Issue 41

P. Gallo et alii, Frattura ed Integrità Strutturale, 41 (2017) 456-463; DOI: 10.3221/IGF-ESIS.41.57 461 C ONCLUSIONS he present paper proposed an extension of the method presented by Nuñez and Glinka [13] for blunt U-notches, to a blunt V-notches. The key to getting the extension to blunt V-notches is the substitution of the Creager and Paris [15] equations with the more general Lazzarin and Tovo [16] equations that allow an unified approach to the evaluation of linear elastic stress fields in the neighbourhood of crack and notches. The main advantage of the new formulation is that it permits a fast evaluation of the stresses and strains at notches under creep conditions, without the use of complex and time-consuming FE non-linear analyses. It is presented for blunt V-notches but also valid for U- notches. Moreover, the localized creep formulation can be easily derived neglecting the contribution of the far field. The results have shown a good agreement between numerical and theoretical results. Thanks to the extension to blunt V- notches, all geometries can be easily treated with the aim of the numerical method developed. Although Lazzarin and Tovo equations are valid also in case of sharp V-notches (i.e. for a notch radius that tends to be zero), the values of stress and strain are no longer suitable as characteristic parameters governing failure. As well known, in fact, these local approaches failed when the stress fields tends toward infinity (such as for crack or sharp notches), and the development of alternative solutions becomes crucial. The evaluation of stress and strain at some points ahead of the notch tip may be a possible way to address the problem. Different methods are available in literature dealing with this matter, for example based on energy local approaches such as Strain Energy Density [23-25]. This parameter could be useful also to characterize creeping conditions if combined with the present model, giving the possibility to include in the analysis also cracks and sharp V-notches. However, some points remain open: -order singularity variation with time: when considering creeping conditions, the singularity order does not assume a constant value, but varies with time. -evolution against time from elastic to elastic-plastic or fully plastic state of the system, especially when dealing with high temperature. Because of the promising results showed in the preliminary analyses, the authors still devoting effort to overcome the problems cited previously and to combine successfully the proposed model for the prediction of stresses and strain with the SED averaged over a control volume, in order to give a useful and more general tool when dealing with notches subjected to creep, regardless of the specimen geometries. R EFERENCES [1] Cui, L., Wang, P., Crack initiation behavior of notched specimens on heat resistant steel under service type loading at high temperature, Frattura ed Integrita Strutturale, 10(38) (2016) 26-35. [2] Gallo, P., Berto, F., High temperature fatigue tests and crack growth in 40CrMoV13.9 notched components, Frattura ed Integrita Strutturale, 9(34) (2015) 180-189. [3] Kotousov, A., Berto, F., Lazzarin, P., Pegorin, F., Three dimensional finite element mixed fracture mode under anti- plane loading of a crack, Theor. Appl. Fract. Mech., 62(1) (2012) 26-33. [4] Radaj, D., Berto, F., Lazzarin, P., Local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches, Eng. Fract. Mech., 76(8) (2009) 1109-1130. [5] Berto, F., Campagnolo, A., Gallo, P., Brittle Failure of Graphite Weakened by V-Notches: A Review of Some Recent Results Under Different Loading Modes, Strength Mater., 47 (2015) 488–506. [6] He, Z., Kotousov, A., Berto, F., Effect of vertex singularities on stress intensities near plate free surfaces, Fatigue Fract. Eng. Mater. Struct., 38 (2015) 860–869. [7] Sih, G.C., Redemption of the formalism of segmented linearity: multiscaling of non-equilibrium and non- homogeneity applied to fatigue crack growth, Fatigue Fract. Eng. Mater. Struct. 38 (2015) 621–628. [8] Ayatollahi, M.R., Razavi, S.M.J., Rashidi Moghadam, M., Berto, F., Mode I fracture analysis of Polymethylmetacrylate using modified energy—based models, Phys. Mesomech. 18(5) (2015) 53-62. [9] Ayatollahi, M.R., Rashidi Moghaddam, M., Razavi, S.M.J., Berto, F., Geometry effects on fracture trajectory of PMMA samples under pure mode-I loading, Eng. Fract. Mech., 163 (2016) 449–461. [10] Ayatollahi, M.R., Razavi, S.M.J., Sommitsch, C., Moser, C., Fatigue life extension by crack repair using double stop- hole technique, Mater. Sci. Forum, 879 (2017) 3-8. [11] Razavi, S.M.J., Ayatollahi, M.R., Sommitsch, C., Moser, C., Retardation of fatigue crack growth in high strength steel S690 using a modified stop-hole technique, Eng. Fract. Mech., 169 (2017) 226–237. T