is reached at $t=t_s$, and the solidified fraction is evaluated on a volume basis.
Riser design: $t_{riser}/t_{cast}=(M_{riser}/M_{cast})^n$. If the riser freezes after the casting, it feeds molten metal to compensate solidification shrinkage to the end, preventing shrinkage porosity.
How to read it
In the animation, watch how fast the outer solid shell (pale blue) thickens while the central liquid core (orange) shrinks.
On the time-vs-modulus curve, read where the current operating point sits and how steeply time rises as modulus increases.
On the casting-vs-riser bars, confirm the riser freezes later than the casting (its bar extends further right). If reversed, raise the riser modulus ratio.
Learn Chvorinov solidification by dialogue
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Does a casting freeze from the outside? In the animation the edges turn blue while the centre stays orange the longest.
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Yes. Heat escapes through the mold wall, so a solid shell forms at the surface and thickens inward. Shell thickness grows as the square root of time (parabolic law), so it is fast early and slow later. The centre, which freezes last, is the hot spot.
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Why does the modulus M=V/A set the solidification time? Why not volume alone?
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Volume stores heat and surface area releases it, so the ratio V/A is what matters. A sphere is M=r/3, a cube M=side/6. Spread the same volume thin and M drops, so it freezes faster. Chvorinov’s rule t=B·M² means time goes as the square of that ratio.
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What is the riser for? There is an extra reservoir of metal beside the casting.
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Metal shrinks as it freezes, and without make-up metal a cavity (shrinkage porosity) forms inside. Design the riser to freeze after the casting and it feeds molten metal the whole time the casting solidifies. That is why the riser modulus is larger. On the comparison bars, the riser should extend further right than the casting.
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How much larger should the riser be?
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The rule of thumb is a riser modulus about 1.2× the casting. At n=2 the time becomes 1.2²≈1.44×, giving ample margin. Drop the ratio to 1.0 with the slider and you will see the riser and casting freeze almost together, the risky case. Calibrate for the actual alloy and mold in the end.
Real-world applications
Initial riser sizing: back-calculate the required riser modulus from the casting modulus.
Comparing how thickness changes affect solidification time: quickly check how a design change alters freezing.
Screening design options before CAE casting (solidification) analysis: estimate hot-spot locations across concepts.
Common misconceptions and cautions
Volume alone does not set solidification time; the ratio to cooling area (modulus) dominates.
Do not count gating or non-cooling faces in the cooling area (avoid over-estimation); count only the effective mold-contact area.
The constant B varies strongly with alloy, mold, and superheat, so calibrate it with measurements. Chvorinov’s rule is for first-pass screening; combine detailed analysis, standards, and measured data for final decisions.
FAQ
Read solidification time and modulus first. Then use the cross-section animation to see how the shell grows, and the casting-vs-riser comparison to confirm the riser freezes after the casting. Check whether the cooling area is sufficient for the volume.
In Chvorinov’s rule t=B·M^n the solidification time goes as a power of the modulus. Modulus is volume over cooling area, larger for chunkier castings, which freeze more slowly. A sphere gives M=r/3 and a cube M=side/6.
The riser must solidify after the casting. A larger riser modulus lengthens its solidification time so it feeds molten metal until the casting freezes, preventing shrinkage porosity. A riser modulus of about 1.2× the casting is common for margin.
Chvorinov’s rule is an empirical relation where solidification time scales with a power of modulus V/A. Alloy, mold, superheat, and riser details need separate checks. Final decisions still require standards, measured data, detailed analysis, and vendor limits.
How to Use
Enter the casting volume [cm³] (e.g. 500 cm³ for a steel part)
Enter the cooling area [cm²] (e.g. 800 cm² for a complex shape)
Set the mold constant B (slider 0.02–8 min/cm²; roughly 1–3 for sand)
Adjust the exponent n (typically 1.5–2.5, near 2.0 for sand)
Watch the shell grow outside-in in the animation while solidification time [min] and modulus update in real time
Worked Example
Ductile iron (FCD450) thick section: V=800 cm³, A=1200 cm², B=1.6 min/cm², n=2. Modulus M=V/A=0.667 cm. Chvorinov’s rule t=B×M^n gives t≈1.6×(0.667)²≈0.71 min (≈43 s). A riser modulus 1.2× larger gives about 1.44× the time, feeding metal until the casting freezes. Calibrate B for the actual alloy, mold, and superheat.
Practical Notes
Count only mold-contact area; exclude internal gating (avoid over-estimation)
For large casings (V>2000 cm³), raise B (slow-cooling correction)
Riser sizing: apply about a 1.3× safety factor on solidification time (anti-shrinkage)
Aluminum A356 uses B ≤ 8; faster cooling than steel (≈3× conductivity)
For complex gating, pre-check the effect of ±20% area variation via sensitivity
