PSI - Issue 72

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

550

2, = [ + + (− (1− )) 1⁄ (∆ )− ]

(8)

In this equation: - ∆ is the lower strain range, - ∆ is the higher strain range, - = ( 0 ) , 0 is the threshold value for lifetime, - = ( 0 ) , 0 represents the endurance fatigue limit, - is the Weibull shape parameter, - is the Weibull scale parameter, and - is the Weibull location parameter, which defines the zero-percentile curve. Rege and Pavlou (2017) proposed a new damage accumulation model based on nonlinear iso-damage curves. According to these authors, the fatigue damage resulting from the th step of cyclic loading is described by the equation: =( ) ( ) =( − − ) ( ) (9) In this equation: - ( ) is a function of the stress amplitude for the th step of cyclic loading being considered, - represents the number of cycles at the knee point of the S-N curve, - signifies the fatigue life for cyclic loading with constant stress amplitude, , - indicates the number of load cycles applied at load step . Aeran et al. (2017) introduced a new nonlinear fatigue damage model based on S-N curves, which relies on a specific model parameter. This parameter can be determined using design S-N curves included in established design standards. Dias et al. (2019) presented a parametric probabilistic approach for evaluating cumulative fatigue damage. This approach is based on the double linear damage rule, where the coordinates of the knee point are defined using a joint probability density function generated by a Kernel density estimator. Additionally, uncertainty quantification is conducted using Monte Carlo simulations. Chen et al. (2023) examined a nonlinear fatigue damage accumulation model under variable amplitude loading. This model considers the loading sequence effect by employing an exponential function based on the load cycle ratio. It proposes using the material's static toughness as a damage parameter. Yu et al. (2025) introduced an enhanced cumulative fatigue damage model that incorporates toughness exhaustion and new considerations for residual strength, treating these as dual state parameters. This preliminary research proposes a probabilistic stress-life prediction method for a structural component or connection subjected to variable amplitude loading, based on non-linear damage accumulation. The approach utilises the damage model developed by Huffman and Beckman (2013), which models non-linear damage by calculating the damage incurred during each loading cycle, considering the damage state at the time of that cycle. This model assumes that damage accumulation behaves similarly to crack growth. As a result, any specific reversal to a tensile stress in a variable amplitude stress history will lead to greater damage later in the loading history than at the beginning. The probabilistic analysis employed in this non-linear damage accumulation fatigue model is grounded in probabilistic local fatigue fields for constant amplitude fatigue data, as proposed by Castillo and Fernández-Canteli (2009). Furthermore, this approach requires numerical modelling of both the crack initiation and propagation phases for the structural component or connection being analysed, in order to obtain accurate fatigue life predictions. In this research, the non-linear damage model proposed by Huffman and Beckman (2013) can be generalised to incorporate stress- and energy-based criteria. This methodology can be applied to experimental fatigue data from structural components and connections subjected to constant and variable amplitude loading, leveraging known fatigue properties of the materials involved, specifically strain life data and fatigue crack growth data under constant amplitude conditions.