Introduction
Mechanical components generally operate under cyclic stresses of varying amplitude during their lifetime. Fatigue phenomena are generated by these stresses and it is the main cause of failure of mechanical components during operation. Assessing fatigue damage is a critical issue, and it is one of the most common structural engineering problems. In general, fatigue damage accumulation theories can be divided into two categories: (1) linear damage accumulation theories and (2) nonlinear damage accumulation theories.
To predict the remaining life of these components, it is important to establish a method for assessing the accumulation of fatigue damage. For many years, design engineers have used Miner’s rule and its modifications to predict the fatigue life of components under variable loading11. In the linear approach, the work absorbed for each fatigue cycle is assumed to be constant and independent of one another. Nor does it take into account stress damage below the fatigue limit and the interaction between applied loads. This can lead to an order of magnitude difference between the predicted life and the test life, and such calculations may be unconservative2-4. Several researchers have tried to modify Miner’s rule, but predictions of life expectancy based on it are often unsatisfactory because of its inherent flaws5. Marco and Starkey6first proposed a nonlinear load-related damage rule, denoting the damage accumulation as , whereis a factor depending on theth loading.
More recently, Kwofie and Rahbar8-9 developed a novel approach to nonlinear damage accumulation based on S-N curves, referred to as the K-R model. Kwofie and Rahbar introduced the concept of fatigue driving forces that lead to fatigue damage in this model. The fatigue driving stress is a function of the cyclic stress, the number of loading cycles, and the fatigue life. This value increases with increasing loading cycles until a critical maximum driving stress is reached at the time of fracture. Residual fatigue life can be predicted by equating the fatigue driving stresses to produce cycles equivalent to the previous loading. It does not require much characterization of the material and the parameters of the model are only related to the S-N curve of the material. Later, Zuo10 et al. made a further study based on the K-R model and proposed a new nonlinear damage accumulation rule to improve the inherent flaws in the linear damage accumulation rule and to keep it simple in its application. The main advantages of the model are its ease of use, it only requires S-N curves, and it does not require any additional material properties to account for the effects of the loading history of the material.
It has been found that in addition to the loading sequence effects to be taken into account, the load interaction effects can also impact fatigue damage at multiple stages. Abrupt changes in load amplitude under different loading sequences can cause changes in the damage evolution of subsequent load cycles, which in turn affects the remaining life of the structure. Schijve, Yarema11 and Batsoulas12 noted that the number of damage nuclei will lead to a load interaction effect that is greater at higher loading stresses. In addition, the number of damage nuclei produced by different loading stress levels will lead to variations in damage accumulation and this effect will increase with larger differences between stress levels.
Considering the loading interaction effects, with reference to the literature13,14, Zhu15 introduced a load ratio between each loading stage to describe the loading interaction effects, making an improvement to the K-R model. In order to study the loading interaction effects on damage accumulation, Peng16 analyzed that after undergoing high-loading cycling, the damage evolution curve under low-loading cycling will be shifted based on its damage evolution curve of constant amplitude loading and this shift has a promoting effect on damage accumulation, while the opposite is true for low-high loading, providing an intuitive theoretical explanation for loading interaction effects.
The objective of this study is to present a new modified fatigue driving stress model that accounts for the loading interaction effects and is used to predict the remaining life under variable amplitude fatigue loading. The validity of this model is also verified by comparing it with Miner’s rule and other models based on fatigue driving stress theory through fatigue tests of variable amplitude on several materials.
Models based onfatigue driving stress theory