Issue 48

V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 48 (2019) 77-86; DOI: 10.3221/IGF-ESIS.48.10 83 1 * 1 0 1 cr n cr cr n C K BI L          (13)     1 0 cr n cr cr n C K BI L     (14) where C* is the C -integral. The value of this line integral corresponding secondary creep deformation used in [10] as the relevant loading parameter to characterize the local stress-strain rate fields at any instant around the crack front in a cracked body subjected to extensive creep conditions             ds x u n dxW C i j ij 1 2 *    (15) where the first term in Eq.(15) is the strain energy rate density (SERD) for power-law hardening creep [11,12] 0 1 kl cr cr cr cr cr cr ij ij e e cr n W d n              (16) and  is an arbitrary counterclockwise path around the crack tip and the Cartesian coordinate system x i is centered at the crack tip. Substitution of Eq. (16) into Eq. (15) leads to the expression for C* -integral   1 * cos sin cos 1 cr cr cr cr cr n cr cr cr cr cr cr r r e rr r rr r cr n u u u u C Br d r d n r r                                                                (17) Similarly to the plastic problem, Eqn. (13) for the creep stress intensity factor include a governing parameter for power- law nonlinear viscous materials in the form of cr n I -integral which can be obtained using the numerical method elaborated by the authors [8]. This method was extended by Shlyannikov and Tumanov [13] to analyze the fracture resistance characteristics of creep-damaged material. According to this method, the cr n I -integral value can be determined directly from the FEA distributions of the displacement rate  cr i u and dimensionless angular stress   cr ij functions     , , , , , , cr FEM n cr cr cr I t n t n d             (18)       1 , , , cos sin 1 1 cos 1 cr cr cr n FEM cr cr cr cr cr cr r cr cr e rr r r cr cr cr cr cr rr r r cr n du du t n u u n d d u u n                                                                 (19)   1 0 0 0 0 1 cr cr cr cr cr cr n n n n cr cr cr cr cr cr cr n cr i i e i e i e i n cr cr cr e e e cr u u u du u r L L dt L BL K                                            (20) where t is creep time,   e is the von Mises equivalent stress and     0 cr cr e e . In Eqs.(19,20) a dot over a displacement quantity denotes a time differentiations. The  -variation angular functions of the suitably normalized functions   ij and  i u and correspondingly governing parameter cr n I -integral depend on the damage function  and creep exponent n . In the traditional models for creep or creep-fatigue crack growth rate prediction the I n -integral is a function only the creep