PSI - Issue 75

Thomas Constant et al. / Procedia Structural Integrity 75 (2025) 660–676 Author name / Structural Integrity Procedia 00 (2025) 000–000

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Appendix A. Pseudocode illustrating the procedure for multiaxial critical plane fatigue damage assessment

Algorithm 1 Pseudo-code description of the m B model. Require: m A ( x A ) (see eq 1) , x B = { σ ′ f , ϵ ′ f , R p 0 . 2 , k t } , E , ν , b , c , K ′ , n ′ 1: L d ← []

▷ Empty list to store computed damage for each node k

2: for k ∈N c do

▷ Loop for all nodes in the critical location

3: σ local ( t ) = k t σ k ( t ) , t ∈ 0 , T ▷ Application of concentration factor k t to account for geometric singularities in critical locations 4: ϵ local ( t ) = 1 E (1 + ν ) σ local ( t ) − ν Tr( σ local ( t )) I ▷ Assumption of linearity and isotropy 5: if σ eq ( t ) ≥ R P 0 . 2 then ▷ Elastoplastic correction of the strain tensor by the Ramberg-Osgood model ( f RO ) if σ eq exceeds R P 0 . 2 6: ϵ corrected ( t ) = f RO ( ϵ local ( t ) , K ′ , n ′ ) 7: else 8: ϵ corrected ( t ) = ϵ local ( t ) 9: end if 10: L d ( n ( θ )) ← [] ▷ Empty list to store computed damage for each candidate plane defined by its normal vector n ( θ ) 11: for θ ∈ 0 ,θ max do ▷ Loop for each candidate plane oriented with an angle θ from the material coordinate system, and of normal vector n ( θ ) 12: Projection of ϵ corrected ( t ) and σ corrected ( t ) on the candidate plane of normal vector n ( θ ), t ∈ 0 , T 13: Evaluation of the shear γ ( t ) and normal ϵ n ( t ) strain histories, t ∈ 0 , T 14: Rainflow counting of these strain histories to extract fatigue cycles { ∆ γ ( j ) max , ∆ ϵ ( j ) n ,σ n , mean , n j } j ∈ 1 , n cycle 15: Evaluation of individual cyclic damages d ( j ) = n j N ( j ) f from equation 9 . 16: Linear accumulation of damage for the candidate plane with normal n ( θ ) using Miner’s rule: d n ( θ ) = n cycle j = 1 n j d ( j ) 17: L d ( n ( θ )) ← L d ( n ( θ )) ∪ d n ( θ ) ▷ Update of the list of computed damage on candidate planes 18: end for 19: L d ← L d ∪ max L d ( n ( θ )) ▷ Update of the list of computed damage for each node k . The candidate plane of normal n ( θ ) experiencing the highest damage is defined as the critical plane 20: end for 21: d = max( L d ) ▷ The node experiencing the highest damage defines the location of crack nucleation in the critical regions of the system 22: return d ▷ The damage scalar value associated with a critical location