PSI - Issue 80

M. Elkhodbia et al. / Procedia Structural Integrity 80 (2026) 187–194

191

Author name / Structural Integrity Procedia 00 (2023) 000–000

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Fig. 1. Schematic illustration of a (a) standard DCB specimen and (b) the double tapered wedge TM0177 (2016).

Table 1. Geometric dimension specifications for the standard DCB specimen, as per ANSI / NACE TM0177-2016 Method D TM0177 (2016) (dimension values are in mm). L B B n h S E = F J D K N a i [ = J − F ] 101.6 12.7 7.62 12.70 2.39 6.35 38.10 4.85 3.18 6.35 31.75

3.1. Numerical procedure

Finite element analysis (FEA) is employed to simulate the DCB test using the coupled chemo-thermo-mechanical phase-field model assuming elasto-plasticity. A quarter-section model leverages symmetry, as shown with boundary conditions and mesh in Fig. 2. The model uses approximately 190,000 tetrahedral elements for the DCB and 8,000 for the wedge, with mesh refinement near the expected crack path. The simulation involves wedge insertion (modeled with contact and friction, µ = 0 . 3) to achieve a constant arm displacement δ = 0 . 5 mm, representative for P110 steel tests TM0177 (2016). Subsequently, crack growth is simulated over 336 hours under fixed displacement, applying time-dependent hydrogen concentration boundary conditions C inv ( t ) derived from the permeation experiments of Vera et al. Vera and Case (1997) for P110 steel in NACE solution A at di ff erent temperatures (Fig. 3a). As shown in Fig. 3b, The temperature-dependent hydrogen di ff usivity D 0 ( T ) specific to P110 steel are modeled via the Arrhenius relation: D 0 ( T ) = D ref exp − E a RT , (21) and fitted to data from Vera and Case (1997). The simulation captures hydrogen accumulation and phase field ( ϕ ) evolution (Fig. 4a, b show example contours). Finally, the wedge lift-o ff load P is simulated by extracting the wedge, allowing calculation of K ISSC via Eq. (20), replicating the experimental post-processing (Fig. 4c shows a typical simulated lift-o ff curve). The coupled system is implemented in COMSOL Multiphysics via a staggered iterative scheme, solving each sub problem sequentially and ensuring convergence across the coupled fields (more information on the numerical imple mentation is available in Elkhodbia and Barsoum). Simulations were performed for P110 steel using the material parameters detailed in Table 2, including the temperature-dependent di ff usivity parameters ( D ref , E a ) fitted from Vera et al. Vera and Case (1997). Simulations were run at the experimental temperatures (24, 36, 58, 95 C). Fig. 4d compares the predicted K ISSC values from both the original elastic model Elkhodbia and Barsoum and the current elasto-plastic model against the experimental data from Vera et al. Vera and Case (1997). The experimental data exhibit a clear trend of increasing K ISSC with tem perature, signifying reduced SSC susceptibility at higher temperatures. Both simulation models successfully capture this important qualitative behavior. The original elastic model (obtained from Elkhodbia and Barsoum), provides re sults that are already in good agreement with the experimental observations. However, the predictions from the new elasto-plastic model yield K ISSC values that are consistently slightly lower than those from the elastic model across the studied temperature range. As depicted in Fig. 4d, these lower values predicted by the elasto-plastic framework appear to align more closely with the mean experimental data points, suggesting an improvement in accuracy. 3.2. Results and discussion