PSI - Issue 75

Andrew Halfpenny et al. / Procedia Structural Integrity 75 (2025) 219–233 Author name / Structural Integrity Procedia (2025)

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7

max ={ ∆ (1− max ) if > max max otherwise

(20)

3. Retardation Models Elber (1971) observed that, following a tensile overload, the surfaces of a fatigue crack remained in contact even after the application of smaller tensile loads, with consequent reduction of the crack growth rate. This phenomenon is known as crack retardation. This phenomenon was attributed to the large plastic deformation region produced by the tensile overload around the crack tip causing the material to expand in this region due to plastic strain. Consequently, when the tensile overload ceases, the expanded material, due to the containment induced by the surrounding elastic material, applies a residual compressive stress to the surfaces of the crack pushing them close together (Fig. 2a). Crack propagation resumes if and when the stress at the crack tip overcomes the residual compressive stress caused by the tensile overload. The pre-compression remains effective until the crack has overgrown the plastic zone created by the tensile overload. According to the Paris law (Eq. 2), the crack growth rate

can be expressed as: = ∙ (∆ )

(21)

with the effective stress intensity range defined as: ∆ = max − (22) where is the stress intensity needed to overcome the residual compressive stress caused by the tensile overload.

(a)

(b)

Fig. 2 . Plasticity in the crack wake after Elber (a) and illustration of the plastic zone in Willenborg’s retardation model (b).

Other phenomena can also be observed: