Issue 35

L. C. H. Ricardo et alii, Frattura ed Integrità Strutturale, 35 (2016) 456-471; DOI: 10.3221/IGF-ESIS.35.52 459 Barsom [19] and the contribution of this term is  p =K/  (  ) for a sharp elliptic or hyperbolic notch with a crack-tip radius,  . The above equations can now be used to obtain the principal stresses after the simplifying assumptions of negligible contributions of T rr and f(  ,r,  ) are assumed. Hence, the principal stresses, as derived from Eq. (5), become:   1 2 3 21 cos 1 sin 2 2 2 1 cos 1 sin 4 2 2 2 0 K r K r                                                          (6) This, in conjunction with the von Mises and Tresca yield criteria, gives the expressions for the plastic zone shape as follows: von Mises:   2 2 2 2 2 2 2 3 sin ( ) (1 2 ) 1 cos( ) 4 2 ( ) 3 1 sin ( ) cos( ) 4 2 ys p ys K r K                                 (7) Tresca: 2 2 2 2 2 2 2 2 2 2 2 cos sin 2 2 2 ( ) cos 1 2 sin 2 2 2 cos 1 sin 2 2 2 ys p ys ys K r K K                                                                              (8)   min max ( ) 1 m c C K da dN K K K K          max ( ) m c C K da dN K K    1 max ( ) ( ) m m da C K K dN    Table 1 : Empirical crack growth equations for constant amplitude loading [14]. Plane Stress Plane Strain Plane Stress Plane Strain Plane Stress Plane Strain