A modelling framework for coupled hydrogen diffusion and mechanical behaviour of engineering components

Abstract

In this paper, we propose a finite element formulation for solving coupled mechanical/diffusion problems. In particular, we study hydrogen diffusion in metals and its impact on their mechanical behaviour (i.e. hydrogen embrittlement). The formulation can be used to model hydrogen diffusion through a material and its accumulation within different microstructural features of the material (dislocations, precipitates, interfaces, etc.). Further, the effect of hydrogen on the plastic response and cohesive strength of different interfaces can be incorporated. The formulation adopts a standard Galerkin method in the discretisation of both the diffusion and mechanical equilibrium equations. Thus, a displacement-based finite element formulation with chemical potential as an additional degree of freedom, rather than the concentration, is employed. Consequently, the diffusion equation can be expressed fundamentally in terms of the gradient in chemical potential, which reduces the continuity requirements on the shape functions to zero degree, C 0 , i.e. linear functions, compared to the C 1 continuity condition required when concentration is adopted. Additionally, a consistent interface element formulation can be achieved due to the continuity of the chemical potential across the interface-concentration can be discontinuous at an interface which can lead to numerical problems. As a result, the coding of the FE equations is more straightforward. The details of the physical problem, the finite element formulation and constitutive models are initially discussed. Numerical results for various example problems are then presented, in which the efficiency and accuracy of the proposed formulation are explored and a comparison with the concentration-based formulations is presented. Keywords Hydrogen embrittlement (HE) • Hydrogen enhanced local plasticity (HELP) • Hydrogen enhanced decohesion (HEDE) • Chemical potential • Galerkin method • Interface/cohesive model Nomenclature HEDE Hydrogen enhanced decohesion HELP Hydrogen enhanced local plasticity HE Hydrogen embrittlement HID Hydrogen induced decohesion α Number of trapping sites in a trap β L Number of interstitial sites per solvent atom B Elsiddig Elmukashfi

Progress and opportunities in modelling environmentally assisted cracking

“…Recent efforts have been devoted to tackling stage 2: resolving the electrochemical-diffusion interface. Models have been presented that provide as input the lattice chemical potential [46][47][48][49], a more rigorous approach than prescribing a constant hydrogen concentration. More importantly, a new generalised formulation has been proposed to resolve the electrochemistry-diffusion interface, enabling quantifying the flux of hydrogen from the local pH and overpotential [50].…”

General model for the kinetics of solute diffusion at solid-solid interfaces

“…Within the context of a continuous function that is discretized in a FVM model, the variation in chemical potential across the saddle point will not be linear, as it is often wrongly assumed (e.g., Ref. [47]), unless both sites are identical in nature. Instead, a condition of equal flux on both sides of J = J − = J + is necessary [48,49], where…”

Coupling a discrete twin model with cohesive elements to understand twin-induced fracture

“…Intergranular fracture is a type of brittle fracture, which involves the nucleation and propagation of cracks along grain boundaries. It is a dominant failure mechanism in as-cast metals (Powell 1994), ultrafine-grained metals (Pippan and Hohenwarter 2016), during stress corrosion (Birbilis and Hinton 2011) and hydrogen embrittlement (Barrera et al 2018;Elmukashfi et al 2020). It takes place in materials in which the stress required to debond the grain boundary interface is lower than the stress to debond atomic planes inside the grains (Jiang et al 2015) or to nucleate and grow microscopic voids (Tvergaard 1981;Cocks and Ashby 1982).…”