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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3. Mechanical modelling: evolution of near-tip stress-strain fields A high-resolution numerical modelling was performed by the finite element method (FEM) to analyze the stress strain state evolution near the crack tip in a rate-independent elastoplastic material with von Mises yield surface and power-law strain hardening, as described elsewhere (Toribio and Kharin, 1998b; 1999; 2000b; 2002; 2004; 2006). A combined isotropic-to-kinematic hardening rule was used. The mechanical characteristics of the material correspond to the steel used in the experimental program (Table 2). The applied loading history consisted of several (up to ten) zero-to-tension cycles in accordance with two of the experimental fatigue programs, namely, K max / K IC = 0.45 and 0.80, followed by rising load corresponding to the SSRT. The nonlinear finite element code MARC was used with updated Lagrangian formulation to account for large geometry changes. Fig. 3 shows the evolution of the hydrostatic stress distribution in the plane of the crack beyond the tip,  =  ( x ), during monotonic loading in the SSRT after fatigue pre-cracking, where x is the distance from the crack tip in the deformed configuration of the solid and thus x =0 represents the crack tip itself, i.e., the surface of the solid which determines the boundary condition for the problem of hydrogen diffusion in the solid. This Fig. 3 provides a first insight — based on mechanical considerations — into the consequences of fatigue pre-stressing on the posterior HAC behaviour of the steel. For the lowest (zero) level of externally applied SIF K = 0 (Fig. 3a; unloading phase; end of fatigue pre-cracking and beginning of the SSRT), the two residual hydrostatic stress laws are negative, i.e., compressive residual stresses are generated in the close vicinity of the crack tip as a consequence of the fatigue pre-cracking procedure, the two distributions of hydrostatic stress  =  (x) being similar for the two pre-cracking levels K max / K IC = 0.45 and 0.80. The stronger compressions are associated with the heaviest fatigue pre-cracking level K max = 0.80 K IC . The hydrostatic stress just at the crack tip (boundary condition for the hydrogen diffusion problem) is negative for the two pre-cracking regimes of K max = 0.45 and 0.80 K IC . For an intermediate level of externally applied loading in the SSRT (applied K = 0.30 K IC ), clear differences may be observed between the two distributions of hydrostatic stress (those associated with fatigue pre-cracking levels of K max = 0.45 and 0.80 K IC ), especially in the close vicinity of the crack tip, which implies a different rate of hydrogen transport to prospective fracture nuclei by stress assisted diffusion according to which hydrogen is driven by the hydrostatic stress gradient d  /d x . For increasing level of externally applied SIF during SSRT (applied K = 0.60 K IC and applied K = 0.80 K IC ) all compressions become tensions. In addition, the hydrostatic stress just at the crack tip (boundary condition for the hydrogen diffusion problem) is now positive for the two pre-cracking regimes of K max = 0.45 and 0.80 K IC . Again the hydrostatic stress profiles after pre-cracking with K max = 0.45 and 0.80 K IC show that hydrogen is ―pumped‖ towards the peak of the distributions, i.e., towards the maximum hydrostatic stress point. In the case of the strongest fatigue program ( K max = 0.80 K IC ) it is seen in Fig. 3b (applied K = 0.30 K IC , initial stages of SSRT) that residual stresses remain compressive in an extended area beyond the crack tip and, even more important, there is a negative gradient of hydrostatic stress d  /d x <0 that delays hydrogen diffusion towards the inner points, prevents hydrogen degradation of the material therein, and increases the fracture load in hydrogen. Hydrogen diffusion assisted by stress fields is governed by two factors: (i) the hydrostatic stress at the crack tip itself (boundary condition for the hydrogen diffusion problem); (ii) the hydrostatic stress gradient as a driving force for hydrogen entry and diffusion into the material. The two factors are conditioned by the maximum SIF during the fatigue pre-cracking that influence the posterior SSRT at different levels of applied K . Another assumption of increasing trapping of hydrogen as a consequence of heavier fatigue pre-cracking is also consistent with the observed beneficial effect of K max on posterior HAC resistance: accumulated mechanical pre damage in the cyclic plastic zone delays the hydrogen delivery due to an increase of the dislocation density and thus of the number of potential traps for hydrogen therein. Thus the experimental fact of better HAC performance for higher K max (Fig. 1) can in part be attributed to this phenomenon of hydrogen trapping. The higher the K max -level, the larger the region of elevated density of traps and the lower the hydrogen permeation rate.