Abstract
The diffusion of hydrogen in metals is of interest due to the deleterious influence of hydrogen on material ductility and fracture resistance. It is becoming increasingly clear that hydrogen transport couples significantly with dislocation activity. In this work, we use a coupled diffusion-crystal plasticity model to incorporate hydrogen transport associated with dislocation sweeping and pipe diffusion in addition to standard lattice diffusion. Moreover, we consider generation of vacancies via plastic deformation and stabilization of vacancies via trapping of hydrogen. The proposed hydrogen transport model is implemented in a physically based crystal viscoplasticity framework to model the interaction of dislocation substructure and hydrogen migration. In this study, focus is placed on hydrogen transport and trapping within the intense deformation field of a crack tip plastic zone. We discuss the implications of the model results in terms of constitutive relations that incorporate hydrogen effects on crack tip field behavior and enable exploration of hydrogen embrittlement mechanisms.
Issue Section:
Special Issue: The Behavior of Crystalline Materials: In Honor of Professor Hussein Zbib
References
1.
Johnson
, W. H.
, 1875
, “On Some Remarkable Changes Produced in Iron and Steel by the Action of Hydrogen and Acids
,” Nature
, 11
(281
), pp. 393
.2.
Myers
, S. M.
, Baskes
, M.
, Birnbaum
, H.
, Corbett
, J. W.
, DeLeo
, G.
, Estreicher
, S.
, Haller
, E. E.
, Jena
, P.
, Johnson
, N. M.
, and Kirchheim
, R.
, 1992
, “Hydrogen Interactions with Defects in Crystalline Solids
,” Rev. Mod. Phys.
, 64
(2
), pp. 559
–617
. 3.
Barthélémy
, H.
, 2012
, “Hydrogen Storage–Industrial Prospectives
,” Int. J. Hydrogen Energy
, 37
(22
), pp. 17364
–17372
. 4.
Gangloff
, R. P.
, and Somerday
, B. P.
, 2012
, Gaseous Hydrogen Embrittlement of Materials in Energy Technologies: The Problem, Its Characterisation and Effects on Particular Alloy Classes
, Elsevier
, New York
.5.
Popov
, K.
, and Nechai
, E.
, 1967
, “Theory of Hydrogen Embrittlement of Metals
,” Soviet Materials Science: A Transl. of Fiziko-khimicheskaya mekhanika materialov/Academy of Sciences of the Ukrainian SSR
, 3
(6
), pp. 459
–473
. 6.
Ghermaoui
, I.
, Oudriss
, A.
, Metsue
, A.
, Milet
, R.
, Madani
, K.
, and Feaugas
, X.
, 2019
, “Multiscale Analysis of Hydrogen-Induced Softening in FCC Nickel Single Crystals Oriented for Multiple-Slips: Elastic Screening Effect
,” Sci. Rep.
, 9
(1
), pp. 1
–10
. 7.
Beacham
, C.
, 1972
, “A New Model for Hydrogen-Assisted Cracking (Hydrogen. Embrittlement)
,” Metall. Trans.
, 3
, pp. 437
–451
.8.
Birnbaum
, H. K.
, and Sofronis
, P.
, 1994
, “Hydrogen-Enhanced Localized Plasticity—A Mechanism for Hydrogen-Related Fracture
,” Mater. Sci. Eng. A
, 176
(1–2
), pp. 191
–202
. 9.
Lynch
, S.
, 1979
, “Hydrogen Embrittlement and Liquid-Metal Embrittlement in Nickel Single Crystals
,” Scr. Metall.
, 13
(11
), pp. 1051
–1056
. 10.
Lynch
, S.
, 1988
, “Environmentally Assisted Cracking: Overview of Evidence for an Adsorption-Induced Localised-Slip Process
,” Acta Metall.
, 36
(10
), pp. 2639
–2661
. 11.
Lynch
, S.
, 1989
, “Metallographic Contributions to Understanding Mechanisms of Environmentally Assisted Cracking
,” Metallography
, 23
(2
), pp. 147
–171
. 12.
Petch
, N.
, and Stables
, P.
, 1952
, “Delayed Fracture of Metals Under Static Load
,” Nature
, 169
(4307
), pp. 842
–843
. 13.
Pfeil
, L. B.
, 1926
, “The Effect of Occluded Hydrogen on the Tensile Strength of Iron
,” Proc. R. Soc. Lond. A.
, 112
(760
), pp. 182
–195
.14.
Troiano
, A.
, 1973
, “General Keynote Lecture, Hydrogen in Metals
,” Proc. Int. Conf. on the Effects of Hydrogen on Materials Properties and Selection and Structural Design
, Champion, PA
, Sept. 23–27, 1973
.15.
Hatano
, M.
, Fujinami
, M.
, Arai
, K.
, Fujii
, H.
, and Nagumo
, M.
, 2014
, “Hydrogen Embrittlement of Austenitic Stainless Steels Revealed by Deformation Microstructures and Strain-Induced Creation of Vacancies
,” Acta Mater.
, 67
, pp. 342
–353
. 16.
Nagumo
, M.
, 2004
, “Hydrogen Related Failure of Steels—A New Aspect
,” Mater. Sci. Technol.
, 20
(8
), pp. 940
–950
. 17.
Sofronis
, P.
, and McMeeking
, R. M.
, 1989
, “Numerical Analysis of Hydrogen Transport Near a Blunting Crack Tip
,” J. Mech. Phys. Solids
, 37
(3
), pp. 317
–350
. 18.
Charles
, Y.
, Nguyen
, H. T.
, and Gaspérini
, M.
, 2017
, “Comparison of Hydrogen Transport Through Pre-Deformed Synthetic Polycrystals and Homogeneous Samples by Finite Element Analysis
,” Int. J. Hydrogen Energy
, 42
(31
), pp. 20336
–20350
. 19.
Hassan
, H. U.
, Govind
, K.
, and Hartmaier
, A.
, 2019
, “Micromechanical Modelling of Coupled Crystal Plasticity and Hydrogen Diffusion
,” Philos. Mag.
, 99
(1
), pp. 92
–115
. 20.
Hüter
, C.
, Shanthraj
, P.
, McEniry
, E.
, Spatschek
, R.
, Hickel
, T.
, Tehranchi
, A.
, Guo
, X.
, and Roters
, F.
, 2018
, “Multiscale Modelling of Hydrogen Transport and Segregation in Polycrystalline Steels
,” Metals
, 8
(6
), p. 430
. 21.
Ilin
, D. N.
, Saintier
, N.
, Olive
, J.-M.
, Abgrall
, R.
, and Aubert
, I.
, 2014
, “Simulation of Hydrogen Diffusion Affected by Stress-Strain Heterogeneity in Polycrystalline Stainless Steel
,” Int. J. Hydrogen Energy
, 39
(5
), pp. 2418
–2422
. 22.
Miresmaeili
, R.
, Saintier
, N.
, Notsu
, H.
, Olive
, J.-M.
, and Kanayama
, H.
, 2010
, “One-Way Coupled Crystal Plasticity-Hydrogen Diffusion Simulation on Artificial Microstructure
,” J. Comput. Sci. Technol.
, 4
(2
), pp. 105
–120
. 23.
Saintier
, N.
, Awane
, T.
, Olive
, J.-M.
, Matsuoka
, S.
, and Murakami
, Y.
, 2011
, “Analyses of Hydrogen Distribution Around Fatigue Crack on Type 304 Stainless Steel Using Secondary Ion Mass Spectrometry
,” Int. J. Hydrogen Energy
, 36
(14
), pp. 8630
–8640
. 24.
Dadfarnia
, M.
, Martin
, M. L.
, Nagao
, A.
, Sofronis
, P.
, and Robertson
, I. M.
, 2015
, “Modeling Hydrogen Transport by Dislocations
,” J. Mech. Phys. Solids
, 78
, pp. 511
–525
. 25.
Murakami
, Y.
, Kanezaki
, T.
, Mine
, Y.
, and Matsuoka
, S.
, 2008
, “Hydrogen Embrittlement Mechanism in Fatigue of Austenitic Stainless Steels
,” Metall. Mater. Trans. A
, 39
(6
), pp. 1327
–1339
. 26.
Hashimoto
, M.
, and Latanision
, R.
, 1988
, “The Role of Dislocations During Transport of Hydrogen in Hydrogen Embrittlement of Iron
,” Metall. Trans. A
, 19
(11
), pp. 2799
–2803
. 27.
Cortes
, R.
, Valiente
, A.
, Ruiz
, J.
, Caballero
, L.
, and Toribio
, J.
, 1997
, “Finite-Element Modeling of Stress-Assisted Hydrogen Diffusion in 316L Stainless Steel
,” Mater. Sci.
, 33
(4
), pp. 491
–503
. 28.
Van Leeuwen
, H.
, 1974
, “The Kinetics of Hydrogen Embrittlement: A Quantitative Diffusion Model
,” Eng. Fract. Mech.
, 6
(1
), pp. 141
–161
. 29.
Love
, G.
, 1964
, “Dislocation Pipe Diffusion
,” Acta Metall.
, 12
(6
), pp. 731
–737
. 30.
San Marchi
, C.
, Somerday
, B. P.
, and Robinson
, S. L.
, 2007
, “Permeability, Solubility and Diffusivity of Hydrogen Isotopes in Stainless Steels at High Gas Pressures
,” Int. J. Hydrogen Energy
, 32
(1
), pp. 100
–116
. 31.
Nair
, S.
, Jensen
, R.
, and Tien
, J.
, 1983
, “Kinetic Enrichment of Hydrogen at Interfaces and Voids by Dislocation Sweep-in of Hydrogen
,” Metall. Trans. A
, 14
(2
), pp. 385
–393
. 32.
Schuster
, G.
, and Altstetter
, C.
, 1983
, “Fatigue of Stainless Steel in Hydrogen
,” Metall. Trans. A
, 14
(10
), pp. 2085
–2090
. 33.
Wang
, Y.
, Connétable
, D.
, and Tanguy
, D.
, 2015
, “Hydrogen Influence on Diffusion in Nickel From First-Principles Calculations
,” Phys. Rev. B
, 91
(9
), p. 094106
. 34.
Wen
, M.
, Fukuyama
, S.
, and Yokogawa
, K.
, 2004
, “Hydrogen-Affected Cross-Slip Process in FCC Nickel
,” Phys. Rev. B
, 69
(17
), p. 174108
. 35.
Angelo
, J. E.
, Moody
, N. R.
, and Baskes
, M. I.
, 1995
, “Trapping of Hydrogen to Lattice Defects in Nickel
,” Modell. Simul. Mater. Sci. Eng.
, 3
(3
), pp. 289
–307
. 36.
Tanguy
, D.
, Wang
, Y.
, and Connétable
, D.
, 2014
, “Stability of Vacancy-Hydrogen Clusters in Nickel From First-Principles Calculations
,” Acta Mater.
, 78
, pp. 135
–143
. 37.
Myers
, S.
, Nordlander
, P.
, Besenbacher
, F.
, and Nørskov
, J.
, 1986
, “Theoretical Examination of the Trapping of Ion-Implanted Hydrogen in Metals
,” Phys. Rev. B
, 33
(2
), pp. 854
–863
. 38.
Hirth
, J.
, and Lothe
, J.
, 1982
, Theory of Dislocations
, Wiley
, New York
.39.
Li
, S.
, Li
, Y.
, Lo
, Y.-C.
, Neeraj
, T.
, Srinivasan
, R.
, Ding
, X.
, Sun
, J.
, Qi
, L.
, Gumbsch
, P.
, and Li
, J.
, 2015
, “The Interaction of Dislocations and Hydrogen-Vacancy Complexes and Its Importance for Deformation-Induced Proto Nano-Voids Formation in α-Fe
,” Int. J. Plast.
, 74
, pp. 175
–191
. 40.
Kays
, W. M.
, 2012
, Convective Heat and Mass Transfer
, Tata McGraw-Hill Education
, New York
.41.
Hart
, E.
, Hoffman
, R.
, and Turnbull
, D.
, 1957
, “Self-Diffusion in Dilute Binary Solid Solutions—II
,” Acta Metall.
, 5
(2
), pp. 74
–76
. 42.
Chen
, Y.
, and Schuh
, C. A.
, 2007
, “Geometric Considerations for Diffusion in Polycrystalline Solids
,” J. Appl. Phys.
, 101
(6
), p. 063524
. 43.
Frank
, F.
, 1950
, Report of the Symposium on the Plastic Deformation of Crystalline Solids
, Carnegie Institute of Technology
, Pittsburgh
, p. 150
.44.
McLellan
, R. B.
, 1979
, “Thermodynamics and Diffusion Behavior of Interstitial Solute Atoms in Non-Perfect Solvent Crystals
,” Acta Metall.
, 27
(10
), pp. 1655
–1663
. 45.
Tien
, J.
, Thompson
, A. W.
, Bernstein
, I.
, and Richards
, R. J.
, 1976
, “Hydrogen Transport by Dislocations
,” Metall. Trans. A
, 7
(6
), pp. 821
–829
. 46.
Fukai
, Y.
, 2003
, “Formation of Superabundant Vacancies in M–H Alloys and Some of Its Consequences: A Review
,” J. Alloys Compd.
, 356–357
, pp. 263
–269
. 47.
Kocks
, U. F.
, Argon
, A. S.
, and Ashby
, M. F.
, 1975
, “Thermodynamics and Kinetics of Slip
,” Prog. Mater. Sci.
, 19
, pp. 1
–281
.48.
Mughrabi
, H.
, 1979
, “Microscopic Mechanisms of Metal Fatigue
,” Proceedings of the 5th International Conference on Strength of Metals and Alloys, Aachen, Germany, Vol. 3, pp. 1615
–1638
.49.
Louthan
, M.
, Jr, Donovan
, J.
, and Caskey
, G.
, Jr, 1975
, “Hydrogen Diffusion and Trapping in Nickel
,” Acta Metall.
, 23
(6
), pp. 745
–749
. 50.
Lee
, S.-M.
, and Lee
, J.-Y.
, 1986
, “The Trapping and Transport Phenomena of Hydrogen in Nickel
,” Metall. Trans. A
, 17
(2
), pp. 181
–187
. 51.
Chen
, D.
, 2018
, Personal Communication
.52.
Liang
, Y.
, Ahn
, D.
, Sofronis
, P.
, Dodds
, R.
, Jr, and Bammann
, D.
, 2008
, “Effect of Hydrogen Trapping on Void Growth and Coalescence in Metals and Alloys
,” Mech. Mater.
, 40
(3
), pp. 115
–132
. 53.
Zheng
, H.
, Rao
, B.
, Khanna
, S.
, and Jena
, P.
, 1997
, “Electronic Structure and Binding Energies of Hydrogen-Decorated Vacancies in Ni
,” Phys. Rev. B
, 55
(7
), pp. 4174
–4181
. 54.
Myers
, S.
, Richards
, P.
, Wampler
, W.
, and Besenbacher
, F.
, 1989
, “Ion-Beam Studies of Hydrogen-Metal Interactions
,” J. Nucl. Mater.
, 165
(1
), pp. 9
–64
. 55.
Castelluccio
, G. M.
, and McDowell
, D. L.
, 2017
, “Mesoscale Cyclic Crystal Plasticity With Dislocation Substructures
,” Int. J. Plast.
, 98
, pp. 1
–26
. 56.
Yagodzinskyy
, Y.
, Saukkonen
, T.
, Kilpeläinen
, S.
, Tuomisto
, F.
, and Hänninen
, H.
, 2010
, “Effect of Hydrogen on Plastic Strain Localization in Single Crystals of Austenitic Stainless Steel
,” Scr. Mater.
, 62
(3
), pp. 155
–158
. 57.
Polák
, J.
, and Man
, J.
, 2014
, “Fatigue Crack Initiation—The Role of Point Defects
,” Int. J. Fatigue
, 65
, pp. 18
–27
. 58.
Polák
, J.
, and Sauzay
, M.
, 2009
, “Growth of Extrusions in Localized Cyclic Plastic Straining
,” Mater. Sci. Eng. A
, 500
(1–2
), pp. 122
–129
. 59.
Differt
, K.
, and Essmann
, U.
, 1993
, “Dynamical Model of the Wall Structure in Persistent Slip Bands of Fatigued Metals I. Dynamical Model of Edge Dislocation Walls
,” Materials Science and Engineering: A
, 164
(1–2
), pp. 295
–299
.60.
Essmann
, U.
, Gösele
, U.
, and Mughrabi
, H.
, 1981
, “A Model of Extrusions and Intrusions in Fatigued Metals I. Point-Defect Production and the Growth of Extrusions
,” Philos. Mag. A
, 44
(2
), pp. 405
–426
. 61.
Essmann
, U.
, and Mughrabi
, H.
, 1979
, “Annihilation of Dislocations During Tensile and Cyclic Deformation and Limits of Dislocation Densities
,” Philos. Mag. A
, 40
(6
), pp. 731
–756
. 62.
Davoudi
, K. M.
, and Vlassak
, J. J.
, 2018
, “Dislocation Evolution During Plastic Deformation: Equations vs. Discrete Dislocation Dynamics Study
,” J. Appl. Phys.
, 123
(8
), p. 085302
. 63.
Schafler
, E.
, Steiner
, G.
, Korznikova
, E.
, Kerber
, M.
, and Zehetbauer
, M.
, 2005
, “Lattice Defect Investigation of ECAP-Cu by Means of X-Ray Line Profile Analysis, Calorimetry and Electrical Resistometry
,” Mater. Sci. Eng. A
, 410–411
, pp. 169
–173
. 64.
Ungár
, T.
, 2006
, “Subgrain Size-Distributions, Dislocation Structures, Stacking-and Twin Faults and Vacancy Concentrations in SPD Materials Determined
,” Materials Science Forum
, 503–504
, pp. 133–140
.65.
Xu
, S.
, Xiong
, L.
, Chen
, Y.
, and McDowell
, D. L.
, 2016
, “An Analysis of Key Characteristics of the Frank-Read Source Process in FCC Metals
,” J. Mech. Phys. Solids
, 96
, pp. 460
–476
. 66.
ABAQUS, F.
, 2009
, software V6. 9
, Simulia Corp.
, Providence, RI
, Simulia, Inc.67.
Gobbi
, G.
, Colombo
, C.
, Miccoli
, S.
, and Vergani
, L.
, 2019
, “A Fully Coupled Implementation of Hydrogen Embrittlement in FE Analysis
,” Adv. Eng. Software
, 135
, p. 102673
. 68.
Irwin
, G.
, 1968
, “Linear Fracture Mechanics, Fracture Transition, and Fracture Control
,” Eng. Fract. Mech.
, 1
(2
), pp. 241
–257
. 69.
Anderson
, T. L.
, 2017
, Fracture Mechanics: Fundamentals and Applications
, CRC Press
, Boca Raton, FL
.70.
Ebisuzaki
, Y.
, Kass
, W.
, and O'keeffe
, M.
, 1967
, “Diffusion and Solubility of Hydrogen in Single Crystals of Nickel and Nickel—Vanadium Alloy
,” J. Chem. Phys.
, 46
(4
), pp. 1378
–1381
. 71.
Rice
, J. R.
, 1987
, “Tensile Crack Tip Fields in Elastic-Ideally Plastic Crystals
,” Mech. Mater.
, 6
(4
), pp. 317
–335
. 72.
Bitzek
, E.
, and Gumbsch
, P.
, 2013
, “Mechanisms of Dislocation Multiplication at Crack Tips
,” Acta Mater.
, 61
(4
), pp. 1394
–1403
. 73.
Alcalá
, J.
, Očenášek
, J.
, Nowag
, K.
, Esqué-de los Ojos
, D.
, Ghisleni
, R.
, and Michler
, J.
, 2015
, “Strain Hardening and Dislocation Avalanches in Micrometer-Sized Dimensions
,” Acta Mater.
, 91
, pp. 255
–266
. 74.
Kiener
, D.
, and Minor
, A.
, 2011
, “Source Truncation and Exhaustion: Insights From Quantitative In Situ TEM Tensile Testing
,” Nano Lett.
, 11
(9
), pp. 3816
–3820
. 75.
Sun
, S.
, Shiozawa
, K.
, Gu
, J.
, and Chen
, N.
, 1995
, “Investigation of Deformation Field and Hydrogen Partition Around Crack Tip in FCC Single Crystal
,” Metall. Mater. Trans. A
, 26
(3
), pp. 731
–739
. 76.
Doshida
, T.
, and Takai
, K.
, 2014
, “Dependence of Hydrogen-Induced Lattice Defects and Hydrogen Embrittlement of Cold-Drawn Pearlitic Steels on Hydrogen Trap State, Temperature, Strain Rate and Hydrogen Content
,” Acta Mater.
, 79
, pp. 93
–107
. 77.
Ritchie
, R. O.
, 1999
, “Mechanisms of Fatigue-Crack Propagation in Ductile and Brittle Solids
,” Int. J. Fract.
, 100
(1
), pp. 55
–83
. 78.
Taggart
, R.
, Wahi
, K.
, and Beeuwkes
, R.
, 1976
, Properties Related to Fracture Toughness
, V.
Weiss
and W.
Warke
, eds., ASTM International
, West Conshohocken, PA
.79.
Farkas
, D.
, Duranduru
, M.
, Curtin
, W.
, and Ribbens
, C.
, 2001
, “Multiple-Dislocation Emission From the Crack Tip in the Ductile Fracture of Al
,” Philos. Mag. A
, 81
(5
), pp. 1241
–1255
. 80.
Puttick
, K.
, 1959
, “Ductile Fracture in Metals
,” Philos. Mag.
, 4
(44
), pp. 964
–969
. 81.
Castelluccio
, G. M.
, Geller
, C. B.
, and McDowell
, D. L.
, 2018
, “A Rationale for Modeling Hydrogen Effects on Plastic Deformation Across Scales in FCC Metals
,” Int. J. Plast.
, 111
, pp. 72
–84
. 82.
Eshelby
, J. D.
, 1957
, “The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems
,” Proc. R. Soc. London, A
, 241
(1226
), pp. 376
–396
. 83.
Mura
, T.
, 2013
, Micromechanics of Defects in Solids
, Springer Science & Business Media
, Dordrecht, The Netherlands
.84.
Sauzay
, M.
, and Kubin
, L. P.
, 2011
, “Scaling Laws for Dislocation Microstructures in Monotonic and Cyclic Deformation of FCC Metals
,” Prog. Mater. Sci.
, 56
(6
), pp. 725
–784
. 85.
Kuhlmann-Wilsdorf
, D.
, 1962
, “A New Theory of Work Hardening in Crystals
,” Trans. Met. Soc.
, 218
, p. 962
.86.
Estrin
, Y.
, Toth
, L.
, Molinari
, A.
, and Bréchet
, Y.
, 1998
, “A Dislocation-Based Model for All Hardening Stages in Large Strain Deformation
,” Acta Mater.
, 46
(15
), pp. 5509
–5522
. 87.
Arsenlis
, A.
, and Parks
, D. M.
, 2002
, “Modeling the Evolution of Crystallographic Dislocation Density in Crystal Plasticity
,” J. Mech. Phys. Solids
, 50
(9
), pp. 1979
–2009
. 88.
Patra
, A.
, and McDowell
, D. L.
, 2012
, “Crystal Plasticity-Based Constitutive Modelling of Irradiated BCC Structures
,” Philos. Mag.
, 92
(7
), pp. 861
–887
. 89.
Kubin
, L. P.
, Canova
, G.
, Condat
, M.
, Devincre
, B.
, Pontikis
, V.
, and Bréchet
, Y.
, 1992
, “Dislocation Microstructures and Plastic Flow: A 3D Simulation
,” Solid State Phenom.
, 23–24
, pp. 455
–472
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