Continuum Damage Model for Hydrogen Embrittlement in Ferritic Steels

TL;DR

This work develops a Nano-Void Coalescence (NVC)–inspired continuum damage model for hydrogen embrittlement in ferritic steels by embedding hydrogen-enhanced localization and vacancy stabilization within a Gurson plasticity framework. The model is two-way coupled to trap-mediated hydrogen diffusion, solved in a staggered ABAQUS UMAT formulation, with calibration on X65 linepipe steel and validation against hydrogen-charged round-bar tensile tests. Key contributions include a hydrogen-softening flow law $\sigma_{flow}(\bar{\epsilon^p}, C_H)$ with a critical hydrogen concentration $C_c$ and an additional hydrogen-driven void nucleation term $df_{nucleation,H}=B \; d\bar{\epsilon^p} \; C_H$, jointly enabling prediction of ductility loss and elongation. The approach provides a physically grounded, numerically implementable tool for assessing hydrogen-induced damage in pipeline steels and informs materials integrity management in hydrogen environments.

Abstract

Hydrogen embrittlement of metals and alloys, particularly steels, has been an important scientific and engineering challenge in the Oil and Gas industry for many years. It impacts the integrity and performance of a wide range of structures and equipment such as downhole tubulars and pipelines in sour service in the Upstream (U/S) and hydro-processing reactors in the Downstream (D/S). In addition, the rapidly growing interest in hydrogen as an energy carrier for fuel cells and mobility or as a clean fuel/heat source for hard to decarbonize industrial processes, draws attention to this key challenge of materials integrity in handling hydrogen. The fundamental understanding of failure mechanism(s) and the capability to model material behavior is important for managing the integrity and for repurposing existing infrastructure for transporting hydrogen as well as for extending the life of structures. To that extent, the present work develops a robust mathematical model to estimate the strength degradation and embrittlement due to hydrogen in steels. The model incorporates hydrogen affected constitutive response of material, within the framework of finite element method. The modified constitutive response is a Gurson plasticity based continuum damage model and incorporates two vital aspects of NVC failure theory. These key aspects are (i) hydrogen enhanced localized dislocation plasticity, and (ii) hydrogen enhanced vacancy stabilization forming nano-voids. The deformation and damage in the material is coupled with trap mediated hydrogen diffusion. Calibration of damage model parameters is performed for X65 commercial linepipe steel. Finally, capability of the damage model is demonstrated with numerical simulation of round bar tensile tests on X65 steel under hydrogen exposure. The numerical simulations are shown to be in excellent agreement with experimental results.

Figures (7)

• Figure 1: Numerical tensile stress-strain reponse for round bar specimen using Gurson user material (UMAT) developed in this work and Abaqus in-built Gurson constitutive model.
• Figure 2: Strain-hardening for the model material with various exposures of hydrogen. $C_{rel}=0.0$ indicates no hydrogen and $C_{rel}$ indicates critical amount of hydrogen. With the modified hardening law, the material softens as the exposure of hydrogen increases.
• Figure 3: Tensile stress-strain response of round bar specimen with the effect of hydrogen induced softening.
• Figure 4: Variation of void nucleation df from breaking carbides and hydrogen with effective plastic strain. Hydrogen contribution is plotted for various values of $H-V$ complex parameter $B$. Y-axis represents the increment of void nucleation.
• Figure 5: Tensile stress-strain response of round bar specimen with the effect of hydrogen induced void nucleation.