Three-dimensional constraint-based void-growth model for high temperature hydrogen attack

K. Vijayvargia, M. Dadfarnia, P. Sofronis, M. Kubota, A. Staykov, K. Wada, J. A. Pugh, T. J. Eason

Research output: Contribution to journalArticlepeer-review


High temperature hydrogen attack (HTHA) is degradation of steels exposed to hydrogen gas at high temperatures and pressures. Hydrogen in steels reacts with carbon from carbides to produce methane gas bubbles typically on grain boundaries which grow and coalesce, leading to loss of strength and fracture toughness. Current design practice against HTHA is based on the Nelson curves which define the conditions for safe operation in a temperature/hydrogen-partial-pressure diagram. Nelson curves are phenomenological in nature and do not account for the underlying failure mechanism(s), material microstructure, carbide stability, and applied stresses. In light of experimental evidence of predominant cavitation ahead of cracks reported by Martin et al. (Acta Mater 140:300–304, 2017), it is expected that void growth is accelerated by the triaxial stresses associated with microstructural flaws. To this end, we propose a three-dimensional, axisymmetric, constraint-based void-growth model extending the “one-dimensional” model of Dadfarnia et al. (Int J Fract 219:1–17, 2019). The present model is shown to yield satisfactory agreement with the available experimental data from hydrogen attack of 2¼Cr–1Mo steel at temperatures ranging from 500 to 600 °C. In addition, the model is used to construct Nelson type curves in the temperature/hydrogen-partial-pressure diagram. These curves represent failure times for given applied stresses and triaxiality. The proposed methodology can be viewed as providing a step toward improving the current design practice against HTHA while maintaining the simplicity of the original Nelson curve approach.

Original languageEnglish (US)
Pages (from-to)203-228
Number of pages26
JournalInternational Journal of Fracture
Issue number2
StatePublished - Oct 2023
Externally publishedYes


  • Carbon steel
  • Constrained void growth
  • Hydrogen attack
  • Modelling
  • Triaxiality

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Mechanics of Materials


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