PSI - Issue 52

D. Kujawski et al. / Procedia Structural Integrity 52 (2024) 293–308 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 5 where B is the specimen’s thickness, = ( 2 Δ ) is the change in potential energy when crack increases from ( a) to ( a+da) . Assuming that crack flanks begin to contact at P cl = nP max the corresponding energy is = 2 ( 2 Δ ) (5) Thus, the effective amount of the potential energy, dU eff , available for crack extension is: =(1− 2 )( 2 Δ ) (6) where n = P cl /P max . The corresponding normalized effective potential energy released is: ( ) =1− 2 (7) Figure 3 illustrates the relation for normalized (K eff /K max ) tip and ( / ) tip versus P cl /P max for Elber’s model (Elber), single asperity (SA), partial crack closure (2/pi), and potential energy release (dU). 297

Fig.3 Dependence of normalized crack tip driving force on normalized crack closure. An inspection of Fig. 3 indicates that the Elber’s model shields the crack tip the most, followed by (2/p) model, then the potential energy rate and single asperity model. It is seen from Fig. 3 that the contribution from (dU) and (SA) models on the crack tip shielding is very small if (P cl /P max) < 0.3. It worth noting that for the last 50 years, it was inferred that a single parameter driving force  K eff , given by Eq. (1) is sufficient to analyze fatigue damage and to model fatigue crack growth (FCG) behavior via the classical Paris-Erdogan relationship (often referred as the Paris law): = (∆ ) (8) where C and m are the fitting parameters. Thus, according to crack closure hypothesis, FCG data from different R-