A coupled diffusion and cohesive zone modelling approach for numerically assessing hydrogen embrittlement of steel structures

Highlights

• Critical review of current models.

• Finite element results reveal significant impact on the choice of modelling basis and input parameters.

• The models are able to reproduce single experimental behaviour of hydrogen induced cracking.

• To date, the transferability of the modelling approach is limited.

Abstract

Simulation of hydrogen embrittlement requires a coupled approach; on one side, the models describing hydrogen transport must account for local mechanical fields, while on the other side, the effect of hydrogen on the accelerated material damage must be implemented into the model describing crack initiation and growth. The present study presents a review of coupled diffusion and cohesive zone modelling as a method for numerically assessing hydrogen embrittlement of a steel structure. While the model is able to reproduce single experimental results by appropriate fitting of the cohesive parameters, there appears to be limitations in transferring these results to other hydrogen systems. Agreement may be improved by appropriately identifying the required input parameters for the particular system under study.

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.