Scaling Relationships of Vibration-Based Fatigue Testing

In advanced aerospace structures, including gas turbine engines, components are subjected to vibratory loading over many flight hours, making them vulnerable to high cycle fatigue. Thus, for a material to be safely used in these applications, it must first be characterized for its ability to withstand high cycle fatigue. To characterize these materials more quickly, vibration-based methods can quickly accumulate fatigue cycles by exciting a cantilevered plate specimen at one of its resonant modes until failure. For fatigue tests exceeding 1000 Hz, a resonant mode known as the “two-stripe” mode is often used, so named for its two node lines which extend from the clamped edge of the specimen to the opposite free edge. The two-stripe mode is especially desirable due to its existence at high frequencies and the presence of a large uniaxial bending stress along its free edge. In particular, the mode meets two key criteria: (1) the resonant frequency is sufficiently isolated from other neighboring modes such that they do not interfere with the mode shape, and (2) the ratio of stresses between the free edge of the plate and the clamped edge of plate is significantly greater than 1, such that fatigue failure occurs predictably in a place where it can be monitored by instruments.

Vibration-based fatigue testing with the two-stripe mode has predominantly been performed using square plate specimens, but in principle rectangular plates are equally valid. There has been little research done in determining how alternative dimensions impact the performance. Thousands of modal analysis simulations using ANSYS show that, while square plates meet the criteria, a rectangular plate having a length-to-width ratio of 1.37 inches may provide more favorable results. The purpose of this work is to validate the ANSYS simulations using a 1000 lb shaker from Data Physics Inc and a selection of plate dimensions from the modal analysis experiments. The plates are monitored with a laser vibrometer and subjected to sine sweeps to identify the frequencies of the two-stripe and other neighboring modes, thus validating the frequency isolation criteria. Select plates are further monitored by a pair of strain gauges to validate their stress ratios, thus validating the stress ratio criteria. Having validated the simulations, recommendations are given for how to quickly select preferable plate dimensions when planning a test around the operating frequencies of the test equipment. It is also found that the maximum strain in the plates appears to be a function only of plate thickness and the length-to-width ratio, not the overall size, which suggests that vibration-based fatigue testing can be extended to substantially higher frequencies when paired with a faster shaker.