1. The Ohio State University
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

2. 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. 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

3. Local stress field Stress Field External applied stress Dislocation
configuration
Microstructure
Stress Field
Misfit stress
Dislocation stress
Dislocation movement
Microstructure evolution
Initial channel filling and relaxation: PF dislocation model
Rafting: PF binary diffusion model
Stress due to modulus mismatch
Modulus mismatch between /’
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.

4. Starting configuration

5. Dislocation structure

7. 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

8. Positive misfit under tension
Time evolution of g' particles in a Ni-Al alloy with +0.3% misfit under 152MPa tensile stress along [001].

9. Time evolution of g' particles in a Ni-Al alloy with -0
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.

10. Chemical potential plot
Chemical potential difference in different channels caused by channel dislocations is about 30~50J/mol

11. Effective Medium Approximation Equivalent strain approach
D.Y. Li, L.Q. Chen, Scripta Materialia, Vol.37,No.9,pp ,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) Phil Mag,  Vol:  85 , Issue:  2–3 ,( 2005)

12. 2D simulation of rafting due to inhomogeneous modulus
Hard precipitate
Soft precipitate
Positive misfit
Negative misfit
Comp
Ten
Com t*
Initial relaxed: misfit: +/-1.6%) Modulus mismatch: 18%
Applied stress: +/-0.03C440

13. Negative misfit: -1.6% Modulus mismatch: 18%
Applied stress: +/-0.03C440
No applied stress
hard precipitate
No applied stress
Soft precipitate

14. Plastic V.S. Elastic N P Hard precipitate Soft precipitate N P
Channel dislocation induced rafting with homogeneous modulus
Positive misfit
Negative misfit
Comp
Ten
Com N P
competition
Rafting caused by inhomogeneous modulus
Hard precipitate
Soft precipitate
Positive misfit
Negative misfit
Comp
Ten
Com N P

15. Questions?