Hydrogen embrittlement is a complex phenomenon, involving several lengthand timescales, that affects a large class of metals. It can significantly reduce the ductility and load-bearing capacity and cause cracking and catastrophic brittle failures at stresses below the yield stress of susceptible materials. Despite a large research effort in attempting to understand the mechanisms of failure and in developing potential mitigating solutions, hydrogen embrittlement mechanisms are still not completely understood. There are controversial opinions in the literature regarding the underlying mechanisms and related experimental evidence supporting each of these theories. The aim of this paper is to provide a detailed review up to the current state of the art on the effect of hydrogen on the degradation of metals, with a particular focus on steels. Here, we describe the effect of hydrogen in steels from the atomistic to the continuum scale by reporting theoretical evidence supported by quantum calculation and modern experimental characterisation methods, macroscopic effects that influence the mechanical properties of steels and established damaging mechanisms for the embrittlement of steels. Furthermore, we give an insight into current approaches and new mitigation strategies used to design new steels resistant to hydrogen embrittlement.

In the present work, a mathematical model and computer programs were developed for numerical simulation of the processes of nucleation and growth of the ␣ -phase Widmanstätten plates during the course of the ␤ ⇒ ␣ phase transformation in a Ti-6Al-4V alloy. The ␣ -phase appearance at the grain boundary of ␤ phase is described by a numerical procedure for random nucleation as a function of the vanadium concentration and the temperature. The rate at which an interface moves depends both on the intrinsic mobility and on the rate at which diffusion can remove the excess of vanadium atoms ahead of the interface. The finite-element method (FEM) was used for solving the diffusion equation on the domain occupied by ␤ phase. The elements chosen have dimensions in both space and time. A computer code based on the finite-element modeling and the volume of fluids method was developed to trace the movement of the ␣ /␤ interface. The influences of the cooling rate and the temperature of isothermal exposure on the Widmanstätten morphology were simulated and analyzed. The developed models and program packages are capable of one-dimensional (1-D) and two-dimensional (2-D) simulations of the morphology of the ␤ ⇒ ␣ phase transformation in Ti-6Al-4V alloy for continuous cooling with any cooling path and for an arbitrary combination between continuous cooling and isothermal exposure.

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We present calculations of free energy barriers and diffusivities as functions of temperature for the diffusion of hydrogen in α-Fe. This is a fully quantum mechanical approach since the total energy landscape is computed using a new self consistent, transferable tight binding model for interstitial impurities in magnetic iron. Also the hydrogen nucleus is treated quantum mechanically and we compare here two approaches in the literature both based in the Feynman path integral formulation of statistical mechanics. We find that the quantum transition state theory which admits greater freedom for the proton to explore phase space gives result in better agreement with experiment than the alternative which is based on fixed centroid calculations of the free energy barrier. We also find results in better agreement compared to recent centroid molecular dynamics (CMD) calculations of the diffusivity which employed a classical interatomic potential rather than our quantum mechanical tight binding theory. In particular we find first that quantum effects persist to higher temperatures than previously thought, and conversely that the low temperature diffusivity is smaller than predicted in CMD calculations and larger than predicted by classical transition state theory. This will have impact on future modeling and simulation of hydrogen trapping and diffusion.