PSI - Issue 46

Jakub Šedek et al. / Procedia Structural Integrity 46 (2023) 69–74 Jakub Šedek / Structural Integrity Procedia 00 (2021) 000–000

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The crack opening displacement (COD) during monotonic loading for load ratio σ y / σ flow from 0.1 to 0.45 is shown in Fig. 3 a) for plane strain and in Fig. 3 b) for specimen thickness B = 1.25 mm, that represent solution close to plane stress under higher loads ( α gS = 1.2). The SYM solution of COD uses the constraint factor α gS determined from FE model at corresponding load levels. The plain strain plot also contains the FE results of Dugdale approach for the crack. This analysis is fully elastic with the constant traction on crack lips with the magnitude of ασ yield , where α gS is used for α . The traction is applied only in the plastic region of the plastic zone. 4. Discussion The FE analysis of M(T) specimen was carried out to determine the plastic constraint factor and to utilize the factor for appreciating the stress state at the crack tip. The elements in the crack plane ahead of the crack tip were used to determine the constraints by taking into account elements inside or also under the plastic zone. The value of global constraint factor α gS differs especially under plain strain being lower compared with α g referred in Newman (1993). The plot of α gS versus the ratio B/r p 2 is presented to show the tendency to form uniform dependency. The boundary problems show the value of α gS being 1.15 for plane stress and around 2 for plain strain conditions. The COD is used to compare FEM and SYM solutions with α gS applied as constraint factor. For plain strain, the elastic-plastic FEM, elastic FEM-Dugdale and SYM results are presented. The solution close to plane stress conditions is represented by thin specimen with the elastic-plastic FEM and SYM. Under plane strain, the match of CODs is slightly better for both FEM variants than for SYM. Around the crack tip, the FEM and SYM results are generally very close. Nevertheless, the grater the load, the grater the deviation can be seen from the figures of COD. Behind the crack tip, the COD tends to be higher, contrary to the front, where COD is slightly lower in comparison to FEM Dugdale. The trend of concave shape of crack lips is preserved as well as the convex shape for the SYM and Dugdale’s approach in front of the crack tip. 5. Conclusions The analysis of the crack tip plasticity was carried out from the point of view of constraint factor α . The FE model of M(T) specimen using three crack length configurations and several load levels was utilized. Modified process for global constraint factor determination was proposed and it was shown, that using constraint factor α gS in the SYM yields good match of COD results for both, plane strain and plane stress conditions. The value of α gS at plane stress was 1.15 and around 2 for plain strain conditions. Although the constraint factor α gS represents average over the plastic zone, the constant value is widely used in crack growth prediction models, despite that using other more sophisticated plastic constraint development over plastic zone was introduced in SYM. Still, nowadays in engineering practice, the constant constraint factor is being chosen based on trial-and-error process of correlation experimentally data of crack growth and prediction model. Generally, the process of constraint factor determination, e.g., based on FEM with at least idealized condition, should be available. Acknowledgements This research work was carried out with the institutional support from the Ministry of Industry and Trade of the Czech Republic (Order account no.: IFRAM5, DČZ: DKRV01). References Branco R., Antunes F.V., Costa J.D., 2015. A review on 3D-FE adaptive remeshing techniques for crack growth modelling, Engineering Fracture Mechanics, Vol. 141, pp. 170-195, ISSN 0013-7944, https://doi.org/10.1016/j.engfracmech.2015.05.023. Braut S., Sikanen E., Nerg J., Sopanen J., Bozic Z., 2021. Fatigue life prediction of Electric RaceAbout (ERA) traction motor rotor, Procedia Structural Integrity Vol. 31 pp. 45–50, doi.org/10.1016/j.prostr.2021.03.024. Dirika H., Yalçinkaya T., 2018, Crack path and life prediction under mixed mode cyclic variable amplitude loading through XFEM, International Journal of Fatigue Vol. 114, pp. 34-50, doi.org/10.1016/j.ijfatigue.2018.04.026 Dugdale D.S., 1960. Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, pp. 100–104. Fatigue & Fracture Associates, 2013. FASTRAN, A Fatigue Crack Growth Life-Prediction Code Based on the Crack-Closure Concept, Version 5.4.