PSI - Issue 23

Oleg Naimark / Procedia Structural Integrity 23 (2019) 245–250 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

249

5

specific nonlinearity (metastability) of free energy release in the presence of non-locality effects of defects interaction that allows the explanation of transition from damage localization to the fatigue crack nucleation stage. The K  - independent area of fatigue crack initiation corresponds to the transition to the blow-up damage kinetics with explosive jump from structure dependent scales of defects int a to macroscopically recognized 0 a . The power law reflects the self-similar (blow-up) stage of damage kinetics over c L scale that allows to estimate 0 a ~ c L . This length is related to the stress based scenario of fatigue crack nucleation. Starting from this scales 0 a the singularity related to the stress intensity factor 0 K  is combined with the blow-up singularity (5), that provides fatigue crack kinetics up to the scale l a . The drop of the crack velocity is the consequence of subjection of crack kinetics to the stress intensity factor th K  according to the Paris law. The process zone scale in this case is associated with the H L length. Mentioned scenario was illustrated by Betekhtin et al. (2017) for morphological images of crack nucleation and propagation in the conditions of Very High Cycle fatigue.

Fig. 2. Fracture surface of Ti6Al4V alloy in Very High Cycle fatigue regime with the images of characteristic areas of fracture surface.

Criticality of fatigue damage-failure transition corresponds to self-similar pattern of fracture surface that was studied by Betekhtin et al. (2017) calculating spatial (scaling) invariant (the Hurst exponent) of the fracture surface roughness for the identification of characteristic areas in Fig. 2. Crack velocity da dN is given in this case by the intermediate asymptotic solution





pz          eff K K sc L l



K     

a eff N l sc E l sc  

d

,

,

(7)

 

d



where α and β are the power exponents for the areas 2 and 3 (Fig. 2) in the range of scales [ l sc , L pz ] corresponding to multiscale correlation of defect induced roughness. The Paris law follows from (7) for eff K K   for the scales

, corresponding to the TCD effective scales eff L .

(L

pz sc l

L

 ) ,

eff

6. Discussion

Multiscale mechanisms of damage-failure transitions in metals are studied for Very High Cycle Fatigue. By correlating with results of experimental and structural studies, a theoretical approach is developed to describe characteristic stages of damage- failure kinetics corresponding to the “fish - eye” area nucleation, small crack growth and the Paris crack propagation in pre-damaged material. Experimentally estimated scales and power exponents were used in the constitutive laws as the structure sensitive parameters for characteristic damage-failure transition stages. The explanation of intermediate asymptotic nature of damage localization kinetics, small crack growth and the Paris crack advance was proposed in the link to the nonlinearity of free energy release and defect induced structural roughness scaling of fracture surface.