Université Libre de Bruxelles Faculty of Applied Sciences
Department of Matter and Materials
Materials Science and Electrochemistry Group
Supervisor Jean – Luc Delplancke Co Supervisor Antoine Pourbaix Academic year 2005 – 2006
HYDROGEN EMBRITTLEMENT OF
FERROUS MATERIALS
Mioara Elvira Stroe
Supervisor
Dr. Jean Luc Delplancke
Co – supervisor Antoine Pourbaix
Local Members of the Jury Dr. Luc Segers
Dr. Marie–Paule Delplancke Dr. Marc Degrez
Invited Members of the Jury
Dr. Patrick Toussaint Industeel Belgium, Group Arcelor
Dr. Mihai Popa Institute of Physical Chemistry “I.G. Murgulescu”, Romania
Belgium, January 2006
To Luiza, Cris,
Anastasis and Anouka
Preface
This thesis is submitted to the Faculty of Applied Sciences at the Université Libre de Bruxelles, Belgium, in order to fulfil the requirements for obtaining the Ph.D. degree in Applied Sciences.
This study was financed by Industeel Belgium, in the frame of a broader research program between Industeel Belgium and CEBELCOR
Acknowledgements
I am deeply indebt to Antoine Pourbaix, co – supervisor of this thesis, for guiding me during all these years. His clarity of spirit and enthusiasm continuously amazed me and inspired me. I thank him for constantly encouraging me and for the extensive discussions that helped me to find the way.
By his support I could visit some laboratories abroad (NPL in UK, Statoil Norway, ECP France) and to participate to several conferences.
I would like to thank Jean Luc Delplancke, the head of Department of Materials Science and Electrochemistry for hosting me in his Department and for all support he granted me in the past four years.
I like to acknowledge Industeel Belgium, and particularly Patrick Toussaint and Jean Jacques Dufrane for financial and scientific support.
I am very glad that I found in Renée Scherer, Jacques Kissel and Suzanne de Kegel not only very kind colleagues but also friends. My work and my stay here was more pleasant due to their presence.
I enjoyed collaborating with Jean Dille, Roger D’Haens, Lionel Canet, Olivier van de Vyver and Victor Wertz from the Department of Materials Science and Electrochemistry.
I would like to thank to Catherine Dagbert from Ecole Centrale Paris. Part of fractional thermal degassing tests presented in Section 7.2. were performed with her assistance.
I am pleased to mention the good collaboration with Vincent Ligier to whom I thank for helping me with measurements by fractional thermal degassing at CRMC Industeel Creusot and also with many useful advices.
I thank to Liane Smith (Intetech Ltd. UK) and Stein Olsen (Statoil Norway) for the insights on the industrial aspects of the problem of hydrogen embrittlement.
I like to thank to my sister and my parents for encouraging me all this time. The holydays and their phone calls cheered me up whenever was needed.
My gratitude goes to my friend Tarik Bouali whose determined character and keen sense of detail were an example for me.
ABSTRACT
This work deals with the damage due to the simultaneous presence of hydrogen in atomic form and stress – straining.
The aim of this work is twofold: to better understand the hydrogen embrittlement mechanisms and to translate the acquired knowledge into a more appropriate qualification test.
The phenomena of hydrogen entry and transport inside the metals, together with the different types of damages due to the presence of hydrogen, are presented.
The analysis of the most important models proposed up to now for hydrogen embrittlement (HE) indicated that the slow dynamic plastic straining is a key factor for the embritteling process. There is a synergistic effect of hydrogen – dislocations interactions: on one hand hydrogen facilitates the dislocations movement (according to the HELP mechanism) and on the other hand dislocations transport hydrogen during their movement when their velocity is lower than a critical value.
This work is focused on supermartensitic stainless steels, base and welded materials. The interest on these materials is due to their broad use in offshore oil production.
First, the material’s characterisation with regards to hydrogen content and localisation was performed. This was conducted in charging conditions that are representative of industrial applications.
Because of previous industrial experience it was necessary to find a more appropriate qualification test method to asses the risk of HE.
In this work we proposed the stepwise repeated slow strain rate test (SW R – SSRT) as a qualification test method for supermartensitic stainless steels.
This test method combines hydrogen charging, test duration, plastic, dynamic and slow strains. Thus, this test method is coherent with both the model HELP proposed for hydrogen embrittlement and the observations of industrial failures.
The stepwise repeated slow strain rate test (SW RSSRT) is interesting not only as a qualification test of martensitic stainless steels, but also as a qualification test of conditions for using these materials (type of straining, range of strain and stress, strain rate, hydrogen charging conditions, etc.).
RESUME
Ce travail se rapporte à l’endommagement provoqué par la présence simultanée de l’hydrogène sous forme atomique et une contrainte (appliquée où résiduelle).
Ce travail a comme but une meilleure compréhension du mécanisme de la fragilisation par l’hydrogène (FPH) et la recherche d’un essai de qualification qui soit cohérent avec ce mécanisme.
Les phénomènes liés à l’entrée et au transport de l’hydrogène au sein des métaux, ensemble avec les différents types d’endommagements dus à la présence de l’hydrogène, sont présentés.
L’analyse des modèles proposés jusqu’au présent pour la fragilisation par l’hydrogène (FPH) suggère que la déformation lente plastique dynamique est le facteur clé pour le processus de la fragilisation. Il y a un effet synergétique des interactions entre l’hydrogène et les dislocations: d’un coté l’hydrogène facilite le mouvement des dislocations (d’après le modèle HELP) et d’un autre coté les dislocations transportent l’hydrogène pendant leur mouvement, pourvu que leur vitesse soit en dessous d’une valeur critique.
Le travail a été conduit sur des aciers supermartensitiques, matériau de base et soudé. L’intérêt pour ces matériaux réside de leur large utilisation dans la production du pétrole en offshore.
D’abord, le matériau a été caractérisé du point de vu de la teneur et de la localisation de l’hydrogène. Les essais ont été conduits dans des conditions représentatives pour les cas industriels.
L’expérience industrielle d’auparavant indique qu’il est nécessaire de trouver un test de qualification plus approprié pour estimer la susceptibilité à la fragilisation par l’hydrogène.
Dans ce travail on propose un essai de traction lente incrémentée (SW R – SSRT) comme méthode de qualification pour les aciers supermartensitiques.
L’essai combine le chargement en hydrogène, la durée d’essai, la déformation lente, plastique et dynamique. Donc, cette méthode d’essai est cohérente avec le modèle HELP proposé pour FPH et les observations des accidents industriels.
Cet essai est intéressant pas seulement comme essai de qualification pour les aciers supermartensitiques, mais aussi comme essai de qualification pour les conditions d’utilisation des ces matériaux (type de déformation, niveau de déformation et contrainte, vitesse de déformation, conditions de chargement en hydrogène, etc.).
TABLE OF CONTENT
NOTATION
1. INTRODUCTION ………..
1.1. ORIGIN AND AIMS OF THE WORK 1.2. STRUCTURE OF THE WORK
2. HYDROGEN ENTRY AND TRANSPORT IN METALS ………
2.1. HYDROGEN ADSORPTION
2.1.1. ELECTROCHEMICAL CHARGING
2.1.2. CHARGING FROM GASEOUS HYDROGEN ATMOSPHERE 2.1.3. THE INFLUENCE OF SURFACE STATE ON ADSORPTION
2.2. HYDROGEN ABSORPTION
2.2.1. ATOMIC HYDROGEN TRANSFER (CLASSICAL MECHANISM)
2.2.2. DIRECT TRANSFER OF H+ THROUGH THE INTERFACE (MODEL PROPOSED BY CROLET ET AL.)
2.3. HYDROGEN TRANSPORT IN MATERIAL 2.3.1. DIFFUSION
2.3.1.1. IDEAL DIFFUSION, FICK’S LAW 2.3.1.2. TEMPERATURE EFFECTS
2.3.1.3. DIFFUSION UNDER STRESS GRADIENT 2.3.2. TRAPPING
2.3.3. TRANSPORT OF HYDROGEN BY MOVING DISLOCATIONS 2.4. SUMMARY OF HYDROGEN IN METALS
3. TYPES OF DAMAGES DUE TO HYDROGEN ………..
3.1. HYDROGEN INDUCED CRACKING (HIC) AND STEPWISE CRACKING (SWC)
1.
3.
5.
7.
10.
10.
15.
18.
18.
19.
22.
23.
23.
23.
25.
26.
26.
28.
30.
33.
36.
3.2. STRESS ORIENTED HYDROGEN INDUCED CRACKING (SOHIC)
3.3. HYDROGEN REACTION WITH THE METAL MATRIX (HYDRIDE FORMATION)
3.4. HYDROGEN REACTIONS WITH NON METALLIC PHASES
3.5. HYDROGEN EMBRITTLEMENT (HE ) OR HYDROGEN STRESS CRACKING (HSC)
3.6. SULPHIDE STRESS CRACKING (SSC)
4. HYDROGEN EMBRITTLEMENT ………..
4.1. DECOHESION MECHANISM
4.1.1. THERMODYNAMIC ASPECTS OF INTERFACIAL DECOHESION
4.1.2. ELECTRONIC DISTRIBUTION IN H – METAL SYSTEMS 4.1.3. EXPERIMENTAL OBSERVATIONS
4.1.4. CONCLUSIONS FOR THE DECOHESION MECHANISM
4.2. PLASTICITY MODEL: HYDROGEN ENHANCED LOCALISED PLASTICITY “HELP”
4.2.1. HYDROGEN SHIELDING EFFECT
4.2.1.1. HYDROGEN EFFECT ON THE INTERACTIONS
BETWEEN DISLOCATIONS
4.2.1.2. INTERACTIONS BETWEEN DISLOCATIONS AND
AN IMPURITY ATOM IN THE PRESENCE OF HYDROGEN
4.2.2. MICROSCOPIC OBSERVATIONS 4.2.3. MACROSCOPIC OBSERVATIONS
4.2.4. CONCLUSIONS FOR THE HELP MECHANISM
4.3. CONCLUSIONS ON THE PARAMETERS AND ON THE MODELS PROPOSED FOR HYDROGEN EMBRITTLEMENT
5. INDUSTRIAL ASPECTS AND NEED FOR A HE TEST METHOD ...
5.1. HISTORIC OF SUPERMARTENSITIC STAINLESS STEEL USE IN OFF SHORE
37.
38.
39.
39.
40.
41.
44.
44.
48.
48.
49.
50.
51.
52.
55.
55.
60.
61.
61.
65.
67.
5.2. FAILURES DUE TO HYDROGEN EMBRITTLEMENT 5.3. NEED FOR A HE TEST METHOD
6. MATERIALS AND EXPERIMENTAL TECHNIQUES ………
6.1. MATERIAL DESCRIPTION
6.1.1. OVERVIEW OF GENERAL MECHANICAL PROPERTIES 6.1.2. CHEMICAL COMPOSITION AND MICROSTRUCTURE 6.1.3. WELD DESCRIPTION
6.2. EXPERIMENTAL METHODS
6.2.1. PERMEATION METHOD 6.2.2. THERMAL DEGASSING
6.2.2.1. FRACTIONAL THERMAL DEGASSING 6.2.2.2. TOTAL DEGASSING
6.2.3. NANOINDENTATION METHOD 6.2.4. MECHANICAL TESTS
6.2.4.1. CONSTANT LOAD TEST
6.2.4.2. SLOW STRAIN RATE TEST (SSRT)
6.2.4.3. REPEATED SLOW STRAIN RATE TEST (RSSRT)
6.2.4.4. STEPWISE REPEATED SLOW STRAIN RATE TEST
(SW RSSRT)
7. EXPERIMENTAL RESULTS ……….
7.1. PERMEATION TESTS RESULTS
7.2. RESULTS FOR THERMAL DEGASSING TESTS 7.2.1. FRACTIONAL THERMAL DEGASSING 7.2.2. TOTAL DEGASSING
7.2.3. CONCLUSIONS OF THERMAL DEGASSING TESTS 7.3. RESULTS OF NANOINDENTATION TESTS
7.4. RESULTS OF MECHANICAL TESTS
7.4.1. RESULTS FOR CONSTANT LOAD TESTS
69.
71.
73.
75.
75.
77.
78.
81.
81.
88.
88.
89.
91.
94.
94.
96.
99.
100.
103.
105.
118.
118.
121.
121.
122.
127.
127.
7.4.2. RESULTS OF SLOW STRAIN RATE TESTS 7.4.3. REPEATED SLOW TRAIN RATE TESTS RESULTS
7.4.4. STEPWISE REPEATED SLOW STRAIN RATE TESTS RESULTS
8. DISCUSSION ………
8.1. HYDROGEN DISLOCATIONS INTERACTIONS 8.2. THE EMBRITTLING PHENOMENON: FROM HELP TO
EMBRITTLEMENT
8.3. BEHAVIOUR OF VARIOUS FERROUS MATERIALS IN THE PRESENCE OF HYDROGEN
8.4. PROPOSAL FOR SPECIFIC HE TESTS FOR MARTENSITIC MATERIALS
8.5. RESULTS OF HE TESTS USED IN THIS WORK
8.6. SW RSSRT AS A QUALIFICATION TEST FOR MARTENSITIC STEELS AND FOR OPERATING CONDITIONS
9. CONCLUSIONS ………...
10. REFERENCES ……….
11. APPENDICES ………..
APPENDIX 1. HYDROGEN EVOLUTION REACTIONS ……….
APPENDIX 2. THERMODYNAMIC AND KINETIC ASPECTS OF THE
INTERFACIAL DECOHESION ………..
APPENDIX 3. ATOM SUPERPOSITION AND ELECTRON DELOCALISATION MOLECULAR ORBITAL METHOD (ASED – MO) ………
APPENDIX 4. HYDROGEN SHIELDING EFFECT ………..
128.
148.
161.
171.
173.
175.
175.
177.
178.
181.
183.
189.
201.
203.
213.
227.
229.
NOTATION
Roman letters
A A.R.
AFM b C0
CE CL D Dok
E Ea
Er
F 2Fk* G GTAW h Hnano
[H]
[H+] HAZ HE HELP HIC HID i i0
J Jabs Jads Jdes Jdsb
Jss
Surface Area reduction
Atomic force microscopy Burgers vector
Subsurface concentration Counter electrode
Constant load test Diffusion coefficient
Preexponential term for kink diffusion Potential
Activation energy
Reduced elastic modulus Faraday constant
Free energy of formation of a double – kink on a dislocation Shear modulus
Gas tungsten arc welding Depth
Nanohardness
Concentration of hydrogen atoms on the metallic surface Concentration of hydrogen cations in solution
Heat affected zone Hydrogen embrittlement
Hydrogen enhanced localised plasticity Hydrogen induced cracking
Hydrogen induced decohesion Current density
Exchange current density Flux
Flux of absorbed hydrogen atoms Flux of adsorbed hydrogen atoms Flux of desorbed hydrogen atoms
Flux of hydrogen atoms diffusing out from the bulk of material Steady state flux
k ki
l l L m ni
Ni
No
Nr
Ns
P Pnano
PGMAW Qk
r R RE R SSRT S Snano SCE SCC SEM SOHIC SSC SSRT SW M SSRT SW R SSRT t
T TEM TTF UTS vcr V VH
Boltzmann’s constant Rate constant for reaction i Dislocation length
Strain increment Membrane thickness Mass
Stoichiometric coefficient of species i Density of irreversible traps
Number of interstitial sites occupied by hydrogen Density of reversible traps
Number of interstitial sites in the matrix Hydrogen partial pressure
Indentation load
Pulse gas metal arc welding Activation energy for kink diffusion Distance in polar coordinates Gas constant
Reference electrode
Repeated slow strain rate test Sieverts constant
Stiffness
Saturated calomel electrode Stress corrosion cracking Scanning electron microscopy
Stress oriented hydrogen induced cracking Sulphide stress cracking
Slow strain rate test
Stepwise monotonic slow strain rate test Stepwise repeated slow strain rate test Time
Temperature
Transmission electron microscopy Time to failure
Ultimate tensile strength Critical velocity of dislocation Mean molar volume
Molar volume of hydrogen
Greek letters x
W WB
WE YS YS0.2%
Distance
Activation energy
Bonding energy between hydrogen and trap Working electrode
Yield strength Offset yield strength
αi Transfer coefficient of reaction i β Proportionality constant
γ Proportionality constant
δ Separation distance between two layers of the interface δc Critical separation distance
∆l Strain to failure
ε Strain
η Overpotential
θ Coverage degree
θ0 Equilibrium coverage degree θL Occupancy of the interstitial sites θr Occupancy of the reversible sites
µ Bulk modulus
ν Poisson’s coefficient
σ Stress
σh Hydrostatic stress
τ Shear stress
ϕ (χ, δ) Cohesive function φ Angle in polar coordinates
1. INTRODUCTION
1. INTRODUCTION
1. INTRODUCTION
1.1. ORIGIN AND AIMS OF THE WORK
Several cracking accidents occurred recently in offshore exploitations that were attributed to hydrogen embrittlement (HE).
The structures involved are flowlines and equipments installed on the bottom of the sea.
These flowlines are protected against corrosion by cathodic protection with aluminium – indium (AlIn) or aluminium – zinc – indium (AlZnIn) sacrificial anodes and by heavy duty coatings.
The flowlines are subjected to elastic and plastic deformations during laying and during operation: reeling and dereeling, laying, movements on the sea bed due to marine streams, thermal expansion, pressure tests, or accidental interference with fishing activities.
The materials of the pipelines that experienced failure are martensitic and supermartensitic stainless steels (SMSS) and duplex stainless steels (DSS).
Of course, these materials are known to be sensitive to hydrogen embrittlement.
However, extensive design analysis and qualification testing [1] indicate that they are appropriate for this application. In particular extensive long-term testing showed no cracking under constant load and under constant plastic deformation (four point bend tests) at – 1050 mV to – 1200 mV versus saturated calomel electrode (SCE).
As these materials are much more cost effective than carbon steel, their use has markedly increased in the recent past [2] and is planned to increase further in the future.
These cracking accidents came as a surprise to many operators, because the materials passed all the qualification tests and because, currently, there are about 2000 km of such SMSS and DSS pipelines in operation and only few accidents occurred.
This work has two main purposes:
¾ a better understanding of the hydrogen embrittlement mechanisms involved in the failures,
1. INTRODUCTION
¾ in case the HE tests used appear non appropriate, find better qualification tests that better reflect the mechanisms and parameters involved in HE.
This study is focused on martensitic stainless steels, due notably to a marked trend for a broader use of this material.
In principle two approaches can be considered:
¾ a detailed fundamental analysis of the HE phenomena, to see the factors that may cause failures,
¾ a comprehensive analysis of the accidents.
Since a comprehensive analysis of the industrial accidents is not currently available, this study was conducted mostly on the basis of an analysis of the fundamental aspects of hydrogen embrittlement.
Extensive work was conducted and several models were proposed for hydrogen embrittlement. But, none of the models proposed up to now can explain all the observed phenomena or the role of all factors.
For example, the hydrogen content was often considered as the main factor (as in the decohesion and the adsorption models, see section 4). The stress level is also considered in most studies. But the loading mode, the local H accumulation and the local stress concentration in the bulk of the material were not always given due consideration.
It was thus felt necessary to revisit the existing models with the aim of identifying and analysing the influencing parameters.
Hydrogen embrittlement is a loss of mechanical properties due to the presence of hydrogen in atomic form and stress. A significant decrease of ductility and /or fracture strength, delayed fracture and absence of metal loss are typical features of HE.
In fact, this work showed that the fundamental approach combined with the real life test parameters and with the analysis of the actual failures proved to be interestingly coherent.
1. INTRODUCTION
1.2. STRUCTURE OF THE WORK
After the presentation of the origin and the aims of this work (Section 1.1.), the most important aspects of the hydrogen entry and behaviour inside the materials are presented in Section 2.
In Section 3. a summary of different damages due to hydrogen is presented. This chapter aims to identify the characteristics of Hydrogen Embrittlement (HE) in comparison with other types of hydrogen damages. HE is the consequence of simultaneous presence of hydrogen in atomic form and stress.
Several models were proposed up to now for hydrogen embrittlement. An analysis of the most important is presented in Section 4. The factors involved in these models and that must be considered for testing materials, were identified.
The industrial context at the origin of this work and the need for specific tests are described in Section 5.
This study is focused on supermartensitic stainless steels. The description of the materials and the experimental methods selected and used to characterise the materials for HE is given in Section 6.
The results are presented in Section 7.
The discussion (Section 8) addresses the test methods that are coherent with the mechanisms for hydrogen embrittlement and analyses the results, with a comparison with the real conditions of failures.
Section 9 (Conclusions) summarises the important factors for hydrogen embrittlement that are derived from the HELP model, how these factors can be included in a specific test procedure for HE, how the results of a test proposed here are coherent with the models and with the industrial experience.
1. INTRODUCTION
2. HYDROGEN ENTRY AND
TRANSPORT IN METALS
2. HYDROGEN IN METALS
2. HYDROGEN IN METALS
In this section the different steps involved in hydrogen entry and transport through the material are presented.
The first step is hydrogen adsorption on the material surface.
As source of hydrogen, electrochemical evolution of hydrogen by cathodic polarisation, corrosion reaction or gaseous hydrogen atmosphere can be mentioned.
In this work two cases are analysed: cathodic protection in aqueous solution (Section 2.1.1.) and adsorption from gaseous hydrogen atmosphere (Section 2.1.2.).
The influence of metallic surface state on the hydrogen adsorption is analysed in Section 2.1.3.
The adsorbed atoms could then undergo absorption, passing through the metallic interface. This step leads to accumulation of a subsurface hydrogen concentration, C0. The C0
dependency on applied potential or current (for electrochemical charging) and pressure (for charging from gaseous hydrogen atmosphere) is presented in Section 2.2.
The next process is the transport of hydrogen through the material. The different aspects, like diffusion, trapping and the hydrogen transport by moving dislocations are presented in Section 2.3.
2. HYDROGEN IN METALS
2.1. HYDROGEN ADSORPTION
The adsorbed hydrogen atoms can be formed by different paths, according to the source of hydrogen.
By cathodic polarisation or corrosion reaction, electroadsorbed species are formed on the metallic surface whereas in the presence of a gaseous atmosphere the molecular hydrogen can undergo physisorption or chemisorption.
2.1.1. ELECTROCHEMICAL CHARGING
In solution under cathodic polarisation, the hydrated hydrogen cations, H3O+, are transported by diffusion / migration towards the cathode. There, the cation undergoes reduction and becomes atomic hydrogen, H.. The atomic hydrogen can recombine to form molecular hydrogen, H2 that leaves the metallic surface.
For the reduction of hydrogen ions two different reaction mechanisms are possible, depending on the nature of the metal:
A. Volmer – Tafel mechanism (electrochemical reduction followed by chemical recombination)
adsorbed k
k
hydrated e H
H
↔
−
+ +− 1
1
Volmer reaction (2.1.)
2
2
2
H H
H
k
k adsorbed
adsorbed
↔
−
+ Tafel reaction (2.2.)
B. Volmer – Heyrovsky mechanism (electrochemical reduction followed by electrochemical recombination)
adsorbed k
k
hydrated e H
H
↔
−
+ +− 1
1
Volmer reaction (2.1.)
2
3
3
H e
H
H k
k adsorbed
hydrated
↔
−
+ + +− Heyrovsky reaction (2.3.)
2. HYDROGEN IN METALS
Depending on the nature of the metal, the different mechanisms of hydrogen reduction could take place. The paths followed by hydrogen reduction reaction on different metals are given in Table 2.1.
For iron and steels the most probable mechanisms are coupled reduction – chemical combination or slow reduction – fast electrochemical as noted in Table 2.1.
Table 2.1. Mechanisms followed by hydrogen reduction on different metals [3]
Metal Mechanism Fe A : Coupled reduction, recombination
or
B :Slow reduction, fast electrochemical Ti B: Fast reduction, slow electrochemical Pd A : Fast reduction, slow recombination
Pt A : Fast reduction, slow recombination Ni A : Slow reduction, fast recombination
For each of the two mechanisms, the reactions and the dependency of the degree of coverage, θ, on the current or potential will be described.
θ is necessary to calculate the subsurface concentration C0.
The subsurface concentration, C0, is an important factor as it determines the hydrogen content in the material (see Section 2.2. and 2.3.). It also determines the filling of reversible traps, as will be presented in Section 2.3.
A. Volmer – Tafel mechanism
The first reaction (Volmer reaction) is the cathodic reduction of hydrated cations to form atomic hydrogen that remains adsorbed on the metallic surface.
The second reaction is the recombination of atomic hydrogen to form molecular hydrogen and is a purely chemical reaction.
2. HYDROGEN IN METALS
The general expression for the rate of an electrochemical reaction is:
RT rev F E E i e
n Ci RT
W ke rate
))
( −
Π −
= −
α
(2.4.)
Assuming that the Volmer reaction is the rate determining reaction, the expression for the potential – current density dependency can be written as:
[ ]
−
−
− +
= − α η
α η
RT V F H
RT k VF H
k
i (1 )
exp
exp 1
1
1 (2.5.)
The concentration of atomic hydrogen adsorbed on the surface, [H], is proportional to the degree of coverage, θ. The reduction of hydrogen cation H+ occurs only on the sites that are not covered by adsorbed hydrogen atoms. This part is equal to (1 – θ), so the second term on the right side of equation (2.5.) is directly proportional to (1 – θ).
The current – potential relationship becomes:
−
−
−
−
= − α η
θ α η
θ RT
V F RT k
VF k
i (1 )
exp ) 1 (
exp 1
1
1 (2.6.)
By introducing the exchange current density for Volmer reaction, i0,V, and the overvoltage expressions, η, the equation (2.6.) becomes:
−
− −
− −
= α η
θ η θ
α θ
θ
RT F RT
i F
i V V (1 V)
1 exp exp 1
0 0
, 0
1 (2.7.)
2. HYDROGEN IN METALS
The equation (2.7.) expresses the dependence of the degree of coverage on the current density i1 .
The Tafel reaction is a pure chemical reaction, so its rate constant does not depend on the potential. The reaction rate is given by:
[ ]
(1 ) ²2 2 2
2 =− =k −θ −k−θ
dt H Fd
i (2.8.)
At equilibrium, i.e. when the overall rate is zero, the degree of coverage reaches the equilibrium value, θ0, given by:
² )
1
( 0 2 2 0
2 2 ,
0 =k −θ =k−θ
i (2.9.)
For the Volmer – Tafel mechanism when the rate is determined by the Volmer reaction, the degree of coverage is (See Appendix 1 ):
2 , 0 0 1 1
i
− i
=θ
θ (2.10.)
where i0,2 is the reaction exchange current density for the equilibrium value of the potential.
B. Volmer – Heyrovsky mechanism (electrochemical reduction followed by electrochemical recombination (Figure 2.2.)
adsorbed k
k
hydrated e H
H
↔
−
+ +− 1
1
Volmer reaction (2.1.)
2
3
3
H e
H
H k
k adsorbed
hydrated
↔
−
+ + +− Heyrovsky reaction (2.3.)
2. HYDROGEN IN METALS
The Heyrovsky reaction (2.3.) consists of the reduction of a hydrated hydrogen cation with a hydrogen atom that is adsorbed on the metallic surface, with the formation of molecular hydrogen. This equation is also an electrochemical reaction, as well as the Volmer reaction (2.1.). The rate of the reaction is potential dependent.
The rate of the cathodic partial reaction is proportional to the degree of coverage, θ, and the hydrogen cations concentration, [H+]. The reversal reaction is proportional to the molecular hydrogen concentration, [H2], and the free part of the surface (1 – θ). The rate of reaction (2.3.) is given by:
[ ] [ ]
−
−
−
−
= − + α η
θ α η
θ RT
H F H
RT k HF H
k
i (1 )
exp exp
) 1
( 3
2 3
3 (2.11.)
For the Volmer – Heyrovsky mechanism, θ depends on the current density of each partial reaction involved, as both of them are charge transfer reactions.
Considering the equations (2.5.) and (2.11.) and for large overvoltage, the degree of coverage becomes independent of the potential. E.g. for high cathodic overvoltage, θ is expressed as:
H V
i i
, 0
, 0 0 0
1 1 1
θ θ θ
+ −
= (2.12.)
where i0,V and i0,H are the exchange current densities for the Volmer and Heyrovsky reactions respectively.
The hydrogen coverage on the metal substrate depends both on the mechanism of hydrogen evolution on the metal (A or B) and on the charging conditions (current density or potential).
2. HYDROGEN IN METALS
2.1.2. CHARGING FROM GASEOUS HYDROGEN ATMOSPHERE
The model proposed by Wang in 1936 [4] and then improved by other authors [5 – 10] for the dissociative chemisorption of gaseous hydrogen is presented in Figure 2.1.
The process involves several steps:
a. The gas molecule strikes the material surface and splits into atoms that adhere there.
adsorbed
H
H2 ↔2 (2.13.)
The flux of adsorbing atoms is second order in (1 – θ) and could be expressed by:
P k
Jads = ads(1−θ)² (2.14.)
b. There is a reversal reaction of recombination of adsorbed atoms with the formation of molecular hydrogen, which leaves the metallic surface. The desorbing flux is second order in θ, since two adjacent atoms are needed to recombine:
θ²
des
des k
J = (2.15.)
c. The adsorbed atoms could traverse the metallic interface and become absorbed atoms. The corresponding flux is:
γθ
abs =
J (2.16.)
2. HYDROGEN IN METALS
d. The atoms inside the material could diffuse out to the surface and the flux is proportional to the subsurface hydrogen concentration, C0, and the fraction of unoccupied surface sites, through which hydrogen can diffuse out:
) 0
1
( C
Jdsb =β −θ (2.17.)
The net flux has the following form:
² )²
1
( θ desθ
ads P k
k
J = − − (2.18.)
) 0
1
( C
J =γθ −β −θ (2.19.)
At equilibrium, there is no net flux. The degree of coverage, θ0, and subsurface hydrogen concentration, C0, can be deduced as:
k P k
des
= ads
− 0
0
1 θ
θ (2.20.)
k P C k
des
eq ads β
= γ
,
0 (2.21.)
The expression for the concentration is known as the Sieverts’ law:
P S
C0,eq = (2.22.)
where S is Sieverts’ constant that depends on the kinetics of adsorption and desorption processes:
β γ
des ads
k
S = k (2.23.)
2. HYDROGEN IN METALS
This model explains quantitatively how the net flux changes with the external gas pressure.
The Sieverts’ law shows that the subsurface hydrogen concentration is proportional to the square root of the hydrogen atmosphere pressure.
In Figure 2.2. an example of this dependency is presented for carbon steel at different temperatures [11]. On the ordinate the flux units are presented, as the flux is proportional to the subsurface concentration (see section 6. 1. Permeation test method).
J ads =kads(1–θ )²P
J dsb = β(1–θ )C0
J des = kdesθ²
J abs = γ θ
gas interface metal bulk
Figure 2.1. Fluxes involved in the hydrogen adsorption and absorption from gaseous atmosphere
0 5 10 15 20 25
0 50 100 150 200 250 300
square root of hydrogen pressure (Pa1/2)
Flux (in arbitrary units)
Figure 2.2. Hydrogen flux – hydrogen pressure dependency at different temperatures for carbon steel [11]
413 K 483 K
533 K 633 K 698 K
2. HYDROGEN IN METALS
This type of charging can take place in the same time with electrochemical charging: (for instance: pipelines at great depths, cathodically protected, with simultaneous electrochemical charging and charging from gaseous H2 from bubbles at high hydrostatic pressure).
2.1.3. THE INFLUENCE OF SURFACE STATE ON THE ADSORPTION Presence of promoters for hydrogen entry
An important aspect of hydrogen behaviour is the substantial enhancement of absorption in the presence of specific compounds. These compounds such as S2-, HS –, H2S, As etc., hinder the recombination of hydrogen atoms on the metallic surface and therefore enhance the absorption reaction.
These compounds are usually referred to as poisons.
Even small quantities of poison strongly increase the hydrogen uptake. In Table 2.2. the hydrogen amount penetrating the material for constant charging current, when the amount of sulphide in solution increases, is presented [12].
Table 2.2. Hydrogen uptake function of sulphide content in solution [12]
[S2–], ppm Hydrogen penetrating the steel (%)
3.5 x 10 – 3 1.6
1.3 x 10 – 2 2.4
2.75 x 10 – 2 5.8
3.6 x 10 – 1 25.6
Oxide films formed on the metallic surface are barriers for H absorption and are hindering the hydrogen passage through the interface [13 – 17].
2.2. HYDROGEN ABSORPTION
With regard to the passage of hydrogen through the metallic interface, with the accumulation of a subsurface concentration, C0, two mechanisms were proposed up to now:
2. HYDROGEN IN METALS
¾ one mechanism considers that the same species (atomic H) adsorbed on the surface lead to molecular and absorbed hydrogen (classical mechanism presented in Section 2.2.1.)
¾ Crolet et al. recently suggested that hydrogen is passing in ionic form (H+) directly through the metallic interface to form a solid solution (Section 2.2.2.)
2.2.1. ATOMIC H TRANSFER (CLASSICAL MECHANISM)
After the reduction of hydrogen cations, a part of the hydrogen atoms that are adsorbed on the metallic surface will recombine to form molecular hydrogen that leaves the surface.
Another part of adsorbed hydrogen atoms will undergo an absorption reaction inside the material, according to the equilibrium:
absorbed
adsorbed H
H ↔ (2.24.)
The direct reaction, of passage of atomic hydrogen through the interface, depends on the surface coverage (θ) and on the number of available sites in the subsurface that hydrogen can occupy.
The consequence is the accumulation of hydrogen under the metallic surface, leading to a concentration C0.
The reversal reaction, of hydrogen passage form the subsurface towards the surface can take place.
The rate for the reversal reaction is proportional to the subsurface concentration and to the concentration of empty sites on the surface through which hydrogen could be desorbed (1 – θ ).
The rate of the overall reaction is:
) 1 (
1 0 0 θ
θ − −
−
= k C
N k N
i des
s abs
abs (2.25.)
2. HYDROGEN IN METALS
At equilibrium (i abs = 0) and for small coverage degree θ and small degree of saturation, the subsurface concentration of hydrogen C0 is proportional to the degree of coverage:
C0
k
kabsθ = des (2.26.)
or:
θ K
C0 = (2.27.)
where K is the ratio of the rate constants for the direct and reversal reaction of the hydrogen passage through the interface (2.24.).
The equation (2.27.) shows that the subsurface concentration of hydrogen, C0, is a function of the degree of coverage, θ.
We remind here that in the previous section we saw that θ depends on the charging conditions (current density and potential) and also on the temperature.
Thus, the concentration of hydrogen in the material will also be depending on these parameters.
Assuming that the passage of hydrogen through the interface (2.24.) is the slowest step, then, for the Volmer - Tafel mechanism the relationship between the subsurface concentration and the charging current can be found considering that reactions (2.1.) and (2.2.) are at equilibrium, thus:
[ ]
(1 )exp 2 ²1 θ α η kθ
RT H F
k
i =
−
= + (2.28.)
Replacing θ from (2.28.) into (2.27.) leads to the value of C0 :
k i K C
2 0
= 1 (2.29.)
2. HYDROGEN IN METALS
The subsurface concentration C0 depends not only on the charging current, but also on the kinetics of hydrogen evolution (through k2).
The square root dependence on the charging current is followed up to certain value of the current density. Above a limiting value, the subsurface concentration of hydrogen becomes independent of the charging current (Figure 2.3.). This corresponds to the saturation of the surface ( θ = 1).
In the presence of promoters (or poisons) this square root dependency is followed up to high values of charging current density as presented in Figure 2.3 [18].
Thus, the subsurface concentration, C0, depends on the charging conditions (applied current or potential), on temperature, pH, state of the surface (presence of poisons, presence of oxides, other species than hydrogen adsorbed on the surface).
1,0E+00 1,0E+01 1,0E+02 1,0E+03
1,0E+00 1,0E+01 1,0E+02 1,0E+03 1,0E+04
i1/2 (µA/cm²)
Ct (ppm wt)
1,0E-05 1,0E-04 1,0E-03 1,0E-02
C0 (ppm wt)
Figure 2.3. Example of experimental hydrogen content – charging current density dependency. Tests were conducted on 22Cr duplex stainless steel in a chloride solution without H2S (1) and saturated with H2S (2) [18].
(1) (2)
2. HYDROGEN IN METALS
2.2.2. DIRECT TRANSFER OF H+ THROUGH THE INTERFACE (MODEL PROPOSED BY CROLET ET AL.)
In the classical mechanism presented above, it is considered that the same adsorbed atoms lead either to molecular hydrogen evolution or to atomic hydrogen absorbed in the material.
Crolet [19 – 21] considers that a hydrated hydrogen cation looses its water atmosphere and will proceed directly through the interface. Thus, the subsurface concentration is given by the passage of H+ (in ionic form) through the interface.
In this new model for hydrogen absorption the species that are leading to molecular hydrogen (atomic hydrogen adsorbed on the surface) are different from the ones that are undergoing absorption.
The equilibrium (2.24.) is written as:
+
+ ↔ metal
hydrated H
H (2.30.)
The direct transfer of the proton H+ could take place not only from H+ from water, but also by deprotonation of other complexes adsorbed on the surface: H2S becomes HS- ,and similarly for H3As, H3P, HSCN, HF.
The severity of these species with regard to cracking increases with decreasing stability of these complexes. Thus, the adsorbed HS-ads, is not an inhibitor for recombination reaction (2.2.) or (2.3.) but a catalyst for the direct transfer of H+ through the interface (reaction 2.30.):
+
−
− +
+
→
→ +
metal adsorbed
adsorbed
adsorbed adsorbed
hydrated
H HS
S H
S H HS
H
2
2
(2.31.)
2. HYDROGEN IN METALS
This mechanism gives a new explanation of the damaging effects of H2S and other poisons: these species favour the direct transfer of H+ in the metal without decreasing the recombination of atomic H.
This new direct transfer mechanism does not necessarily exclude the classical mechanism, where atomic hydrogen is passing through the interface.
Apparently more studies are still conducted on these interesting questions.
2.3. HYDROGEN TRANSPORT WITHIN THE MATERIAL
In the following, the diffusion laws are presented for the ideal case of diffusion without trapping. Then the different types of traps that can be encountered in a real material are presented, with the expression for diffusion in the presence of traps. In the last subsection hydrogen diffusion inside the material under other gradients than composition gradient is presented.
2.3.1. DIFFUSION
2.3.1.1. Ideal diffusion, Fick’s laws
Due to its small volume, a hydrogen atom can diffuse and occupy the interstitial sites inside the material (Figure 2.4.).
(a) (b)
Figure 2.4. Octahedric interstitial sites of face centred cubic (a) and body
2. HYDROGEN IN METALS
The face-centred cubic (f.c.c.) lattice has one octahedral interstitial site per metal atom and two tetrahedral interstitial sites per metal atom in the unit cell.
The body-centred cubic (b.c.c.) lattice has three octahedral interstitial sites per metal atom and six tetrahedral interstitial sites per metal atom in the unit cell. In the f.c.c. lattice the octahedral positions (O) have the largest free volume, whereas in the b.c.c. lattice the tetrahedral sites (T) are the largest. In Table 2.3. several metals with crystallographic structure and preferred occupied sites are presented [22].
Table 2.3. Interstitial sites occupied by hydrogen in different metals [22]
Host lattice Crystallographic structure Occupied sites
α – Fe b.c.c. T
γ – Fe f.c.c. O
Pd f.c.c. O Ta b.c.c. T V b.c.c. T Nb Rhomb. T
where T are tetrahedral sites and O octahedral sites .
The subsurface concentration, C0, determines a concentration gradient that is the driving force for the diffusion.
The diffusion obeys the Fick’s laws:
Fick’s first law for diffusion:
x D C
J ∂
− ∂
= (2.32.)
and
Fick’s second law for diffusion:
²
² x D C t C
∂
= ∂
∂
∂ (2.33.)
where D is the diffusion coefficient for the ideal case , where diffusion takes place without trapping.
2. HYDROGEN IN METALS
For a given material the diffusion coefficient is constant. Some values of the diffusion coefficient for different materials are presented in Table 2.4.
Table 2.4. Diffusion coefficient of hydrogen in different materials at room temperature
Material D (cm²/s) Ref.
Carbon steel 2.5 x 10 – 6 [11]
Ferritic stainless steel 10 – 7 [23]
Austenitic stainless steel 2.15 x 10 – 12 [33]
Martensitic stainless steel 2 x 10 – 9 [24 – 28]
Duplex stainless steel 10 –9 – 10 – 10 (depending on the ferrite / austenite ratio)
[23, 29 – 32 ]
2.3.1.2. Temperature effect
The diffusion coefficient has an exponential expression dependence with the temperature:
−
= kT
D E
D 0exp a (2.34.)
In Figure 2.5. the diffusion coefficient – temperature dependency for different steels is presented [33].
1,00E-14 1,00E-10 1,00E-06 1,00E-02
0 100 200 300 400
temperature (°C)
D (m²/s)
C steel duplex austenitic
Figure 2.5. Evolution of diffusion coefficient (D) with the temperature for different steels [33]
2. HYDROGEN IN METALS
The interstitial hydrogen is reversible, therefore at room temperature it can diffuse out from the metal.
The diffusion coefficients (apparent and real) and the subsurface concentration, C0, can be easily measured and calculated from permeation experiments (See Section 6.).
2.3.1.3. Diffusion under stress gradient
When a stress is applied, hydrogen diffuses under stress gradient toward the places of high stress. The diffusion flux depends not only on the concentration gradient, but also on the stress gradient according to equation:
−
−
=
−
grad h
RT V gradc c D
J σ (2.35.)
Stress – induced hydrogen diffusion takes place whether the inhomogeneous stress is caused by applied forces or residual stresses.
Due tot the stress gradient, the diffusion of hydrogen can take place even when hydrogen distribution is uniform inside the material (grad c = 0).
2.3.2. TRAPPING
In real cases, the hydrogen atoms are not located only in the interstitial positions, but they are trapped by the different defects inside the material.
Any metallurgical defect inside the material can act as a trap for hydrogen.
According to their energy, traps are divided into reversible, for which the energy is low and hydrogen can leave easily the trap, and irreversible (or deep traps) where more energy has to be provided for hydrogen release.
Examples of traps are presented in Table 2.5.
