PSI - Issue 52

D. Kujawski et al. / Procedia Structural Integrity 52 (2024) 293–308 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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analysis showed that the contribution from a single asperity (SA) contact (illustrated in Fig. 1b) contributes only about 0.21K cl . This results in m =0.21 in Eq. (2) and was in good agreement with the conclusion drawn earlier by Vasudevan et al. (1992) analysis where m was 0.25. Recently, Pippan and Hohenwarter (2017) have provided a review on the PICC, OICC and RICC phenomena. By using multiple rigid asperities contacting the crack flanks at the same K cl (similar to a rigid wedge) the calculated crack tip shielding contribution was about 0.7K cl (corresponding to m =0.7), which is very similar to Paris et al. (1999) analysis of a rigid wedge contact (illustrated in Fig. 1c), called (2/  or 2/pi) partial crack closure, suggesting its effectiveness at the crack tip of (2/  )K cl = 0.64K cl or m =0.64 in Eq. (2). Depending on the contact types (single or multiple rigid asperities) the m varied from 0.21 to 0.7. It is worth noting that roughness induced asperities are not rigid material but exhibit elastic-plastic behavior since they are ductile and deformable, therefore the m-value may significantly reduce the actual effect of theoretically calculated crack tip shielding.

Fig. 2 Illustrations of (a) Elber’s model, (b) single asperity (SA) model, (c) partial closure model ( 2/p) due to rigid wedge, and (d) potential energy released (dU) model Another form of crack driving force, equivalent to the Griffith model, is an energy release rate, , which is the energy available for an incremental crack extension. For a load control loading, as it is illustrated in Fig.1d, the energy release rate is expressed as: = 1 ( ) = 2 ( Δ ) (4)