RIP - ICME and CorrosionCorrosion modeling using 3D probabilistic

cellular automata based model

Cristian Perez-Brokate1,2, Dung di Caprio2,

Damien Feron1,3, Jacques de Lamare1 et

Annie Chausse3

1 CEA/DEN/DPC/SCCME2 IRCP - Chimie Paris

3

cristian.perez-brokate@chimie-paristech.fr

March 7th 2016

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Outline

1 Introduction

2 Cellular Automata

3 Corrosion Model

4 Results

5 Conclusions and Perspectives

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 2

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Outline

1 Introduction

2 Cellular Automata

3 Corrosion Model

4 Results

5 Conclusions and Perspectives

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 3

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Introduction

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 4

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Introduction

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 4

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Introduction

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 4

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Introduction

Electrochemical reactions:- Anode: Metal oxidation

AnodeM+

Cathode

H20

- Cathode: Environment reduction

1/2 H2 + OH-

Cathode

- Cathode: Environment reduction

Electrolyte

e-

e-

ΔV

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 4

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Localized Corrosion

Corrosion depends on the distribution of anodic and cathodicreactions

Localized Corrosion:

Concentration of reactions

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Localized Corrosion

Can lead to loss of material functionality

Stochastic behavior (nucleation, electrochemical reactionlocalization)

Difficult to predict

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Localized Corrosion

Can lead to loss of material functionality

Stochastic behavior (nucleation, electrochemical reactionlocalization)

Difficult to predict

Cl-

Metal

Electrolyte

Cl-

Oxide

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 6

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Localized Corrosion

Can lead to loss of material functionality

Stochastic behavior (nucleation, electrochemical reactionlocalization)

Difficult to predict

a)

100μm

b)

di Caprio [2011]

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Outline

1 Introduction

2 Cellular Automata

3 Corrosion Model

4 Results

5 Conclusions and Perspectives

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Cellular Automata definition

1 d:Lattice dimension (d=3 for our case)

2 StateMaterial : Metal, Reactive or PassiveElectrolyte : Acidic, Basic or Neutral

3 Transition function:From state t −→ t + 1

4 Neighborhood :Moore or Neumann (or other)

d=1

d=2

d=3

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 8

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Cellular Automata definition

1 d:Lattice dimension (d=3 for our case)

2 StateMaterial : Metal, Reactive or PassiveElectrolyte : Acidic, Basic or Neutral

3 Transition function:From state t −→ t + 1

4 Neighborhood :Moore or Neumann (or other)

NeutralBulk

Reactive

Passive

Acidic

Basic

Metal: Solution:

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 8

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Cellular Automata definition

1 d:Lattice dimension (d=3 for our case)

2 StateMaterial : Metal, Reactive or PassiveElectrolyte : Acidic, Basic or Neutral

3 Transition function:From state t −→ t + 1

4 Neighborhood :Moore or Neumann (or other)

Dissolution:

Reactive Solution

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 8

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Cellular Automata definition

1 d:Lattice dimension (d=3 for our case)

2 StateMaterial : Metal, Reactive or PassiveElectrolyte : Acidic, Basic or Neutral

3 Transition function:From state t −→ t + 1

4 Neighborhood :Moore or Neumann (or other)

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Cellular Automata & Corrosion

1 Simple transition rules describecomplex systems

2 Adapted to model stochasticphenomena due to the inclusion ofprobabilities in the transition function T

3 Mesoscopic approach of corrosion(lattice cell size = 10 nm - 10 µm)

4 Simulation of morphological evolutionof interfaces

5 Adapted to parallel programing (agroup of cells per processor, GPU cardshas more processors)

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 9

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Cellular Automata & Corrosion

1 Simple transition rules describecomplex systems

2 Adapted to model stochasticphenomena due to the inclusion ofprobabilities in the transition function T

3 Mesoscopic approach of corrosion(lattice cell size = 10 nm - 10 µm)

4 Simulation of morphological evolutionof interfaces

5 Adapted to parallel programing (agroup of cells per processor, GPU cardshas more processors)

Figure: Brownian motion is astochastic phenomenon

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 9

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Cellular Automata & Corrosion

1 Simple transition rules describecomplex systems

2 Adapted to model stochasticphenomena due to the inclusion ofprobabilities in the transition function T

3 Mesoscopic approach of corrosion(lattice cell size = 10 nm - 10 µm)

4 Simulation of morphological evolutionof interfaces

5 Adapted to parallel programing (agroup of cells per processor, GPU cardshas more processors)

10µm

5mm

512 blocks

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 9

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Cellular Automata & Corrosion

1 Simple transition rules describecomplex systems

2 Adapted to model stochasticphenomena due to the inclusion ofprobabilities in the transition function T

3 Mesoscopic approach of corrosion(lattice cell size = 10 nm - 10 µm)

4 Simulation of morphological evolutionof interfaces

5 Adapted to parallel programing (agroup of cells per processor, GPU cardshas more processors)

a)

100μm

b)

di Caprio [2011]

Taleb & Sta�ej [2011]

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 9

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Cellular Automata & Corrosion

1 Simple transition rules describecomplex systems

2 Adapted to model stochasticphenomena due to the inclusion ofprobabilities in the transition function T

3 Mesoscopic approach of corrosion(lattice cell size = 10 nm - 10 µm)

4 Simulation of morphological evolutionof interfaces

5 Adapted to parallel programing (agroup of cells per processor, GPU cardshas more processors)

multipleprocessors

thousands of processors

CPU

GPU

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 9

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Outline

1 Introduction

2 Cellular Automata

3 Corrosion Model

4 Results

5 Conclusions and Perspectives

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Outline

3 Corrosion ModelPhysical description of corrosionCellular automata modelAlgorithm

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Physical description of corrosion

Electrochemical reactions

Chemical reaction Environment condition CommentAnodic

M + H2O −→ MOHaq + H+ + e− Acid / Neutral Metal oxidation + Cation hydrolysis

M + OH− −→ MOHsolid + e− Basic Precipitation of the hydroxide (Passivation)Cathodic

H+ + e− −→ 12H2 Acid / Neutral Reduction of hydrogen

H2O + e− −→ 12H2 + OH− Basic Reduction of water

Anaerobic condition (No oxygen considered), no cations

Diffusion

Chemical reaction Comment

H+ + OH− −→ H20 Neutralization

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Outline

3 Corrosion ModelPhysical description of corrosionCellular automata modelAlgorithm

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Corrosion model

Anode:

Oxidation site

Cathode:

Reduction site

e-

Electron

Transfer

Neutral

Metal

Reactive

Passive

Acidic

Basic

Metal:

Solution:

Phenomena included:

Corrosion (anodic and cathodic sites)

Electrolyte diffusion (stochastic method)

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Corrosion

Anodic and cathodic reactions are spatially separated.Controlled by probability (Psse)

Chemical reaction Cellular Automata Rule Environment conditionAnodic

M + H2O −→ MOHaq + H+ + e− Reactive −→ Acid Acid / Neutral

M + OH− −→ MOHsolid + e− Reactive + Basic −→ Passive + Neutral BasicCathodic

H+ + e− −→ 12H2 Surface + Acid −→ Surface + Neutral Acid / Neutral

H2O + e− −→ 12H2 + OH− Surface + Neutral −→ Surface + Basic Basic

Anodic reaction leads to more acidicenvironment and further corrosion.

Cathodic reaction leads to basic environmentand promote passive layer.

Basic environment

Acidic environment

Metal Acid

Metal+Basic Metal+Neutral

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Electrolyte diffusion

Random walk

(Ndiff ) diffusion iterations for one anodic and cathodicreactions

Neutralization of acid and basic sites

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Outline

3 Corrosion ModelPhysical description of corrosionCellular automata modelAlgorithm

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Flowchart

Return pit morphology

Diffusion

SSE reactions

Initialize grid

i < tn

Verify connectivity and select cathodic and anodic sites

j < Ndiff

j=j+1

i=i+1

PSSE

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Outline

1 Introduction

2 Cellular Automata

3 Corrosion Model

4 Results

5 Conclusions and Perspectives

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

General Corrosion

Metal

NeutralSolution

SurfaceReactive

Number of cells x(256)

Numberof cells y

(256)

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

General Corrosion1 Uniform corrosion2 Separation of acid and basic zones.3 Accelerated corrosion, cathodic reaction concentration.4 Separation of peninsula and slowing down of corrosion.

0

2

4

6

8

10

12

14

0 100 200 300 400 500 600 700 800 9000

1000

2000

3000

4000

5000

6000

7000

Corroded

Sites

×106

Number

ofreactions

Number of time steps

1

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

General Corrosion1 Uniform corrosion2 Separation of acid and basic zones.3 Accelerated corrosion, cathodic reaction concentration.4 Separation of peninsula and slowing down of corrosion.

0

2

4

6

8

10

12

14

0 100 200 300 400 500 600 700 800 9000

1000

2000

3000

4000

5000

6000

7000

Corroded

Sites

×106

Number

ofreactions

Number of time steps

2

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

General Corrosion

1 Uniform corrosion

2 Separation of acid and basic zones.

3 Accelerated corrosion, cathodic reaction concentration.

4 Separation of peninsula and slowing down of corrosion.

0

2

4

6

8

10

12

14

0 100 200 300 400 500 600 700 800 9000

1000

2000

3000

4000

5000

6000

7000

Corroded

Sites

×106

Number

ofreactions

Number of time steps

3

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 21

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

General Corrosion

1 Uniform corrosion

2 Separation of acid and basic zones.

3 Accelerated corrosion, cathodic reaction concentration.

4 Separation of peninsula and slowing down of corrosion.

0

2

4

6

8

10

12

14

0 100 200 300 400 500 600 700 800 9000

1000

2000

3000

4000

5000

6000

7000

Corroded

Sites

×106

Number

ofreactions

Number of time steps

4

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Metal thickness loss

Neutral

Bulk

Reactive

Passive

Acid

Basic

Metal:

Solution:

Non reactive

hloss

NXNY

+ +

Metal Loss

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Influence of Ndiff

Ndiff is the ratio of corrosion and diffusion rate.Conditions: constant electrochemical reaction probabilityPsse and dissolution probability Pdiss .

0

100

200

300

400

500

0 5000 10000 15000 20000

Met

alth

icknes

slo

ss

Number of time steps

Ndiff

200250300350

Neutralization increases when Ndiff increases.Cristian PEREZ — Research in Progress Symposium — March 7th 2016 23

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Influence of dissolution probability Pdiss

Constant Ndiff and electrochemical reaction probabilityPsse .

0

100

200

300

400

500

600

700

800

900

0 1000 2000 3000 4000 5000 6000 7000

Met

alth

icknes

slo

ss

Number of time steps

Larg

eis

land

det

ach

men

t

Pdiss

0.10.51.0

Dissolution probability has no major influence in metalloss.

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Influence of dissolution probability Pdiss

Constant Ndiff and electrochemical reaction probabilityPsse .

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 1000 2000 3000 4000 5000 6000 7000

Num

ber

ofIs

lands

Time step

Larg

eis

land

det

ach

men

t

Pdiss

0.10.51.0

0

5

10

15

20

25

0 1000 2000 3000 4000 5000 6000 7000

Aver

age

size

ofis

lands

Time step

Pdiss

0.10.51.0

Small island size

Number of islands increases when dissolution probabilitydecreases.

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Experimental comparison

Metal islands predicted in the model are observed in theliterature

100 µm

Figure: Corrosion of nickel alloyobserved after exposure in anincinerator of organic wastes[Di Caprio et al., 2011]

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Outline

1 Introduction

2 Cellular Automata

3 Corrosion Model

4 Results

5 Conclusions and Perspectives

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Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

Conclusions and Perspectives

Cellular Automata modeling is adapted to simulatestochastic anodic and cathodic reaction.

Cellular Automata simulates the morphological evolutionof generalized corrosion.

The model describes the apparition of metal island ingeneralized corrosion.

Quantification of island detachment and comparison withexperimental results.

Cristian PEREZ — Research in Progress Symposium — March 7th 2016 28

Thank you

Questions ?

Introduction Cellular Automata Corrosion Model Results Conclusions and Perspectives

References I

[Di Caprio et al., 2011] Di Caprio, D., Vautrin-Ul, C., Stafiej, J., Saunier, J., Chausse, A., Feron, D., and Badiali,J. P. (2011).Morphology of corroded surfaces: Contribution of cellular automaton modelling.Corrosion Science, 53(1):418–425.

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