PSI - Issue 23

Oleg Naimark / Procedia Structural Integrity 23 (2019) 245–250

246

Author name / Structural Integrity Procedia 00 (2019) 000 – 000

2

cycle gas turbine engine resource, by Nicolas (1999). It was noted by Cowles (1996), that the series of catastrophes caused by the failure of gas turbine engines, combined with the high cost of resource assessment and the potential cost of developing new material structures, stimulated promising approaches in life-time predictions. T he “criticality” concepts was proposed by Naimark (2016) for the study of stages of multiscale damage-failure transition. Mughrabi (2006), Mughrabi and Höppel (2010) underlined, that the definition of initiation and propagation stages of fatigue cracks is one of the key problems of fatigue fracture and is determined by the methodology for studying the damage kinetics, nucleation and propagation of cracks. The role of the initiation stage is especially important for giga-cycle regimes, which are characterized by the emergence of “ fish-eye ” zones of fatigue crack foci in the bulk of the material. Moreover, it was noted by Bathias and Paris (2005) that the stage of fatigue crack propagation in VHCF is less significant than the time of fatigue crack initiation. The existence of two singularities related to the stress field at the crack tip and blow-up kinetics of damage localization is considered by Oborin et al. (2019) as the physical basis for the interpretation of the Theory of Critical Distances (TCD) proposed by Taylor (2008). The free energy metastability of solid with defects and corresponding free energy release explain the conception of the Finite Fracture Mechanics (FFM) in the presence of the finite amplitude energy barrier. The variety of crack paths is analyzed as duality of inherently linked two types of singularities related to the singularity of multiscale damage kinetics under crack nucleation and singularity of stress field at the crack tip as the classical framework of fracture mechanics. Mughrabi (2013) mentioned that fatigue damage is traditionally associated with microplastic deformations during cyclic loading, initiating various microstructural mechanisms determining the durability depending on the nature and initial structure of material. For ductile metals, a special type of fatigue (cyclic) deformation localization (persistent slip bands - PSB) is observed, that traditionally leads to the initiation of cracks in the near-surface zone. Thus, the opposite to HCF case is characteristic for VHCF, when the central attention is paid not to the crack propagation stage, but to multiscale damage localization associated with defects (localized plastic shears, microcracks, pores). It is also noted by Mughrabi (2006), that the stages of fatigue damage-failure transition are characterized by the “irreversibility” effects initiated by multiscale localized slips that play a key role in the nucleation of a fatigue crack. 3. Duality of singularities in crack nucleation and propagation The subject of fatigue damage-failure transition is one whose roots go back to the classical work by Griffith (1921). According to the Griffith ’s theory the additional characteristics of the crack resistance were introduced in the form of the energy of the development of the new surface at the crack tip. The energy U of elastic materials with a crack is represented in the form (Fig.1, curve 1) 2. Fatigue crack initiation in VHCF

2 2 4 a E           2 2 a

U

 

(1)

where  is the surface energy;  is the applied stress; a is the crack length; E is the elastic modulus. The Griffith conception was developed by Irwin (1957) and proposed the force version of the crack stability (the stress intensity factor) related to the intermediate self-similar singular solution for the stress field at the crack tip area

1 2 ( ), ij 



K r f

K a   





,

(2)

ik

I

I

 , r are the coordinates of point,

( )  ij f is the  dependence in the first term

I K is the stress intensity factor,

where

of asymptotical solution.