PSI - Issue 68

D. Linn et al. / Procedia Structural Integrity 68 (2025) 1259–1265

1265

D. Linn, W. Becker / Structural Integrity Procedia 00 (2024) 000–000

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resp. Fig. 7. Coupled stress and energy criterion, plotted for a temperature load of ∆ T = − 189K.

For the example of a patch on a substrate under a temperature change of − 100 K, the incremental energy release rate can now be calculated for any crack length ∆ a and is shown in Figure 6 (right), again in comparison with results of the FEM. The comparison shows that there are good agreements between the results of the analytical model and the FEM. In the next step the coupled stress and energy criterion ((17) and (18)) can be evaluated. For the tensile and shear strength as well as for the fracture toughness, the values for an adhesive Loctite Multibond 330 ( σ c = 35 MPa, τ c = 20 . 2MPa, G IIc = 2 G Ic = 0 . 24Nmm − 1 ) are taken as they were also used in the work by Goglio et al. (Goglio et al. (2008)) and by Stein (Stein (2018)). The plot in Figure 7 shows both criteria for a temperature load of − 189K, which is the smallest load for which both criteria are fulfilled. For a length of x = ∆ a = 2 mm, the stress criterion is greater than one, while the energy criterion just becomes one. This means that a debonding crack of this length forms instantaneously when the configuration is cooled by 189 K. A simplified model of a two-layer system is considered that can be used for di ff erent load cases. For example, a patch on a substrate under thermal load or typical adhesive joints such as a Double Cantilever Beam or a Single Lap Joint. A closed-form analytical approach was used to approximate the displacements and the strain and stress field within the two layers. Here the interlaminar stresses along the interface between both layers are discussed in more detail and show a very good agreement to the FEM. Finally, the initiation of debonding cracks is analyzed within the framework of Finite Fracture Mechanics for the configuration of a patch on a substrate under thermal loading. It is shown that the results with the new approach are in good agreement with the FEM, but provide more understanding of the physical behavior and allow easy parameter studies. The calculations with the analytical model are very e ffi cient, which is reflected in a shorter calculation time (FEM: 70s – Analytical model: 4s). 7. Conclusion Frhaan, W., Bakar, B., Hilal, N., Al-Hadithi, A., 2021. CFRP for strengthening and repairing reinforced concrete: a review. Innovative Infrastructure Solutions 6, 1–13. doi: https://doi.org/10.1007/s41062-020-00417-5 . Goglio, L., Rossetto, M., Dragoni, E., 2008. Design of adhesive joints based on peak elastic stresses. International Journal of Adhesion and Adhesives 28, 427–435. doi: https://doi.org/10.1016/j.ijadhadh.2008.04.001 . special Topic Issue on Structural Adhesive Joints. Hell, S., Weißgraeber, P., Felger, J., Becker, W., 2014. A coupled stress and energy criterion for the assessment of crack initiation in single lap joints: A numerical approach. Engineering Fracture Mechanics 117, 112–126. doi: https://doi.org/10.1016/j.engfracmech.2014.01.012 . Leguillon, D., 2002. Strength or toughness? A criterion for crack onset at a notch. European Journal of Mechanics - A / Solids 21, 61–72. doi: https://doi.org/10.1016/S0997-7538(01)01184-6 . Mendoza-Navarro, L.E., Diaz-Diaz, A., Castan˜eda-Balderas, R., Hunkeler, S., Noret, R., 2013. Interfacial failure in adhesive joints: Experiments and predictions. International Journal of Adhesion and Adhesives 44, 36–47. doi: https://doi.org/10.1016/j.ijadhadh.2013.02.004 . Stein, N., 2018. Analytische und semi-analytische Berechnungsmodelle zur Auslegung von Strukturklebverbindungen. Ph.D. thesis. Technische Universita¨t Darmstadt. Darmstadt. URL: http://tuprints.ulb.tu-darmstadt.de/7649/ . Stein, N., Weißgraeber, P., Becker, W., 2015. A model for brittle failure in adhesive lap joints of arbitrary joint configuration. Composite Structures 133, 707–718. doi: https://doi.org/10.1016/j.compstruct.2015.07.100 . References