PSI - Issue 75

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

237

4

2.2. Cyclic crack tip plasticity model and crack retardation When a crack experiences a tensile overload, a subsequent reduction of the crack growth rate was observed (Elber (1971)). To account for this crack growth retardation, caused by the large plastic deformation region produced around the crack tip by the tensile overload, the ‘Total - Life’ method uses a retardation model based on a multiaxial cyclic crack tip plasticity model proposed by Moftakhar et al. (1995), that in turns makes use of the Neuber rule (Neuber (1961)) and the Ramberg-Osgood cyclic plasticity model (Landgraf et al. (1969)). The crack retardation model needed to determine the retardation stress intensity factor, , involves the calculation of the residual compressive stress ahead of the crack tip and its effect on the crack propagation (Mikheevskiy and Glinka (2009)). According to the law for blunt cracks proposed by Creager and Paris (1967), under the assumption of linear elasticity and Mode I crack opening, the crack-tip opening stress along the crack propagation axis can be expressed as: ( ) = √2 ∙ (1 + ∗ 2 ) (7) To account for the stress redistribution caused in real applications by the plastic yielding occurring ahead of the crack tip, Glinka (1985) introduced a ‘plasticity correction factor’, , defined as: ( ) = 2 + ∗ ∙ (1+ ∆ ) 2 + ∗ ∙√1+ ∆ (8) where is the theoretical plastic zone size determined by solving Eq. 7 for with = (yield strength), while ∆ is the plastic zone increase due to the stress redistribution defined as: ∆ = 1 ∙ [∫ ( ) ∗ 2 − ( − ∗ 2 )]⇒∆ = ( ∗ −2 ) 2 ∙ (2 + ∗ ) (9) This is graphically shown in Fig. 1.

Fig. 1. Effect of stress redistribution at the crack tip. Glinka (2015b) later proposed to use an effective plasticity correction factor, ′ , to account for the decreasing effect of the plasticity correction factor as increases: