Viktor Kharin

Two-Dimensional Numerical Modelling of Hydrogen Diffusion in Metals Assisted by Both Stress and Strain

The present work is based on previous research on the one-dimensional (1D) analysis of the hydrogen diffusion process, and proposes a numerical approach of the same phenomenon in two-dimensional (2D) situations, e.g. notches. The weighted residual method was used to solve numerically the differential equations set out when the geometry was discretized through the application of the finite element method. Three-node triangular elements were used in the discretization, due to its simplicity, and a numerical algorithm was numerically implemented to obtain the hydrogen concentration distribution in the material at different time increments. The model is a powerful tool to analyze hydrogen embrittlement phenomena in structural materials.

A generalised model of hydrogen diffusion in metals with multiple trap types

Continuum modelling of hydrogen diffusion in metals, which accounts for both trapping and an imposed force field, is revisited. A generalised model of hydrogen diffusion and trapping is developed as a continuous interpretation of the discrete random-walk theory. A system of nonlinear equations describing the phenomenon of diffusion with multiple types of traps is derived without the assumption of a local equilibrium among hydrogen populations in dissimilar positions. Lattice-trap interchange kinetics can degenerate into local equilibrium as a limit case. Moreover, certain terms in general equations may be negligible in specific situations. By removing these terms, known particularised models of hydrogen diffusion and trapping are recovered. Determining the terms, which are disregarded in reduced models, enables a straightforward assessment of the applicability of these models. The advantages and limitations of particularised models applied to hydrogen embrittlement analyses are discussed.

Two-dimensional numerical modelling of hydrogen diffusion assisted by stress and strain

This work is based on previous research on the one-dimensional (1D) analysis of the hydrogen diffusion process, and proposes a numerical approach to simulate the phenomenon in two-dimensional (2D) situations, e.g., near notches. The weighted residual method was used to solve numerically the differential equations set out when the geometry was discretized through the application of the finite element technique. This developed procedure can be a suitable practical tool to analyze hydrogen embrittlement phenomena in structural materials.

Hydrogen Diffusion in Metals Assisted by Stress: 2D Numerical Modelling and Analysis of Directionality

Hydrogen diffusion within a metal or alloy is conditioned by the stress-strain state therein. For that reason it is feasible to consider that hydrogen diffuses in the material obeying a Fick type diffusion law including an additional term to account for the effect of the stress state represented by the hydrostatic stress. In this paper the hydrogen transport by diffusion in metals is modelled in notched specimens where loading generates a triaxiality stress state. To this end, two different approaches of stress-assisted hydrogen diffusion, one-dimensional (1D) and two-dimensional (2D), were compared in the vicinity of the notch tip in four notched specimens with diverse triaxiality level at two different loading rates. The obtained results show that the 2D approach predicts lower values of hydrogen concentration than the 1D approach, so that a loss of directionality of hydrogen diffusion, depending on both notch geometry parameters (radius and depth) and loading rate, appears when a 2D approach is considered.

Influence of the Die Bearing Length on the Hydrogen Embrittlement of Cold Drawn Wires

Prestressing steels, obtained by cold drawing, are highly susceptible to hydrogen embrittlement (HE) phenomena. Stress and strain fields produced by cold drawing play an essential role in this process since they affect hydrogen diffusion. Therefore, variations of such fields due to changes in drawing conditions could modify life in-service of these structural components. In this work the effect on HE of a parameter of the wire drawing process, the bearing length, is analyzed by means of diverse numerical simulations by the finite element method (FEM). The results of this work allow the definition of a characteristic value of the die bearing length equal to the wire radius, and demonstrate that the effects of stress-strain fields produced by wire drawing on HE are reduced when the bearing length exceeds such a characteristic value, so that the optimum cold drawing process is that with a bearing length higher than the wire radius.

Effects of Manufacturing-Induced Residual Stresses and Strains on Hydrogen Embrittlement of Cold Drawn Steels

Hydrogen embrittlement (HE) plays a relevant role in the performance of prestressing steel wires. In this framework, the knowledge of residual stresses and plastic strains in wires due to cold-drawing (manufacturing-induced residual stresses), as well as of wires hydrogenation from harsh environments are the keys to successful predictions of wire lives. This paper advances previous analyses of HE in cold-drawn prestressing wires via numerical modelling, first, of the cold-drawing process to gain the distributions of residual stresses and plastic strains, and next, of the stress-strain assisted hydrogen diffusion in wires towards creation the conditions for HE nucleation. Generated results prove the relevant role of residual stress-and-strain field in hydrogen diffusion in the wires, as well as their possible consequences for HE.

A Critical Review of Existing Hydrogen Diffusion Models Accounting for Different Physical Variables

The present paper offers a continuum modelling of trap-affected hydrogen diffusion in metals and alloys, accounting for different physical variables of both macroscopic nature (i.e., related to continuum mechanics, e.g., stress and strain) and microscopic characteristics (material microstructure, traps, etc.). To this end, the model of hydrogen diffusion assisted by the gradients of both hydrostatic stress and cumulative plastic strain, stress-and-strain assisted hydrogen diffusion, proposed and frequently used by the authors of the present paper (Toribio & Kharin) is analysed in addition to other well-known models such as those proposed by (i) McNabb & Foster, (ii) Oriani, (iii) Leblond & Dubois, (iv) Sofronis & McMeeking, (v) Krom and Bakker, showing their physical and mathematical differences and similarities to account for different physical variables.

Hydrogen Embrittlement of Cold Drawn Prestressing Steels: the Role of the Die Inlet Angle

Cold-drawn prestressing steel wires are susceptible to hydrogen embrittlement (HE) in aggressive environments, and the residual stress-strain states generated in wires by the drawing process play the key role there. Hence, the alterations of the stress-strain fields due to the specific features of the drawing procedure affect the serviceability of wires under HE. On the basis of performed numerical simulations of the process of cold drawing with the use of different drawing dies, the paper addresses the effect of the inlet angle of the die on the residual stress-strain fields in the wires. We also deduce their consequences for the hydrogenation of wires and their susceptibility to HE. The reduction of the die inlet angle is shown to be beneficial for the performance of wires.

Hydrogen-Assisted Rolling-Contact Fatigue of Wind Turbines Bearings

This work analyses the effects of hydrogen-assisted rolling-contact fatigue on bearings of wind turbines. To this end, the well-known ball-on-rod test to evaluate the resistance to rolling-contact fatigue was simulated by the finite element method for obtaining the stress-strain state undergone by the bearings considering their in-service conditions. Results of this paper allow a simple estimation of the hydrogen amount in potential damage zones of the specimen.

Numerical analysis of hydrogen-assisted rolling-contact fatigue of wind turbine bearings

Offshore wind parks at locations further from the shore often involve serious difficulties, e.g. the maintenance. The bearings of offshore wind turbines are prone to suffer hydrogen-assisted rolling-contact fatigue (HA-RCF). Three important aspects linked with bearing failures are being extensively researched: (i) rolling contact fatigue (RCF), (ii) influence of carbide particles on fatigue life, and (iii) local microplastic strain accumulation via ratcheting. However, there is no reference related to bearing failure in harsh environment. This way, this paper helps to gain a better understanding of the influence of hydrogen on the service life of offshore wind turbine bearings through a numerical study. So, the widely used RCF ball-on-rod test was simulated by finite element method in order to obtain the stress-strain state inside the bearings during life in service and, from this, to elucidate the potential places where the hydrogen could be more harmful and, therefore, where the bearing material should be improved.