Shuwei Ma, Tresa.M.Pollock

The University of Michigan, Ann Arbor, MI

Ni-Al-Mo Single Crystal Rafting Studies

MEANS Group Meeting, Columbus, OHApril, 4, 2007

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 in γ channels (continuum). Rafting direction is determined only by the sign of lattice misfit and applied load direction.

P type rafting

N type rafting

γ’

γ

/ E

2( ) /E E E

Previous Models of Rafting

Accounting for Local Stress Fields with Phase Field Model

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 /’

Michael Mills’s plot

Phase field modeling was applied to evaluate elastic and plastic driving force in the Ni-Al-Mo system.

Objective

Provide a complete experimental data set in model Ni-Al-Mo single crystals for phase field modeling.

This information includes:

1. Misfit (sign and magnitude)2. Plastic strain processes in matrix3. Elastic modulus4. Diffusion5. Rafting kinetics

References

1. M.Fahrmann, W.Hermann, E, Fahrmann, A.Boegli, T.M.Pollock. Materials Science and Engineering A260 (1999) pp.212-221.

2. O.Paris, M.Fahrmann, E.Fahrmann, T.M.Pollock and P.Fratzl. Acta mater. Vol.45, No.3, 1997, pp.1085-1097.

3. M.Fahrmann, E.Fahrmann, O.Paris, P.Fratzl, and T.M.Pollock. Superalloy 1996, pp.191-200.

4. M.Fahrmann, P.Fratzl, O.Paris, E.Fahrmann and W.C.Johnson. Acta Metall.Mater, Vol.43, No.3, pp.1007-1022.

5. M.Fahrmann, E.Fahrmann, T.M.Pollock, W.C.Johnson. Metallurgical and materials Transactions A. pp.1943-1945.

Many properties have already been measured in a large set of Ni-Al-Mo single crystals

Experimental Methods

1. Observation of rafting and coarsening of ’ precipitate: SAXS (small angle X-ray scattering)Quantitatively image analysis on TEM and SEM ( Fourier Analysis)

2. Misfit measurementHot stage X-ray diffraction on over-aged sample, unconstrained misfit. (210) diffraction.

3. Elastic Constant measurementFree-free beam resonance technique.

4. Diffusion data

Ternary Ni-Al-Mo Phase Diagram

V’60% V’10%

Single Crystal Compositions

Coherency Stress and Precipitate Coarsening in Ni-Al-Mo Alloys

V’0.1

Coherency Stress and Precipitate Coarsening in Ni-Al-Mo Alloys

•The coarsening rate decreases with increasing Mo content of alloy •A change in the rate controlling mechanism of coarsening from long range diffusion of Al to long range diffusion of Mo in this series of alloys.

ktrtr 30

3 )(

13 at% Mo

8 at% Mo5 at% Mo

Misfit And Rafting in Experimental Alloys

Misfit and Rafting in Experimental Ni-Al-Mo system

R1, Positive misfit > 0

R3, Negative misfit, < 0

• Elastic and plastic rafting models can predict these observation.• Do rafting kinetics distinguish elastic and plastic effects?

Young’s Modulus

Elastic Stiffness of and ’ phases in Ni-Al-Mo

Elastic Modulus Mismatch

R3, =-0.5%

R1, =+0.5%

For elastically anisotropic materials, the term E’-E has to be replaced by the differential C*, i.e, (C11-C12)’- (C11-C12)

For Elastic model:

2' )(/)( EEE

-5 0 5 10 15 20 25 30 35 40

1

2

3

4

5

6 Fully rafted

Asp

ect

Ra

tio

Creep Time (hrs)

R3, Ni-13.3Al-8.8Mo (at%)misfit -0.5%, (Fahrmana)

R1, Ni-19.5Al-0.5Mo (at%)Misfit +0.5%, (Ma)

Average Precipitate Aspect Ratio During Creep

R1 alloy with positive misfit has a lower rate of rafting in spite of less Mo. C*

R3>C*R1. Effect of elastic modulus mismatch?

Creep condition: 980°C/130MPa.

For Elastic model:

2' )(/)( EEE

Role of Matrix Plasticity in the Rafting Kinetics

Ni-13.3Al-8.8Mo (at%)Misfit, =-0.5%,V’=0.60

Kinetics and the driving force of rafting are greatly affected by the state of the /’ interfaces.

Microstructure Evolution During Stress Annealing and Aging for Pre-strained interface

•The microstructure in samples pre-strained in tension or compression rafted during subsequent aging in a direction as if the former load was still present, whereas a sample with isotropically relaxed interfaces did not show directional coarsening;

•The microstructure in a sample pre-strained in tension rafted under an applied compressive stress initially in a direction opposite to what is generally observed in compression for this alloy.

Suggestions

• Channel dislocations and modulus mismatch could both affect the rafting. This may be reflected in differences in rafting kinetics.

• It is necessary to combine channel dislocations and modulus mismatch to evaluate their relative contributions via phase field modeling.

• Does phase field modeling have sufficient fidelity to evaluate elastic + plastic driving force in the Ni-Al-Mo system?

THANK YOU!

Microstructure Evolution During Aging (980C/4hrs)

State b

2m

State d

2m

State c

2m

State a

2m

Microstructure Evolution During Compression Creep (980C/130MPa)

1hrs

8hrs

1m

1m 1m

1m

Initially fully coherent(State a)

partially coherent,pre-strain in tension

State b

1m

1m 1m

1m

Microstructure Evolution During Stress Annealing and Aging for Pre-strained interface

Stress annealed in compression

Ordinary ageing