Dynamic stress analysis of the specimen gauge portion with a circular profile for the ultrasonic fatigue test

• Actual stress of hourglass-shaped specimen measured for the ultrasonic fatigue test.
• Compensation factors for the forced vibration and the gauge shape effects.
• Actual fatigue strength determination quantified in a VHCF range.

An hourglass-shaped specimen has been utilized for the ultrasonic fatigue test (UFT) at a resonance frequency around 20 kHz. Although the gauge portion of the actual test specimens was made with a circular arc shape, the stress along the gauge portion has been measured by the conventional stress equation assuming a gauge portion with the form of a hyperbolic cosine. In this study, stress distribution results by finite element analysis (FEA) in forced resonant vibration mode showed that the shape of a circular arc caused considerably higher stresses at the center of the gauge portion than did the hyperbolic cosine. The error of the stress equation occurring due to the difference in the gauge portion profile was compensated for by using the forced vibration factor (C1) and the gauge shape factor (C2). Thus, stress concentration effects in specimens with various gauge lengths were quantified to determine the actual fatigue strength.