Issue 41

V.Shlyannikov et alii, Frattura ed Integrità Strutturale, 41 (2017) 285-292; DOI: 10.3221/IGF-ESIS.41.38 288 where C and m are material constants and multi-axial stress function    f D described by Eqs.(5,6). By assuming that the creep strain rate is governing by the equivalent von Mises stress, the damage accumulation constitutive equation in multi- axial state of stress is used in the form given by Kachanov [9]            1 n eqv eqv B (14) where B and n are constants of the Norton power law equation. C REEP STRESS INTENSITY FACTOR n [10] one unified parameter in the form of a plastic stress intensity factor (SIF) is introduced based on the asymptotic elastic-plastic stress and strain the crack tip fields which gives more accurate the characterization of fracture resistant properties materials and structures under static and cyclic loading than the wide spread two- parametric theories. The plastic SIF takes into account both the in-plane and out-of-plane constraint effects at fracture. Generally, the creep crack-tip singular asymptotic fields in the terms of a creep SIF's under the secondary extensive creep conditions can be modified to obtain a stress, strain and displacement rate for elastic-nonlinear-viscous material properties as the follows [11]                1 1 * 0 0 ; n cr n C K I L   , n cr cr K K (15) For a crack of length 2a in an infinite body and subject to a remote stress  , C* for the plane strain problem is given by [4]               1 * 0 0 0 3 2 n C a n (16) where  0 and   0 are reference stress and strain rate, respectively. Equations for the crack tip asymptotic stress-strain fields for three-dimensional creeping solids through amplitude factor (Eq.15) are a function of a governing parameter in the form of creep I n -integral. The numerical method was introduced by the authors [11] to determine the I n -integral for power-law creeping materials. According to this approach, the dimensionless angular stress   FEM ij and displacement rate  i u functions are directly determined from the FEA distributions            , , ( , , ) FEM FEM n I t n t n d (17)                                                                           1 , , cos sin 1 1 cos 1 FEM FEM n FEM FEM FEM FEM FEM FEM r e rr r r FEM FEM FEM FEM rr r r du du n t n u u n d d u u n (18)                                                    0 1 0 0 0 1 n n n n FEM FEM n FEM FEM FEM FEM FEM FEM i i e i e i e n i n FEM FEM FEM FEM e e e cr u u u du u r L L dt L BL K (19) I