Ning Zhou; Chen Shen; Michael J. Mills ; Yunzhi Wang;

The Ohio State University

AFOSR under MEANS 2

Mechanisms of ’ Rafting in Single Crystal Ni-Base Superalloys

––– A Simulation Study

Modeling of rafting in Ni Base superalloy

•Elastic model

•Plastic-elastic model

Rafting direction is determined by the sign of lattice misfit, modulus

mismatch and applied load direction.

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.

P type rafting

N type rafting

γ’

γ

/ E

2( ) /E E E

Local stress field

External applied stress

Dislocationconfiguration Microstructure

StressField

Misfit stressDislocation stress

Dislocation movement

Microstructureevolution

Initial channel filling and relaxation: PF dislocation model

Rafting: PF binary diffusion model

)( 321

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.

Starting configuration

Dis

loca

tion

stru

ctur

e

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

Negative misfit under tension

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

Positive misfit under tension

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 difference in different channels caused by channel dislocations is about 30~50J/mol

Chemical potential plot

Effective Medium Approximation

Hard precipitate(Modulus mismatch about 40%)

Positive misfit: 0.563%

Discrete Atom Method

Hard precipitate(Modulus mismatch:50%)

Positive misfit: 5.0%

Jong K. Lee, Materials Science & Engineering A238(1997)1-12

D.Y. Li, L.Q. Chen, Scripta Materialia, Vol.37,No.9,pp1271-1277,1997

Yu U. Wang, Yongmei M. Jin, and Armen G. KhachaturyanJ. App Phys. Vol: 92, Number 31 (2002)1351-1360Phil Mag,  Vol:  85 , Issue:  2–3 ,( 2005)261-277

Equivalent strain approach

Hard precipitate Soft precipitate

Positive misfit Negative misfit Positive misfit Negative misfitComp Ten Com Ten Comp Ten Comp Ten

Initial relaxed: misfit: +/-1.6%)Modulus mismatch: 18%

2D simulation of rafting due toinhomogeneous modulus

Applied stress: +/-0.03C440

t*

2( ) /E E E

No applied stress

Soft precipitate

No applied stress

hard precipitate

Negative misfit: -1.6%Modulus mismatch: 18% Applied stress: +/-0.03C44

0

Hard precipitate Soft precipitatePositive

misfitNegative

misfitPositive

misfitNegative

misfitComp Ten Com Ten Comp Ten Comp Ten

N P P N P N N P

Plastic V.S. Elastic

Channel dislocation induced rafting with homogeneous modulus

Positive misfit

Negative misfit

Comp Ten Com Ten

N P P N

Rafting caused by inhomogeneous modulus

/ E

2( ) /E E E

competition