Review ArticleA coupled diffusion and cohesive zone modelling approach for numerically assessing hydrogen embrittlement of steel structures
Introduction
Hydrogen induced degradation of mechanical properties, often termed hydrogen embrittlement (HE), is a well recognized threat for structural steels. It manifests as loss in ductility, strength and toughness, which may result in unexpected and premature catastrophic failures. The phenomenon was first reported by Johnson in 1874 [1], and has later been extensively researched both experimentally [2], [3], [4], [5], [6], [7], [8], [9], [10], [11] and numerically [12], [13], [14], [15], [16], [17], [18], [19], [20], yielding a number of models accounting for the phenomenon. However, no consensus about the basic mechanisms responsible for hydrogen embrittlement is reached yet. Two theories have advanced as the more accepted ones for the case of hydrogen degradation in steel: Hydrogen Enhanced Decohesion (HEDE), in which interstitial atomic hydrogen reduces the bond strength and thus the necessary energy to fracture [21], [22], [23], [24], [25]; and Hydrogen Enhanced Localized Plasticity (HELP), in which atomic hydrogen accelerates dislocation mobility through an elastic shielding effect which locally reduces the shear stress [26], [27], [28], [29], [30]. Today it is seemingly recognized that no single mechanism can comprehensively explain all the phenomena associated with hydrogen embrittlement. Rather it appears that different mechanisms apply to different systems, and that a combination of mechanisms is more likely in many cases.
In recent years, cohesive zone modelling has gained increasing interest as suitable method for modelling hydrogen embrittlement [14], [15], [16], [18], [20], [31], [32], with the possibility of providing increased understanding of the involved process and their interactions combined with reduced time and costs compared to experimental programs. The damage process is classically described by interface elements, which constitutive relation is defined by a cohesive law (traction separation law). Simulation of hydrogen induced degradation requires a coupled approach, including modelling of transient mass transport, plastic deformation, fracture and their interactions. On one side, the models describing hydrogen diffusion must account for local mechanical field quantities; i.e. hydrostatic stress and plastic strain. On the other side, the effect of hydrogen on the accelerated material damage must be implemented into the cohesive law.
The present work presents a review of coupled diffusion and cohesive zone modelling as a method for numerically assessing the hydrogen embrittlement susceptibility of a steel structure. In the first section, established and recent models for hydrogen transport are summarised and discussed. The second section gives an overview of cohesive zone modelling in general and approaches for implementing hydrogen influence. The coupling aspect between hydrogen transport and cohesive zone modelling is discussed and put in conjunction with the presented hydrogen diffusion models. Finally, in the third section, some practical applications of the presented model are discussed.
Section snippets
Hydrogen transport models
The process that results in hydrogen embrittlement includes a transport stage of hydrogen to the site of degradation. In order to predict the degrading effect of hydrogen on the mechanical properties, it is of fundamental importance to correctly assess the hydrogen distribution in the material.
Atomic hydrogen is generally considered to reside either at normal interstitial lattice sites (NILS) or being trapped at microstructural defects like dislocations, carbides, grain boundaries and
A cohesive zone modelling approach to hydrogen embrittlement
Cohesive models were first formulated by Barenblatt [56] and Dugdale [57], who introduced finite non-linear cohesive tractions in front of an existing crack, as a mean to overcome the crack tip stress singularity. To date, the cohesive model is extensively applied for crack propagation analysis using the finite element method. Among the various approaches available, it is appealing in that it requires few parameters and in its universality of applicability [58].
Practical applications of the coupled continuum model
The capability of the model to trustfully predict hydrogen induced crack nucleation and propagation in structural steel applications is of key importance for further developments. An engineering tool, able to partly replace time consuming and costly experimental programs, should be of general validity and provide robustness and transferability to other material systems and environments. While most studies are able to reproduce single experimental results by appropriate fitting to the cohesive
Conclusion
A coupled mass transport and cohesive zone modelling approach for simulating hydrogen induced cracking is described and discussed. Based on calculations, the main findings are summarized as follows:
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The choice of input trap binding energy and trap density formulation have significant impact on the resulting lattice, trapped and total hydrogen distributions, and on the corresponding hydrogen induced reduction of the cohesive strength.
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The use of the Langmuir-McLean isotherm as the necessary
Acknowledgements
The present work was financed by the Research Council of Norway (Petromaks 2 programme, Contract No. 234110/E30), Statoil, Gassco, Technip, POSCO and EDF Induction and performed within the frames of the ROP project (www.sintef.no/rop). The authors gratefully acknowledge the valuable input from Antonio Alvaro, Philippe Mainçon and Vidar Osen.
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