Issue 41

F. Berto, Frattura ed Integrità Strutturale, 41 (2017) 475-483; DOI: 10.3221/IGF-ESIS.41.59 482 Figure 8 : Through the thickness SED distribution for t/a = 0.50, 1, 2, 3. Control radius R 0 = 1.00 mm. C ONCLUSIONS (1) The results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked plates under anti-plane loading. In particular, it is confirmed that mode III does induce coupled mode II c . (2) The influence of plate bending is increasingly important as plate thickness decreases. The anti-plane loading used is a nominal mode III loading. For thin plate it is a mixed modes III and II loading, in which mode III induces mode II c and vice versa. At the present state of the art it is not possible to separate the coupled modes from the applied modes. (3) Bažant and Estenssoro’s analysis works well for the symmetric mode (mode I), but it is incomplete for the asymmetric mode (a combination of modes II and III). (4) Discussion on whether K III tends to zero or infinity as a corner point is approached is futile because, as pointed out by Benthem, K III is meaningless at a corner point. (5) The present results do not confirm the existence of a corner point singularity dominated region within a K -dominated region. It appears that a new field parameter, probably a singularity, is needed to describe the stresses at the plate surfaces. (6) Calculation of the strain energy density (SED) in a control volume at the crack tip shows that the position of the maximum SED is independent of plate thickness. Both for thin plates and for thick ones the maximum SED is close to the lateral surface, where the maximum intensity of the coupled mode II takes place. (7) Under the anti-plane loading used theoretical understanding of the stress field in the vicinity of a corner point is still incomplete. R EFERENCES [1] Kotousov, A., Lazzarin, P., Berto, F., Harding, S., Effect of the thickness on elastic deformation and quasi-brittle fracture of plate components, Eng. Fract. Mech., 77 (2010) 1665-1681. [2] Kotousov, A., Lazzarin, P., Berto, F., Pook, L. P., Three-dimensional stress states at crack tip induced by shear and anti-plane loading, Eng. Fract. Mech., 108 (2013) 65-74. [3] Pook, L. P., Campagnolo, A., Berto, F., Lazzarin, P., Coupled fracture mode of a cracked plate under anti-plane loading, Eng. Fract. Mech., (2015) doi:10.1016/j.engfracmech.2014.12.021. [4] Pook, L. P., A 50-year retrospective review of three-dimensional effects at cracks and sharp notches, Fatigue Fract. Engng. Mater. Struct., 36 (2013) 699-723. [5] Bažant, Z. P., Estenssoro, L. F., Surface singularity and crack propagation, Int. J. Solids Struct., 15 (1979) 405-426. [6] Pook, L. P., Some implications of corner point singularities, Eng. Fract. Mech., 48 (1994) 367-378. [7] Pook, L. P., Linear elastic fracture mechanics for engineers. Theory and applications, WIT Press, Southampton (UK), (2000).