PSI - Issue 75

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

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3.6. Harter-Willenborg Model Harter (2000), proposed to use a modified overload plastic zone size, , in the Willenborg model to account for the effects of compressive underload. The modified overload plastic zone size reduces the retardation effect and is expressed as: = ∙ [1 − 0.9 ∙ | min |] (38) where min is the size of the residual tensile stress zone created by the compressive underload and is determined according to Irwin’s formula (Eq. 23). The Harter-Willenborg model is not able to predict lives shorter than the life with no retardation and does not consider delayed retardation or overshoot. Austen-Willenborg Model Austen modified the Willenborg model to consider delayed retardation, overshooting and compressive underload (nCode (2003)). The resulting Austen-Willenborg model calculates as follows: = ∙√1− − − −( − max ) ∙√1− − − max ∙√1− − (39) 3.7. 4. Looping algorithms Crack growth analysis is an iterative process and when implemented in commercial durability software, the crack growth laws and retardation models previously described are iteratively applied within a looping algorithm, until a termination condition is met. T here are two looping algorithms available called ‘Cycle -by- Cycle’ and ‘Rapid Integration’. ‘ Cycle-by-Cycle ’ looping algorithm The ‘Cycle -by- Cycle’ looping algorithm is the most basic but is also the most comprehensive. It calculates the incremental crack growth for each cycle in turn calculating the instantaneous stress intensity and retardation. The main disadvantage of this algorithm is the longer processing time required to carry out most analyses. The ‘Cycle by- Cycle’ algorithm is most useful where significant retardation is expected and the fatigue life is short, or where semi-elliptical crack growth analysis is required. The ‘Cycle -by- Cycle’ looping algorithm creates a ‘Cycle’ object used to store all the crack growth parameters and initialises the cycle pointer and the initial crack length . The main loop then commences, and iteration continues until some termination condition is met. The ‘Cycle’ object is read in turn by the following algorithms: ‘ Rainflow ’ (get current cycle), ‘ Stress Intensity Factor ’ (calculate SIF for current crack length), ‘ Retardation ’ (calculate ) and ‘ Crack Growth Law ’ (calculate ∆ ). The required output calculated by each algorithm are then 4.1. where = 121 ∙ ( − min ) 2 (40)