PSI - Issue 13

Temma Sano et al. / Procedia Structural Integrity 13 (2018) 1154–1158 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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Fig. 1 Boundary and initial conditions for the present finite element analysis. Table 1 Material constants used in the present analysis. Young's modulus ： E [Pa] 207×10 9 Poisson's ratio : ν 0.3 Initial yield strength ： σ 0 [Pa] 250×10 6 Work-hardening exponent ： n 0.2 Thickness ： h [m] 8.25×10 -4 Crack tip radius : b 0 [m] 5.00 × 10 -6

Subsequently, we performed elastoplastic analysis using the same model and loading condition under the influence of hydrogen, based of Kanayama 2008 and Sasaki 2015. In this analysis, hydrogen is introduced from outside the material, and diffuses to the crack tip during mechanical loading. In order to analyze the plastic zone evolution with the effect of hydrogen, both elastoplastic and hydrogen diffusion analyses were alternatively carried out. A step of coupled analysis consists of increasing the remote stress by 2 MPa and subsequent holding for 0.5 s for hydrogen diffusion. The coupled analysis was performed for 20 steps, corresponding to a final stress of 40 MPa and the total holding time of 10 s. Moreover, we proposed a method for fatigue crack propagation in the finite element analysis. In general, fatigue crack propagation is simulated by node release (Moes 2002). However, the hydrogen diffusion analysis mentioned above requires significant area even at the crack tip, and therefore, a finite curvature of the crack tip is required for simulating fatigue crack propagation under the influence of hydrogen. Since the node release produces a crack tip with infinite curvature, it is not available for the coupled analysis of finite element method and hydrogen diffusion. In this context, we must develop a new way to analyze hydrogen-affected fatigue crack propagation. Figure 2 shows the schematics of our proposed method, namely, the stress field formed in the previous loading cycle was shifted to the crack wake, instead of propagating the crack. The shift in the stress field to the crack wake is regarded as crack propagation in terms of their relative positions. To enable the stress field to shift, we noted the displacement information.

Fig. 2 Proposed method to simulate fatigue crack propagation. More specifically, we attempted to reconstruct the stress field using the displacement data, as schematically shown in Fig. 3. First, the material was loaded in the same manner as Fig. 1 (Fig. 3(a)). Then, for a target node, we found a point that proceeded by Δ a in the direction of crack propagation (Fig. 3(b)). Subsequently, from the nearest three points surrounding the point that proceeded, we interpolated the displacement at the point (Fig. 3(c)). The obtained displacement data were provided to the target node (Fig. 3(d, e)). The same procedures (b) to (e) were performed for all the nodes.