A phase field model for hydrogen-assisted fatigue

We present a new theoretical and numerical phase field-based formulation for predicting hydrogenassisted fatigue. The coupled deformation-diffusion-damage model presented enables predicting fatigue crack nucleation and growth for arbitrary loading patterns and specimen geometries. The role of hydrogen in increasing fatigue crack growth rates and decreasing the number of cycles to failure is investigated. Our numerical experiments enable mapping the three loading frequency regimes and naturally recover Paris law behaviour for various hydrogen concentrations. In addition, Virtual S-N curves are obtained for both notched and smooth samples, exhibiting a good agreement with experiments.

[1]  R. Ritchie,et al.  Modeling the Hydrogen Effect on the Constitutive Response of a Low Carbon Steel in Cyclic Loading , 2021, Journal of Applied Mechanics.

[2]  N. Fleck,et al.  A fracture criterion for the notch strength of high strength steels in the presence of hydrogen , 2014 .

[3]  Wei Tan,et al.  Phase field predictions of microscopic fracture and R-curve behaviour of fibre-reinforced composites , 2020, Composites Science and Technology.

[4]  Emilio Mart'inez-Paneda,et al.  Phase field modelling of fracture and fatigue in Shape Memory Alloys , 2020, Computer Methods in Applied Mechanics and Engineering.

[5]  A. J. Mcevily,et al.  Hydrogen-assisted cracking , 1991 .

[6]  B. Bourdin,et al.  Numerical experiments in revisited brittle fracture , 2000 .

[7]  A. Chambolle An approximation result for special functions with bounded deformation , 2004 .

[8]  Yuhei Ogawa,et al.  Hydrogen-assisted, intergranular, fatigue crack-growth in ferritic iron: Influences of hydrogen-gas pressure and temperature variation , 2020 .

[9]  Zhiliang Zhang,et al.  Cohesive zone simulation of grain size and misorientation effects on hydrogen embrittlement in nickel , 2017 .

[10]  R. Gangloff,et al.  Gaseous hydrogen embrittlement of materials in energy technologies Volume 2 , 2012 .

[11]  E. Mart'inez-Paneda,et al.  Analysis of the influence of microstructural traps on hydrogen assisted fatigue , 2020, 2008.05452.

[12]  D. Halm,et al.  Controlling factors and mechanisms of fatigue crack growth influenced by high pressure of gaseous hydrogen in a commercially pure iron , 2021 .

[13]  Vinh Phu Nguyen,et al.  A phase-field regularized cohesive zone model for hydrogen assisted cracking , 2020 .

[14]  Emilio Mart'inez-Paneda,et al.  A cohesive zone framework for environmentally assisted fatigue , 2017, 1711.09965.

[15]  Chuanjie Cui,et al.  A phase field formulation for dissolution-driven stress corrosion cracking , 2020, ArXiv.

[16]  Emilio Mart'inez-Paneda,et al.  Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme , 2019, Theoretical and Applied Fracture Mechanics.

[17]  W. Gerberich,et al.  On the influence of internal hydrogen of fatigue thresholds of HSLA steel , 1983 .

[18]  Lallit Anand,et al.  Hydrogen in metals: A coupled theory for species diffusion and large elastic–plastic deformations , 2013 .

[19]  Laura De Lorenzis,et al.  A review on phase-field models of brittle fracture and a new fast hybrid formulation , 2015 .

[20]  H. Waisman,et al.  A unified model for metal failure capturing shear banding and fracture , 2015 .

[21]  M. Ortiz,et al.  A quantum-mechanically informed continuum model of hydrogen embrittlement , 2004 .

[22]  F. Bolzoni,et al.  Fatigue behavior of hydrogen pre-charged low alloy Cr–Mo steel , 2016 .

[23]  D. McDowell,et al.  A rationale for modeling hydrogen effects on plastic deformation across scales in FCC metals , 2018, International Journal of Plasticity.

[24]  GetFEM , 2020, ACM Transactions on Mathematical Software.

[25]  M. Williams,et al.  On the Stress Distribution at the Base of a Stationary Crack , 1956 .

[26]  Brian P. Somerday,et al.  Technical Reference on Hydrogen Compatibility of Materials , 2008 .

[27]  Marco Paggi,et al.  A phase field approach enhanced with a cohesive zone model for modeling delamination induced by matrix cracking , 2020 .

[28]  C. F. Niordson,et al.  Strain gradient plasticity modeling of hydrogen diffusion to the crack tip , 2016, 1711.05616.

[29]  W. Eddy,et al.  A Statistical , 2008 .

[30]  Thomas J. R. Hughes,et al.  A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects , 2016 .

[31]  Emilio Mart'inez-Paneda,et al.  Strain gradient plasticity-based modeling of hydrogen environment assisted cracking , 2016, 1711.06179.

[32]  Richard P. Gangloff,et al.  Corrosion fatigue crack propagation in metals , 1990 .

[33]  Zdenko Tonković,et al.  A residual control staggered solution scheme for the phase-field modeling of brittle fracture , 2019, Engineering Fracture Mechanics.

[34]  Gilles A. Francfort,et al.  Revisiting brittle fracture as an energy minimization problem , 1998 .

[35]  Jean-Jacques Marigo,et al.  Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments , 2009 .

[36]  A. Turnbull,et al.  Modelling of the hydrogen distribution at a crack tip , 1996 .

[37]  E. Mart'inez-Paneda,et al.  A mechanism-based multi-trap phase field model for hydrogen assisted fracture , 2021, ArXiv.

[38]  J. Scully,et al.  On the suitability of slow strain rate tensile testing for assessing hydrogen embrittlement susceptibility , 2019, Corrosion Science.

[39]  S. Matsuoka,et al.  Slow strain rate tensile and fatigue properties of Cr–Mo and carbon steels in a 115 MPa hydrogen gas atmosphere , 2015 .

[40]  Bai-Xiang Xu,et al.  Current collector Composite anode Separator Composite cathode Current collector Electrons Lithium atoms Lithium ions Discharge Charge Anode particle Electrolyte Cathode particle , 2015 .

[41]  L. De Lorenzis,et al.  A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach , 2018, 1811.02244.

[42]  Jean-Jacques Marigo,et al.  Crack nucleation in variational phase-field models of brittle fracture , 2018 .

[43]  E. Gdoutos,et al.  Fracture Mechanics , 2020, Encyclopedic Dictionary of Archaeology.

[44]  Brian P. Somerday,et al.  A statistical, physical-based, micro-mechanical model of hydrogen-induced intergranular fracture in steel , 2010 .

[45]  A. Cocks,et al.  A modelling framework for coupled hydrogen diffusion and mechanical behaviour of engineering components , 2020, Computational Mechanics.

[46]  M. Paggi,et al.  Phase field modeling of fracture in Functionally Graded Materials: Γ-convergence and mechanical insight on the effect of grading , 2020 .

[47]  Sebastian Toro,et al.  A phase-field model for solute-assisted brittle fracture in elastic-plastic solids , 2017 .

[48]  Philip K. Kristensen,et al.  Applications of phase field fracture in modelling hydrogen assisted failures , 2020, Theoretical and Applied Fracture Mechanics.

[49]  Yukitaka Murakami,et al.  The effect of hydrogen on fatigue properties of steels used for fuel cell system , 2006 .

[50]  Marco Paggi,et al.  Modeling complex crack paths in ceramic laminates: A novel variational framework combining the phase field method of fracture and the cohesive zone model , 2018 .

[51]  Emilio Mart'inez-Paneda,et al.  A phase field formulation for hydrogen assisted cracking , 2018, Computer Methods in Applied Mechanics and Engineering.

[52]  Philip K. Kristensen,et al.  An assessment of phase field fracture: crack initiation and growth , 2021, Philosophical Transactions of the Royal Society A.

[53]  L. Anand,et al.  On modeling fracture of ferritic steels due to hydrogen embrittlement , 2019, Journal of the Mechanics and Physics of Solids.

[54]  M. Arzaghi,et al.  Hydrogen-affected fatigue crack propagation at various loading frequencies and gaseous hydrogen pressures in commercially pure iron , 2019, International Journal of Fatigue.

[55]  Hirshikesh,et al.  Phase field modelling of crack propagation in functionally graded materials , 2019, Composites Part B: Engineering.

[56]  J. M. Alegre,et al.  Coupled hydrogen diffusion simulation using a heat transfer analogy , 2016 .

[57]  Emilio Mart'inez-Paneda,et al.  A phase field model for elastic-gradient-plastic solids undergoing hydrogen embrittlement , 2020, Journal of the Mechanics and Physics of Solids.

[58]  E. Carter,et al.  First principles assessment of ideal fracture energies of materials with mobile impurities: implications for hydrogen embrittlement of metals , 2004 .

[59]  The effect of hydrogen induced surface asperities on fatigue crack closure in ultrahigh strength steel , 1983 .

[60]  Christian Miehe,et al.  A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits , 2010 .

[61]  J. Belzunce,et al.  Effect of hydrogen on the fatigue crack growth rate of quenched and tempered CrMo and CrMoV steels , 2019, International Journal of Fatigue.

[62]  Konstantinos Poulios,et al.  GetFEM , 2020, ACM Trans. Math. Softw..

[63]  S. Matsuoka,et al.  Unified evaluation of hydrogen-induced crack growth in fatigue tests and fracture toughness tests of a carbon steel , 2017 .

[64]  A. Karma,et al.  Phase field modeling of chemomechanical fracture of intercalation electrodes: Role of charging rate and dimensionality , 2019, Journal of the Mechanics and Physics of Solids.

[65]  S. Matsuoka,et al.  Hydrogen trapping and fatigue crack growth property of low-carbon steel in hydrogen-gas environment , 2017 .

[66]  I. M. Robertson,et al.  A microstructural based understanding of hydrogen-enhanced fatigue of stainless steels , 2013 .

[67]  K. Shirvan,et al.  Multiphysics phase-field modeling of quasi-static cracking in urania ceramic nuclear fuel , 2021 .

[68]  Justin D. Dolph,et al.  Measurement and Modeling of Hydrogen Environment-Assisted Cracking in a Ni-Cu-Al-Ti Superalloy , 2016, Metallurgical and Materials Transactions A.

[69]  Nikolas Provatas,et al.  Phase-Field Methods in Materials Science and Engineering , 2010 .

[70]  C. Moriconi,et al.  Cohesive zone modeling of fatigue crack propagation assisted by gaseous hydrogen in metals , 2014 .