PSI - Issue 59

Jesús Toribio et al. / Procedia Structural Integrity 59 (2024) 104–111 Jesús Toribio / Procedia Structural Integrity 00 ( 2024) 000 – 000

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6

2 

2

∆  f = (  /32) (K IC /  Y ) (4) in which  f and ∆  f are respectively the sizes of the monotonic (K=K max ) and cyclic (K=K max ) plastic zones during fatigue pre-cracking and the ratio (K IC /  Y ) is a characteristic of the material. In addition, a dimensionless ratio  c of the critical stress intensity factor (at the end of the SCC test) to the fracture toughness in air may be defined as follows:  c = K C (SCC test) / K IC (air) (5) which is approximately the ratio of the failure load in solution to the failure load in air (Fc/Fo) given in Figs. 1 and 2 (neglecting the subcritical crack growth). Thus the plastic zone size and the end of the SCC tests may be calculated as follows:  c = (  /8) (K IC /  Y ) 2  c 2 (6) This size is relevant to ascertain interactions between crack-tip plasticity and hydrogen and to determine the role of diffusion in the hydrogen transport in pearlitic steel. 4. Chemical analysis: modeling of stress-assisted diffusion of hydrogen 4.1. Theoretical fundamentals: diffusional theory of HAC HAC 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). When also the plastic strain distribution is supposed to affect hydrogen transport by diffusion, then it is named stress-and-strain assisted diffusion of hydrogen (Toribio and Kharin, 2015). In the problem analyzed in the present paper, hydrogen diffuses from the wire surface exposed to hydrogenating environment towards the wire core. Equation (7) shows the dependence of hydrogen diffusion on 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. This equation is just a modified Fick type law where two additional terms are included to include the gradients of hydrostatic stress and plastic strain, as follows: f

  

     

  

( )

   S P ε K K

H RT V

t C



S P ε

  D C DC





(7)

( )



The steady-state solution of the differential equation (7) allows an estimation of the equilibrium concentration of hydrogen ( C eq ). This way, the long-time hydrogen accumulation in the metal can be obtained as follows:

RT V H

  

  

 ( )exp

 C C K eq



(8)

S P ε 0

where C 0 is the equilibrium hydrogen concentration for the material free of stress and strain. According to equation (7) hydrogen is diffused from the wire surface towards the inner zones of the material with lower hydrogen concentration (negative in-wards gradient of hydrogen concentration), higher hydrostatic stress (positive in-wards gradient of hydrostatic stress) and higher hydrogen solubility (positive in-wards gradient of hydrogen solubility).