PSI - Issue 47

Gianmarco Villani et al. / Procedia Structural Integrity 47 (2023) 873–881 G. Villani et al. / Structural Integrity Procedia 00 (2023) 000–000

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6. Conclusions

An energetic approach based on the computation of the elastic strain energy has been developed for the prediction of elliptical crack evolution during crack propagation events. The approach is based on two main hypotheses: the first one regards the geometry assumed by the crack during the propagation (elliptical geometry) and the second one regards the driving force governing the crack propagation. This method allows to compare stationary configurations in order to find the one that implies the minimization of the elastic strain energy. A Matlab ® routine has been carried out to automatically perform the numerical computations, linking a Matlab ® script to manage the elastic strain energy behaviours and the crack shapes, and an ANSYS Mechanical APDL ® script to perform the simulations iteratively. Three di ff erent cases have been analysed: two infinite body with a circular and an elliptical crack subjected to a uniform tension in the bulk and one surface cracked body subjected to bending load. The results in terms of crack evolution have been compared to the literature ones that use a stress intensity factor approach, where the crack propa gation rule is governed by the calculation of the stress intensity factors in correspondence of the two semi-axes. The crack shapes predicted by the energetic approach agree with the literature results in all the three cases. The energetic approach here proposed allows the adoption of rough meshes while the stress intensity factor one requires very refined meshes in correspondence of the crack front. Therefore, not requiring stress intensity factors computation, this method is suitable to study complex geometries and non trivial load combinations. Choi, D., Choi, H., 2005. Fatigue life prediction of out-of-plane gusset welded joints using strain energy density factor approach . Theoretical and Applied Fracture Mechanics 44, 17–27. Fang, X., Hu, C., Du, S., 2006. Strain energy density of a circular cavity buried in semi-infinite functionally graded materials subjected to shear waves. Theoretical and Applied Fracture Mechanics 46, 166–174. Gilchrist, M.D., Smith, R.A., 1991. A Critical Analysis of Crack Propagation Laws. Fatigue Fracture of Engineering Materials Structures 14, 617–626. Hachi, B., Belkacemi, Y., Rechak, S., Haboussi, M., Taghite, M., 2010. Fatigue growth prediction of elliptical cracks in welded joint structure: Hybrid and energy density approach . Theoretical and Applied Fracture Mechanics 54, 11–18. Lin, X., Smith, R., 1997. Shape growth simulation of surface cracks in tension fatigued round bars. International Journal of Fatigue 19, 461–469. Lin, X., Smith, R., 1999a. Finite element modelling of fatigue crack growth of surface cracked plates Part I: The numerical technique. Engineering Fracture Mechanics 63, 503–522. Lin, X., Smith, R., 1999b. Finite element modelling of fatigue crack growth of surface cracked plates Part II: Crack shape change. Engineering Fracture Mechanics 63, 523–540. Liu, Y.P., Chen, C.Y., Li, G.Q.L., Li, J.B., 2010. Fatigue life prediction of semi-elliptical surface crack in 14MnNbq bridge steel. Engineering Failure Analysis 17, 1413–1423. Newman Jr., J., Raju, I.S., 1981. An empirical stress intensity factor equation for the surface crack. Engineering Fracture Mechanics 15, 185–192. Paris, P., Erdogan, F., 1963. A Critical Analysis of Crack Propagation Laws. Journal of Basic Engineering 85, 528–533. Paul, T.K., 1995. Plane stress mixed mode fatigue crack propagation. Engineering Fracture Mechanics 52, 121–137. Sih, G., 1979. An introduction to Fracture Mechanics, Reference Material for the course on Advanced Fracture Mechanics . Lehigh University, Bethlehem, PA . Song, P., Shieh, Y., 2004. Crack growth and closure behaviour of surface cracks . International Journal of Fatigue 26, 429–436. Zhou, X., 2006. Triaxial compressive behavior of rock with mesoscopic heterogenous behavior: strain energy density factor approach . Theoretical and Applied Fracture Mechanics 85, 46–63. References