13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Hydrogen Embrittlement in Metals: Analysis of Directionality of Hydrogen Diffusion Assisted by Stress and Strain Jesús Toribio1,*, Viktor Kharin1, Diego Vergara1, Miguel Lorenzo2 1 Department of Materials Engineering, University of Salamanca, Avda. Requejo 33, 49022 Zamora, Spain 2 Department of Mechanical Engineering, University of Salamanca, Avda. Fernando Ballesteros 2, 37700 Béjar, Spain * Corresponding author: toribio@usal.es Abstract 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. According to this law hydrogen diffuses not only to the points of minimum concentration (driven by its gradient), but also to those of maximum hydrostatic stress (driven by its gradient), the diffusion itself being also conditioned by the gradient of plastic strain. 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 very distinct triaxiality level at two different loading rates. The 2D approach predicts lower values of hydrogen concentration than the 1D approach, so that a loss of directionality of hydrogen diffusion towards the location of highest hydrostatic stress appears in the 2D case. This loss of directionality of hydrogen diffusion depends on both notch geometry parameters (radius and depth) and loading rate (or straining rate). Keywords Hydrogen diffusion, Numerical models, Notched samples, Directionality of diffusion. 1. Introduction Catastrophic fracture of structural materials in harsh environments for lower loading level than in air is caused many times by hydrogen diffusion towards material lattice and accumulation in certain places where damage at microstructural level is produced [1-4]. This phenomenon, known as hydrogen embrittlement (HE) or hydrogen-assisted fracture (HAF), has a key role in prestressed concrete structures due to the high susceptibility of the prestressing steel to this type of fracture [5-7]. At the critical fracture instant, the hydrogen concentration C reaches a critical value Ccr in a certain material locus cr x . The critical value of hydrogen concentration depends on the stress-strain state at the critical instant in the critical place or prospective location for fracture initiation [8]. Thus, the fracture criterion can be expressed as follows: ( , )i i cr cr σ ε C C= in cr x x = , (1) where x is the spatial vector coordinates. In this equation the influence of the stress-strain state on the critical value of hydrogen concentration is included by means of both tensor invariants represented by the principal stresses, σi, and principal plastic strains εi (i = 1, 2, 3). To study this phenomenon, constant-extension-rate tensile (CERT) tests in a hydrogenating environment are commonly used. The mechanical load applied during the test generates a certain stress-strain state in the material according to the geometry of the tested specimen. Although specimens for this type of test could exhibit different shapes, diverse studies [9,10] consider round notched bars as the best suited to the evaluation of these fracture phenomena. Obviously, under CERT test load conditions the stress and strain state varies with time and, consequently, a transient analysis of the hydrogen diffusion must be carried out.
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