PSI - Issue 52

2

Author name / Structural Integrity Procedia 00 (2019) 000 – 000

D. Kujawski et al. / Procedia Structural Integrity 52 (2024) 293–308

294

1. Introduction In structural materials that are subjected to cyclic loading, fatigue cracks typically initiate on the surface and propagate until failure for a smooth tensile sample. For a pre-cracked sample, the cracks begin to grow at low applied stress intensity. For both cases, during this process, a significant portion of the component's fatigue life is consumed as cracks propagate in the threshold regime. The threshold regime is affected by the simultaneous influence of mechanical and chemical effects on damage, where long-time exposure is necessary for this to occur. Figure 1 schematically illustrates the stages to failure in terms of defect/crack size versus time/cycles of service. Key features of this figure show that by the time non-destruction inspection (NDI) finds a crack, the component has lost 80% of its life. Above the NDI limit, cracks enter Paris region where only 20% of the life remains.

Fig. 1 Schematic illustration of the stages to failure in terms of defect/crack size versus time/cycles of service.

Based on the elastic materials behavior, a tension stress applied to a cracked specimen would cause the crack to open and the crack opening displacement would return to zero once the applied load is removed. However, when an elastic plastic material is loaded, Elber (1970) observed that the fatigue crack was closed during unloading, even before the tension stress returned to zero. This unexpected observation, Elber called it as plasticity-induced crack closure (PICC). He postulated that for the PICC an effective range of stress intensity factor (SIF),  K eff , can be calculated as: ∆ = − (1) where K max is the maximum stress intensity factor (SIF) during a load cycle and K op is the SIF when the crack tip is just fully open. Often, K op is replaced or used interchangeably with K cl , which relates to the instance when the crack flanks come into contact. According to PICC model (illustrated in Fig. 2a), any load below K op (or K cl ) is not damaging therefore, the fatigue crack growth rate depends solely on  K eff . Thus, using Eq. (1) one can express the normalized effective SIF range or ‘crack driving force’ as following: ∆ =1− (2)