Solidification time and special casting processes
How castings freeze and shrink, Chvorinov's rule with casting moduli and riser rules, and the special casting processes – shell, investment, lost-foam, permanent-mould, die, low-pressure, squeeze, centrifugal and continuous casting.
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Why it matters
How fast a casting freezes decides its grain size, its strength and whether shrinkage cavities appear in the wrong place – so solidification time is the basis of every riser design. The special casting processes are how the automotive industry makes aluminium wheels and gearbox housings (die and low-pressure casting), turbocharger wheels (investment casting) and cylinder liners (centrifugal casting) with finishes and tolerances that sand moulds cannot reach.
Key ideas
How a casting freezes. Metal poured above its liquidus first loses superheat, then releases latent heat while it solidifies, then cools as a solid. Against the cold mould wall a thin chill zone of fine equiaxed grains forms, then columnar grains grow inward along the heat-flow direction, and in alloys a central equiaxed zone may form. A pure metal or eutectic freezes at one temperature with a smooth front (skin-forming); an alloy with a wide freezing range forms a mushy zone of dendrites and liquid, which is harder to feed and prone to dispersed porosity.
Shrinkage has three parts: liquid contraction (superheat removal), solidification shrinkage (typically a few per cent by volume for steel and aluminium; grey iron can be almost zero or even expand because graphite precipitates) and solid contraction. Risers feed the first two; the pattern's shrinkage allowance covers the third.
Chvorinov's rule. Heat flows out through the casting surface, while the amount of heat to remove is proportional to the volume, so freezing time scales with the modulus M = V/A. For a sand mould the result is t_s = B·(V/A)ⁿ with n ≈ 2. The mould constant B depends on the metal (density, latent heat, superheat) and on the mould material (its thermal conductivity, density and specific heat). Metal moulds extract heat much faster than sand, so B is far smaller for permanent moulds. B is found experimentally – from a test casting or a data book – and is typically of the order of a few s/mm² for sand moulds.
Consequences:
- Of all shapes with the same volume, a sphere has the smallest surface area and freezes slowest; thin plates and fins freeze fastest.
- A riser must have a larger modulus than the section it feeds – a common rule is M_riser ≥ 1.2·M_casting (about 44 % more freezing time). The best practical riser is a cylinder with H ≈ D.
- Directional solidification – freezing should progress from the thinnest, farthest section towards the riser so that a liquid feed path always exists. Chills (metal inserts) speed up freezing locally; insulating sleeves and exothermic toppings slow down the riser.
Special casting processes.
- Shell moulding – resin-coated sand cured on a heated metal pattern forms thin shells; good finish and accuracy, suited to small/medium parts in volume.
- Investment (lost-wax) casting – wax patterns are dipped repeatedly in ceramic slurry and stucco, dewaxed and fired, then poured. Very complex shapes, thin walls, excellent finish, almost any alloy (including superalloys for turbo wheels); costly per part, size limited.
- Lost-foam (evaporative pattern) casting – an expanded polystyrene pattern stays in unbonded sand and vaporises as metal enters; no parting line or cores; used for engine blocks and heads.
- Permanent-mould (gravity die) casting – reusable metal mould filled by gravity; good properties from fast cooling; mainly Al, Mg, Cu alloys.
- Pressure die casting – metal injected at high pressure into hardened steel dies. Hot-chamber machines (injection unit immersed in the melt) suit low-melting alloys such as Zn, Sn, Pb and some Mg; cold-chamber machines (metal ladled into a shot sleeve for each shot) are used for Al, Mg and Cu alloys. Very high rates, thin walls, fine finish; porosity from trapped air limits heat treatment and welding.
- Low-pressure die casting – metal pushed upward from a sealed furnace by gas pressure (about 0.1 bar or so) into the die; quiet filling; aluminium wheels and cylinder heads.
- Squeeze casting – pressure applied during solidification; near-forging properties.
- Centrifugal casting – true centrifugal (no core; hollow shapes such as pipes and cylinder liners, outer skin densest, inclusions collect at the bore and are machined off), semi-centrifugal (axisymmetric solid parts such as wheels and pulleys) and centrifuging (several small cavities around a central sprue).
- Continuous casting – molten steel solidifies in a water-cooled copper mould and is withdrawn continuously as slabs, blooms or billets for rolling.
Formulas
t_s = B·(V / A)ⁿ
t_s = solidification time (s or min), V = volume (m³ or mm³), A = cooling surface area (same length units squared), B = mould constant (s/mm² or s/m² – keep units consistent), n ≈ 2 (some texts use 1.5–2).
t₂ / t₁ = (M₂ / M₁)²
Comparing two castings in the same mould and metal (same B, n = 2); M = V/A.
M_cube = a / 6 M_sphere = D / 6 M_long cylinder = D / 4 M_cylinder (H = D) = D / 6 M_large plate = thickness / 2
All surfaces cooling (for the plate, edges neglected).
M_riser ≥ 1.2·M_casting
Modulus rule for risers (empirical).
G = ω²·R / g N = (60 / 2π)·√(G·g / R)
Centrifugal casting: G = G-factor (dimensionless, take a suitable value from a data book), ω = angular speed (rad/s), R = radius (m), g = 9.81 m/s², N = speed (rpm).
Worked examples
Example 1 (standard) – shape effect. A cube and a sphere each have volume 1.0 × 10⁶ mm³ and are cast in the same sand mould. Compare their freezing times.
- Cube: a = 100 mm, M = a/6 = 16.67 mm.
- Sphere: D = (6V/π)^(1/3) = (6 × 10⁶/π)^(1/3) = 124.07 mm, M = D/6 = 20.68 mm.
t_sphere/t_cube = (M_sphere/M_cube)²= (20.68/16.67)² = 1.54. The sphere takes about 54 % longer.
Example 2 (GATE level) – using a test casting to find B. A 100 mm cube freezes in 10 min in a sand mould. Find B and the freezing time of a cylinder D = 100 mm, H = 150 mm, in the same mould and metal.
- Cube: M = 100/6 = 16.67 mm;
B = t/M²= 600 s/(16.67 mm)² = 2.16 s/mm². - Cylinder: V = (π/4)(100²)(150) = 1.178 × 10⁶ mm³.
- A = πDH + 2(πD²/4) = 47 124 + 15 708 = 62 832 mm².
- M = V/A = 18.75 mm.
- t = 2.16 × 18.75² = 759 s = 12.7 min.
Example 3 – centrifugal casting speed. A cylinder liner of outer diameter 300 mm is cast with a G-factor of 65. ω = √(65 × 9.81/0.15) = 65.2 rad/s, so N = 65.2 × 60/(2π) ≈ 623 rpm.
Common mistakes
- Treating B as universal. It is specific to the metal–mould pair and pouring temperature, and its units follow the length units used for V/A.
- Using the riser's total surface area when one face is attached to the casting (that face does not cool) – read the question's assumption.
- Comparing shapes by volume instead of modulus.
- Assuming a bigger riser always helps; a riser placed where no feed path exists cannot feed.
- Mixing up hot-chamber and cold-chamber die casting: aluminium is cold-chamber because molten Al attacks the immersed steel injection parts.
- Forgetting that in true centrifugal casting the impurities gather at the inner surface, not the outer.
For GATE ME
Expect Chvorinov ratio problems (two shapes in the same mould, finding B from a test casting, riser size for a given safety factor), moduli of cubes, cylinders, spheres and plates, and matching questions: process ↔ product ↔ alloy (hot vs cold chamber, investment, centrifugal, shell, lost-foam, continuous casting). Practise writing V and A for composite shapes and deciding which faces cool.
Quick check
- For the same volume, which freezes slowest: cube, sphere or plate?
- If the modulus doubles, how does freezing time change?
- Which die-casting machine is used for aluminium?
- A 60 mm cube freezes in 3 min. How long does a 120 mm cube take in the same mould?
- In true centrifugal casting, where do inclusions collect?
Answers: 1. Sphere; 2. Four times; 3. Cold-chamber; 4. 12 min; 5. At the inner (bore) surface.
Interview questions
All Engineering Materials and Manufacturing Processes interview questionsTry answering each one aloud before you open it.
1.What is solidification time in the context of casting processes?Concept
Solidification time is the duration required for a molten metal to transition from a liquid to a solid state within a mold. It is a critical factor in casting processes as it affects the microstructure and mechanical properties of the final product. The solidification time is influenced by factors such as the thermal properties of the metal, the mold material, and the geometry of the casting.
2.Explain Chvorinov's rule and its significance in casting.Concept
Chvorinov's rule states that the solidification time of a casting is t_s = B·(V/A)ⁿ, with n ≈ 2, where V/A is the casting modulus and B is a mould constant that depends on the metal (latent heat, density, superheat) and the mould material's ability to absorb heat. It follows because the heat to remove scales with volume while the heat flows out through the surface area. Its main use is riser design: a riser must have a larger modulus than the section it feeds (typically about 1.2 times) so that it freezes last and keeps feeding shrinkage.
3.Why is it important to control the solidification time in casting processes?Application
Controlling the solidification time is crucial because it affects the quality and properties of the final casting. A controlled solidification process can minimize defects such as porosity, shrinkage, and internal stresses. It also influences the grain structure, which in turn affects the mechanical properties like strength and ductility. Proper control ensures that the casting meets the desired specifications and performance criteria.
4.What is investment casting and where is it typically used?Concept
Investment casting, also known as lost-wax casting, is a process where a wax pattern is coated with a refractory ceramic material to create a mold. Once the ceramic material hardens, the wax is melted away, leaving a cavity for molten metal to be poured into. This process is used for producing complex and detailed components with high dimensional accuracy, such as turbine blades, jewelry, and dental fixtures.
5.Explain the difference between sand casting and die casting.Concept
Sand casting involves creating a mold from a sand mixture, into which molten metal is poured. It is suitable for large and complex shapes but has a rough surface finish. Die casting, on the other hand, uses a metal mold and is typically used for high-volume production of small to medium-sized parts with a smooth surface finish. Die casting provides better dimensional accuracy and surface finish compared to sand casting.
6.What happens if the cooling rate is too fast during the solidification process?Application
Fast cooling gives finer grains and usually higher strength, which is why chills and metal moulds are used deliberately. But if it is too fast the metal may freeze before the mould is full (misrun or cold shut), thin sections may freeze off and cut the feed path so shrinkage cavities form elsewhere, and steep thermal gradients cause residual stress, distortion or hot tears. In cast iron, very fast cooling suppresses graphite and gives hard, brittle chilled (white) iron at the surface.
7.Why is directional solidification important in casting processes?Application
Directional solidification means the casting freezes progressively from the sections farthest from the riser towards the riser, so every region that is still shrinking stays connected to liquid metal. If a thick section is isolated by thinner sections that freeze first, its shrinkage cannot be fed and a shrinkage cavity forms there. Designers achieve it by placing risers at heavy sections, tapering sections towards the riser, and using chills to speed up freezing and insulating sleeves or exothermic toppings to slow down the riser.
8.Calculate the solidification time for a casting with a volume of 0.002 m³ and a surface area of 0.1 m², given a mould constant B = 2 s/mm² and n = 2.Numerical
Modulus V/A = 0.002/0.1 = 0.02 m = 20 mm. Using Chvorinov's rule, t = B·(V/A)² = 2 s/mm² × (20 mm)² = 800 s ≈ 13.3 min. The units of B must match the length unit used for the modulus; a mould constant of only a few s/m² would give an unrealistic sub-second time.
9.What is centrifugal casting and what are its advantages?Concept
Centrifugal casting is a process where molten metal is poured into a rotating mold. The centrifugal force pushes the metal against the mold walls, creating a dense and uniform casting. This process is advantageous for producing cylindrical parts like pipes and rings, as it reduces impurities and porosity. It also allows for the production of parts with a fine-grained microstructure and good mechanical properties.
10.If a casting has a high volume-to-surface area ratio, how does it affect the solidification time?Application
A high volume-to-surface area ratio means that the casting has a larger volume relative to its surface area. According to Chvorinov's Rule, this results in a longer solidification time because the heat takes longer to dissipate through the smaller surface area. This can lead to a coarser grain structure and potentially more defects if not properly managed.
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