PSI - Issue 59

Jesús Toribio et al. / Procedia Structural Integrity 59 (2024) 137–144 Jesús Toribio / Procedia Structural Integrity 00 ( 2024) 000 – 000

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Fig. 3. Hydrostatic stress distributions ahead of the crack tip during monotonic loading at SSRT after fatigue pre-cracking at K max /K IC = 0.45 (dashed lines) and 0.80 (solid lines) at progressive applied K levels indicated in the figures. The distance x from the crack tip is measured in the deformed configuration and the sequential test instants (load levels) are indicated in the figures in relation to the fracture toughness K IC 4. Hydrogen diffusion modelling: evolution on near-tip hydrogen concentration distributions 4.1. Theoretical fundamentals: diffusional theory of HAC HE phenomena can be analyzed in terms of hydrogen diffusion through material lattice (lattice diffusion). As explained above, it is usually assisted by the stress field in the material, and specifically by the trace of the stress tensor, i.e., by the hydrostatic stress term, so that it is properly stress-assisted diffusion of hydrogen (Van Leeuwen, 1974; Toribio and Kharin, 1997a; 1997b; 1997c; 1998a; 2000a). When also the plastic strain distribution is supposed to affect hydrogen transport by lattice diffusion, then it is named stress-and-strain assisted diffusion of hydrogen (Toribio and Kharin, 2012; 2013a; 2013b; 2013c; 2013d; 2013e; 2015; 2017). Hydrogen diffusion is driven by the stress and strain state represented by, namely: (i) the in-wards gradient of hydrostatic stress and (ii) the in-wards gradient of strain-dependent hydrogen solubility, respectively. It is a modified Fick type law with two extra terms:

  

     

  

( )

   S P ε K K

H RT V

t C



S P ε

  D C DC





(1)

( )



with the meanings of symbols given in the above references. The steady-state solution of the differential equation leads to the equilibrium concentration of hydrogen ( C eq ). The long-time hydrogen accumulation in the metal is:

RT V H

  

  

 ( )exp

 C C K eq



(2)

S P ε 0