Piezo-electric ultrasonic fatigue machines are used to carry out fatigue tests more rapidly than what is possible using other technologies, at a frequency of $20\text{kHz}$. The very high cycle fatigue (VHCF) domain can be studied with these machines as ${10}^9$ cycles are reached within 14 h when specimens are loaded at stress amplitudes below the yield stress or conventional fatigue strength. The estimation of stress in specimens fatigued at high frequency is a current challenge when adopting this technology. This paper discusses the accuracy and reliability of three methods used to estimate stress amplitudes in specimens subjected to VHCF tests at a high loading frequency. Two historically used methods using strain gauges and a laser vibrometer are discussed and compared with a third, recently developed method based on time-resolved in situ X-ray diffraction (XRD). The three methods are applied to estimate the stress amplitude in a pearlitic steel specimen. The experimental artifacts and uncertainties are evaluated quantitatively to compare the benefits and limits of the methods. The experimental results show that the three methods correctly estimate the stress amplitudes applied to fatigued specimens.

压电超声波疲劳机用于执行疲劳测试比使用其他技术更快，频率为 $20\text{千赫}$. 可以使用这些机器研究甚高周疲劳 (VHCF) 域，如${10}^9$当试样以低于屈服应力或常规疲劳强度的应力幅度加载时，循环在 14 小时内达到。在采用该技术时，估计高频疲劳试样的应力是当前的挑战。本文讨论了用于估计在高加载频率下进行 VHCF 测试的试样的应力幅值的三种方法的准确性和可靠性。讨论了两种历史上使用应变计和激光测振仪的方法，并与最近开发的基于时间分辨原位 X 射线衍射 (XRD) 的第三种方法进行了比较。应用这三种方法来估计珠光体钢试样中的应力幅值。对实验工件和不确定性进行定量评估，以比较这些方法的优点和局限性。