Predicting Microstructure-Creep Resistance …...2015/04/27 · Predicting Microstructure-Creep...
Transcript of Predicting Microstructure-Creep Resistance …...2015/04/27 · Predicting Microstructure-Creep...
Predicting Microstructure-Creep Resistance Correlation in High Temperature Alloy over Multiple Time Scales
Prof. Vikas Tomar (PI) & Hongsuk Lee &Sudipta Biswas
Prof. Jian Luo (co-PI) & Naixie Zhou
School of Aeronautics and Astronautics, Purdue University
University of California, San Diego & Clemson University
Program Manager: Dr. Jason HissamGrant No. : DEFE0011291
Long Term Creep in Microstructures
Sobotka, 1985, AISI 316 LN Steel
Long Term Creep in Microstructures
Igarashi, 2011
Proposal Research Workflow
Nanocrystalline Ni and Bulk W Based Alloy Control Sample
Preparation
Theoretical Framework to Characterize GB Segregation
In‐Situ Microstructural Testing of GB Evolution and Strength
Microstructure Level Multiscale Modeling to Predict Effect of GBs on Embrittlement, Creep, and rupture
Task‐1
Task‐3
Task‐4
Task‐2
Task 1: Fabrication and Characterization of Control
Samples
UC San Diego
Task 1, Part A: Nanocrystalline Ni and Ni‐W Foils (Synthesized by Electrodeposition)
Task 1, Part B: Bulk W based Alloys (Synthesized by Ball Milling + SPS)
Task 1: Fabrication and Characterization of Control Samples – Part APreparing Nanocrystalline Ni and Ni‐W Specimens
for Mechanical Test
Chemicals Weight(g/L)NiSO4.6H2O 300NiCl2.6H2O 45H3BO3 45
Saccharine 5Sodium Lauryl Sulfonate(CH3(CH2)11OSO2Na)
0.25
Current Time (ms)
Peak(A/cm2)
ForwardsOn 5 0.4
off 15
Temperature: 65 ºC
Deposition time: 30 min to 2h
Power SuppliesEl‐Sherik, et al., J of Materials Science 30, 5743 (1995)
1
Slide 6
1 Jian Luo, 4/17/2015
Free‐Standing Nanocrystalline Ni Specimens
free‐standing, mirror‐like
40 m
UniformCrack‐free
Nanocrystalline Ni
Cu Substrate(dissolved afterwards)
Grain Size (from the Scherrerequation) is ~18 nm.
The image of the “apple” from iPhone
30min 120min60min
20 μm
p
Two‐step to Prepare Bulk Nanocrystalline W Alloys
NanocrystallinePowders
Bulk NanocrystallineMaterial
High Energy Ball Milling Spark Plasma Sintering
Pressureless Sintering
W-5 at.% Ni W-5 at.% Co
W-5 at. % Re W-5 at.% Cu
1200⁰C, 5h 1200⁰C, 5h
1200⁰C, 5h 1200⁰C, 5h
Grain Size: 600 nm Grain Size: 820 nm
Grain Size: 2.2 μm Grain Size: 210 nm
(G) (H)
(I) (J)
Task 1: Fabrication and Characterization of Control Samples – Part B
Bulk Nanocrystalline W Alloys
Ball Milled Powder
Pressureless Sintered Samples
W – Mn Pure W W – Ni
W – Re – NiW – Re W – Ti
1 μm
1 μm
1 μm
1 μm
1 μm
1 μm
Task 1: Fabrication and Characterization of Control Samples – Part B
Bulk Nanocrystalline W Alloys
Spark Plasma Sintered Samples
Task 1, Part B Extension – Testing of Bulk Nanocrystalline Specimen (Currently in Progress @ UCSD)
Creep Test Setup
INSTRON Instrument Equipped with Heating Furnace
Planned Experiments:• The creep tests for the specimens pure W, W‐5%Ni, W‐5%Ti, W‐5%Co, W‐5%Re and W‐5%Cu will be performed at elevated
temperature 400 ̊C and/or 750 ̊C.• Creep data will be collected to evaluate the mechanical properties of the W alloys with different doping elements.• Moreover, the microstructure evolution of creep tested W alloys specimens will be characterized by SEM and TEM.
(a.)
(b.) (c.)
Task 2-High Temperature Nanoindentation Tests
Task 3: A New Theoretical Framework to Characterize GB Segregation
UC San Diego
Task 3, Part A: The Classical GB Segregation Model (Assessments of W alloys with the Wynbaltt‐ChatainModel)
Task 3, Part B: Non‐Classical High‐T GB Segregation (Coupled with GB Premelting/Interfacial Disordering
Task 3, Part A: Classical GB Segregation ModelAssessment of W based Alloys by the Wynblatt‐Chatain Model
zv
zvzp
GB
Twisted angle Δθ
1 21
1
1 1
0.5 ( ) 2 1(1 )2
2 ( )
p v
BB AA v el Ssegv vi
iel S p i v i v i
zX z X z XQ e e z E
Q z X QzH
E zX z X z X z X
i = 1
i > 1
bonding energy difference strain energySolute‐dopant interactions
exp1 1
segi i
i
X X HX X kT
A Mclean type segregation equation
Bulk compositionith layer composition
Segregation Enthalpy
2GB ii
X X GB absorption
W‐Co (Co‐doped W) Alloy
0 1 2 3
0.4
0.6
0.8
1.0
GB/(
0) GB
X (%)0 1 2 3
0
1
2
3
4
(m
onol
ayer
s)
X (%)
2 4500
1000
1500
2000
2500
W
T (K)
Co (%)
solubility limit
BCC
BCC + Mu
BCC + Liq
Phase diagram
1250 K
1500 K1750 K
GB energy GB absorption
W‐Cr Alloy
0 5 10 15 20 25
0.4
0.6
0.8
1.0
GB/(
0) GB
X (%)0 5 10 15 20 25
0
1
2
3
4
(m
onol
ayer
s)
X (%)
5 10 15 20500
1000
1500
2000
2500
W
T (K)
Cr (%)
Phase diagram
BCC
BCC#1 + BCC#2
1250 K
1500 K 1750 K
GB energy GB absorption
0 2 4 6 8
0.6
0.8
1.0
GB/(
0) GB
X (%)
Phase diagram
1250 K
1500 K 1750 K
0 1 2 3 4 5 6 7 8 90
1
2
3
4
(m
onol
ayer
s)
X (%)
2 4 6 8500
1000
1500
2000
2500
W
T (K)
Fe (%)
BCC
BCC + Mu
BCC + Liq
GB energy GB absorption
W‐Fe Alloy
2 4 6 8500
1000
1500
2000
2500
W
T (K)
Zr (%)
0 1 2 30
1
2
3
4
(m
onol
ayer
s)
X (%)0 1 2 3
0.0
0.2
0.4
0.6
0.8
1.0
GB/(
0) GB
X (%)
1250 K
1500 K1750 K
Phase diagram
BCC
BCC + W2Zr
BCC + Liq
GB energy GB absorption
W‐Zr Alloy
Task 3: A New Theoretical Framework to Characterize GB Segregation
Task 3, Part B: High‐T Segregation + GB Disordering
Multiscale modeling to characterize microstructure‐dependent creep Tomar et al. at Purdue
Develop a thermodynamic framework to predict a “new” type of high‐T(premelting‐like) GB segregationLuo et al. at Clemson/UCSD Discovered by the Luo group
Appl. Phys. Lett. 2005Acta Mater. 2007
Computed GB Diagrams to RepresentLevels of GB Disorder
Prior Relevant StudiesThermodynamic Model for High-T GB Disordering
W‐Ni
See: related review article “Developing Interfacial Phase Diagrams for Applications in Activated Sintering and Beyond: Current Status and Future Directions”Journal of the American Ceramic Society95: 2358 (2012)
The Model for Ternary Alloys
(0) (0), 2 / 3
0
C C C CGB i GB i i j i j
i i j
QX X XC V
(0)2 / 3
0
1 1 1.92
C fuse L L L L L C C Ccl cl i i j i j i j i j i j i j
i i j i j i jX H X X X X X RT
C V
(0)cl=2 GB
reference energyi‐j interfacial energy entropy due to near interface ordering
excessive interaction energyInterfacial energies
Bulk free energy of undercooled liquid
(mol) L Lamorph ( )L C
film i ii
G G X X
Miedema type model modified to use CALPHAD parameters
Multicomponent free energy function built based on binary CALPHAD database
Task 3A: A New Theoretical Framework to Characterize GB Segregation
The Effects of Co‐Doping on Enhancing or Suppressing GB Disorder
The effects of adding a co‐alloying element X to W‐Ni
Assumptions:
Xmix ideally with W and Ni
Xmix ideally with Ni and ( ‐ ) = +50 kJ/molBCCW-X L
W-XZhou & Luo,Acta Materialia 2015
Change the melting point of the co‐alloying element X
Task 3A: A New Theoretical Framework to Characterize GB Segregation
The Effects of Co‐Doping on Enhancing or Suppressing GB Disorder
Change W‐X interaction parameters
Zhou & Luo,Acta Materialia 2015
The effects of adding a co‐alloying element X to W‐Ni
Task 4: Multiscale Models for Rupture Strength and Long Term Creep
Quantum Mechanics Based on
Thermodynamics
Models of Rupture Based on GB Strength
Models of Creep Evolution While Incorporating Interface Physics
and Mechanics
Predictions Validated with in‐situ and ex‐situ experiments
[ Vivek K. Gupta and et al., 2007 ]
(100) (210)W+NI~0.6 nm
x
y
z
(100) (210)W+NI
NI W
Quantum mechanical calculation of GB Strength
time step: 5 a.u. , total 2000 steps
cutoff energy for wavefunction : 350 eV
Nose-Hoover thermostat : 300K, 400K, 500K, 600K
electronic fake mass for CPMD : 400 a.u.
number of k-points for integration over Brillouin zone : 32x32x32
Becquart and et al., 2006
Perdew and et al., 1996
Nose and Shuichi, 1984
Hoover and William, 1985
Monkhorst and Pack., 1996
Vanderbilt and David, 1990
Yield strength: at strain 4%, First peak: at strain 12%Yield strength and first peak’s values have dependent on the Ni volume fraction.Second peak: at strain 18%The second peak’s values are not depend on the Ni volume fraction.Ultimate tensile strength : strain of 12~18%The maximum tensile strength is not affected by Ni volume fraction for the unsaturated W-Ni.
[1] At strain of 0.18
[2] At strain of 0.12
[3] At strain of 0.04
[1][2]
[3]
Stress – strain relation (1) Unsaturated Ni - W
Yield strength: at strain 4%, First peak: at strain 16%Yield strength and first peak’s values have dependent on the Ni volume fraction.Second peak: at strain 24%The second peak’s values have the largest dependence on the Ni volume fraction.Ultimate tensile strength : strain of 16~24%The maximum tensile strength is not affected by Ni volume fraction for the saturated W-Ni.
[1][2]
[3]
[1] At strain of 0.24
[2] At strain of 0.16
[3] At strain of 0.04
(2) Saturated Ni - W
Saturated
Unsaturated
1.00
0.80
0.60
0.400.20
0.00
EL
EC
TR
ON
DE
NSI
TY1.00
0.80
0.60
0.400.20
0.00EL
EC
TR
ON
DE
NSI
TY
1.00
0.80
0.60
0.400.20
0.00
1.00
0.80
0.60
0.400.20
0.00
EL
EC
TR
ON
DE
NSI
TY
Electron density distribution
MAX. STRESS
DOS
MAX. STRESS
DOS
Unsaturated SaturatedElectron density of states (f-orbital)
EL
EC
TR
ON
DE
NSI
TY
Pure W
Unsaturated
Saturated
Pure W
Saturated
Unsaturated
Γ Η ΝΓPhonon dispersion
(ξξ0)
(ξ00)
Saturated
Unsaturated
Trend line
Trend line
max
wgntf
CDCE
ideal
,1max
: Maximum tensile strength of W-Ni alloy: Idealistic maximum tensile strength of W: Surface energy of W: Atomic level cohesive energy of W
ideal
CE
ntf ,
wg
Prediction of peak tensile strength
0.6nm2nm
60nm
60nm
[ V. Gupta et al, 2007 ]135 μm
t = 10 μm
80 μm
Bi-granular model
Polycrystalline model
Continuum scale model(1) Nano-scale model
(2) Micro-scale model[ V. Gupta et al, 2007 ]
How does this prediction apply to continuum scale fracture?
Grain Grain boundary
Crack propagation of GB
4.5E-5 0.013 0.015 0.018Time-step increment
Material model of grains and GBs
[ V. Gupta et al, 2007 ]
Fracture toughness inside the GBFracture toughness in crack initiation
W AKS-W WL NI-W
200 nm GB
400 nm GB
800 nm GB
200 nm GB400 nm GB
800 nm GB
W : TungstenAKS-W : Potassium doped tungstenWL : Tungsten with 1 wt% La2O3
[ B. Gludovatz and et al., 2010 ]
Fracture toughness analysis
Effect of length-scale :
Brittleness index estimation
0.30.03 3
B = 3.3L-1/2
WC/Co [Evan and Charles, 1976]
WC [Lawn and Marshall, 1979]
0 3 2200 6000
NomenclatureB* brittleness index (no unit)L lengthscale (μm)T max. tensile strength (fracture strength)H hardness (GPa)Kc fracture toughness (MPa m^1/2)t GB thickness (μm)p Ni fraction (no unit)
LKHB
c 1* α = 3.3 for W-Ni
Brittleness index of GBs
Measurement of GB embrittlement has been obtained using the revised brittleness index. This provides an absolute range of qualitative measurement to describe the brittleness without considering the length scale limitations.
θ = 90 ̊ θ = 80 ̊ θ = 70 ̊ θ = 60 ̊ θ = 50 ̊
θ = 40 ̊ θ = 30 ̊ θ = 20 ̊ θ = 10 ̊
GB angle from -90 to 90 degree
Inter-granular failure is represented as 1Trans-granular failure is represented as -1
Crack propagation in different angled GBs
Failure index : An index (between -1 and 1) to describe failure type, which can be either inter-granular failure or trans-granular failure.
a = 4.45b = -4.2c = -0.00024
2cTTbaFIGrain
GB
Using the heavi-side function
0 ,10 ,1
][FIFI
FIH
Inter-granular failure
Trans-granular failure
Trans-granular failure
[ Zbigniew Pedzich, 2012 ]
Validation and Conclusion
Perfect inter-granular failure has occurred.Contains crack path with maximum GB angle of 67 ̊. GB strength property can be predicted.
According to the failure index prediction, given microstructure has max. tensile strength ratio between GB and grain as
2cTTbaFIGrain
GB
.803.0 GrainGB TT
For various failed morphologies of polycrystalline W-Ni, GB’s strength property can be predicted using the derived failure type criteria.
Evolution: Previous Works Microstructure evolution has been observed through experimental studies
Groza, 2000; Hong, 2003; Dahl, 2007
Simulation developed replicating the whole sintering process Maizza, 2007; Vanmeensel, 2005
Kinetic Monte Carlo simulation applied to microstructural evolution: Probabilistic approach, depends on random sampling Olevsky, 2004
Phase field modeling has been done to identify sintering mechanisms, external loading not considered Wang, 2006; Liu, 2011; Deng, 2012
Consolidation kinetics has been captured experimentally Bruson, 1984; Grigoryev, 2009; Tang, 2013
Modelling Approach
Cahn Hilliard Allen-Cahn
Chemical Potential
Temp. Effect
Elastic Energy
Chemical Potential
Elastic Energy
Mobility as a fnof density & order param
Order paramto be obtained by solving AC eqn.
Eigen strain as a function of density and order parameter
Consideration of external pressure/loading
Plasticity not considered
Interfacial Energy
Interfacial Energy
Logerithmicfunction
Absolute temperature & boltzmanconstant to be multiplied
Constant co-efficient
Independent of CH eqtn
Eigen strain to be used
Captures effect of external loading
Modeling Approach
• Rectangular grid will be created• Corresponding Element types will assigned
Mesh
• The phase field variables will be assigned• Initial structure is created with assigned initial condition• All the constants & their values can also be assigned in material section
Functions
• Define the total free energy expressions, use in‐built Allen‐Cahn & Cahn‐Hilliard equations• Calculate derivatives & give them as input
Kernels
• Define solver type: Finite Difference Method• Assign pre‐conditioning if required
Executioner
• Micro‐structural images• Plot for temporal evolution of phase field variable• Calculate evolution of grain size
Post‐process
Moose Simulation
Simulation Details: Test Run
Simulation block: 100X60; Particle Radius: 20 & 20;
Grid Size: 0.5
Total Time: 60 with Time Step: 1.0
Maximum displacement applied 35 µm
0
10
20
30
40
50
60
0 10 20 30 40 50 60 70
Applied Load
Time
T = 300 K
T = 1500 K
T = 300 K
Test Results: DensityVariation w/o load
Initial Condition Time = 0.5
Time = 20.5 Time = 60.0
Test Results: DensityVariation w/ load
Initial Condition Time = 1.0
Time = 14 Time = 35.0
Summary
All Tasks on Schedule A Grain Boundary Diagram Based Approach for long
term GB evolution identified A Brittleness Index parameter identified to predict
effect of GB on microstructural Strength Control sample manufacturing process established In‐situ and ex‐situ experimentation protocols
established 4 international journal publications, 1 PhD graduate, 3
supported students with grant in second year