# Assessment of Fatigue Life and Failure Criteria in Ultrasonic Testing Through Thermal Analyses
###### Abstract  
An experimental study was conducted to analyze temperature evolution during very high cycle fatigue tests. The temperature-number of cycles (T-N) curve is typically divided into three phases: **Phase I**--a rapid temperature increases at the start of the test, **Phase II**--temperature stabilization, and **Phase III**--a sharp temperature rise at the test's end, coinciding with specimen fracture. The high frequencies used in ultrasonic fatigue testing can induce self-heating in specimens, but the thermal effects are not yet fully understood. Temperature is known to influence the fatigue performance of materials. To explore this, specimens were subjected to varying stress levels and intermittent loading conditions while monitoring temperature evolution using infrared thermography. The T-N curves were obtained, and S-N curves were constructed for specimens tested at room temperature. All tests were performed under fully reversed loading conditions. The experimental data were used to evaluate models commonly applied in conventional fatigue testing. Additionally, the temperature gradient at the beginning of the ultrasonic fatigue test and the heat dissipation per cycle were estimated and analyzed as potential fatigue damage parameters. These findings indicate that parameters derived from the T-N curve have significant potential for predicting very high cycle fatigue life. v 2024 2025 20  
This study was made possible through extensive experimental results obtained using an ultrasonic frequency fatigue machine (20 kHz), which significantly reduced testing time [3, 4, 5, 6]. The development of this technology has greatly advanced the evaluation of very high cycle fatigue (VHCF), becoming crucial for designing structures and mechanical components capable of enduring high cycle counts throughout their service life. As mentioned, VHCF testing employs ultra-high-frequency loading, reducing test duration. However, elevated stress levels during testing can lead to significant temperature increases in the specimens, a phenomenon documented by several authors [6, 7, 8, 9, 10, 11]. Under certain conditions, excessive heating may result in specimen burning, adversely affecting the material's fatigue performance. The prediction of fatigue life for metallic materials remains a topic of ongoing research, with most studies relying on experimental data to fit predictive models. Traditionally, the fatigue life is estimated using the S-N curve, a method introduced by [PERSON] that is widely applied and well established in the literature. However, the S-N curve can be influenced by various operational factors, including frequency, temperature, stress levels, and environmental conditions [1, 2, 12]. Fatigue occurs when mechanical energy (work input) is transferred to a specimen. Part of this energy accumulates within the material, while the rest dissipates as heat, causing temperature increases during fatigue testing. When the specimen's temperature stabilizes, it indicates that the energy is fully dissipated [13, 14, 15]. Recently, thermodynamic approaches to understanding fatigue behavior have gained attention, particularly for analyzing self-heating phenomena in materials subjected to cyclic loading. These studies primarily focused on low cycle fatigue (LCF) and high cycle fatigue (HCF) regimes, proposing models correlating fatigue behavior with energy dissipation and temperature evolution. This paper aims to investigate temperature evolution, fatigue performance, and material behavior under VHCF testing using thermodynamic concepts. The objectives include the following:  
* Conducting experimental tests under various stress levels and intermittent loading conditions (different pulse and pause times) while monitoring temperatures using infrared (IR) thermography to develop temperature (T)-number of cycles (N) curves. * Estimating temperature gradients at the onset of fatigue testing (R\({}_{\Theta}\)) from the T-N curves and analyzing their dependence on stress levels and effective frequency (f\({}_{\text{eff}}\)).