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Modelling Internal Corrosion of High Temperature Alloys
Ulrich Krupp
Institute of
Materials Design and
Structural Integrity
GTT Annual Workshop and User Meeting 2-4 July 2014
Acknowledgment Katrin Jahns Institute of Materials Design and Structural Integrity Martin Landwehr, Prof. Dr. Jürgen Wübbelmann Institute of Computer Engineering University of Applied Sciences Osnabrück, Germany Dr. S.-Y. Chang, Dr. Robert Orosz, Dr. Vicente Trindade, Prof. H.-J. Christ University of Siegen, Germany Financial Support: German Science Foundation DFG German Ministry of Education and Research (BMBF),
European Fonds for Regional Development (EFRE) GTT Technologies, Herzogenrath, Germany
Outline
What is Internal Corrosion?
Wagner's Theory of Internal Oxidation
Limitations of the Classical Theory
Numerical Treatment of Internal Oxidation and Nitridation
- Finite Difference
- Cellular Automata
What is Internal Corrosion?
high-temperature corrosion:
superficial scale
alloy AB
gas phase (O,N,S,C..)
metal oxide (AO) DO/A
DO
internal oxide (BO)
+ internal oxidation
alloy AB
gas phase (O,N,S,C..)
metal oxide (BO)
selective oxidation
DO
DB
Transition from Internal to External Oxidation Oxidation of Ni-Cr Alloys (100h, 1000°C, air)
Cr2O3
NiO
5%Cr
Cr2O3
20%Cr
50µm depends on:
cCr/DCr/T
Material Degradation by Internal Corrosion
30µm internal AlN
internal Al2O3
superficial Cr2O3
500µm
internal nitridation (AlN)
(Natural Gas Burner Tube, alloy 601)
gas and steam turbines, heat exchangers, chemical reactors,
exhaust systems, metallurgy, heat treatment …
Material Degradation during Cyclic Oxidation at 1100°C
20µm cracks
Al2O3 spallation
Al depletion
transition to
non-protective NiO
internal
Al2O3/Cr2O3
internal
AlN/TiN
Wedge-Shaped Specimen CMSX-4 at 1100°C
Carl Wagner's Theory of Internal Oxidation
Depth of the Internal Precipitation Zone x
C. Wagner, Z. Elektrochemie, 21 (1959) 773
alloy AB
c
cB
cO
BOn
c
x
10s
OB BO ccDD
cO s
cB 0
for
Carl W. Wagner (1901-1977)
DO
tc
Dc0
B
O
s
O2 2
nx
Carl Wagner's Theory of Internal Oxidation
Depth of the Internal Precipitation Zone x
alloy AB
c
cB
cO
BOn
c
x
tc
c
D
D2
0
B
s
O
B
2
O2
nx 11
B
O D
D
cO s
cB 0
for
DO DB
erf
2erf1
O
0O
tDxcc s
)( erfc
)2erfc(1
BO
B0
BBDD
tDxcc
xx
n
xx x
cD
x
cD B
BO
O
Diffusion of O and B:
Mass Balance at x:
C. Wagner, Z. Elektrochemie, 21 (1959) 773
Carl Wagner's Theory of Internal Oxidation
Transition from Internal to External Oxidation
alloy AB
c
cB
cO
BOn
c
x
cO s
cB 0
DO DB
dtx
c
V
AD
V
fAd
mm
BBx
Mass Balance: Mole fraction BOn
B flux to reaction front
C. Wagner, Z. Elektrochemie, 21 (1959) 773
OxB
mOs
O
*0
B2 VD
VDc
gc
n
with g*: crit. volume fraction
of oxide
Limitations of Wagner's Analytical Approach
One type of precipitates of high thermodynamic stability
(solubility product )
0OB nNNKSP
Constant boundary conditions - no changes in
temperature, gas composition etc. possible
One-dimensional - nucleation and growth kinetics / changes
in the diffusion path are neglected
Effective diffusivity - through complex microstructure,
e.g.,DGB>Dbulk
Nucleation and Growth of Internal Precipitates (TiN and AlN in NiCr20Al2Ti2, 1000°C, 150h, N2)
Energy Balance: interface energy
free energy change DG
strain energy DGs
(defect site annilhilation energy)
G. Böhm, M. Kahlweit, Acta Met., 12 (1964) 641
D. J. Young: High Temperature Oxidation and Corrosion of Metals, Elsevier 2008
i
i
isV AGGVG DDD
Supersaturation
AlN
TiN
Finite-Difference Treatment of Diffusion
2
2
x
cD
t
c
t
txcttxc
t
c
tx D
D
,,
,
2
,
2
2
,,2,
x
txxctxctxxcD
t
c
tx
D
DD
Dx Dxx
t
t+ tDc( + )x,t tD
txxctxctxxcx
tDtxcttxci ,,2,,,
2DD
D
DD
Finite-Difference Treatment of Diffusion
txxctxctxxcx
tDtxcttxc ,,2,,,
2DD
D
DD
m
j
jjjj GGGcG1
idnon,id,pure,
= min !
computational thermodynamics
ChemApp + system data
(GTT technologies)
Dx Dxx
t
t+ tDc( + )x,t tD
ChemAppprocessor
Dx Dxx
t
t+ tD
c( +2 )x,t tDChemAppprocessor
Krupp et al., Mater. Corr., 57 (2006) 263
U. Buschmann , Dissertation, Univ. Siegen 2008
2D Finite-Difference Treatment of Diffusion (Crank Nicolson implicit approach)
Dxl
Dyl
Dxr
Dyr
x
y
t
t+ tD
master
slaves
1 2 3 4 5 6
C – Main program
Parallelization (e.g. PVM, GPU/CUDA)
FD diffusion calculation
ChemApp / system
data base initialisation
distributed equilibrium
calculations
user interface
(individual CPUs)
Krupp et al., Mater. Corr., 57 (2006) 263
D=f(x,y) (e.g. PVM)
bulk and gb diffusion
Finite-Difference Simulation of Internal Precipitation of Cr-Nitrides of Moderate Stability (NiCr20, 800°C, N2)
10µm 0
5
10
15
20
25
0 10 20 30 40 50
0,0000
0,0001
0,0002
0,0003
0,0004
0,0005
0,0006
CrN
Cr
N
cCr/CrN [at.%] cN [at.%]
distance from surface [µm]
Oxidation of Low-Cr Steels (X60)
(1.43wt% Cr, 550°C, air)
Fe2O3
Fe3O4
Fe3O4
FeCr2O4
gold marker
inner
scale
outer
scale
intergranular
Cr2O3 V. Trindade, PhD thesis 2006
2D Simulation of Internal Oxidation
FeCr2O4
Fe3O4/
y [m·10-5]
y [m·10-5] x [m·10-5]
x [m·10-5]
original surface inner oxide scale thickness
grain boundaries
FeCr2O4
Inner Oxide-Scale Growth (X60)
(1.43wt% Cr, 550°C, air)
time [h]
inner oxide-scale thickness [µm]
0 10 20 30 40 50 60 70 800
5
10
15
20
25
experiment (d=10µm)
simulated (d=10µm)
simulated (d=30µm)
simulated (d=100µm)
inner
oxid
e sc
ale
thic
knes
s [µ
m]
time [h]
experiment
simulation (grain size 10µm)
(grain size 30µm)
(grain size 100µm)
The Cellular Automata Approach
Dividing Space into Lattice
cf. Rapaz, Bellet, Deville: Numerical Modeling in MSE, Springer 1998
Defining a Neighbourhood
(von Neumann, Moore)
0
Defining State Variables
(e.g.: 0,1)
1
0 0 0
0 0 0
0 0
0 0 0 0 0
0 0
0 0 0 0 0 0
0 0 1 0 0 0
0 0
0 0
0
0
0
0
Defining Transition Rules (applied simultaneously to all cells)
1
1
The Cellular Automata Approach (Chopard and Droz)
Probabilities
Chopard and Droz, Cellular Automata Modeling of Physical Problems, Cambridge Univ. Press 1998
0
0
2
2
2
N144
1
4
1
pp
pp
ppD
ballistic
movement reflection
deflection
deflection
incoming nitrogen
p1
p2
p3
p0
ppp 31
12 20 pppDiffusion Coefficient
tx n
T
n
X ,with
Diffusion Profile (Chopard and Droz)
concentration
location x
cellular automata
analytical solution
tD
xctxc s
2erf1,
The Cellular Automata Approach for Internal Precipitation (Zhou and Wei)
Initialization
Zhou and Wei, Scripta Mater., 37 (1997) 1483
solvent: inert (I)
solute: active element (B)
nitride (BN)
nitrogen (N)
Transition: B+N=>BN:
(Implementation ChemApp possible)
Diffusion: N stepwise to the right
B every 20th iteration to the left
Stable state (AN)
Zhou and Wei, Scripta Mater., 37 (1997) 1483
Transition pT: pT
Transition pTr: pT
r
The Cellular Automata Approach for Internal Precipitation (Zhou and Wei)
Internal Precipitation (Zhou and Wei) + N- Diffusion (Chopard and Droz)
location y (arbitrary units)
location x (arbitrary units)
location y (arbitrary units)
location x (arbitrary units) 512 x 512 cells
20000 iterations
(increased B counter diffusion)
512 x 512 cells
1500 iterations
Precipitation + N Diffusion (Chopard and Droz) + B Diffusion in the Internal Precipitation Zone
solvent (inert)
active element B
nitride (BN)
0
0
nitride sink (min 5 nitrides within R=5cells)
Precipitation + B Diffusion in the Internal Precipiation Zone – Concentration Profile
concentration (cells / 512cells)
location x
active
element B
nitride
BN
Precipitation + B Diffusion in the Internal Precipitation Zone – Penetration Depth
square root of exp. time [h-0.5]
incubation
time: non-stable
precipitates
penetration
depth x [µm]
(Ni-20Cr-6Ti
1000°C, N2)
Grain boundary diffusion
location y (arbitrary units)
512 x 512 cells
3000 iterations Ttot=100h, T=800°C
location x (arbitrary units)
DGB>Dbulk
Conclusions and Future Aspects
Classical Wagner theory is limited to special scenarios
Finite Difference: easy combination with ChemApp
Cellular Automata:
-nucleation and growth
-3D effects: various diffusion paths (e.g., GB/bulk diffusion
Problems to be solved:
-combination of small and large concentrations
-implementation of ChemApp
more info: [email protected]