Issue 52

A.V. Tumanov et alii, Frattura ed Integrità Strutturale, 52 (2020) 299-309; DOI: 10.3221/IGF-ESIS.52.23 302 determined for the cracked body with a finite size. In the case of full three-dimensional cracked body, the p I -factor in Eqn. (8) changes not only with the strain hardening exponent n p but also with the position along the crack front. In Eqn. (9), the stress tensor and invariant are both normalized by the yield stress: and ij ij y kk kk y         . More detail in determining the p I factor for different elastic-plastic cracked body configurations are given by Refs. [15-18]. In a first approximation the crack growth as a static cracks sequence is considered. Thus, the path independent J-integral can be obtained from: 2 2 1 (1 ) K J E    (10) Substitution Eqns. (6) and (8) into (7) give a possibility to obtain the critical distance where the strain energy density reaches a critical value: 2 2 1 1 (1 ) 1 p p n n y f p e c n r K n E W           (11) The fatigue crack growth rate can be calculated by substitution Eqns. (5) and (11) into (1) directly, it leads to the following relationship: 2 1 2 2 2 2 1 1 2 0 0 (1 ) 1 1 2 ln( )( ) p f p p n r n n p y e f p f y e p fatigue p t c f f n r K da dr a K dN n EU EW N N N                                       (12) C REEP DAMAGE ACCUMULATION n this study the classical Kachanov-Rabotnov power law is used for the creep damage accumulation description. According to this model, the strain rate during creep is [1-2]: 1 cr e e cr n B             (13) and the creep damage accumulation rate is: 1 m cr e cr cr d D dt             (14) where B and cr n are material constants of the Norton power law constitutive equation, D and m – are material properties. The damage variable  indicate the measure of creep damage with 0   denoting the undamaged state and 1   the fully damaged state. The creep damage increment cr   at time t  can be obtained by integrating the expression (14): .     1 1 3 1 1 m m cr D t C m               . (15) where 3 C - is integration constant. This constant can be determined from the initial state. I