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