PSI - Issue 80

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

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

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Fig. 4. Simulation results for P110 DCB test validation against Vera et al. Vera and Case (1997): Representative (a) hydrogen concentration and (b) phase-field ( ϕ ) contours after 336h exposure (T = 25 °C example); (c) Simulated lift-o ff curve for determining K ISSC ; (d) Final validation comparing predicted K ISSC (elastic Elkhodbia and Barsoum vs. elasto-plastic) with experimental data across temperatures.

more complete representation of the energy balance during fracture and provides a slightly more conservative (lower K ISSC ) estimate, while o ff ering the capability to analyze scenarios where plasticity e ff ects are expected to be more pro nounced. Overall, the validation confirms the capability of both model formulations to capture the essential physics governing temperature-dependent SSC, with the elasto-plastic extension o ff ering a refinement in accuracy by account ing for plastic energy contributions.

4. Conclusion

This paper extended a chemo-thermo-mechanical phase-field framework for SSC to incorporate elasto-plastic defor mation for the purpose of DCB test modeling. Building upon a prior thermo-elastic model Elkhodbia and Barsoum, the primary enhancement involved modifying the fracture driving force to include contributions from stored plastic energy alongside elastic energy. Validation simulations of DCB tests for P110 steel in sour service were compared against experimental data Vera and Case (1997). Both the original elastic and the extended elasto-plastic models accurately captured the experimentally observed reduction in SSC susceptibility (increasing K ISSC ) with increasing temperature. The elasto-plastic formulation yielded slightly lower, more conservative K ISSC predictions that aligned closely with experimental means, demonstrating improved accuracy by accounting for plastic energy contribution dur ing fracture. However, the relatively small di ff erence between the models for this specific SSC scenario suggests that temperature-dependent hydrogen transport and fracture toughness degradation are the dominant factors controlling the macroscopic fracture threshold. The distinctions between predictions from the elasto-plastic model and a purely elastic counterpart would become more pronounced in scenarios characterized by lower hydrogen concentrations (and consequently, reduced H 2 S severity). Under such conditions, the material retains a greater degree of its inherent duc tility and fracture toughness, allowing plasticity to have a more substantial role in the fracture process. Experimental studies on high-strength steels, such as C110 and similar grades, under varying H 2 S conditions have indeed indicated that the material’s capacity for plastic deformation is less compromised at lower H 2 S levels compared to high H 2 S environments Liu and Case (2022); Cancio et al. (2010). Nonetheless, the successful integration of plasticity pro-