Survival probability of structures under fatigue: a data-based approach

Abstract

This article addresses the probabilistic nature of fatigue life in structures subjected to cyclic loading with variable amplitude. Drawing on the formalisation of Miner's cumulative damage rule that we introduced in the recent article [Cartiaux, Ehrlacher, Legoll, Libal and Reygner, Prob. Eng. Mech. 2023], we apply our methodology to estimate the survival probability of an industrial structure using experimental data. The study considers both the randomness in the initial state of the structure and in the amplitude of loading cycles. The results indicate that the variability of loading cycles can be captured through the concept of deterministic equivalent damage, providing a computationally efficient method for assessing the fatigue life of the structure. Furthermore, the article highlights that the usual combination of Miner's rule and of the weakest link principle systematically overestimates the structure's fatigue life. On the case study that we consider, this overestimation reaches a multiplicative factor of more than two. We then describe how the probabilistic framework that we have introduced offers a remedy to this overestimation.

Figures (4)

• Figure 1: S-N curve used for each sensor. In loglog coordinates, it is piecewise linear, with the slopes $-1/3$ and $-1/5$ prescribed by Part 1-9 of Eurocode 3. The curve is then entirely characterised by the detail category$\Delta \sigma_C$, which is the severity for which the NCF assumes the value $2 \times 10^6$.
• Figure 2: Survival probability of each monitored zone (in colour) and of the structure (in black), as a function of time (for $C_\mathrm{s}=1$ and $\Delta \sigma_C = 36\, \mathrm{MPa}$). The curves are computed with the deterministic equivalent damage approximation, and the Monte Carlo approximation for the survival probability of the structure is displayed with dots. The quantiles of order $p=0.05$ of the lifetimes of the zones and of the structure are represented by the vertical dotted lines. The curves for the zones 1, 2 and 7 are essentially lying one on top of each other (and likewise for the curves of the zones 4 and 8, and also for the curves of the zones 3, 5 and 6).
• Figure 3: Histograms of the daily cumulative damages at each sensor. The $y$-axis provides the percentage of days (over the monitoring period) for which the observed cumulative damage lies into the corresponding class. For sensors OS3-Back-Left, OS5-Support-Right and OS6-Support-Left, the percentage of days with no cumulative damage is $84\%$, $94\%$ and $92\%$, respectively. On these days, either no cycle has been recorded at all, or all associated severities are below the cut-off limit of the S-N curve (see Figure \ref{['fig:sn']}).
• Figure 4: Correlations between the daily cumulative damages recorded at each sensor.

Theorems & Definitions (3)

• Remark 2.1
• Remark 3.1
• Remark 3.2