PSI - Issue 57

Baran Yeter et al. / Procedia Structural Integrity 57 (2024) 133–143 Baran Yeter & Feargal Brennan / Structural Integrity Procedia 00 (2023) 000 – 000

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The Wheeler retardation model introduces a retardation factor, C p, which is a function of the relative crack growth along the overload-induced plastic zone. This model can be integrated with the Paris law. Thus, the modified Paris law based on the Wheeler yield zone model can be expressed as (Wheeler, 1972): ( ) = ( eff , ) (3) eff , = HSS √ (4) where C and m are material constants, and the stress intensity factor is described based on the geometric function Y , the stress range Δ σ , and the current crack size a i , which becomes a c after enough number of cycles N t to cause fast fracture failure. The geometric function used for a tubular joint must account for the complex stress field occurring as a result of boundary effects such as loading, non-uniform stress field, and specimen and crack geometries, which can be derived using experimental and finite element analyses (Etube et al., 1999). = 0 + ∑ ( , , , , . .) =1 = 0 + ∑ =1 (5) ={ [ + − ] , + < + 1 , + ≥ + (6) where C p varies from 0 to 1, depending on the location of the crack tip in a previously created larger zone, and it is denoted as: = 1 ( ) 2 (7) = 1 ( ) 2 (8) where a i represents the current crack length corresponding to the i th cycle, r pi denotes the current plastic zone size, corresponding to the i th cycle, a OL is the crack length at which overload was applied, r pi is the plastic zone created by overload, and μ is the Wheeler empirically adjustable exponent, taken merely as the value that fits the best to the test loading data (Skinn et al., 1994). The terms defining the Wheeler retardation model are illustrated in Fig. 5.

Fig. 5. Representation of the Wheeler yield-zone model

Table 3. Mechanical and Fracture properties offshore steel (Air condition) used in the tubular joint (JCSS, 2006) Parameter Units Value Material constant, C - 4.91e-12 Material exponent, m - 3.1 Critical SIF MPa.m l/2 69 Yield stress MPa 355