Types of loading and the definition of a cycle

As fatigue damage is caused by loading a structure with alternating loads over a period of time, it is useful to define common types of load histories.

One channel of a load history is either of constant amplitude or variable amplitude. Constant amplitude loading is cyclic loading to the same load amplitude, and may include a mean stress for the cycles. Variable amplitude loading is anything other than constant amplitude loading. Examples of constant and variable amplitude loading histories are shown in the figures Constant Amplitude Load History and Variable Amplitude Load History below.

Constant Amplitude Load History

Variable Amplitude Load History

The definition of a cycle for constant amplitude loading is straightforward and follows the definition from trigonometry. In the figure Constant Amplitude Load History (above) the properties used to define a cycle are presented:

Property	Symbol	Formulae
Maximum or peak	Lu
Minimum or valley	L1
Range	ΔL
Amplitude	La
Mean Load	Lm
R-ratio	R

Note:

For stress or strain histories, the definitions are similar: just exchange the symbol L with σ or ε.

For variable amplitude loading, a complete cycle may not be as readily identified because of the possibility of sub-cycles superimposed on a larger amplitude cycle. To avoid any ambiguity, the definition of a full cycle will be taken as a load sequence that produces a closed loop in the stress-strain response of the material. The determination of cycles from loading histories are discussed in more detail in Damage-based data reduction methods.

For load histories with multiple channels, there are additional classifications of proportional or non-proportional loading. A proportional multiple channel load history has a constant of proportionality among each of the channels in the set (figure Proportional Multiple Channel Load History below), and is in contrast to non-proportional multiple channel load history (figure Non-Proportional Multiple Channel Load History below), where there is not a single constant of proportionality among each of the channels in the set.

Proportional Multiple Channel Load History

Non-Proportional Multiple Channel Load History

The terms uniaxial and multiaxial are sometimes used with regard to loading histories and stress histories. The meaning of the terms will depend on the context in which they are used. In some cases, they will refer to load histories with single or multiple load channels, respectively, and in other cases the terms will refer to the description of the local stress state at a point in the structure.

Another term that is often used in the context of load histories is block cycle loading or block loading. Any load history that repeats itself can be considered a block of loading. For example, the variable amplitude history in the figure Variable Amplitude Load History (see Concepts in common) may correspond to the load response of a component for one lap of a test track. If multiple laps give the same load response, then the history of figure Variable Amplitude Load History could be used repeatedly to yield the same fatigue result as a history containing all of the laps. In this case, the load history of figure Variable Amplitude Load History would be considered as one block.

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Types of loading and the definition of a cycle, Simcenter 3D 2021.1 Series

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