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Kasetsart University
Dr.Peerapong Triyacharoen Department of Materials Engineering
213211: Imperfection
75
Solidification
Kasetsart University
Dr.Peerapong Triyacharoen Department of Materials Engineering
213211: Imperfection
76
Schematic Solidification Stages
Formation of Nuclei Growth of nuclei into crystals Completely solidified
Nucleation Growth
Kasetsart University
Dr.Peerapong Triyacharoen Department of Materials Engineering
213211: Imperfection
77
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
Kasetsart University
Dr.Peerapong Triyacharoen Department of Materials Engineering
213211: Imperfection
78
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
Kasetsart University
Dr.Peerapong Triyacharoen Department of Materials Engineering
213211: Imperfection
79
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.
Kasetsart University
Dr.Peerapong Triyacharoen Department of Materials Engineering
213211: Imperfection
80
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
Kasetsart University
Dr.Peerapong Triyacharoen Department of Materials Engineering
213211: Imperfection
81
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
Kasetsart University
Dr.Peerapong Triyacharoen Department of Materials Engineering
213211: Imperfection
82
Casting or Ingot Structure
Kasetsart University
Dr.Peerapong Triyacharoen Department of Materials Engineering
213211: Imperfection
83
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)
Kasetsart University
Dr.Peerapong Triyacharoen Department of Materials Engineering
213211: Imperfection
84
Effect on Structure and PropertiesmsktSDAS =
k and m = constants depending on the metal composition
Secondary Dendrite Arm Spacing:
Aluminum alloy
Kasetsart University
Dr.Peerapong Triyacharoen Department of Materials Engineering
213211: Imperfection
85
Effect on Structure and Properties (con.)
Aluminum casting alloy
Kasetsart University
Dr.Peerapong Triyacharoen Department of Materials Engineering
213211: Imperfection
86
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.