Solidification - Kasetsart...

Kasetsart University

Dr.Peerapong Triyacharoen Department of Materials Engineering

213211: Imperfection

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Solidification




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Schematic Solidification Stages

Formation of Nuclei Growth of nuclei into crystals Completely solidified

Nucleation Growth




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Nucleation

vGr ∆= 3π34

Embryo

Nucleus

γππ 23 4 rGrG vT +∆=∆34

r = radius of embryo or nucleus

∆Gv = volume free energy

γ = specific surface free energy




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Homogeneous Nucleation• Occurs when the undercooling (∆T) becomes large

enough to cause formation of a stable nucleus.

THT

Gr

f

m

v ∆∆−=

∆−=

γγ 22*

r* = critical radiusTm = melting temperature∆T = undercooling (Tm – T)∆Hf = latent heat of fusion

represents the heat given up during the liquid-to-solid transformation




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Heterogeneous Nucleation• Occurs in a liquid on the surfaces of its container,

insoluble impurities, or other structural material which lower the critical free energy required to form a stable nucleus.




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Glasses• Amorphous (glassy) solid• Insufficient time for nuclei to form and grow by

rapid cooling (rapid solidification processing)

Tg Tm Temperature

Den

sity

Crystalline Solid

Glass

Undercooled liquid

Liquid




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Growth MechanismsNeed to remove two types of heat:

1. Specific heat: required to change temperature of a unit weight of the material by one degree.

2. Latent heat of fusion

Planar Growth Dendritic Growth




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Casting or Ingot Structure




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Solidification TimeTime required to completely solidify for a simple casting (ts) :

n

s AVBt ⎟

⎠⎞

⎜⎝⎛= Chvorinov’s rule

B = mold constant, depending on the properties and initial temperature of both the metal and the mold

V = volume of the castingA = surface area of the casting in contact with the moldn = constant (usually about 2)




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Effect on Structure and PropertiesmsktSDAS =

k and m = constants depending on the metal composition

Secondary Dendrite Arm Spacing:

Aluminum alloy




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Effect on Structure and Properties (con.)

Aluminum casting alloy




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Example: Design of an Aluminum CastingDesign the thickness of an aluminum casting whose length is 12 in. and

width is 8 in., in order to produce a tensile strength of 40,000 psi. The mold constant in Chvorinov’s rule for aluminum alloys cast in a sand mold is 45 min/in2.

n

s AVBt ⎟⎠⎞

⎜⎝⎛=

Solution • Required SDAS = 0.007 cm to obtain a T.S. = 42,000 psi

• Required solidification time = 300 s or 5 min

B = 45 min/in2 V = (8)(12)(x) = 96x

A = (2)(8)(12) + (2)(x)(8) + (2)(x)(12) = 40x + 192

22

1924096)min/45(min5 ⎟

⎠⎞

⎜⎝⎛

+=

xxin ⇒ 333.0)45/5(

1924096

==⎟⎠⎞

⎜⎝⎛

+xx ⇒ x = 0.77 in.

Solidification - Kasetsart...

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