Issue 50

P. Livieri et alii, Frattura ed Integrità Strutturale, 50 (2019) 613-622; DOI: 10.3221/IGF-ESIS.50.52 617 Figure 3 : Mesh for Riemann sums In a previous work [20], we showed that the stress intensity factor can be expressed in the following form: ( ') ( , ') ( ') ( ) I I K Q K Q Q C O        (17) where 3 2 2 2 2 1 3 3 2 C J I                   (18) with 0 sin I d      , 1 0 J th d      and 1 2        is the well-known Riemann function evaluated in 0.5 (C=0.930). If we know the polar equation of the crack border ( ) R  , it is convenient to discretise the angle  instead of the arc length s . Now we consider: 2 2 ( ) ( ) ' ( ) R R       (19) The coefficients (16) assume the form 1 2 2 ( ) jk jk m B Q P m              (20) where P m is the point of the contour corresponding to m   . The coefficient C is then replaced by: 3 2 2 0.889 0.038 ( ) cos ( ) D              (21) where α indicates the position of Q’ for a given origin on the crack border. The condition Q  can be given in terms of a Fourier series as a function of ( ) R R   , so that:   0 ( ) cos sin r r R A r B r        (22)