Probabilistic model of fatigue damage accumulation of materials based on the principle of failure probability equivalence

Abstract

Fatigue damage accumulation model plays a critical role in life prediction and anti-fatigue design of material. It is still a challenging issue to accurately quantify its development process and probabilistic characteristics. In this study, a probabilistic model of fatigue damage accumulation is presented based on Weibull distribution and reliability analysis theory. Firstly, the general rule of fatigue damage accumulation is analyzed, and three basic assumptions about fatigue life and fatigue damage are drawn. Subsequently, two typical fatigue reliability analysis models are elaborated, and a probabilistic model of fatigue damage accumulation is proposed based on the principle of failure probability equivalence. Finally, three sets of experimental data of aluminum alloy are utilized to verify the proposed model. The results show that the proposed model is capable of quantifying the dynamic probability characteristics of fatigue damage accumulation. Moreover, the proposed model has high calculation accuracy, and it can be easily established based on fatigue life data of material.

Introduction

Engineering structures and materials are usually subjected to the cyclic loading during their service, and fatigue failure becomes one of their main failure modes [1], [2]. Fatigue failure of materials may cause huge economic losses, and even result in catastrophic accidents. Under such circumstances, fatigue resistance of material becomes a serious issue from both the economic and safety point of views. In practical engineering, the concept of fatigue damage accumulation is generally adopted to quantify the failure process of material under cyclic loading [3], [4]. Fatigue damage gradually accumulates with the increase of loading times, and fatigue fracture will eventually occur when accumulated fatigue damage exceeds its critical value. In engineering applications, a reliable fatigue damage accumulation model is strongly expected in life prediction and anti-fatigue design of materials [5], [6], [7], [8], [9].

Over the past few decades, considerable studies that focused on fatigue damage accumulation of materials have been carried out, and a variety of fatigue damage accumulation models have been developed [10], [11], [12]. In general, the existing fatigue damage accumulation models can be classified into two categories, micro-mechanism models [13], [14] and macro-phenomenological models [15], [16]. From the fault physics point of view, fatigue failure of material involves a series of complex micro-mechanisms, and its quantitative modeling seems to be a particularly challenging issue. To investigate fatigue damage mechanisms of material under tension–tension cyclic loading, Zhao et al. [17] presented a statistical model of fatigue damage accumulation based on continuum damage mechanics theory. Liu et al. [18] proposed a novel fatigue damage modeling approach based on critical plane method and continuum damage mechanics theory. To reveal the damage evolution law of materials with voids and cracks, Kim et al. [19] developed a damage mechanics model based on the effective stress and crack theory. Wu et al. [20] presented a constitutive-damage model to explore the fatigue fracture mechanisms of materials based on strain-controlled fatigue test results.

It should be noted that the detailed information on failure mechanisms (such as details about crack initiation and propagation) is generally required to establish the micro-mechanism damage models. However, such micro-mechanism information may be not fully available in practical engineering. Besides, the micro-mechanism damage models are difficult to apply in engineering due to their complexity. In contrast, the macro-phenomenological damage models (such as Miner's rule) are preferred due to their simplicity and practicality. To account for the loading sequence effects, Lv et al. [21] proposed a modified nonlinear fatigue damage accumulation model based on performance degradation of materials. Zhu et al. [22] presented a nonlinear fatigue damage accumulation model based on a damage function related to isodamage curves and remaining life. To characterize all the fatigue regimes of materials, Correia et al. [23] developed a generalized Kohout-Věchet model of different fatigue damage parameters. Yu [24] presented an improved nonlinear fatigue damage accumulation model based on Manson–Halford theory.

Although much progress has been made in macro-phenomenological damage models of materials [25], [26], most of these models can not quantify the inherent dispersion of fatigue damage accumulation [27], [28], [29], [30]. Because of the randomness of internal defects and the diversity of fatigue damage mechanisms of materials, the accumulated fatigue damage at a given loading times generally shows a large dispersion. To quantify the probabilistic characteristics of fatigue damage, Pinto et al. [31] presented a probabilistic fatigue damage accumulation model to calculate fatigue life of material under step-stress conditions. Zhu et al. [32] proposed a probabilistic approach for modeling fatigue damage based on a one-to-one transformation technique. Sun et al. [33] developed a statistically consistent fatigue damage model based on Monte Carlo sampling method and Miner’s rule. Luo et al. [34] proposed a novel probabilistic modeling approach for fatigue damage accumulation, and then it was applied to predict fatigue life of material under random loading. Shen et al. [35] presented a probabilistic model of fatigue damage accumulation to account for the randomness of external loads and fatigue resistance of materials. However, most of these existing models are developed based on experimental data and subjective experiences, which has the disadvantages of lacking mathematical derivation and theoretical basis.

In this study, the general rule of fatigue damage accumulation is analyzed, and some basic assumptions about fatigue damage accumulation and fatigue life are presented. The two-parameter Weibull distribution is utilized to quantify the probabilistic characteristics of fatigue damage and fatigue life, and two typical fatigue reliability analysis models are elaborated. A probabilistic model of fatigue damage accumulation is proposed based on the principle of failure probability equivalence, and three sets of experimental data of aluminum alloy are utilized to validate the proposed model.