PSI - Issue 25

Marco Maurizi et al. / Procedia Structural Integrity 25 (2020) 268–281 M. Maurizi nd F. Be to / S ructural Integrity Procedia 00 (2019) 00 – 00

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9

(a)

(b)

Fig. 4: Coupled Mode 0 induced by in-plane shear loading. (a) FE example of local out-of-plane mode (Mode 0) generated by Mode II loading. (b) Induced singular Mode 0 (denoted as K C III ( z )) and primary Mode II stress intensity factor (normalized) variation along the thickness and influence of Poisson’s ratio. The weak e ff ect of Poisson’s ratio on the primary Mode II is not shown.

(2011a) for cracked plates.

4.1.1. Scale e ff ect The 3D stress e ff ect zone is located near the crack / notch tip within a radial distance from it equal about to half of the plate thickness, as previously mentioned. After that, the singular stress field can be described by the 2D William’s solution in plane stress conditions; therefore, a K-dominant zone incorporates the 3D a ff ected area. Based on this consideration and extending the definition of NSIF of Mode III of Eq. (13) to Mode 0, the coupled out-of-plane mode (notch) stress intensity factor K N 0 ( z ) must be necessarily related to that remotely applied K ∞ II such that (He et al. (2016)):

0

, ν ,

z h

K N

( λ 2 − λ 0 ) F

0 ( z ) = K ∞ II h

(19)

where h is the plate thickness and F 0 ( z / h , ν ) is a dimensionless function dependent on z and Poisson’s ratio. For the crack case, λ II = λ 0 , the Mode 0 NSIF coincides with the stress intensity factor and it does not depend on the thickness. The strength of the dependence from the plate thickness reaches maximum for 2 α = 104 ◦ (see Fig. 3), where K N 0 ∝ K ∞ II h 0 . 3 . Moreover, taking into account the asymptotic near crack-tip William’s expansion for the stress field applied remotely as boundary condition, the following expression can be obtained:

f 0 n

, ν b n h

∞ n = 0

z h

K N

n ,

0 ( z ) =

(20)