Issue 35

G. Gobbi et alii, Frattura ed Integrità Strutturale, 35 (2016) 260-270; DOI: 10.3221/IGF-ESIS.35.30 264 compares the trends of the applied force versus the vertical load line displacement (F-V LL ) represented in Fig. 2, obtained from experimental toughness tests and from the numerical cohesive model simulating the same loading condition. Force, F, is evaluated at the center of the loading pin, and it corresponds to the load cell measurement. Displacement, V LL , is measured at the node where the clip-on-gauge is experimentally located. In this way, experimental data can be directly compared with the numerical outputs. Simulation of hydrogen effect The decreasing of the mechanical performances of a steel due to the embrittlement effect are strictly related to hydrogen content. Therefore, to simulate correctly this phenomenon it is necessary to take into account properly the total amount of hydrogen present into the material. As already highlighted in the introduction, the concentration of hydrogen inside the steel lattice consists of two contributions: the interstitial lattice sites content and the trapped hydrogen content. To estimate both these contributions, a three-steps model is implemented. Once the total hydrogen concentration is calculated, it is then used to reduce the cohesive law, simulating hydrogen embrittlement effect. The first step is a stress analysis used to calculate the hydrostatic stress field into the specimen. The second step, instead, consists of a mass diffusion analysis in which a redistribution of an initial hydrogen concentration, selected according to the experimental values equal to 1.5 ppm at the free surfaces [17], is computed based on the hydrostatic stress field previously calculated. The equation used by Abaqus to solve the diffusion analysis is the following, with the omission of the temperature term that is not considered: * P p J s D k x x               (3) where J * is the flux, s is the solubility, D is the diffusivity of the material, φ is the normalized concentration over the solubility, k P is the term that induces diffusion due to the hydrostatic effect and p is the hydrostatic stress. Tab. 1 summarizes the values of the parameters used in the model. It should be pointed out that the scientific literature only reports experimental values of the apparent diffusion coefficient D H for the current steel. Thus, this was the value implemented into the model. The concentration obtained from this analysis refers only to the “free” hydrogen present in the interstitial lattice sites, C L . Solubility s Diffusivity D Gibbs free energy 0 b g  Gas constant R 0.071 ppm mm N -1/2 1.62·10 -5 mm 2 /s 30 kJ/mol 8.314 J K -1 mol -1 Table 1 : Values of parameters adopted in the three simulations of the cohesive zone model. Finally, the last step is a stress analysis with cohesive elements implementation to simulate the fracture behavior. In this simulation, also the trap site concentration is computed. As indicated in the introduction, influence of traps on hydrogen embrittlement is certainly important; however, the characterization of trap type, density, binding energy and occupancy is a demanding task that has to be performed at smaller scales. In order to simplify this problem and to include this contribution in the finite elements codes, we consider here only hydrogen low energy traps and we assume that these are related to the plastic strain. In fact, starting from results presented in [6], the work by [15] proposed the following relation between the trap content and the plastic strain:   49.0 0.1 T P L C C      (4) This relation was proposed for high and low strength steels, from physical-chemical analytical relations and numerical models [6]. It is implemented in the third analysis using the plastic strain calculated during the simulation. The total bulk hydrogen concentration, C , resulted from the sum of interstitial lattice sites C L and the traps sites C T is related to the surface concentration in the cohesive zone through [21]: