Issue 41

V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 41 (2017) 31-39; DOI: 10.3221/IGF-ESIS.41.05 35 and to determine the accuracy of this type of calculation, which will be used later for the general 3D problem to provide for the plastic SIF. Figure 6 : Typical FEM-mesh for cylindrical hollow specimens with semi-elliptical surface crack. Figure 7 : FEM crack front geometry: initial (a) , intermediate (b, c) , final (d) . The distributions of I n -integral along the crack front were used to determine the plastic SIF Kp . For cylindrical hollow specimens the plastic SIF Kp in pure Mode I can be expressed directly in terms of the corresponding elastic SIF K 1 using Rice’s J-integral as follows:       2 2 1 1 0 ' ' n n P K J I K E E      (1)         1/ 1 1/ 1 2 2 2 1 1 1 1 0 0 ( / ) ( / ) ; ( / ) , ,( / ) , ,( / ) n n p FEM FEM n n K a w Y a w K K Y a w I n a w I n a w                                      (2) where 1 1 / K K w  is normalized by a characteristic size of cracked body elastic stress intensity factor and E 'E  for plane stress and   2 ' 1 E E    for plane strain. In the above equations,  and n are the hardening parameters, a w   is the dimensionless crack length, w is characteristic size of specimen (for our case that is specimen diameter),  is the nominal stress, and  0 is the yield stress. The procedure for calculating of the governing parameter of the elastic–plastic stress–strain fields in the form of I n -integral for the different specimen geometries by means of the elastic–plastic FE- analysis of the near crack-tip stress-strain fields suggested by [1-3]. In this case, the numerical integral of the crack tip field I n changes not only with the strain hardening exponent n but also with the relative crack length b/D and the relative crack depth a/D :