Solidification Processing

1
Solidification Processing

• Lecture 25 Phase field models

2
Sharp interface model
3
Phase-field model
No need to chase interface location One set of
governing equations for everywhere
4
Phase field model

• Construct Ginzburg-Landau free energy
• Deriving governing equations
• Determination of parameters
• Numerical calculation of governing equations
• Interpreter numerical results

5
Free energy
6
Free energy density
7
Free energy density
8
Interface anisotropy
FCC
9
Free energy density
10
Free energy density
11
Governing equation
12
Governing equation
13
Governing equation
14
Governing equation
At equilibrium
15
Driving force
16
Parameters determination
The parameters ???, ??? and M??? in the
phase-field equation are to be matched with the
interface energy ???, interface thickness 2???
and interface propagation rate v???. ??? and ???
are determined at equilibrium condition and M???
is determined at dynamic steady condition. From
the knowledge of alloy thermodynamics, an
equilibrium state implies that the amount of each
individual phase is not changed and the common
tangent law is satisfied. For a planar interface
at equilibrium condition, the equilibrium
phase-field parameter ??e obeys the following
equation according to equation (25.16) after
taking account the relationship of ??1-??
17
Parameters determination
18
Parameters determination
19
Parameters determination
20
Parameters determination
21
Parameters determination
22
Numerical solution