Crystal Viscoplasticity Creep-Fatigue Interaction Model for CMSX-8 Ernesto A. Estrada Rodas1 and Richard W. Neu1,2

1The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology

2Materials Science and Engineering, Georgia Institute of Technology

Introduction CMSX-8 has primarily two phases, an ordered intermetallic L12 phase known as g’ and a disordered phase known as g. Under creep, the deformation mechanisms that take place on each phase are unique to each phase:

Motivation

Components in the hot section of Industrial Gas Turbines (IGTs) are subject to a very hostile environments, and creep and fatigue loads. The push for increased efficiency leads to even higher operating temperatures which also affect the microstructure. Commercial software is limited to non-interaction creep and plasticity and cannot account for microstructure evolution. An enhanced crystal viscoplasticity (CVP) model is needed to enhance the design and maintenance of hot section materials and components.

Implementation as an Abaqus User Material Subroutine (UMAT)

Future work

Creep-fatigue interaction studies and preliminary model calibration

1

2

12 24

( ) ( ) ( ) ( ) ( ) ( )

' 1

1 13

ˆ ˆˆ ˆin in in in in

Lf f

g g g

g g

L F F d n d n

Deformation can be best represented by assuming an additive effect in the deformation:

2

2 2 2

( ) ( ) ( ) ( ) ( ) ( )1101

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( )1121

( ) ( ) ( )1 1 1

exp

exp

pass oromis cslipin

misattack

L pass APBslipin

L L L attack

Q Vb F sign

kT

Qb F

g

g g g

g

g

( )2

( ) ( )cV

signkT

600

700

800

900

1000

1100

1200

1300

0 200 400 600 800 1000

Te

mp

era

ture

[C

]

Stress [MPa]

Influence of stress and temperature on modes of creep deformation

CMSX-4 Primary

CMSX-8 Primary

CMSX-4 Tertiary

CMSX-8 Tertiary

CMSX-4 Rafting

CMSX-8 Rafting?

Tertiary

Creep Rafting Primary

Creep

[Reed, 2006; Ma, Dye, and Reed, 2008, CMSX-8 Data]

Tertiary – dislocation activity restricted to

a/2<110> form operating on {111} slip

planes in the g channels

Primary – g’ particles are sheared by

dislocation ribbons of overall Burgers vector

a<112> dissociated into superlattice partial

dislocations separated by a stacking fault;

shear stress must be above threshold stress

(about 550 MPa)

Rafting – transport of matter constituting

the g phase out of the vertical channels and

into the horizontal ones (tensile creep case)

[Ma, Dye, and Reed, 2008]

[Ma, Dye, and Reed, 2008]

The inelastic strain rates include creep mechanisms and the backstress to model creep-fatigue, dislocation densities and inelastic strain are used as ISV:

0

5

10

15

20

25

30

0 500 1000 1500

Cre

ep

Str

ain

[%

]

Time [hrs]

871 °C, 448 MPa

CMSX-8 Exp. 1

CMSX-8 Exp. 2

CMSX-4 Ma et al. Model

CMSX-8 Model

0

5

10

15

20

25

30

0 100 200 300 400 500

Cre

ep

Str

ain

[%

]

Time [hrs]

871 °C, 551 MPa

CMSX-8 Exp. 3

CMSX-8 Exp. 4

CMSX-4 Ma et al. Model

CMSX-8 Model

0.0

0.5

1.0

1.5

2.0

0 25 50 75 100

Cre

ep

Str

ain

[%

]

Time [hrs.]

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1,000

Cre

ep

Str

ain

[%

]

Time [hrs]

950 °C, 250 MPa

CMSX-8 Exp. 5CMSX-8 Exp. 6CMSX-4 MacLahan et al.CMSX-4 Matan et al.CMSX-4 Ma ModelCMSX-8 Model

0

5

10

15

20

25

30

0 100 200 300 400 500

Cre

ep

Str

ain

[%

]

Time [hrs]

1065 °C, 124 MPa

CMSX-8 Exp. 7CMSX-8 Exp. 8CMSX-8 Exp. 9CMSX-8 Exp. 10CMSX-4 Ma ModelCMSX-8 Model

Low cycle creep-fatigue tests provide with very useful data for calibration of the model:

150

200

250

300

350

400

450

500

0 1 2 3

Str

ess [M

Pa

]

Hold [min.]

Cycle 1 Cycle 2

Cycle 3 Cycle 4

Stress relaxation

1st 10 cycles

Half life

hysteresis

Creep, fatigue and creep-fatigue experimental data will be used to calibrate the CVP model parameters, preliminary it has been calibrated for pure creep:

A single finite element representative volume element is used to simulate deformation of dogbone specimens:

Abaqus single element

Degrees of freedom used to model a single element under uniaxial tension

The CVP is embedded in a UMAT which defines the material model at each integration point. A modified Newton-Rhapson algorithm is used to solve for the inelastic strains on each slip system at each time step:

•A Newton-Rhapson step is always performed on the level function with greatest RMSE.

•A Newton-Rhapson step on level function “A” is flopped to a Newton-Rhapson step on level “B” every time a Newton-Rhapson step or line search step applied on level function “A” increases the error on level function “B”.

•If a Newton-Rhapson step or line search increases the error in both flow rules, then the process is restarted with a decreased time increment

o Finalize calibration of the model using creep-fatigue data

o Include the effect of alloying composition and microstructure evolution: Include effect of Re% on diffusivity Use data from aged microstructures in the CVP and

incorporate a microstructure evolution model o Prepare a reduced order model to ease implementation

of the CVP on industry applications o Study environmental effects and propose relations to

account for their effect on life

This material is based upon work supported by the Department of Energy under Award Number DE-FE0011722