Issue 49

G. Meneghetti et alii, Frattura ed Integrità Strutturale, 49 (2019) 53-64; DOI: 10.3221/IGF-ESIS.49.06 54 I NTRODUCTION ealing with cracks under in-plane mixed mode I+II loading conditions, according to Williams [1], the local stress fields expressed in terms of Cartesian stress components as functions of the polar coordinates ( r , θ ), with origin at the crack tip (Fig. 1a), can be written in the following form:             xx I II yy xy θ 1 3 θ 1 3 cos - sin θ sin θ -2sin - sin θ cos θ 2 2 2 2 2 2 σ K K θ 1 3 1 3 σ = cos + sin θ sin θ + sin θ cos θ 2 2 2 2 2 2πr 2πr τ 1 3 θ 1 3 sin θ cos θ cos sin θ sin 2 2 2 2                                                                                    1/2 1 +T 0 +O(r ) 0 θ 2                                   (1) With reference to cracks under mode III loading conditions, the asymptotic, singular stress distributions have been determined by Qian and Hasebe [2], following Williams’ procedure [1]. The local stress field in terms of Cartesian stress components as functions of the polar coordinates ( r , θ ), with origin at the crack tip (Fig. 1b), is the following: xz 1/2 III yz θ -sin τ 2 K= +O(r ) τ θ 2πr cos 2                                (2)   Figure 1 : Cartesian stress components and polar coordinates with origin at the crack tip for (a) in-plane mixed mode I+II crack problem and (b) out-of-plane mixed mode I+III crack problem. The mode I and mode II Stress Intensity Factors (SIFs) can be defined according to Gross and Mendelson [3] by means of Eqns. (3) and (4), respectively.   0.5 0 0 2 lim I yy r K r             (3)   0.5 0 0 2 lim II xy r K r             (4) D σ nom τ nom 2a W = 10 ·2a L = W (a) r crack bisector σ xx σ yy τ xy θ τ nom y x a D = 10 ·a L = D crack bisector M t a 2α=0° M t F F r θ τ yz σ yy σ xx τ xy τ xz σ zz y x z (b)