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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where C 0 is the equilibrium hydrogen concentration for the material free of stress and strain. 4.2. Crack-tip hydrogen diffusion assisted by stress and strain fields

The results of the large-deformation elastoplastic stress-strain field simulations considered in the previous paragraphs (cf. Fig. 3) were taken as the input data. Diffusion modelling was performed in one-dimensional (1D) approximation along the x -axis or crack line. The following data were considered in the computations: ambient temperature T = 293 K , V H = 2.10 – 6 m 3 /mol and D = 10 – 12 m 2 /s. The applied loading rate in modelling the rising load SSRT was taken to be dK/dt = 0.25 MPa . m 1/2 /s. The results of the diffusion calculations, shown in Fig. 4, are valid for whichever particular value of D provided the loading rate is adjusted to maintain the constant ratio D/ ( dK/dt ), as it follows from the similitude criteria for the transport, so that availability of the exact value of D for the steel under consideration is not a crucial matter Analysis of the diffusion was performed during the rising load phase from K = 0 after pre-cracking to K = K IC , i.e., during the diffusion time t R = K IC / ( dK/dt ).

Fig. 4. Hydrogen concentration distributions ahead of the crack tip during constant-rate 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. 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 . The generated numerical results about crack tip hydrogen diffusion presented in Fig. 4 and complementary stress evolution data in Fig. 3 show that in the very close vicinity of the entry surfaces x < ~ 2…4  m the concentration patterns C ( x , t ) for fixed diffusion times t (or applied load levels K = dK/dt . t ) are quite similar to the respective stress profiles  ( x ), so that the steady-state equilibrium concentration is approximately achieved at this depths under the tried loading rate. In deeper material points, a more or less significant delay of hydrogenation due to heavier fatigue pre-cracking is observed.