PSI - Issue 57

Giovanni M. Teixeira et al. / Procedia Structural Integrity 57 (2024) 670–691 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

679

10

Otherwise, for > the crack closure stress is obtained from: Δ = ( () ( 2 ′ () 1 ′ ) )

Fig. 8. Definition of effective stress and strain ranges.

(32)

And the effective stress range is determined from: Δ =

(33)

Taking crack closure into account has the effect of turning the results less conservative in those scenarios where the stresses are predominantly compressive.

2.2. Crack Tip Opening Displacement The correlation between the cyclic J-integral and the crack-tip opening displacement provides the basis for Equations 34 and 35 below as per Equation 19. In equation 21 the stress range and the viscoplastic strain range are measured from a stabilized cycle, usually at half-life. Then: Δ = ′ TMF (34) So that TMF = 1 0 (1.45 Δ 2 +2.4 Δ ⋅ Δ √1+3 ′ ) (35) ′ is the Ramberg-Osgood exponent. ′ and ′ are both related to the yielding limit by the expression [16]: 0 =2 ⋅ ′ ⋅ 0.002 ′ (36)