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MESOSCALE DEFORMATION

Modeling Long-term Creep Performance for Welded Nickel-base Superalloy Structures for Power Generation Systems

Chen Shen1, Monica Soare1, Pengyang Zhao2, Akane Suzuki1, Vipul Gupta1, Timothy Hanlon1, Yunzhi Wang2, Samuel Thamboo1

1 GE Global Research, 1 Research Circle, Niskayuna, NY 12309; 2 Ohio State University, 2041 College Road, Columbus, OH 43210

Phase identified Description Spatial characteristics

g’ Primary strengthening precipitates,

Ni3(Al,Ti) type

Dendrite core: spherical

Interdendritic: coarser, cuboidal

TiN Primary nitrides (MN) Homogeneously disperse

(TiMoCr)C Primary carbides (MC) Preferentially interdendritic

s TCP phase, rich in Cr,Mo,Ni

Detrimental intermetallic

Depletes refractory elements

Globular, preferentially interdendritic

(TiMo)2SC Carbosulphide Adjacent to s

Mo,Cr-carbides Lamellar g/carbide,

Secondary carbides M23C6, M6C

(* Matysiak, H. et al, 2013)

As-solidified phase observation (VIM + Investment casting)*

Orowan equation serves as the kinetic

equation linking the macroscopic shear

rate and microscopic dislocation activities:

𝛾 𝛼 = 𝜌𝑀𝛼𝑏𝑣𝛼 = 𝜌𝑀

𝛼𝑏𝑣𝛼 𝜎, 𝑇, 𝑆𝑖 , 𝑃𝑖 , …

𝛾 𝛼 - Shear rate on slip system 𝛼 𝜌𝑀𝛼 - Mobile dislocation density of slip system 𝛼

𝜎 - Applied stress

𝑇 -Temperature 𝑆𝑖 - State variables, e.g., dislocation densities

and 𝛾′ volume fraction 𝑃𝑖 - Material properties, e.g., modulus and APB

energy.

𝑣𝛼 𝜎, 𝑇, 𝑆𝑖 , 𝑃𝑖 , … = 𝑣glide𝛼 𝜎, 𝑇, 𝑆𝑖 , 𝑃𝑖 , 𝑄slip

𝛼 , if 𝑅escape ≫ 𝑅glide, e. g. tensile

𝑣climb𝛼 𝜎, 𝑇, 𝑆𝑖 , 𝑃𝑖 , 𝑄self

𝛼 , if 𝑅escape ≪ 𝑅glide, e. g. creep

Dislocation sources

Dislocation sources

Escape via climb: reaction rate = 𝑹𝐞𝐬𝐜𝐚𝐩𝐞

Glide through obstacles: reaction rate = 𝑹𝐞𝐬𝐜𝐚𝐩𝐞

(Dyson, 2009)

(Ma, 2006)

Heterogeneous deformation

Dislocations

Statistically-stored dislocations (SSDs)

Mobile

Immobile

Geometrically-necessary

dislocations (GNDs)

Immobile

𝜎 𝜎 Homogeneous

structure -> stress field

• Equal densities of “+” and “-”

dislocations accumulated • No long-range influence

𝜎 𝜎

• Significant stress gradient leading to a net density of one sign of dislocations

• Introduced both a curvature as well as a strain

Plasticity carriers: 𝛾 𝛼 = 𝜌𝑀

𝛼𝑏𝑣𝛼

Origin of shear resistance for 𝜌𝑀

𝛼 in FCC crystals, influencing 𝑣𝛼

Task 2 Task 3 Task 4 Task 5

Develop a physics-based, microstructure-informed model for accurately

predicting long-term creep behavior for heterogeneous weld structure

H282*

• High firing temperature for improved fuel efficiency

• Combustor materials - creep strength, oxidation & corrosion resistance

• Long-term creep prediction a key challenge

• Physics-based modeling of creep life for AUSC steam turbine rotor alloy HA282 in prior DOE program

• Challenge: heterogeneous (weld) microstructure, higher temperature (1500-1700˚F)

FZ

HAZ

Representative volume

element (RVE) in weldment

Precipitate microstructure

• 𝛾′ volume fraction,

distribution

FFT-based crystal plasticity (image-based, full-field)

Polycrystal response

Intr

a-g

ran

ula

r b

eh

av

ior

Constitutive model Continuum mechanics

Microstructure and property heterogeneities

Potential drop measurement

Digital image correlation

Creep deformation modes

• Intermediate stresses: dislocation climb-bypass • High stresses: g' shearing • Low stresses (high T): diffusional creep

Secondary Creep

Precipitate-dislocation

interaction. Climb/Diffusion

Tertiary Creep

Grain boundary cavitation

Primary Creep

Strain hardening

dislocation-dislocation

interaction

IN740 (Casias Ph.D Thesis)

𝜺 𝒔𝒆𝒄

𝜺𝒑𝒓𝒊𝒎𝒂𝒓𝒚

𝜆

𝜺𝒄𝒓𝒆𝒆𝒑 = 𝜺𝒅𝒊𝒔𝒍𝒐𝒄 + 𝜺𝒅𝒊𝒇𝒇𝒖𝒔𝒊𝒐𝒏

𝜺 𝒅𝒊𝒇𝒇𝒖𝒔𝒊𝒐𝒏 = 𝒄𝑳𝝈 + 𝒄𝑩 𝝈+𝜺 𝑩𝑫+𝜺 𝑺𝑫

𝒄𝑩 = 𝟑𝝅𝑭𝟒𝑫𝑩𝜹𝑩𝜴

𝒅𝒌𝑩𝑻 𝒄𝑳 = 𝑭

𝟏𝟐𝑫𝒗𝜴

𝒌𝑩𝑻𝒅𝟐

𝜺 𝒅𝒊𝒔𝒍𝒐𝒄 = 𝑨𝝆(C) 𝒇 𝟏 − 𝒇𝝅

𝟒𝒇− 𝟏 𝒔𝒊𝒏𝒉 𝑩

𝝈𝒆𝒇𝒇 − 𝝈𝒑−𝝈𝟎

𝑴𝒌𝑻𝝀𝒃𝟐

𝝈𝒆𝒇𝒇 =𝝈𝒂𝒑𝒑𝒍𝒊𝒆𝒅(𝟏+𝜺

𝒄𝒓𝒆𝒆𝒑)

𝟏−𝑫𝒔

𝝈𝒑 = 𝑬𝒇

𝟏 − 𝒇𝜺 𝒅𝒊𝒔𝒍𝒐𝒄 𝟏 − (𝟏 + 𝟐𝒇)

𝝈𝒑

𝟐𝒇𝝈𝒆𝒇𝒇

𝝈𝒑 =𝜸𝑨𝑷𝑩

𝟐𝒃

𝟏𝟐𝜸𝑨𝑷𝑩𝒇𝒓

𝝅𝑮𝒃𝟐− 𝒇

𝝈𝒐=0.25MG(T)b 𝝆, 𝝆= 𝝆(C)

(Dyson, 2009)

For climb

For precipitate shearing

For D-D interaction

Constitutive creep model

INTRODUCTION MICROSTRUCTURE MACROSCALE DEFORMATION

This work is supported by Department of Energy (Award # DE-FE0024027) and GE Power & Water.

We gratefully thank Vito Cedro, Steve Pope, Srikanth Kottilingam, Jeffrey Roberts, Deepak Saha, Michael

Knussman, Rebecca Casey, Michael Gilhooly, Thomas Bigelow for technical discussions and support.

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER

ACKNOWLEDGMENT

after solution & aging

Ni Cr Co Mo Ti Al

EPMA fit k 1.04 0.97 1.08 0.86 0.74 0.90

Scheil 1.06 0.98 1.04 0.68 0.62 1.14

𝐶𝑠 = 𝑘𝐶0 1 − 𝑓𝑠𝑘−1

Micro-segregation

Dendrite core Interdendritic

(20ksi)

Welded HA282

L+g

L+g+MC

L+g+MC+M6C

L+g+MC+s

L+g+MC+s+M3B2

L

Scheil simul.

Diffusion simul.

Lever rule

(HA282)

(×1000)