Issue 32

N. Bisht et alii, Frattura ed Integrità Strutturale, 32 (2015) 1-12; DOI: 10.3221/IGF-ESIS.32.01 5 Figure 6 : Representation of crack with coordinate system. Evaluating Eq. (1-3) at 0 180    and dropping the higher order terms Eq. (1-3) yields:   II K r u 1 k 2G 2π   (4)   2 2 I K r v k G   (5) 2  2 III K r w G   (6) For full crack models Eq. (4-6) can be reorganized to | | 2 I v G K k r    (7) | | 2 1 II u G K k r     (8) | | 2 III w K G r    (9) where Δv, Δu and Δw are the motions of one crack face with respect to the other. k= 3−4ν, for plane strain or axisymmetric; (3−ν)/ (1+ ν) for plane stress; where ν is Poisson's ratio. The final factor v r  is evaluated based on the nodal displacements and locations. For practical purposes the value of v r  is approximated by limiting the value of v r  by simply evaluating the following expression for a small fixed value of r (small in relation to the size of the crack) as: | |  v A Br r   (10) At point I shown in Fig.7, v=0 Hence, in the limiting condition