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

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

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.

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 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 Equivalent strain approach 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 Soft precipitate Positive misfit Negative misfit Comp Ten Com t* Initial relaxed: misfit: +/-1.6%) Modulus mismatch: 18% Applied stress: +/-0.03C440

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 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

Questions?