Issue34

G Meneghetti et alii, Frattura ed Integrità Strutturale, 34 (2015) 109-115; DOI: 10.3221/IGF-ESIS.34.11 114 MM = 0.37 ( ϕ = 30°), 11 for MM = 0.50 ( ϕ = 45°) and 16 for MM = 0.63 ( ϕ = 60°). In particular the minimum a/d ratio to assure the validity of the proposed method increases as the mode II loading becomes dominant, that is as the mode mixity ratio (MM) defined by Eq. (7) increases. A similar behavior has been observed in the previous paragraph and in [10], with reference to K * FE and K ** FE . 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 1 10 100 1000 a/d W PSM /W FEM   R   mm     a  0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 1 10 100 1000 a/d W PSM /W FEM   R   mm     b  0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 1 10 100 1000 a/d W PSM /W FEM 2  = 0°  = 45° R 0 = 0.1 mm    c   0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 1 10 100 1000 a/d W PSM /W FEM   R   mm     d  Figure 4 : Ratio between the SED based on the elastic peak stresses ( PSM W ) and the SED derived from the FE analyses ( FEM W ) for a crack (2α = 0°) under mixed mode (I+II) loading: (a) ϕ = 0° (MM = 0), (b) ϕ = 30° (MM = 0.37), (c) ϕ = 45° (MM = 0.50) and (d) ϕ = 60° (MM = 0.63). C ONCLUSIONS n the present contribution (*), a link between the averaged SED approach and the peak stress method in the case of cracks subjected to mixed mode (I+II) loading has been investigated:  On the basis of the peak stress method, some expressions useful to estimate the mode I and mode II SIFs, recently derived for pure modes of loading, have been verified also in the case of mixed mode (I+II) crack problems.  Since the normal and tangential peak stresses are proportional to the mode I and mode II SIFs, a link can immediately be established with the SED parameter by means of Eqs. (3), (4) and (5). By substituting the PSM-based relationships in the closed-form expressions of the averaged SED it appears that the latter can be directly estimated by means of the elastic peak stresses evaluated at the crack tip.  The ratio between the SED based on the elastic peak stresses and the SED derived from the FE analyses converge to a unit value for a ratio a/d greater than a value between 3 (MM = 0) and 16 (MM = 0.63). The minimum a/d ratio to assure the validity of the proposed method increases with increasing the mode mixity ratio (MM).  The usefulness of the SED expression based on the elastic peak stresses is that (i) only the elastic peak stresses numerically evaluated at the crack tip are needed and the definition of a control volume is no longer required; I