PSI - Issue 59

Jesús Toribio et al. / Procedia Structural Integrity 59 (2024) 145–150 Jesús Toribio / Procedia Structural Integrity 00 (2024) 000 – 000

147

3

3. Mechanical analysis The FEM analysis allows a determination of stress-strain distributions in the samples for increasing levels of externally applied load (remote stress) on the specimens. On the basis of this mechanical analysis , the distribution of hydrogen concentration will be obtained ( chemical analysis ). The load-displacement curves F - u are shown in Fig. 2 up to the maximum load F max (after this value the load decreases). The maximum displacement u max is greater for shallow notches than for deep ones, and there is a sort of similarity between the curves corresponding to different notch depth.

100

100

80

80

60

60

R/D=0.04

R/D=0.40

40

40

0 0.0 0.5 1.0 1.5 2.0 2.5 C/D=0.1 C/D=0.2 C/D=0.3 C/D=0.4

0 0.0 0.5 1.0 1.5 2.0 2.5 C/D=0.1 C/D=0.2 C/D=0.3 C/D=0.4

F (kN)

F (kN)

20

20

u (mm)

u (mm)

Fig. 2. Load-displacement curves F - u for specimens with sharp and blunt notches of different depths.

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

c

 

        D c M c Mc

(1)

,



t

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

(2)

,



RT

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:

H RT      V

c c 

0 exp

(3)

,

r



