Mechanisms of ’ Rafting in Single
Crystal Ni-Base Superalloys
––– A Simulation Study
AFOSR under MEANS 2
Ning Zhou; Chen Shen;
Michael J. Mills ; Yunzhi Wang;
The Ohio State University
Modeling of rafting in Ni Base superalloy
•Elastic model
Rafting direction is determined by the
sign of lattice misfit, modulus
mismatch and applied load direction.
 ( E   E ) /  E
2
γ’
P type rafting
•Plastic-elastic model
γ
Take into account the contribution from
plastic deformation inγchannels. And the
rafting direction is determined only by the
sign of lattice and applied load direction.
N type rafting
 /  E
Local stress field
Initial channel filling and
relaxation: PF dislocation model
Dislocation
configuration
External
applied stress
Dislocation stress
Misfit stress
Microstructure
Stress
Field
Dislocation
movement
•
•
•
Rafting: PF binary
diffusion model
Modulus mismatch
between /’
    ( 1   2   3 )
Microstructure
evolution
Rafting induced by channel dislocations for a homogeneous modulus system
Rafting purely due to modulus mismatch with no channel dislocations
Combining channel dislocations and modulus mismatch to evaluate their relative
contributions.
Starting configuration
Dislocation structure
Negative misfit under tension
Time evolution of g' particles in a Ni-Al alloy with -0.3% misfit under 152MPa tensile stress along [001].
Dislocations from different slip systems are represented by different colors
Positive misfit under tension
Time evolution of g' particles in a Ni-Al alloy with +0.3% misfit under 152MPa tensile stress along [001].
Time evolution of g' particles in a Ni-Al alloy with -0.3% misfit under 152MPa tensile stress along [001].
t=3.6 hrs; t=7.2 hrs; t=10.7 hrs.
Dislocations from different slip systems are represented by different colors
Time evolution of g' particles in a Ni-Al alloy with +0.3% misfit under 152MPa tensile stress along [001].
t=3.6 hrs; t=7.2 hrs.
Chemical potential plot
Chemical potential difference in different channels caused by channel dislocations is about 30~50J/mol
Effective Medium Approximation
D.Y. Li, L.Q. Chen, Scripta Materialia, Vol.37,No.9,pp1271-1277,1997
Hard precipitate
(Modulus mismatch about 40%)
Positive misfit: 0.563%
Discrete Atom Method
Jong K. Lee, Materials Science & Engineering A238(1997)1-12
Hard precipitate
(Modulus mismatch:50%)
Positive misfit: 5.0%
Equivalent strain approach
Yu U. Wang, Yongmei M. Jin, and Armen G. Khachaturyan
J. App Phys. Vol: 92, Number 31 (2002)1351-1360
Phil Mag, Vol: 85 , Issue: 2–3 ,( 2005)261-277
2D simulation of rafting due to
inhomogeneous modulus
Hard precipitate
Positive misfit
Comp
Ten
Soft precipitate
Negative misfit
Com
Ten
Positive misfit
Comp
Ten
Negative misfit
Comp
t*
Initial relaxed: misfit: +/-1.6%)
Modulus mismatch: 18%
Applied stress: +/-0.03C440
 ( E   E ) /  E
2
Ten
Negative misfit: -1.6%
Modulus mismatch: 18%
Applied stress: +/-0.03C440
No applied stress
hard precipitate
No applied stress
Soft precipitate
Plastic V.S. Elastic
Channel dislocation induced rafting with homogeneous modulus
Positive
misfit
Negative
misfit
Comp
Ten
Com
Ten
N
P
P
N
 /  E
competition
Rafting caused by inhomogeneous modulus
Hard precipitate
Soft precipitate
Positive
misfit
Positive
misfit
Negative
misfit
Negative
misfit
Comp
Ten
Com
Ten
Comp
Ten
Comp
Ten
N
P
P
N
P
N
N
P
 ( E   E ) /  E
2