PSI - Issue 75

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

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3.4. Modified Generalised Willenborg Model Brussat (1974) proposed an extension of the Generalised Willenborg model proposed by Gallagher (1974) to consider the effects of compressive underload. This model is also documented in NASA (1999). Brussat modified the expression of the parameter as: = { 2.523 ∙ 0 1 + 3.5 ∙ (0.25 − ) 0.6 if <0.25 1 otherwise (33) where is the ratio of underload stress to overload stress and 0 is the value of for =0 . The parameter 0 is a material parameter determined experimentally, with typical values ranging between 0.2 and 0.8 as described in Mettu et al. (1999). Brussat also proposed an alternative definition of the minimum effective stress intensity factor, min : min = { max ( min − ′ ,0) if min >0 min otherwise (34) This retardation model does not account for delayed retardation or overshoot. B ased on Walker’s crack growth law , Chang and Engle (1984) also extended the Generalised Willenborg model proposed by Gallagher (1974) to consider the effects of compressive underload. The model is expressed as: = { ∙ [∆ ∙ (1 − ) −1 ] for ∆ >∆ ℎ and ≥ 0 ∙ [ max ∙ (1+ 2 ) ] for ∆ >∆ ℎ and < 0 0 for ∆ <∆ ℎ (35) 3.5. Walker-Chang-Willenborg Model

with

{ + if > + − if < − otherwise

=

(36)

where + and − are the cut-off values for positive and negative stress ratios, respectively. Also, the threshold stress intensity range, ∆ ℎ , is defined as: ∆ ℎ =∆ 0 ∙ (1 − ∙ ) where is a fitting parameter and ∆ 0 is the stress intensity range at =0 . This retardation model does not include delayed retardation or overshoot.

(37)