An important aspect to fatigue design is ensuring that the load spectrum is representative of the stresses and strains actually experienced by the component during service. The distribution and number of stress cycles, and the order in which the loads are applied define the stress spectrum loading. For example, stress spectrum loading is used for testing spherical tanks for transporting liquid natural gas and for assessing fatigue performance of aircraft wings. Service load spectra can be estimated from typical operating conditions experienced by the component. This can be achieved by monitoring strain at critical regions of the component under service loads. For the purpose of life prediction, the spectrum loading is simplified.
Standard air spectra programs are available to simulate the load sequence for aircraft transport and military aircraft (e.g. Transport WIng STandard (TWIST) and Fighter Aircraft Loading STAndard For Fatigue Evaluation (FALSTAFF)). TWIST was designed to simulate the loading spectra for transport wing tension skins near the main landing gear attachment. The loading program allows for different types and levels of gust loadings. Both TWIST and FALSTAFF are available as commercial software packages.
Metal airframes are generally fatigue tested under spectrum loading conditions to a minimum of two lifetimes to ensure adequate fatigue life. A high structural reliability is generally guaranteed if the fatigue life of the structure is 2-4 times the lifetime of the structure. However, the high variability associated with fatigue life of composites means that the 2-4 lifetime fatigue criteria may not be sufficiently reliable, and hence the need to use larger life factors for fatigue design.
Figure 9: Blocking of constant amplitude cyclic stresses
The most common tool for estimating the fatigue life of a structure under continuous or block-spectrum loading conditions (Figure 9) is Palmgren-Miner (or Miner’s) rule. This rule estimates fatigue life by the following expression (see also Figure 10):
(4)
where Ng is the fatigue life under spectrum of loads, ai is the fraction of fatigue life for each stress load σi and Ni is the fatigue life at constant stress amplitude for stress level σi . For metallic structures, the accuracy of Miner’s rule is probably sufficient for preliminary design with test conformation required for fatigue-critical final designs.
Figure 10: Schematic of Palmgren-Miner rule
The Palmgren-Miner rule is only relevant when predicting the extent of damage induced under constant amplitude fatigue loading, which may be either continuous or blocked (see Figure 9). For bonded composite joints, Palmgren-Miner rule tends to be generally unreliable, providing non-conservative estimates of fatigue life. However, empirically derived values might prove useful to design. The order (i.e. load sequence) in which the stresses are applied can be expected to affect the fatigue life. There are indications that severe fatigue growth occurs due to load interactions [7]. The dependence of fatigue life on load sequence can be attributed to the effect of cumulative damage on the residual strength of the material. Modelling of this process is difficult.
A new model incorporating a ‘cycle mix’ factor [7] has been proposed for predicting fatigue life of bonded joints subjected to variable amplitude fatigue. The results obtained using this approach indicates a significant improvement in fatigue lifetime predictions.
Note: The basic principle for adhesive fatigue design is to ensure that the overlap length of the joint is sufficient to enable the adhesive shear stress to decay to near-zero to make the joint resistant to creep and load rate effects [8].
Next: General Approaches to Fatigue Design
