Issue 48

F. V. Antunes et alii, Frattura ed Integrità Strutturale, 48 (2019) 666-675; DOI: 10.3221/IGF-ESIS.48.63 674 gratefully acknowledged. The authors would also like to thank the DD3IMP in-house code developer team for providing the code and all the support services. R EFERENCES [1] Paris, P.C. and Erdogan, J. (1963). Critical analysis of crack growth propagation laws, J. Basic Eng. 85D, pp. 528–534. [2] Rice, J.R. 1967). Mechanics of crack tip deformation and extension by fatigue, In: Fatigue crack propagation. Philadelphia: ASTM STP 415, pp. 256–271. [3] Elber, W. (1970). Fatigue crack closure under cyclic tension, Eng. Fract. Mech. 2, pp. 37-45. [4] Lugo, M. and Daniewicz, S.R. (2011). The influence of T-stress on plasticity induced crack closure under plane strain conditions, Int. J. Fatigue 33, pp.176–185. [5] Donald, K. and Paris, P.C. (1999). An evaluation of  K eff estimation procedure on 6061-T6 and 2024-T3 aluminum alloys, Int J Fatigue 21, pp. S47–57. [6] Kujawski, D. (2001) Enhanced model of partial crack closure for correlation of R-ratio effects in aluminum alloys, Int J Fatigue 23, pp. 95–102. [7] Christopher, C.J., James, M.N., Patterson, E.A. and Tee, K.F. (2007). Towards a new model of crack tip stress fields, Int J Fract 148, pp. 361–371. [8] Antunes, F.V., Sousa, T., Branco, R. and Correia, L. (2015). Effect of crack closure on non-linear crack tip parameters, Int. Journal of Fatigue 71, pp. 53–63. [9] Kawabata, T., Tagawa, T., Sakimoto, T., Kayamori, Y., Ohata, M., Yamashita, Y., Tamura, E., Yoshinari, H., Aihara, S., Minami, F., Mimura, H. and Hagihara, Y. (2016). Proposal for a new CTOD calculation formula, Eng. Fract. Mech. 159, pp. 16–34. [10] Laird, C. and Smith, G.C. 1962). Crack propagation in high stress fatigue, Philos. Mag. 8, pp. 847–857. [11] Toribio, J. and Kharin, V. (2013). Simulations of fatigue crack growth by blunting–re-sharpening: Plasticity induced crack closure vs. alternative controlling variables, Int. J. Fatigue 50, pp. 72–82. [12] Pelloux, R.M. (1970). Crack Extension by alternating shear, Eng Fract. Mech. 1, pp. 170-174. [13] Neuber, H. (1961). Theory of stress concentration for shear strained prismatical bodies with arbitrary non-linear stress-strain law. J Appl Mech 28, pp. 544–50. [14] Molski, K. and Glinka, G. (1981). A method of elastic–plastic stress and strain calculation at a notch root. Mater Sci Eng 50, pp. 93–100. [15] Lazzarin, P., Berto, F., Gomez, F.J. and Zappalorto, M. (2008). Some advantages derived from the use of the strain energy density over a control volume in fatigue strength assessments of welded joints, Int. J. Fatigue 30, pp. 1345– 1357. [16] Ellyin, F. (1997) Fatigue Damage, Crack Growth and Life Prediction, Chapman & Hall, London. [17] Neuber, H. (1958) Theory of Notch Stresses: Principles for Exact Calculation of Strength with Reference to Structural Form and Material, Springer, Berlin, Germany. [18] Peterson, R.E. (1958) Notch sensitivity, in: G. Sines, J.L. Waisman (Eds.), Metal Fatigue, McGraw Hill, New York, pp. 293–306. [19] Susmel, L. and Taylor, D. (2011). The theory of critical distances to estimate lifetime of notched components subjected to variable amplitude uniaxial fatigue loading, Int. J. Fatigue 33, pp. 900–911. [20] Antunes, F.V., Rodrigues, S.M., Branco, R. and Camas, D. (2016). A numerical analysis of CTOD in constant amplitude fatigue crack growth, Theoretical and Applied Fracture Mechanics 85, pp. 45–55. [21] Williams, J.C. and Starke, Jr. E.A (2003). Progress in structural materials for aerospace systems, Acta Mater. 51, pp. 5775–5799. [22] Wei, L., Pan, Q., Huang, H., Feng, L. and Wang, Y. (2014) Influence of grain structure and crystallographic orientation on fatigue crack propagation behavior of 7050 alloy thick plate, Int Journal of Fatigue 66, pp. 55–64. [23] Voce, E. (1948). The relationship between stress and strain for homogeneous deformation, J. Inst. Metals 74, pp. 537–562. [24] Chaboche, J.L. (2008). A review of some plasticity and viscoplasticity constitutive theories, International Journal of Plasticity 24, pp. 1642–1693. [25] Miller, K.J. (1982). The short crack problem, Fatigue Engng. Mater. Struct. 5, pp. 223–232. [26] Tanaka, K., Nakai, Y. (1983). Propagation and non-propagation of short fatigue cracks at a sharp notch, Fatigue Engng. Mater. Struct. 6, pp. 315–327.