Issue 33

J. Toribio et alii, Frattura ed Integrità Strutturale, 33 (2015) 434-443; DOI: 10.3221/IGF-ESIS.33.48 435 N UMERICAL MODELING he study was divided into two uncoupled analysis. On one hand, the numerical simulation by means of a commercial finite element (FE) code was used for obtaining the stress and strain states after six revolutions of the bar. From the results of such an analysis, a simple estimation of the hydrogen accumulation for long time of exposure to hydrogenating environment was carried out allowing the estimation of the potential hydrogen damage places. The geometry analysed consist in a steel bar of length L = 6 mm and diameter d = 9.53 mm which rotates in contact with three equidistant steel balls of diameter D = 12.70 mm which apply a point load of F = 300 N over the bar surface as reflects the scheme of Fig. 1a. The complete 3D geometry can be simplified to a half just considering the symmetry plane r -  shown in Fig. 1b and applying the corresponding boundary conditions as restricted displacement on the bar axial direction for all the nodes placed inside the symmetry plane. Thus, an important save of computing time is achieved optimizing the available resources. In addition, the geometry of the contacting balls can be also simplified considering the symmetry plane r - z of such components. Taking this into account, only a quarter of the whole geometry of the ball is modelled, as can be seen in Fig. 1b. (a) (b) Figure 1 : (a) Scheme of analysed geometry for a ball on rod test and (b) 3D geometry. The numerical modelling of the ball-on-rod test (six revolutions) was carried out considering the material constitutive law to be elastic perfectly plastic corresponding to a steel with the following material properties for both, rod and balls: Young modulus, E = 206 GPa, Poisson coefficient,  = 0.3 and material yield stress  Y = 2065 MPa. The analysis was carried out considering the isotropic strain hardening of the material and updated Lagrange procedure. According to the Hertz theory considering only the elastic response of the components [16], a very localized effect can be expected in the contact zone between rod and balls. According to this, a ball pressuring a cylinder must undergo a contact pressure of 5.5 GPa with a elliptic contacting zone whose axis length are 160  m and 231  m respectively. A very refined mesh is required near the rod surface, whereas a coarser mesh was considered out of such a zone since the local effect of contact vanishes at the rod core. Thus, elements were homogenously distributed over a depth from the rod surface about 1 mm. This way, in this refined zone, the size of these elements is 43 x 52 x 280  m in the radial, circumferential and axial directions. Regarding the meshing of the balls, the same type of elements was used, assuming a refined zone at the contact zone with element sizes similar to those used for the cylindrical bar. A point load of 300 N was placed at each ball centre and was progressively applied during the first rotation of the rod. Taking this into account, diverse meshes with linear hexaedric element of 8 nodes were considered until the required convergence on results was achieved. The optimum mesh (Fig. 2) consists in 154000 elements: 130000 for meshing the rod and 24000 for meshing the three balls. From results of the mechanical simulation, a simple estimation of the behaviour against HA-RC-MF of the bar can be carried out considering that hydrogen diffusion proceeds from the bar surface to inner points as a function of the gradients of both hydrostatic stress (  ) and hydrogen solubility ( K s  ) [17-19]: T