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Microstructure-Sensitive Crystal Viscoplasticity for Ni-base Superalloys
(with application to long-term creep-fatigue interactions)
Award DE-FE0011722August 2013 August 2017 (including NCE)
Program Manager: Dr. Patcharin Burke
PI: Richard W. NeuThe George W. Woodruff School of Mechanical Engineering
School of Materials Science & EngineeringGeorgia Institute of Technology
Atlanta, GA [email protected]
University Turbine Systems Research WorkshopVirginia Tech
November 1-3, 2016
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Hot Section Gas Turbine Materials
Land-based gas turbines drive to increase service
temperature to improve efficiency; increase life; with minimal increase in cost
replace large directionally-solidified Ni-base superalloyswith single crystal superalloys
Power Output: 375 MW
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Superalloys airfoils are subject to a continuation of process during service due to sustained hostile environment and loading.Understanding the influence of the microstructure and its evolution on TMF, creep and fatigue and their interactions is key todelivering better turbine designs
t
R = 0 t
R = -
[Epishin et al., 2010]
PressureTemperature
Time
PressureTemperature
Enginestart-up
Engineshut-down
Hot Section Gas Turbine Materials
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
PSPP Map for Ni-base Superalloy Airfoils
PROCESS STRUCTURE PROPERTIES
Creep Rate
Elastic Modulus
Yield Strength
Resistance to Environment Degradation
FatigueStrength
FractureToughness
Dendritic structure Primary arm spacing Secondary arm spacing Misorientation
Vacancy concentration
and phases Shape Size Volume fraction Mismatch and
Secondary size
Other Features: Crystal structure APB Energy Texture Eutectic pools Casting pores Freckles High angle grain boundaries Carbides
Dislocations Density in and Configurations Distributions
Load profile
Temperature profile
Environment profile
Composition:Ni, Co, W, Ta, Al, Cr, Re, Ti, Mo , Hf, C, B,
Age Treatment
Casting andSolidification
Solution Treatment
Continuation of Process During Service
PERFORMANCE
MaximumCreep-Rupture Life
MaximumThermomechanical
Fatigue Life
CTE
MinimalCost
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Influence of Service Conditions on Microstructure, Properties, & Performance
PROCESS STRUCTURE PROPERTIES
Creep Rate
Elastic Modulus
Yield Strength
Resistance to Environment Degradation
FatigueStrength
FractureToughness
Dendritic structure Primary arm spacing Secondary arm spacing Misorientation
Vacancy concentration
and phases Shape Size Volume fraction Mismatch and
Secondary size
Other Features: Crystal structure APB Energy Texture Eutectic pools Casting pores Freckles High angle grain boundaries Carbides
Dislocations Density in and Configurations Distributions
Load profile
Temperature profile
Environment profile
Composition:Ni, Co, W, Ta, Al, Cr, Re, Ti, Mo , Hf, C, B,
Age Treatment
Casting andSolidification
Solution Treatment
Continuation of Process During Service
PERFORMANCE
MaximumCreep-Rupture Life
MaximumThermomechanical
Fatigue Life
CTE
MinimalCost
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Role of Chemical Composition
PROCESS STRUCTURE PROPERTIES
Creep Rate
Elastic Modulus
Yield Strength
Resistance to Environment Degradation
FatigueStrength
FractureToughness
Dendritic structure Primary arm spacing Secondary arm spacing Misorientation
Vacancy concentration
and phases Shape Size Volume fraction Mismatch and
Secondary size
Other Features: Crystal structure APB Energy Texture Eutectic pools Casting pores Freckles High angle grain boundaries Carbides
Dislocations Density in and Configurations Distributions
Load profile
Temperature profile
Environment profile
Composition:Ni, Co, W, Ta, Al, Cr, Re, Ti, Mo , Hf, C, B,
Age Treatment
Casting andSolidification
Solution Treatment
Continuation of Process During Service
PERFORMANCE
MaximumCreep-Rupture Life
MaximumThermomechanical
Fatigue Life
CTE
MinimalCost
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Single Crystal Alloy being Investigated for IGT Applications
CMSX-8: 1.5% Re "alternative 2nd gen alloy" replacing 3.0% Re containing alloys (e.g., CMSX-4, PWA1484)
[Wahl and Harris, 2012]
Strength
Creep
Alloy
Cr
Co
Mo
W
Al
Ti
Ta
Re
Hf
C
B
Zr
Ni
Mar-M247LC-DS
8.4
10.0
0.7
10.0
5.5
1.0
3.0
-
1.5
0.07
0.015
0.05
Bal
CM247LC-DS
8.1
9.2
0.5
9.5
5.6
0.7
3.2
-
1.4
0.07
0.015
0.01
Bal
CMSX-4
6.5
9.0
0.6
6.0
5.6
1.0
6.5
3.0
0.1
-
-
-
Bal
SC16
16
0.17
3.0
0.16
3.5
3.5
3.5
-
-
-
-
-
Bal
PWA1484
5.0
10.0
2.0
6.0
5.6
-
9.0
3.0
0.1
-
-
-
Bal
CMSX-8
5.4
10.0
0.6
8.0
5.7
0.7
8.0
1.5
0.2
-
-
-
Bal
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Influence of Temperature, Loading Direction and Crystal Orientation on Modulus and Strength
-1.5 -1 -0.5 0 0.5 1 1.5
strain [%]
-1000
-500
0
500
1000
stre
ss [M
Pa]
Virgin CMSX-8 monotonic response in the dir
20 C
750 C
950 C
1025 C
1100 C
1100 C
1025 C
950 C
750 C
20 C
Increasing
Temperature
Increasing
Temperature
-1.5 -1 -0.5 0 0.5 1 1.5
strain [%]
-1000
-500
0
500
1000
stre
ss [M
Pa]
Virgin CMSX-8 monotonic response in the dir
Increasing
Temperature
750 C
750 C
1100 C
20 C
20 C
1100 C
Increasing
Temperature
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Thermomechanical Fatigue (TMF)
Linear In-Phase (IP) Linear Out-of-Phase (OP)
Time, t
Stra
in,
(%)
Thermal StrainMechanical StrainTotal Strain
Cold
Tension
Compression
Hot
Time, t
Stra
in,
(%)
Thermal StrainMechanical StrainTotal Strain
Cold
Tension
Compression
Hot
Hardening Process
Plastic Deformation
Plastic Deformation
Creep
Oxidation
Cyclic Ageing and Coarsening effects
Hardening Process
Plastic Deformation
Cyclic Ageing and Coarsening effects
Plastic Deformation
Creep
Oxidation
=0 =180
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Effect of Tmin on OP TMF of CMSX-4
[Arrell et al., 2004]
3x
2x drop
[Kirka, 2014]
CMSX-4 [001]
CM247LC DS in Longitudinal Dir.
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Life Modeling Approach
Damage Mechanism Modules
Fatigue
Creep-Fatigue
Environment-Fatigue
CreepRatchetting
Dominant Damage
Deformation Response
Load
ing
Par
amet
er
Life
Accurrate representations of the deformation responsehighly critical for predicting crack formation
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Primary Objectives of UTSR Project
Creep-fatigue interaction experiments on CMSX-8
Influence of aging on microstructure and creep-fatigue interactions
Microstructure-sensitive, temperature-dependent crystal viscoplasticity to capture the creep and cyclic deformation response
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Major Activities and Accomplishments
Characterize creep-fatigue interactions on CMSX-8 Creep-fatigue Thermomechanical fatigue Creep (either tension or compression) followed by fatigue Fatigue followed by creep
Characterize the influence of aging on microstructure and creep-fatigue interactions
Experimentally establish the creep-fatigue interactions in a single-crystal Ni-base superalloy that is being targeted for use in industrial gas turbines (CMSX-8)
TMF life: In-Phase (R=0) vs Out-of-Phase (R=-inf)
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Conventional Creep-Fatigue (baseline)
0.30
0.50
0.70
0.90
1.10
1.30
1.50
100 1000 10000
Stra
in ra
nge
[%]
Cycles to Failure
Effect of hold on LCF life: R = -
(T = 950 [C], R = -1)(T = 1100 [C], R=-1)(T = 950 [C], R = -, hold = 3 min.)(T = 1025 [C], R = -, hold = 3 min.)(T = 1100 [C], R = -, hold = 3 min.)
1100 [C]
950 [C]
950 [C]
1000 [C]1025 [C]
0.30
0.50
0.70
0.90
1.10
1.30
1.50
100 1000 10000
Stra
in ra
nge
[%]
Cycles to Failure
Effect of hold on LCF life: R = 0
(T = 950 [C], R = -1)(T = 1100 [C], R = -1)(T = 950 [C], R = 0, hold = 3 min.)(T = 1025 [C], R = 0, hold = 3 min.)(T = 1100 [C], R = 0, hold = 3 min.)
950 [C]
950 [C]
1000 [C]
1025 [C]
1100 [C]
t
R = 0
t
R = -
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Conventional Creep-Fatigue (baseline)
t
R = 0
t
R = -
0.3
0.5
0.7
0.9
1.1
1.3
1.5
100 1000 10000
Stra
in ra
nge
[%]
Cycles to Failure
Life for low cycle creep-fatigue
(T = 950 [C], R = 0, hold = 3 min.)(T = 950 [C], R = -, hold = 3 min.)(T = 1025 [C], R = 0, hold = 3 min.)(T = 1025 [C], R = -, hold = 3 min.)(T = 1100 [C], R = 0, hold = 3 min.)(T = 1100 [C], R = -, hold = 3 min.)
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Cycle Evolution
150
200
250
300
350
400
450
500
0 0.5 1 1.5 2 2.5 3
Stre
ss [M
Pa]
Hold [min.]
Cycle 1 Cycle 2
Cycle 3 Cycle 4
Stress relaxation
1st 10 cycles
Stress evolution
T = 1100 C, R = 0, = 1.0 %
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Crack Characteristics
R = 0, T = 1100C, = 0.8%Nf = 1420
R = -, T = 1100C, = 0.8%Nf = 980
t
R = 0
t
R = -
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Half-life at 1025 C
= 1.0 [%]
= 0.8 [%]
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Half-life at 1100 C
= 1.0 [%]
= 0.8 [%]
Plastic strain range alone does not
explain life data at high temperatures.A Coffin-Manson
relations would not be sufficient
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Primary Objectives of UTSR Project
Creep-fatigue interaction experiments on CMSX-8
Influence of aging on microstructure and creep-fatigue interactions
Microstructure-sensitive, temperature-dependent crystal viscoplasticity to capture the creep and cyclic deformation response
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Major Activities and Accomplishments
Stress-free and stress-assisted (rafting) aging experiments under tensile and compressive stresses
Establishing process-structure linkages using physical models, 2-point statistics and PCA
Microstructure-sensitive Crystal Viscoplasticity (CVP) Model to Determine Service Process-Structure-Property Linkages
t0 tf
virgin evolved
Experiments & Models to Predict Current State of Microstructure (Service Process-Structure Linkages)
Sensitivity of Local Composition on Diffusivity for Input in Aging and Viscoplasticity Models
Thermo-CalcDICTRA
Databases: TCNi5 / MOBNi2
Composition segregation in and phase
Determination of composition sensitive effective diffusivity to characterize aging activation energy and diffusivity parameter in viscoplasiticity models
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Microstructure Evolution in Blades
2 cm
Dis
tanc
e fro
m R
oot
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Rafting and Coarsening of
[Epishin et al., 2008]
N-raft
P-raft
CMSX-4
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
High-Throughput Stress-assisted Aging
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Aged Microstructure under Compressive Stress
Compression Creep Frame
5um
P-Raft
Ceramic Compression Creep Extensometer
Bottom Holder
Top Holder
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Physical Models to Describe Aging Behavior
Physical aging models
Rafting Coarsening
, = . .
900 C
950 C1100 C
Experimental data pointsLSW Model
3- 0 3 =
= 0
LSW model:
8 = 269.4 /
= ( 0)
A (m/h) Q (kJ/mol)
UT(J/mol.MPa.Kn) n
CMSX-8 2.0105 206 0.033 1.525CMSX-4 9.31104 222 0.19 1.294
Saturated level of rafting
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
2-point Correlation Method
2-point correlation A statistical representation of the microstructure that provides a magnitude measure in addition to the associated spatial correlation.
2-point correlations (,) capture the probability density associated with finding an ordered pair of specific local state at the head and tail of a randomly placed vector into the microstructure.
[Niezgoda, Fullwood and Kalidindi, 2008]
Cross-correlationDefined by (, ). The function gives the probability that a random vector of length x start in one phase and end in the other.
(a) An example of two phase microstructure (b) Cross-correlation for the black and white phases at the head and tail of a vector [Fullwood, Niezgoda, Adams, Kalidindi, 2010].
(a) (b)
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
2-point Correlation Application to CMSX-8
precipitate and channel sizes are determined from the first peak and valley of the probabilistic curve of the corresponding micrograph.
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Quantifying the Current Aged State
Stress decreasing
Reduced order representation of aged microstructures using PCA of 2-point spatial correlations
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Influence of Variation in Composition
Thermo-CalcDICTRA
Databases: TCNi5 / MOBNi2
Composition sensitive diffusivity parameter
Aging behavior Temperature-dependent constitutive models
=642
9
= 0, (
)
Coarsening effective diffusivity
LSW model
Diffusivity parameter
Composition segregationThermo-Calc
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Influence of Composition on Diffusivity
Interdiffusion coefficients of Ni-x binary systemsDICTRA
= 0, (
) = =1
Composition variation (Re) effect on effective diffusivityof the complex Superalloy system
DICTRA
Molar fraction of element x
Effective activation energy/Coarsening activation energy = 275.9 KJ/mol
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Primary Objectives of UTSR Project
Creep-fatigue interaction experiments on CMSX-8
Influence of aging on microstructure and creep-fatigue interactions
Microstructure-sensitive, temperature-dependent crystal viscoplasticity to capture the creep and cyclic deformation response
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
[Ma, Dye, and Reed, 2008]
Distinct deformation in the and phasesIn : 12 octahedral slip systems
moving as dislocation ribbons
deformationIn : 12 octahedral slip
systems active
deformation
Deformation predictions sensitive to the and phase attributes
Alloy structure
[Shenoy, Tjipowidjojo, and McDowell, 2008]
0 100 200 300 400 500
time [hrs]
0
10
20
30
40
cree
p st
rain
[%]
Tertiary creep: 950 C, Stress = 400 MPa
0.09 m
0.10 m
0.11 m
Channel thickness:
0 500 1000 1500
time [hrs]
0
1
2
3
4
5
6
cree
p st
rain
[%]
Primary creep: 750 C, Stress = 680 MPa
0.13 m
0.14 m
0.15 m
Channel thickness:
Microstructure-sensitive Crystal Viscoplasticityfor Single-Crystal Ni-base Superalloys
0 0.2 0.4 0.6 0.8 1
strain [%]
-800
-600
-400
-200
0
200
400
600
800
stres
s [MP
a]
Creep-fatigue test at T =1025 C 801-15B
First 10 cycles CMSX-8[B/C]UMAT
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Crystal Viscoplasticity Kinematic Relations
Kinematic relations includingtemperature dependence
Macroscopic plastic velocity gradient
Deformation gradient
Velocity gradient
In : 12 octahedral slip systems active
In : 12 octahedral slip systems moving as dislocation ribbons
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Creep Deformation Mechanisms of Superalloys
600
700
800
900
1000
1100
1200
1300
0 200 400 600 800 1000
Tem
pera
ture
[C]
Stress [MPa]
CMSX-4 PrimaryCMSX-8 PrimaryCMSX-4 TertiaryCMSX-8 TertiaryCMSX-4 RaftingCMSX-8 Rafting?
Tertiary Creep
Rafting Primary Creep
Tertiary dislocation activity restricted toa/2 form operating on {111} slip planes in the channels
Primary particles are sheared by dislocation ribbons of overall Burgers vector a dissociated into superlattice partial dislocations separated by a stacking fault; shear stress must above threshold stress (about 550 MPa)
Rafting transport of matter constituting the phase out of the vertical channels and into the horizontal ones (tensile creep case)
[Reed, 2006; Ma, Dye, and Reed, 2008, CMSX-8 Data]
Influence of stress and temperature on modes of creep deformation
[Ma, Dye, and Reed, 2008]
[Ma, Dye, and Reed, 2008]
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Inelastic Shear Strain Rate
Crystal Viscoplasticity (CVP) Rate Eqn
Evolution Equations
Inelastic Velocity Gradient
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Orientation Sensitivity
[Ma, Dye, and Reed, 2008]
Primary creep performancebased on experiments
[MacKay and Meier, 1982]
CMSX-4
Creep strain in tertiary regime900C/400MPa (111 hr)
Creep strain in primary regime750C/600MPa (111 hr)
CMSX-4 Model Predictions
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Creep in different orientations
0 200 400 600 800 1000 1200 1400 1600
time [hrs]
0
5
10
15
20
25
30
35
40
cree
p st
rain
[%]
Temp = 950[C], Stress = 250[MPa]
Data
CVP
CVP
CVP
CVP
CVP
CVP
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Primary and Tertiary Creep
0
5
10
15
20
25
30
0 500 1000 1500
Cree
p St
rain
[%]
Time [hrs]
871 C, 448 MPaCMSX-8 Exp. 1CMSX-8 Exp. 2CMSX-4 Ma et al. ModelCMSX-8 Model
0
5
10
15
20
25
30
0 200 400 600
Cree
p St
rain
[%]
Time [hrs]
871 C, 551 MPaCMSX-8 Exp. 3CMSX-8 Exp. 4CMSX-4 Ma et al. ModelCMSX-8 Model
0.0
0.5
1.0
1.5
2.0
0 50 100Cr
eep
Stra
in [%
]
Time [hrs]
Zoom in: 871 C, 551 MPaCMSX-8 Exp. 3CMSX-8 Exp. 4CMSX-4 Ma et al. ModelCMSX-8 Model
Primary, secondary and tertiary creep can be
captured with the model
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
TMF validation
First 10 cycles: IP-TMF [100-1100-100] C, R = 0, = 2.83[/]
Stabilized hysteresis: OP-TMF [100-850-100] C, R = -, = 2.83[/]
Very good agreement predicting TMF
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
TMF validation
Stabilized hysteresis: IP-TMF [100-1100-100] C, R = 0, = 2.83[/]
Stabilized hysteresis: OP-TMF [100-850-100] C, R = -, = 2.83[/]
Very good agreement predicting TMF
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
If we considering activation energy for plastic flow Q0 a function of %Re, the diffusivity parameter could take the form of:
Since Re segregates almost exclusively in the channels, the Activation energy in the phase can be modified to account for Re content as follows:
( ) exp for2
o mQ TT TRT
=
Incorporating the Influence of Re Content
[Miller, 1976; Shenoy et al., 2005]
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The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Remaining Plans for Project
Exercise new CVP codes (1) displacement-controlled algorithm coded in FORTRAN as UMAT for
ABAQUS (suitable for 3D analysis of detailed features, but computationally expensive)
(2) stress-controlled algorithm coded in MATLAB (limited to 1D loadings, but computationally cheap; utility in alloy design; early design iterations)
Characterize aged microstructure and its analysis Establish protocols for reduced-order modeling of the current state of the
microstructure using spatial correlations and principal component analysis Develop PSP linkage models using PC values for describing current state
of the microstructure Creep-fatigue interaction life analysis relationships using all new data Disseminate research
Archival journal articles Intern with Siemens Energy Workshops and Conferences (UTSR, ASME, )
Ernesto Estrada Rodas complete Ph.D. studies in 2017
Microstructure-Sensitive Crystal Viscoplasticity for Ni-base Superalloys(with application to long-term creep-fatigue interactions) Award DE-FE0011722August 2013 August 2017 (including NCE)Program Manager: Dr. Patcharin BurkeHot Section Gas Turbine Materials Slide Number 3Slide Number 4Slide Number 5Slide Number 6Single Crystal Alloy being Investigated for IGT ApplicationsSlide Number 8Thermomechanical Fatigue (TMF)Effect of Tmin on OP TMF of CMSX-4Life Modeling ApproachPrimary Objectives of UTSR ProjectMajor Activities and AccomplishmentsConventional Creep-Fatigue (baseline)Conventional Creep-Fatigue (baseline)Cycle EvolutionCrack CharacteristicsHalf-life at 1025 CHalf-life at 1100 CPrimary Objectives of UTSR ProjectSlide Number 21Microstructure Evolution in BladesRafting and Coarsening of High-Throughput Stress-assisted AgingAged Microstructure under Compressive StressPhysical Models to Describe Aging Behavior2-point Correlation Method2-point Correlation Application to CMSX-8Quantifying the Current Aged StateInfluence of Variation in CompositionInfluence of Composition on DiffusivityPrimary Objectives of UTSR ProjectSlide Number 33Crystal Viscoplasticity Kinematic RelationsCreep Deformation Mechanisms of SuperalloysCrystal Viscoplasticity (CVP) Rate EqnOrientation SensitivityCreep in different orientationsPrimary and Tertiary CreepTMF validationTMF validationIncorporating the Influence of Re ContentRemaining Plans for Project