PSI - Issue 72

José A.F.O. Correia / Procedia Structural Integrity 72 (2025) 547–556

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(FEM) to model the initiation phase, considering a local analysis based on a local fatigue criterion (e.g., stress, strain, energy), and fracture mechanics using the Paris law or local unified approach to model the crack propagation phase (Step 2). - Generate probabilistic S-N fields under constant amplitude loading for a structural detail or connection under consideration following Step 1 and Step 2. The experimental S-N curve under constant amplitude loading and the predicted p-S-N fields for a component or connection must be compared (Step 3). - Generate probabilistic S-N fields (p-S-N) under variable amplitude loading employing a non-linear fatigue damage model suggested by Huffman and Beckman (2013) using the material fatigue data under constant amplitude loading for both fatigue phases, where a probabilistic local fatigue field is obtained and employed (Step 4). - Validate the proposed methodology by comparing the predicted p-S-N fields and the experimental S-N data under variable amplitude loading.

ε

a -N data at constant amplitude loading (material – small smooth specimens)

S-N data at constant amplitude loading (Structural Detail)

S-N data at variable amplitude loading (Structural Detail)

p=0

B = Log N 0

p=0.05

Log 

p=0.5

p=0.95

C = log  0

LogN f

Cyclic stress-strain properties

Experimental S-N data vs Predicted P-S-N Fields (variable amplitude loading)

Generalized probabilistic model applied for several fatigue damage variables

Local Analysis Neuber rule or FEM

Experimental S-N data vs. Predicted P-S-N Fields (constant amplitude loading)

Non-linear accumulation fatigue model proposed by Huffman & Beckman

Fig. 6. Proposed methodology for predicting probabilistic S-N fields at variable amplitude loading considering the non-linear damage modelling.

5. Concluding remarks This preliminary research proposed a probabilistic S-N prediction under variable amplitude loading based on a non-linear damage model and probabilistic local fatigue modelling to be applied to the components and connections. In this methodology, the probabilistic local fatigue model, a generalisation proposed by Correia et al. (2017), can be used to model the probabilistic fields of the fatigue-life strength of material fatigue data under strain-controlled conditions. Numerical modelling must support this methodology to predict S-N fields, including fatigue phases – crack initiation and propagation – applied to components and connections under constant amplitude loading. Given known load block spectra, the non-linear accumulation fatigue model suggested by Huffman and Beckman (2013) can generate the probabilistic S-N strength of components and connections under variable amplitude loading, supported by the suggested numerical modelling. This approach appears promising for obtaining probabilistic S-N fields of structural components and connections under random loading, based on material fatigue data, and validated against a small sample of experimental data of fatigue strength obtained from the constant and variable amplitude loading for these connections and structural details under consideration.