PSI - Issue 75

Andrew Halfpenny et al. / Procedia Structural Integrity 75 (2025) 234–244 Author name / Structural Integrity Procedia (2025)

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where Δ =√Δ 2 −Δ Δ +Δ 2 . 2.3. Cycle counting and memory rules Another fundamental aspect is to determine how the compressive residual stress field ahead of the crack tip and the consequent crack retardation evolve as the crack propagates. According to Mikheevskiy (2009), in a plate of infinite width and under the simpler case of constant amplitude loading, a new residual compressive zone of length forms ahead of the crack tip at every cycle. As the crack propagates, the residual stresses from the previous cycles create a zone of constant compressive stress along the surface of the crack as illustrated in Fig. 3. Mikheevskiy (2009) proposed that the retardation effect of a given cycle decreases following a trapezoidal shape (full effect over a distance of 2 3 followed by a linear decrease over the remaining 1 3 distance) as shown in Fig. 3.

Fig. 3. Effect of the residual compressive stress on the propagating crack under constant amplitude loading.

Glinka and Shen (1991) proposed to calculate the effective stress intensity factor at the crack tip, due to a trapezoidal block of residual compressive stress, using “Universal Weight Functions”. Therefore, the retardation stress intensity factor due to an idealised trapezoidal stress block (Fig. 4a), , can be defined as: =∫ 2 √2 ( ( − ) ) 2 1 (13)

(a)

(b)

Fig. 4. Idealised trapezoidal stress block along the surface of a crack (a) and effect of the residual compressive stress on the propagating crack under variable amplitude loading (b).