Issue 33

J. Toribio et alii, Frattura ed Integrità Strutturale, 33 (2015) 434-443; DOI: 10.3221/IGF-ESIS.33.48 441 The discussion about HA-RC-MF is focused in the quantitative analysis of the hydrogen amount in radial, hoop and axial directions by applying the steady-state solution of the diffusion equation shown in eq. (3) to the distributions of the components of the stress tensor and plastic strain shown in Figs. 2 and 4 respectively. Thus, Fig. 9 shows the radial laws of hydrogen concentration along diverse radial planes considering the stress and strain states shown in Figs. 5 and 6, whereas Figs. 10 and 11 shows the distribution of hydrogen concentration in the hoop and axial directions respectively. According to these results, for long time of exposure to the hydrogenating environment, the hydrogen amount at the rod surface vicinity (within the stress and strain affected zone of the rod, i.e., for depths from the rod surface lower than 1 mm) is progressively increased with the circumferential distance to the contacting ball. Thus, for the plane where the ball is contacting the rod, a huge reduction of the hydrogen amount is observed due to the high compressive stresses produced by the contact pressure (Fig. 6). Consequently, hydrogen diffusion is promoted out of the contact affected zone due to the gradient of both driving forces for hydrogen diffusion: the inwards gradient of plastic strain and the inwards gradient of hydrostatic stress. This effect is also progressively vanished as the distance from the contact plane increases, it being noticeable for planes very close to the contact plane where an important reduction of the hydrogen concentration is also achieved. Nevertheless, for planes with circumferential coordinates higher than 10º from the contact plane, the hydrogen amount at surface is similar than that obtained for higher angle  . The distributions of hydrogen for planes with circumferential coordinate higher than 10º just exhibit slight changes. An interesting issue is observed for these planes from the point of view of HA-RC-MF. At the rod surface vicinity over a depth of 200  m a significant reduction is observed due to the compressive stresses (Fig. 6) with a small plateau of 50  m. Hereafter the hydrogen concentration increases with depth, reaching the maximum value ( C / C 0 = 1.15) of the distribution for a depth of 300  m and for deeper points softly decreases up to the rod core where the concentration associated with thermo-dynamical equilibrium of the material free of stress and strain ( C 0 ) is achieved. So, the potential place of damage would be placed through a zone extended between the balls for depth from surface of 300  m. The hoop distribution of hydrogen for long times of exposure to the hydrogenating environment is presented in Fig. 10, where different depth layers (diverse depths) are depicted, considering the stress and strain states obtained from numerical simulation (Fig. 8). 0 0.2 0.4 0.6 0.8 1 1.2 -40 -20 0 20 40 x=0 x=86  m x=173  m x=216  m x=300  m x=700  m C eq  C 0  (º) Figure 10: Hydrogen distribution for long times of diffusion in the circumferential direction at diverse layers of the rod between the contacting balls. Regarding the hoop distribution of hydrogen concentration shown in Fig. 10, the hydrogen accumulation is placed out of the contacting plane (  = 0º) and surrounding planes where a huge reduction of the hydrogen amount is observed. This reduction becomes lower as the depth from the surface is increased. Out of this zone hydrogen is uniformly distributed for depths up to 86 μ m. For distribution obtained at higher depths, hydrogen is progressively increased for  > 5º, reaching a maximum hydrogen concentration at  = 20º and, hereafter, decreasing slowly. The aforesaid trend is repeated at deeper layers, increasing the maximum hydrogen amount zone as the depth increases (according to the distributions of hydrostatic stress shown in Fig. 6a). For layers placed far from the contact, hydrogen is almost uniformly distributed in the hoop direction, reaching a maximum hydrogen concentration, C / C 0 = 1.13, for a