Opening new doors with Chemistry

THINK SIMULATION!

Advances in Corrosion Simulation Technology

24th Conference October 23-24, 2007

Andre AnderkoGeorge

Engelhardt Margaret Lencka

Scope

• Structure of corrosion simulation technology

• General corrosion model

• Repassivation potential model

• Predicting the effects of heat treatment

• Modeling the propagation and time evolution of localized corrosion

• Development plans

Hierarchy of models for simulating aqueous corrosion

OLI’s Corrosion Simulation Technology

• Stability diagrams• Based entirely on thermodynamics• Predict the tendency of metals to corrode, passivate or remain

immune to corrosion

• General corrosion model• Based on surface electrochemistry• Predicts the rate of general corrosion and corrosion potential

• Repassivation potential model• Based on electrochemistry of local corrosive environments• Predicts the threshold potential above which stable localized

corrosion may occur

• Corrosion propagation and damage evolution model• Based on damage function analysis and deterministic extreme

value statistics• Predicts long-term damage based on short-term data

Electrochemical model for predicting general corrosion rate and corrosion potential

• Partial electrochemical processes in the active state:• Cathodic reactions (e.g., reduction of protons, water

molecules, oxygen, etc.)• Anodic reactions (e.g., oxidation of metals)• Adsorption phenomena

• Active-passive transition influenced by• Acid/base properties of passive oxide films• Temperature• Additional aggressive or inhibitive species

• Synthesis of the processes using mixed potential theory

General corrosion model:Application highlights

• Corrosion of stainless steel in nonoxidizing acids

• Active-passive transition and prediction of depassivation pH

• Effect of oxygen concentration on corrosion potential of a passive alloy

Modeling general

corrosion

• Corrosion rates and corrosion potential of 316L SS in HF solutions

• Prediction is based on calculating partial cathodic and anodic reactions in the active state

0.001

0.01

0.1

1

10

100

0.01 0.1 1 10m HF

Co

rr. R

ate

(m

m/y

)

Pawel (1994) 297 K

Schmitt (2004) 298 K

Ciaraldi et al. (1982) 298 K

Pawel (1994) 323 K

Pawel (1994) 349 K

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12 14m HF

Eco

rr (

V/S

HE

) Schmitt (2004) 298 K,aerated

Schmitt (2004) 298 K,deaerated

Ciaraldi et al. (1982)366 K, deaerated

Corrosion potential Corrosion rate

Corrosion potential and depassivation

pH

• Corrosion potential of 304L SS in aerated solutions

• Predicted polarization curves include active-passive transition and partial processes of O2, H+ and H2O reduction

(3)

(1)

(2)(4)

(3)

(1)

(2)(4)

pH=0.8

pH=1.8

-0.20-0.15-0.10-0.050.000.050.100.150.200.250.300.35

0 1 2 3 4 5 6

pH

Eco

rr /

SH

E

Corrosion potential as a

function of dissolved O2

• Transition between controlling cathodic processes (H2O and O2 reduction) explains the dependence of corrosion potential on dissolved O2

pH=0.013 ppm

pH=0.096 ppm

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

1.E-07 1.E-06 1.E-05 1.E-04 1.E-03m O2

Ec

orr (

SH

E)

Ecorr, exp

Ecorr, cal

Calculating repassivation potential

• Threshold condition: Potential above which localized corrosion can be stabilized

• The model simulates electrochemical processes in a pit or crevice in the limit of repassivation

• It relates the repassivation potential to solution chemistry

Repassivation potential model:Alloys 22, 825, and 316L

• The slope changes as a function of chloride activity

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1 10

aCl

Erp

(S

HE

)

23 C, exp

60 C, exp

95 C, exp

23 C, cal

60 C, cal

95 C, cal

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1 10

a Cl

Erp

(S

HE

)

368 K, exp

353 K, exp

333 K, exp

323 K, exp

303 K, exp

423 K, cal

368 K, cal

353 K, cal

333 K, cal

323 K, cal

303 K, cal

316L825

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1 10 100 1000

a Cl-

Erp

(S

HE

)313 K, exp

333 K, exp

353 K, exp

368 K, exp

378 K, exp

383 K, exp

398 K, exp

423 K, exp

448 K, exp

313 K, cal

333 K, cal

353 K, cal

368 K, cal

378 K, cal

383 K, cal

398 K, cal

423 K, cal

448 K, cal

22

Repassivation potential for mixed chloride – oxyanion systems

• A steep change in slope indicates inhibition at a certain oxyanion concentration

• The transition depends on Cl- concentration and temperature

• At high Cl- concentration, inhibition may not be achieved due to solubility limits

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1 10

M OH-

Erp

(S

HE

)23 C, 0.004 M Cl - exp

23 C, 0.5 M Cl - exp

23 C, 4 M Cl - exp

60 C, 0.04 M Cl - exp

60 C, 0.42 M Cl - exp

23 C, 0.004 M Cl - cal

23 C, 0.5 M Cl - cal

23 C, 4 M Cl - cal

60 C, 0.04 M Cl - cal

60 C, 0.42 M Cl - cal

Erp values above ~0.7 V indicate lack of localized corrosion

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1 10

M NO3-

Erp

(S

HE

)

23 C, 0.42 M Cl - exp

23 C, 3 M Cl - exp

23 C, 4 M Cl - exp

60 C, 0.04 M Cl - exp

95 C, 0.42 M Cl - exp

23 C, 0.42 M Cl - cal

23 C, 3 M Cl - cal

23 C, 4 M Cl - cal

60 C, 0.04 M Cl - cal

95 C, 0.42 M Cl - cal

316L in Cl- + OH-

316L in Cl- + NO3

-

Effect of molybdates on Erp of various alloys:Similar patterns

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1 10

M MoO42-

Erp

(S

HE

) 23 C, 4M NaCl, exp

60 C, 0.04 M NaCl, exp

23 C, 4M NaCl, cal

60 C, 0.04 M NaCl, cal

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1 10

M MoO42-

Erp

(S

HE

) 60 C, 0.4M Cl, exp

60 C, 4M Cl, exp

60 C, 0.4M Cl, cal

60 C, 4M Cl, cal

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1 10

M MoO42-

Erp

(S

HE

)

23 C, 4M NaCl, exp

60 C, 0.04 M NaCl, exp

60 C, 4 M NaCl, exp

23 C, 4M NaCl, cal

60 C, 0.04 M NaCl, cal

60 C, 4 M NaCl, cal

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.0001 0.001 0.01 0.1 1 10

M MoO42-

Erp

(S

HE

) 60 C, 0.4M Cl, exp

60 C, 4M Cl, exp

60 C, 0.4M Cl, cal

60 C, 4M Cl, cal

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1 10

M MoO42-

Erp

(S

HE

)23 C, 0.004 M Cl - exp

23 C, 0.04 M Cl - exp

23 C, 0.42 M Cl - exp

23 C, 4 M Cl - exp

60 C, 0.04 M Cl - exp

60 C, 0.42 M Cl - exp

23 C, 0.004 M Cl - cal

23 C, 0.04 M Cl - cal

23 C, 0.42 M Cl - cal

23 C, 4 M Cl - cal

60 C, 0.04 M Cl - cal

60 C, 0.42 M Cl - cal

316L

600

690

254SMO

2205

Generalized correlation for predicting Erp of stainless steels and nickel-base alloys

• The correlation has been verified for 13 alloys

• It also includes Fe (carbon steel) and Ni as limiting cases

• Correlation includes the effect of oxyanions (OH-, MoO4

2-, VO3-,

NO3-, SO4

2-)

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1 10

aCl

Erp

(SH

E)

22, exp22, generalized276, exp276, generalized625, exp625, generalized825, exp825, generalized690, generalized600, exp600, generalized800, generalized254SMO, exp254SMO, generalizedAL6XN, expAL6XN, generalized2205, generalized316L, exp316L, generalized304L, generalizeds-13Cr, exps-13Cr, generalized

T = 368 K

Effects of heat treatment• Formation of carbides, intermetallics, etc. changes the

microchemistry of alloys and affects corrosion resistance

• A model has been developed to predict alloy composition profiles in the vicinity of the grain boundary as a function of temperature and time of heat treatment• Formation of carbides (M7C3 or M23C6) at the grain

boundaries in Fe-Cr-Ni-Mo-W-N-C alloys • Para-equilibrium between the carbide phase and the alloy

matrix• Growth of the carbide phase as a function of time and

time evolution of the Cr-depleted zone

• Relating the model predictions to corrosion phenomena• Intergranular corrosion• Change in the repassivation potential

Sensitization model:Fundamentals

• At any time, total accumulation of Cr in the carbide is equal to total Cr depletion in the matrix

• Cr concentration at the phase boundary is defined by paraequilibrium

• Cr concentration profile results from diffusion from the grain

• Cr concentration far from the boundary remains essentially identical to bulk concentration (due to large excess of Cr relative to C)

Cr concentration

Distance from grain boundary

r – carbide dimension

r

CCr(z)

z

CCr

Cr

Cr

C

C

0

C

Cr

Calculating Cr depletion profile:Alloy 600

• Cr depletion results from M7C3 precipitation

• At a fixed temperature, the width of depletion zone increases with time; then, self-healing follows

• The model is in good agreement with experiment

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 200 400 600 800 1000

Distance from grain boundary, nm

x(C

r)

T=973 K, t=1h

T=973 K, t=1h, cal

T=973 K, t=10h

T=973 K, t=10h, cal

T=973 K, t=30h

T=973 K, t=30h, cal

T=973 K, t=100h

T=973 K, t=100h, cal

T=873 K, t=250h

T=873 K, t=250h, cal

T=1073 K, t=0.42h

T=1073 K, t=0.42h, cal

Data: Was and Kruger (1985)

Predicting intergranular corrosion

• Depletion parameter: proportional to the area of depletion profile below a certain Cr concentration

• It is calculated directly from the sensitization model

• Rate of intergranular corrosion correlates with the depletion parameter for x(Cr)*=0.120

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 20 40 60 80 100Aging time, h

rate

, mp

y

Streicher test

Huey test

0

24

68

10

1214

16

0 20 40 60 80 100

Aging time, h

De

ple

tio

n p

ara

me

ter

x(Cr)* = 0.12

x(Cr)* = 0.11

x(Cr)* = 0.1

x(Cr)* = 0.09

Standard intergranularcorrosion tests

Alloy 600 heat-treatedat 700 C:Depletion parametersfor various Cr levels

Predicting the repassivation potential: Heat-treated Alloy 825

• The measured Erp is assumed to primarily reflect the localized corrosion of the depleted regions (a pit is more likely to stabilize in an area that is more susceptible to localized corrosion)

• The measurable Erp can be obtained by integration over the depleted zone

• The prediction agrees with the data within experimental uncertainty

95 C0.00266 m Cl-

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

850 900 950 1000 1050 1100

Sensitization temperature

Erp

- E

rp(a

nn

eale

d), V t=15 h, exp

t=100h, exp

t=15h, cal

t=100 h, cal

Predicting Erp for welded alloy 22

• Solidification of welds may lead to segregation patterns of Ni depletion and solute enrichment in interdendritic volumes

• Dendrite cores are then depleted in Cr, Mo and W

• Direct prediction of Erp for annealed and welded samples using the generalized correlation for Erp as a function of alloy composition

95 C

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1E-04 0.001 0.01 0.1 1 10 100

M Cl-

Erp

(S

HE

) Mill annealed, exp

Bulk alloy, predicted

As welded, exp

Welded, predicted

Modeling the propagation of localized corrosion

• Deterministic Extreme Value Statistics • Combining the deterministic and statistical

view of localized corrosion• Prediction of long-term time evolution of localized

corrosion using short-term data• Implemented in Corrosion Analyzer v. 3.0

• New development: Monte Carlo simulation of corrosion damage

Difference between Damage Function Analysis (DFA) and Monte Carlo Simulation of

Corrosion Damage

The main idea of DFA is to regard each corrosion defect (pit, crack) as a “particle” that moves into the metal. Accordingly, the definition of damage function (number of defects for a given penetration) reduces to the solution of a system of balance equations in discontinuous media.

The main idea of the Monte Carlo method is to keep track of each stable pit (or crack) that nucleates, propagates and repassivates on the metal surface. • to effectively describe the progression of damage when

only several pits, or even a single pit, are alive and propagating; all other pits having repassivated.

• to take into account the interaction between a particular individual pit (crack) and the remaining (living) pits (cracks) on the surface in an explicit manner.

Advantages: The method allows us

Disadvantage: The Monte Carlo Method is relatively slow

Algorithm for Monte Carlo Simulation of Corrosion Damage

• Determine the location of the newly born active stable pits (randomly)

• Calculate new dimensions of active pits• Check if any active pit becomes passive due to

repassivation or due to overlapping with other pits• Check if any pit transitions into a crack• Calculate the new dimensions of each crack

In each time step, we need to

These calculations are repeated for every given time until all necessary statistical values are established.

We need models for each stage of damage propagation

Application of Monte Carlo SimulationMean depth of the deepest pit as a function

of time

Time, day

0 100 200 300 400

Max

imum

Pit

Dep

th, m

cm

0

200

400

600

800

1000

Alcan Alloy 2S-O in Kingston Tap Water

Xav -average depth of the largest pit

- standard deviation

Xav

Xav

Xav

Experimental data are taken from P.M. Aziz, Corrosion, 12, 495 (1956).

Experiment

Application of Monte Carlo Simulation:

Corrosion Fatigue

Oxygen Concentration, ppm

0 2 4 6 8 10

Pro

babi

lity

of F

ailu

re

0.0001

0.001

0.01

0.1

1

Lcr = 0.5 cm

Service Life = 15 years

[Cl-] = 350 ppm

Corrosion Fatigue

[Cl-] = 35 ppm

[Cl-] = 3500 ppm

Failure probability for low pressure steam turbine blades as a function of O2 concentration for different Cl- concentrations in electrolyte film during shutdown

Corrosion Analyzer:Underlying Technology at Present

• Thermodynamics of corrosion• Real-solution stability diagrams for alloys can be generated

using both the aqueous and MSE models

• Electrochemistry of corrosion• Computation of corrosion rate, corrosion potential and

repassivation potential• Calculated using the aqueous model for thermophysical

properties• Parameters available for carbon steel, aluminum, stainless

steels (13Cr, 304, 316 and 254SMO) and nickel-base alloys (22, 276, 625, 825, 600, 690, and Ni)

• Propagation of localized corrosion• Deterministic extreme value statistics (in Analyzer 3.0)

Development plans

• Corrosion Analyzer 3.0:• Deterministic extreme value statistics (already

implemented)• Module to predict the effect of heat treatment (to be

implemented)• Monte Carlo simulation of localized corrosion (to be

implemented)

• New technology• Development of electrochemical model parameter for

Cu and Cu-Ni alloys• Extending the electrochemical models to mixed-solvent

systems and coupling them with the thermophysical MSE models