Skip to main content
Log in

Modeling of hydrogen-assisted ductile crack propagation in metals and alloys

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

This paper presents a finite element study of the hydrogen effect on ductile crack propagation in metals and alloys by linking effects at the microstructural level (i.e., void growth and coalescence) to effects at the macro-level (i.e., bulk material deformation around a macroscopic crack). The purpose is to devise a mechanics methodology to simulate the conditions under which hydrogen enhanced plasticity induces fracture that macroscopically appears to be brittle. The hydrogen effect on enhanced dislocation mobility is described by a phenomenological constitutive relation in which the local flow stress is taken as a decreasing function of the hydrogen concentration which is determined in equilibrium with local stress and plastic strain. Crack propagation is modeled by cohesive elements whose traction separation law is determined through void cell calculations that address the hydrogen effect on void growth and coalescence. Numerical results for the A533B pressure vessel steel indicate that hydrogen, by accelerating void growth and coalescence, promotes crack propagation by linking simultaneously a finite number of voids with the crack tip. This “multiple-void” fracture mechanism knocks down the initiation fracture toughness of the material and diminishes the tearing resistance to crack propagation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ahn DC (2006) Mechanics of ductile fracture: void growth by dislocation-loop emission and hydrogen-assisted crack propagation. Ph.D. Dissertation, University of Illinois at Urbana-Champaign, Urbana, Illinois, 2006

  • Ahn DC, Sofronis P, Dodds RH (2007) On hydrogen-induced plastic flow localization during void growth and coalescence. Int. J. Hydrogen Energy, in print

  • Bammann DJ, Sofronis P (2005) A coupled dislocation-hydrogen based model of inelastic deformation. Proceedings of the 11th International Conference of Fracture, Symposium on Hydrogen Embrittlement (CD ROM), Torino, Italy, March 20–25

  • Barenblatt GI (1962). The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7: 55–129

    Article  MathSciNet  Google Scholar 

  • Beachem CD (1972). New model for hydrogen-assisted cracking (hydrogen “embrittlement”). Met Trans 3: 437–451

    Google Scholar 

  • Birnbaum HK, Robertson IM, Sofronis P and Teter D (1997). Mechanisms of hydrogen related fracture—a review. In: Magnin, T (eds) Proceedings of the Second International Conference on Corrosion Deformation Interactions CDI’96, Nice, France, pp 172–189. The Institute of Materials, Great Britian

    Google Scholar 

  • Birnbaum HK and Sofronis P (1994). Hydrogen-enhanced localized plasticity—a mechanism for hydrogen-related fracture. Mat Sci Eng A 176: 191–202

    Article  Google Scholar 

  • Bond GM, Robertson IM and Birnbaum HK (1988). On the mechanisms of hydrogen embrittlement of Ni3Al alloys. Acta Met 37: 1407–1413

    Article  Google Scholar 

  • Brocks W, Klingbeil D, Künecke G, Sun D-Z (1995) Application of the Gurson model to ductile tearing resistance. In: Kirk M, Bakker A (eds) Constraint effects in fracture: theory and applications, ASTM STP 144. American Society for Testing and Materials, Philadelphia, pp 232–252

  • Chateau JP, Delafosse D and Magnin T (2002). Numerical simulations of hydrogen-dislocation interactions in fcc stainless steels. Part I: hydrogen-dislocation interactions in bulk crystals. Acta Met 50: 1507–1522

    Article  Google Scholar 

  • Chen S-H and Gerberich WW (1991). The kinetics and micromechanics of hydrogen assisted cracking in Fe-3 pct Si single crystals. Met Trans A 22: 59–70

    Google Scholar 

  • Chen S-H, Katz Y and Gerberich WW (1990). On the directional dependency of microplasticity for cleavage in Fe-3wt%Si single crystals. Scr Met 24: 1125–1130

    Article  Google Scholar 

  • Chen S-H, Katz Y and Gerberich WW (1991). Crack tip fields and fracture microplasticity in hydrogen-assisted cracking of Fe-3wt pct Si single crystals. Phil Mag A 63: 131–155

    Article  ADS  Google Scholar 

  • Chen X, Kozubowski JA and Gerberich WW (1988). Hydrogen-induced sustained load cracking in single crystal Fe-3 wt. Si. Scr Met 22: 245–248

    Article  Google Scholar 

  • Costa JE and Thompson AW (1981). Effect of hydrogen on fracture behavior of a quenched and tempered medium-carbon steel. Met Trans A 12: 761–771

    Article  Google Scholar 

  • de-Andres A, Perez JL and Ortiz M (1999). Elasto-plastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading. Int J Solids Struct 36: 2231–2258

    Article  MATH  Google Scholar 

  • Delafosse D and Magnin T (2001). Hydrogen induced plasticity in stress corrosion cracking of engineering systems. Eng Fract Mech 68: 693–729

    Article  Google Scholar 

  • Dugdale DS (1960). Yielding of steel sheets containing slits. J Mech Phys Solids 8: 100–104

    Article  ADS  Google Scholar 

  • Gao X, Faleskog J, Shih CF and Dodds RH (1998). Ductile tearing in part-through cracks: experiments and cell-model predictions. Eng Fracture Mech 59: 761–777

    Article  Google Scholar 

  • Gerberich WW, Marsh PG and Huang H (1992). The effect of local dislocation arrangements on hydrogen-induced cleavage. In: Gerberich, WW, Ford, FP, and Staehle, RW (eds) Parkins Symposium on Fundamental Aspects of Stress Corrosion Cracking, pp 191–204. The Minerals Metals & Materials Society, Warrendale, PA

    Google Scholar 

  • Gullerud AS, Koppenhoefer KC, Roy A and Dodds RH (1995). WARP3D: dynamic nonlinear analysis of solids using parallel computers and workstations, Structural Research Series 607, UILU-ENG-95-2012. University of Illinois, Urbana-Champaign

    Google Scholar 

  • Gurson AL (1977). Continuum theory of ductile rupture by void nucleation and growth: Part I—yield criteria and flow rules for porous ductile media. ASME J Eng Mat Tech Ser H 99: 2–15

    Google Scholar 

  • Gutierrez-Solana F, Elices M (1982) High-pressure hydrogen behavior of a pipeline steel. In: Interrante CG, Pressouyre GM (eds) Current solutions to hydrogen problems in steels, Proceedings of the First International Conference on Current Solutions to Hydrogen Problems in Steels, Washinton, DC, November 1–5, 1982, American Society for Metals, Metals Park, Ohio, pp 181–185

  • Hänninen HE, Lee TC, Robertson IM and Birnbaum HK (1993). Direct observations on the role of hydrogen on deformation and fracture of A533B pressure vessel steel. J Mat Eng Perform 2: 807–817

    Article  Google Scholar 

  • Hirth JP (1980). Effects of hydrogen on the properties of iron and steel. Met Trans A 11: 861–890

    Article  Google Scholar 

  • Hirth JP and Carnahan B (1978). Hydrogen adsorption at dislocations and crack is Fe. Acta Metall 26: 1975–1803

    Google Scholar 

  • Holbrook JH, Collings EW, Cialone HJ, Drauglis EJ (1986) Hydrogen degradation of pipeline steels: final report, Brookhaven National Lab., Upton, New York, Department of Energy, Washington, DC. Report: BNL-52049

  • Jiang DE and Carter EA (2004a). Diffusion of interstitial hydrogen into and through bcc Fe from first principles. Phys Rev B 70: 064102–064111

    Article  ADS  Google Scholar 

  • Jiang DE and Carter EA (2004b). First principles assessment of ideal fracture energies of materials: implications for hydrogen embrittlement of metals. Acta materialia 52: 4801–4807

    Article  Google Scholar 

  • Kimura A and Kimura H (1983). Hydrogen embrittlement in high purity iron single crystals. Mat Sci Eng 77: 75–83

    Article  Google Scholar 

  • Koppenhoefer KC and Dodds RH (1998). Ductile crack growth in pre-cracked CVN specimens: numerical studies. Nucl Eng Des 180: 221–241

    Article  Google Scholar 

  • Koplik J and Needleman A (1988). Void growth and coalescence in porous plastic solids. J Mech Phys Solids 24: 835–853

    Google Scholar 

  • Kumnick AJ and Johnson HH (1980). Deep trapping states for hydrogen in deformed iron. Acta Met 28: 33–39

    Article  Google Scholar 

  • Lee TD, Goldenberg T and Hirth JP (1977). Hydrogen and plastic instability in deformed, spheroidized 1090 steel. In: Taplin, DMR (eds) Fracture 1977, International Conference on Fracture, vol 2, pp 243–248. University of Waterloo press, Waterloo

    Google Scholar 

  • Lee TD, Goldenberg T and Hirth JP (1979a). Effect of hydrogen on fracture of U-notched bend specimens of spheroidized AISI 1095 steel. Met Trans A 10: 199–208

    Article  Google Scholar 

  • Lee TD, Goldenberg T and Hirth JP (1979b). Effect of hydrogen on fracture of U-notched bend specimens of quenched and tempered AISI 4340 steel. Met Trans A 10: 439–448

    Article  Google Scholar 

  • Lee TC, Robertson IM and Birnbaum HK (1989). HVEM in situ deformation study of nickel doped with sulfur. Acta Met 37: 407–415

    Article  Google Scholar 

  • Lessar JF and Gerberich WW (1976). Grain size effects in hydrogen-assisted cracking. Met Trans A 7: 953–960

    Article  Google Scholar 

  • Li JCM, Oriani RA and Darken LS (1966). The thermodynamics of stressed solids. Z Physik Chem Neue Folge 49: 271–191

    Google Scholar 

  • Liang Y, Ahn DC, Sofronis P, Dodds RH, Bammann D (2007) Effect of hydrogen trapping on void growth and coalescence in metals and alloys. Mech Mater, in press

  • Liang Y, Sofronis P and Aravas N (2001). Hydrogen induced sher localization of theplastic flow in metals and alloys. Eur J Mech A/Solids 20: 857–872

    Article  MATH  Google Scholar 

  • Liang Y, Sofronis P and Dodds RH (2004). Interaction of hydrogen with crack-tip plasticity: effects of constraint on void growth. Mat Sci Eng A 366: 397–411

    Article  Google Scholar 

  • Lynch SP (1983). Nucleation and Egress of dislocations at crack tips. In: Latanision, RM and Pickens, JR (eds) Atomistics of fracture, pp 955–959. Plenum Press, New York

    Google Scholar 

  • Lynch SP (1988). Environmentally assisted cracking overview of evidence for an adsorption-induced localized-slip process. Acta Met 36: 2639–2661

    Article  Google Scholar 

  • Lynch SP (1989). Metallographic contributions to understanding mechanisms of environ-mentally assisted cracking. Metallography 23: 147–171

    Article  Google Scholar 

  • Lynch SP (1997) A commentary on mechanisms of environmentally assisted cracking. In: Magnin T (ed) Corrosion deformation interactions, CDI’96, No 21, The Institute of Metals, European Federation of Corrosion Publications, pp 206–219

  • McClintock FA (1968). A criterion for ductile fracture by the growth of holes. J Appl Mech 35: 363–371

    Google Scholar 

  • Needleman A (1987). A continuum model for void nucleation by inclusion debonding. J Appl Mech 54: 523–531

    Article  Google Scholar 

  • Needleman A (1990). An analysis of tensile decohesion along an interface. J Mech Phys Solids 38: 289–324

    Article  ADS  Google Scholar 

  • Needleman A (1997). Numerical modeling of crack growth under dynamic loading conditions. Comp Mech 19: 463–469

    Article  MATH  ADS  Google Scholar 

  • Needleman A and Tvergaard V (1987). An analysis of ductile rupture modes at a crack tip. J Mech Phys Solids 35: 151–183

    Article  MATH  ADS  Google Scholar 

  • Needleman A and Tvergaard V (1994). Mesh effects in the analysis of dynamic ductile crack growth. Eng Fract Mech 47: 75–91

    Article  Google Scholar 

  • Nelson HG, Stein JE (1973) Gas phase hydrogen permeation through alpha iron, 4130 steel, and 304 stainless steel from less than 100°C to near 600°C. Report No. NASA TN D-7265, Ames Research Center, Moffet Field, CA 94035

  • Onyewuenyi OA and Hirth JP (1983). Effects of hydrogen on notch ductility and fracture in spheroidized AISI 1090 steel. Met Trans A 14: 259–269

    Article  Google Scholar 

  • Oriani RA (1970). The diffusion and trapping of hydrogen in steel. Acta Met 18: 147–157

    Article  Google Scholar 

  • Oriani RA and Joshphic PH (1974). Equilibrium aspects of hydrogen-induced cracking of steels. Acta Met 22: 1065–1074

    Article  Google Scholar 

  • Oriani RA and Joshphic PH (1979). Hydrogen-enhanced nucleation of microcavities in AISI 1045 steel. Scr Met 13: 469–471

    Article  Google Scholar 

  • Ortiz M and Pandolfi A (1999). A finite deformation irreversible cohesive elements for three-dimensional crack propagationa analysis. Int J Num Meth Eng 44: 1267–1282

    Article  MATH  Google Scholar 

  • Pardoen T and Hutchinson JW (2000). An extended model for void growth and coalescence. J Mech Phys Solids 48: 2467– 2512

    Article  MATH  ADS  Google Scholar 

  • Pardoen T and Hutchinson JW (2003). Micromechanics-based model for trends in toughness of ductile metals. Acta Met 51: 133–148

    Article  Google Scholar 

  • Peisl H (1978). Lattice strains due to hydrogen in metals. In: Alefeld, G and Vokl, J (eds) Hydrogen in metals I, topics in applied physics, vol 28, pp 53–74. Springer-Verlag, Berlin

    Google Scholar 

  • Petti JP and Dodds RH (2005). Ductile tearing and discrete void effects on cleavage fracture under small-scale yielding conditions. Int J Solids Struct 42: 3655–3676

    Article  MATH  Google Scholar 

  • Rice JR and Johnson MA (1970). The role of large crack tip geometry changes in plane strain fracture. In: Kanninen, MF et al (eds) Inelastic behavior of solids, pp 641–672. McGraw-Hill, New York

    Google Scholar 

  • Rice JR and Tracey DM (1969). On the ductile enlargement of voids in triaxial stress fields. J Mech Phys Solids 17: 201–217

    Article  ADS  Google Scholar 

  • Ritchie RO, Sever WL and Wullaert RA (1979). Critical fracture stress and fracture strain models for the prediction of lower and upper shelf toughness in nuclear pressure vessel steels. Met Trans A 10: 1557–1570

    Google Scholar 

  • Robertson IM (2001). The effect of hydrogen on dislocation dynamics. Eng Fract Mech 68: 671–692

    Article  Google Scholar 

  • Robertson IM and Birnbaum HK (1986). HVEM study of hydrogen effects on the deformation and fracture of nickel. Acta Met 34: 353–366

    Article  Google Scholar 

  • Robinson SL and Stoltz RE (1981). Toughness losses and fracture behavior of low strength carbon–manganese steels in hydrogen. In: Bernstein, IM and Thompson, AW (eds) Hydrogen effects in metals, pp 987–995. The Metallurgical Society of AIME, Warrendale, PA

    Google Scholar 

  • Roy YA and Dodds RH (2001). Simulation of ductile crack growth in thin aluminum panels using 3-D surface cohesive elements. Int J Fract 110: 21–45

    Article  Google Scholar 

  • Ruggieri C, Panontin TL and Dodds RH (1996). Numerical modeling of ductile crack growth in 3-D using computational cell elements. Int J Fract 1: 67–95

    Google Scholar 

  • Serebrinsky S, Carter EA and Ortiz M (2004). A quantum-mechanically informed continuum model of hydrogen embrittlement. J Mech Phys Solids 52: 2403–2430

    Article  MATH  ADS  Google Scholar 

  • Siegmund T and Brocks W (1998). Local fracture criteria: lengthscales and applications. J De Physique IV 8: 349–356

    Google Scholar 

  • Siegmund T and Brocks W (1999). Prediction of the work of separation and implications to modeling. Int J Fract 99: 97–116

    Article  Google Scholar 

  • Siegmund T and Brocks W (2000a). The role of cohesive strength and separation energy for modeling of ductile fracture. In: Paris, PC and Jerina, KL (eds) Fatigue and fracture mechanics: 30th Volume ASTM STP 1360, pp 139–151. Americal Society for Testing and Materials, West Conshohocken, PA

    Google Scholar 

  • Siegmund T and Brocks W (2000b). A numerical study on the correlation between the work of separation and the dissipation rate in ductile fracture. Eng Fract Mech 67: 139–154

    Article  Google Scholar 

  • Sofronis P, Liang Y and Aravas N (2001). Hydrogen induced shear localization of the plastic flow in metals and alloys. Eur J Mech A-Solids 20: 857–872

    Article  MATH  Google Scholar 

  • Symons D (1998). The effect of carbide precipitation on the hydrogen-enhanced fracture behavior of alloy 690. Met Trans A 29: 1265–1277

    Article  Google Scholar 

  • Symons D and Thomspon AW (1996). The effect of hydrogen on the fracture of alloy X-750. Met Trans A 27: 101–110

    Article  Google Scholar 

  • Symons D and Thomspon AW (1997). The effect of hydrogen on the fracture toughness of alloy X-750. Met Trans A 28: 817–823

    Google Scholar 

  • Tabata T and Birnbaum HK (1983). Direct observations of the effect of hydrogen on the behavior of dislocations in iron. Scr Met 17: 947–950

    Article  Google Scholar 

  • Tabata T and Birnbaum HK (1984). Direct observations of hydrogen enhanced crack propagation in iron. Scr Met 18: 231–236

    Article  Google Scholar 

  • Taha A and Sofronis P (2001). A micromechanics approach to the study of hydrogen transport and embrittlement. Eng Fract Mech 68: 803–837

    Article  Google Scholar 

  • Takeda Y and McMahon CJ (1981). Strain controlled vs. stress controlled hydrogen induced fracture in a quenched and tempered steel. Met Trans A 12: 1255–1266

    Article  Google Scholar 

  • Tvergaard V (1982). On localization of ductile materials containing spherical voids. Int. J. Fract 18: 237–251

    Google Scholar 

  • Tvergaard V (1990). Material failure by void growth and coalescence. In: Hutchinson, JW and Wu, TW (eds) Advances in applied mechanics, pp 83–151. Academic Press, New York

    Google Scholar 

  • Tvergaard V (2001). Crack growth predictions by cohesive zone model for ductile fracture. J Mech Phys Solids 49: 2191–2207

    Article  MATH  ADS  Google Scholar 

  • Tvergaard V and Hutchinson JW (1992). The relation between crack growth resistance and fracture process parameters in elastic–plastic solids. J Mech Phys Solids 40: 1377–1397

    Article  MATH  ADS  Google Scholar 

  • Tvergaard V and Hutchinson JW (1993). The influence of plasticity on mixed mode interface toughness. J Mech Phys Solids 41: 1119–1135

    Article  MATH  ADS  Google Scholar 

  • Tvergaard V and Hutchinson JW (1996). Effect of strain-dependent cohesive zone model on predictions of crack growth resistance. Int J Solids Struct 33: 3297–3308

    Article  MATH  Google Scholar 

  • Williams ML (1957). On the stress distribution at the base of a stationary crack. J Appl Mech 24: 109–114

    MATH  MathSciNet  Google Scholar 

  • Xia L and Shih CF (1995). Ductile crack growth—I. a numerical study using computational cells with microstructurally-based length scales. J Mech Phys Solids 43: 233–259

    Article  MATH  ADS  Google Scholar 

  • Xia L, Shih CF and Hutchinson JW (1995). A computational approach to ductile crack growth under large scale yielding conditions. J Mech Phys Solids 43: 389–413

    Article  MATH  ADS  Google Scholar 

  • Xu X-P and Needleman A (1994). Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42: 1397–1434

    Article  MATH  ADS  Google Scholar 

  • Xu X-P and Needleman A (1997). Effect of inhomogeneities on dynamic crack growth in an elastic solid. Modelling Simul Mater Sci Eng 5: 489–516

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. Sofronis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ahn, D.C., Sofronis, P. & Dodds, R. Modeling of hydrogen-assisted ductile crack propagation in metals and alloys. Int J Fract 145, 135–157 (2007). https://doi.org/10.1007/s10704-007-9112-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-007-9112-3

Keywords

Navigation