PSI - Issue 28

Jesús Toribio et al. / Procedia Structural Integrity 28 (2020) 2444–2449 Jesús Toribio et al. / Procedia Structural Integrity 00 (2020) 000–000

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4. Chemical analysis The hydrogen diffusion model used in this study was the diffusion equation (assisted by hydrostatic stress) developed by Van Leeuwen (1974), adding stress dependent terms to Fick’s second law of diffusion,

         c D c M c Mc t 

,

(1)



where c is the concentration of hydrogen in the steel, t the time, D the diffusion coefficient of the hydrogen in the metal, M a second coefficient (function of the previous one) and σ the hydrostatic stress. In absence of body forces, the equilibrium requires that Δ σ = 0. The second coefficient M is calculated through the expression : H DV M RT  , (2) V H being the partial molar volume of hydrogen in the metal, R the constant of the ideal gases and T the absolute temperature. The boundary condition corresponds to the Boltzmann distribution as follows: where c 0 is the equilibrium hydrogen concentration in the metal in the absence of any stresses. This equation is also the stationary solution of the diffusion problem. Fig. 4 shows the concentration of hydrogen c / c o in stationary system for deformed sharply notched specimens (dimensionless notch tip radius R/D = 0.04) with different load ratio F / F max with values of the dimensionless notch depths of C/D = 0.1 ( shallow sharp notch ) and C/D = 0.3 ( deep sharp notch ). It is observed how the zone of maximum concentration of hydrogen is in the region near the minimum section of the rod specimen corresponding to the notch tip. The concentration of hydrogen c / c o is plotted against the x -coordinate, which extends along the minimum specimen section and whose origin corresponds to the notch tip itself. The notch geometry has a great influence on the profile of hydrostatic stress, which makes the hydrogen concentration reach higher values in specimens with sharp notches (Toribio and Ayaso, 2004), as in the case of the present paper. For very low loading levels (very small remote stress or externally applied load, F / F max ~ 0.1), the highest concentration of hydrogen is located at the specimen surface of the specimen ( notch tip ) and the maximum value moves into the bar as the load increases. At any rate, the maximum concentration value is achieved in an area in the vicinity of the notch tip, with a pronounced peak and a very strong gradient near the notch. 5. Discussion Fig. 5a plots the boundary ( notch-tip ) concentration of hydrogen c Г / c o represented as a function of the load ratio F / F max . Results show how such a boundary value increases markedly with the remote stress (externally applied load) and slightly decreases with the notch depth, i.e., the equilibrium boundary value of hydrogen concentration is slightly higher for shallow sharp notches. With regard to the possible implications of the present theoretical (numerical) analysis in the matter of experimental aspects of hydrogen embrittlement and notch tensile strength of pearlitic steel, previous research on the topic showed evidence that the fracture process starts in the vicinity of the notch tip, showing a critical zone whose fractographic appearance resembles a sort of microplastic tearing: the so-called tearing topography surface (TTS), as described by Toribio et al. (1991), Toribio and Vasseur (1997) Toribio (1997), Toribio (2012) and Toribio (2018). H RT      V r 0 exp c c    , (3)