The empirical rule that the solidification time of a casting is proportional to the square of the ratio of its volume V to surface area A (the modulus), t = B(V/A)². It is used in sizing risers.
Japanese name: チボリノフの法則
Chvorinov's rule appears in 2 practice questions across 2 topics, including Metals and alloys, Solidification and cast structures.
Answer: B. 16 minutes
For a cube of side a, V/A = a³/(6a²) = a/6, so V/A ≈ 8.3 mm for 50 mm and about 16.7 mm for 100 mm, exactly twice as large. The solidification time is proportional to the square of V/A, so t = 4.0 × 2² = 16 minutes. 8.0 minutes assumes the solidification time is proportional to size, and 32 minutes assumes it is proportional to volume and multiplies by 8. Larger castings take longer to solidify and have coarser structures. Because a riser (the feeder that supplies molten metal) cannot compensate for shrinkage cavities unless it solidifies after the casting, this rule is also the basis for designing risers with a larger V/A than the casting.
Answer: A. About 15 minutes
Even at the same volume, a sphere has the smallest surface area of any shape, so its V/A (modulus) is larger. For a cube of edge a, V/A = a/6 ≈ 0.167a. The radius of a sphere of the same volume is r = (3a³/4π)^(1/3) ≈ 0.620a, so V/A = r/3 ≈ 0.207a, about 1.24 times that of the cube. The solidification time is the square of this, about 1.54 times, giving 10 × 1.54 ≈ 15 minutes. About 12 minutes assumes the time is proportional to V/A, and 10 minutes is the mistake of thinking that the same volume means the same solidification time. A riser must stay liquid longer than the casting it feeds, so it is given a shape that makes V/A large for the amount of metal, such as a sphere or a cylinder with height about equal to its diameter.
Shrinkage cavity Constitutional supercooling Dendrite Dendrite arm spacing Equilibrium partition coefficient Eutectic modification Macrosegregation Scheil equation