13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- The loss of accuracy of 1D approach with regard to the more realistic 2D approach can be quantitatively estimated by a new parameter λ defined as the amount of diffused hydrogen out of the notch geometry plane, thus, λ represents the loss of hydrogen diffusion directionality: (1D) (2D) (1D) λ r r r C C C− = . (4) As a sketch, the 1D approach could be considered as a hollow cylindrical tube through hydrogen diffuses and the 2D approach could be considered as a hollow cylindrical tube with small holes placed in the cylinder walls. So, in first case (1D approach) a fluid that flows inside the cylinder is trapped inside it and is not able to pass through the cylinder walls whilst in second case (2D approach) the fluid can escape out of the cylinder through the holes causing a loss of fluid flux in relation to the first case. To get a clear view of the influence of the parameters defining the different notched geometries on the loss of directionality, in Fig. 3 the distribution of the parameter through the notch symmetry plane is represented for each one of the four notched geometries simulated under the lowest loading rate, 0.001 mm/min, for a exposure time to harsh environment of 80% of the time to fracture in air, t = 0.8 tf. Fig. 3 shows a common trend for notched wires with the same notch tip radius, ρ. For blunt geometries with a higher notch radius (notches C and D) a low loss of directionality is obtained, i.e., the loss of accuracy of the 1D approach is low, cf. Fig. 2, whereas for sharp notches with a low notch radius (notches A and B) the 2D approach is required to obtain an adequate simulation. 0 0.1 0.2 0.3 0.4 0.5 0 0.5 1 1.5 2 A B C D λ depth (mm) u = 0.001 mm/min t = 0.8 t f . Figure 3. Distribution of loss of hydrogen diffusion directionality, through notch symmetry plane for the four notched geometries simulated under an extension rate of 0.001 mm/min at diffusion time t= 0.8tf According to these results, the notch tip radius (ρ) is the parameter governing the amount of hydrogen available for diffusing toward points out of notch symmetry plane in axial direction, with a second order effect of the notch depth (a). Fig. 4 shows a scheme of the diffusion path followed by hydrogen inside the material as a function of the dimensional approach (1D or 2D) to the process of hydrogen diffusion in the solid. The reason why hydrogen diffuses toward the axial direction out of the notch symmetry plane can be attributed to the key role that stress state plays in the hydrogen diffusion assisted by stress model (Eq. 3). According to this model, hydrogen diffuses to the places where the maximum hydrostatic stress appears [17]. In the case of 1D approach these points are placed inside the notch symmetry
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