English
Menu

Solidification and cast structures

Suppose Chvorinov's rule t = B(V/A)² holds (t is the solidification time, V the volume, A the surface area and B a constant). Under the same mold conditions, a cube-shaped casting of a certain volume solidified in 10 minutes. Which is closest to the solidification time of a spherical casting of the same volume?

  1. AAbout 15 minutes
  2. BAbout 12 minutes
  3. C10 minutes
Show answer and explanation

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.

Report an error

Practice this topic Back to topic

More Solidification and cast structures questions

  1. Which is a correct assumption behind the Scheil equation Cs = kC₀(1 − fs)^(k−1) (fs is the fraction solid), which gives the composition of the solid forming during solidification?
  2. An Al-4.0 wt%Cu alloy is solidified. Assume the Scheil equation holds (equilibrium partition coefficient k = 0.17, constant), so the concentration of the remaining liquid rises as CL = C₀(1 − fs)^(k−1). Which is closest to the fraction of liquid remaining when the liquid reaches the eutectic composition of 33.2 wt%Cu (this becomes non-equilibrium eutectic)? On the equilibrium phase diagram, this composition lies within the maximum solubility of the α phase (5.65 wt%).
  3. Which is the correct pairing of additions to a hypoeutectic Al-Si casting alloy and their main effects?
  4. When a regular lamellar eutectic is directionally solidified, the lamellar spacing λ and growth rate V obey λ²V = constant. At a growth rate of 10 µm/s, λ = 2.0 µm. Which is closest to λ when the growth rate is raised to 160 µm/s?
  5. Take the densities of pure aluminum at its melting point (660 °C) as 2.375 g/cm³ for the liquid and 2.55 g/cm³ for the solid. Which is closest to the decrease in volume relative to the liquid volume (solidification shrinkage) when the liquid turns entirely into solid at the melting point?