Issue 20

R. Brighenti et alii, Frattura ed Integrità Strutturale, 20 (2012) 6-16; DOI: 10.3221/IGF-ESIS.20.01 10 A PPROXIMATE SIF S FOR A NOMINALLY - MODE I KINKED CRACK n the case of an infinite cracked plane under a uniform remote stress 0 y  , the SIF of a straight crack of semi-length l aligned with the X-axis is ( ) 0 I y K l     . Assume that such a straight crack is embedded in the stress field (given by Eqs 2-4) within the base material. Such a stress field can be decomposed in the remote uniform uniaxial tensile stress 0 y  and a fluctuating multiaxial stress field ( ) x T  here assumed to be a one-dimensional function of the x coordinate. Furthermore, by observing the courses (reported in Fig. 4) of the stress components due to the presence of inclusions, we can suppose that ( ) x T  is a self- balanced microstress field characterized by a material length d (related to the inclusion spacing), with two non-zero stress components ( / ) y a f x d         and ( / ) xy a f x d         . For the sake of simplicity, we assume     / cos 2 f x d x d   (this could be regarded as a first order approximation through Fourier series of a general periodic function), Fig. 5a. Under the self-balanced microstresses   and   , the SIFs (of the projected crack) are obtained using Buckner’s superposition principle:         0 2 2 2 2 2 2 0 0 0 0 2 2 2 2 2 2 0 0 0 cos 2 2 2 2 2 cos 2 2 2 2 2 l l l I a a a l l l II a a a f x d x d l l l l K dx dx dx l J d l x l x l x f x d x d l l l l K dx dx dx l J d l x l x l x                                                               (5) where J 0 is the zero-order Bessel function [7]. (a) (b) Figure 5 : (a) Self-balanced microstress field and periodically kinked crack. (b) Kinked crack in an infinite plane. I