Stochastic approximation of fatigue damage for in-service monitoring of structures

Abstract

Fatigue is a phenomenon of local degradation resulting from the repetition of low amplitude loads such as wind or waves. It plays a predominant role in the lifetime of aircraft, ships, and o?shore platforms. However, due to material, manufacturing and loading uncertainties [1], it is very di?cult to accurately predict fatigue degradation. Structural health monitoring is a way to obtain in situ measurements and therefore reduce those uncertainties. It requires to develop stochastic damage calculation methods which are able to integrate this information. In this work, we will focus on the evolution of damage during crack initiation for steel structures submitted to polycyclic fatigue. In order to estimate the fatigue damage, the most common approach is based on rain?ow counting assuming a linear damage accumulation (Palmgreen and Miner [2,3]). With this assumption, the loading history has no in?uence on the lifetime of the structure. A second approach, less commonly used in the industry, is based on the Lemaitre and Doghri two-scale fatigue model [4]. Based on the observations of damage localization, two scales are then de?ned: a macroscopic scale with elastic behavior and a microscopic scale with elasto-plastic behavior and a damage evolution law. This approach enables to consider the history of the damage accumulation but leads to high numerical costs.

In order to exploit the two-scale model in a time-dependent stochastic framework, it is then crucial to deal with the following two objectives: identify material random parameters for low failure probabilities [5] and keep numerical costs under control. Here, we propose two strategies to meet these objectives and compare the damage prediction to those obtained using a linear damage accumulation.

[1] O. Pasqualini, F. Schoefs, M. Chevreuil, Measurements and statistical analysis of fillet weld geometrical parameters for probabilistic modelling of the fatigue capacity, Marine Structures 34: 226-248 (2012).

[2] A. Palmgren, Die Lebensdauer von Kugellagern, Z.V.D.I. 68, 339-341 (1924).

[3] M. A. Miner, Cumulative damage in fatigue. J. Appl. Mech. 12, A 159-A164 (1945).

[4] J. Lemaitre, I. Doghri, Damage 90: a post processor for crack initiation, Computer Methods in Applied Mechanics and Engineering, Volume 115, Issues 3ﾖ4 (1994).

[5] B. Rocher, F. Schoefs, M. Fran�ois, A two-scale probabilistic time-dependent fatigue model for offshore steel wind turbines, International Journal of Fatigue, Volume 136 (2020).