... between 80-90% of all structural failures occur through a fatigue mechanism. However, the adoption of fatigue prediction in the finite element community, where most structural engineering decisions are made, has been limited.
According to independent studies by Battelle in 1982, between 80-90% of all structural failures occur through a fatigue mechanism, with an estimated annual cost in the US of about $1.5B. Furthermore Battelle concluded this could be reduced by 29% by application of current fatigue technology. In this section we overview the physical behavior responsible for fatigue from initiation to final component failure.
Fatigue is defined as 'Failure under a repeated or otherwise varying load, which never reaches a level sufficient to cause failure in a single application.' Fatigue cracks always develop as a result of cyclic plastic deformation in a localized area. This plastic deformation often arises, not due to theoretical stresses in a perfect part, but rather due to the presence of a small crack or pre-existing defect on the surface of a component, which is practically undetectable and clearly unfeasible to model using traditional Finite Element techniques.
August Wöhler was the first to study fatigue and propose an empirical approach. Between 1852 and 1870, Wöhler studied the progressive failure of railway axles. He constructed the test rig shown in Figure 1, which subjected 2 railway axles simultaneously to a rotating bending test. Wöhler plotted the nominal stress versus the number of cycles to failure, which has become known as the SN diagram. Each curve is still referred to as a Wöhler line. The SN method is still the most widely used today.
Several effects are notable about the Wöhler line. First, the SN curve is not valid because the nominal stresses are now elastic-plastic. We will show later that fatigue is driven by the release of plastic shear strain energy; therefore above yield, stress loses the linear relationship with strain and cannot be used. Between the transition and the endurance limit (approximately 107 cycles), SN based analysis is valid. Above the endurance limit the slope of the curve reduces dramatically and as such this is often referred to as the 'infinite life' region. In practice, however, this is not really the case. For example, Aluminum alloys do not exhibit infinite life, and even steel does not exhibit infinite life when subjected to variable amplitude loading.
With the advent of modern magnification techniques, fatigue cracks have been investigated in more detail. We now know that a fatigue crack initiates and grows in a two-stage process. In the early stages a crack is seen to grow at approximately 45º to the direction of applied load (following the line of maximum shear stress). After traversing two to three grain boundaries its direction changes and then propagates at approximately 90º to the direction of the applied load. These are known as Stage I and Stage II cracks.
If we observe the development of a Stage I crack at high magnification we see the alternating stress leads to persistent slip bands forming along the planes of maximum shear. These bands slip back and forth, much like a deck of cards, and give rise to surface extrusions and intrusions. The surface intrusions essentially form an 'embryonic' crack. The Stage I crack propagates in this mode until it encounters a grain boundary, at which point it briefly stops until sufficient energy has been applied to the adjacent grain and the process continues.
After traversing two or three grain boundaries the direction of crack propagation now changes into a Stage II mode. In this stage the physical nature of the crack growth is seen to change. The crack itself now forms a macroscopic obstruction to the flow of stress that gives rise to a high plastic stress concentration at the crack tip. It should be noted that not all Stage I cracks evolve to Stage II.
In this section we investigate and explain conceptually the effect of the following parameters on fatigue crack growth rate:
We will see that Stress or Strain range has the most important influence.
From the previous description we notice that in both Stage I and Stage II growth, crack development arises through plastic shear strain on a microscopic scale. Consider, therefore, the plastic shear strain forming along the Stage I slip planes or at the tip of a Stage II crack as a result of the nominal stress time history.
The mean stress (residual stress) will also affect the rate of fatigue damage. Viewed conceptually, if a mean tensile stress is applied to a Stage II crack then the crack is being forced open and any stress cycles applied will therefore have a more pronounced affect. Conversely, if a mean compressive stress is applied then the crack will be forced shut and any stress cycle would first of all have to overcome the pre-compression before any growth could ensue. A similar concept applies for a Stage I crack.
Since fatigue cracks usually initiate from a pre-existing defect at the surface of a component, the quality of the surface will greatly influence the chance of a crack initiating. While most material test specimens have a mirror finish and therefore achieve the best fatigue lives, in practice most components are seldom as good and so we need to modify the fatigue properties. Surface finish has a more significant effect on the fatigue of components subjected to low amplitude stress cycles. The effect of surface finish can be modeled by multiplying the SN curve by the surface correction parameter at the endurance limit.
Surface treatments can be applied to improve the fatigue resistance of a component. These usually work by inducing a residual compressive stress at the surface. Under low amplitude cycles the stresses at the surface are significantly lower or even remain compressive. Therefore the fatigue life is greatly improved. We note, however, that this effect is only true for components subjected to low amplitude stress cycles. If large amplitude cycles were applied then these would start to overcome the pre-compression and the benefit would be lost. The effect of surface treatments can be modeled in the same way as surface quality.
In this section we have attempted to discuss the physics behind fatigue analysis in a practical and conceptual way. The main effects that influence fatigue performance have been addressed. We hope this paper has helped form a clearer picture on the key issues related to fatigue failure.
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