The research on the Very High Cycle Fatigue (VHCF) response of materials is fundamental to guarantee a safe design of structural components. Researchers develop models for the fatigue life in VHCF, aiming at assessing the stress–life relation and, accordingly, the probabilistic S–N (P‐S–N) curves. In the paper, the models for the stress–life relation in VHCF are comprehensively reviewed. The models are classified according to the approach followed for defining the stress–life dependency, that is, power law, probabilistic, fracture mechanics, or Paris law‐based approach. The number of failure modes that can be modeled, the statistical distribution for the fatigue life, and the characteristics of the estimated P‐S–N curves are also reviewed by analyzing the fitting capability of experimental datasets for each model. This review is supposed to highlight the strengths and weaknesses of the currently available models and guide the future research.

It is well-known that many manufacturing parameters affect the quasi-static and the fatigue response of additive manufacturing (AM) parts. In particular, due to the layer-by-layer production, the load orientation, with respect to the building direction, plays a fundamental role for the fatigue response. This paper investigates the fatigue response up to 10⁹ cycles (very high cycle fatigue (VHCF)) of selective laser melting (SLM) AlSi10Mg specimens built in a vertical direction. Ultrasonic tension-compression tests (stress ratio of –1) are carried out on as-built Gaussian specimens with a large loaded volume (2300 mm³). Fracture surfaces are investigated with the scanning electron microscope to analyze the defects originating the VHCF failure. Probabilistic S-N curves are estimated and analyzed. Experimental results confirm that the defect size controls the VHCF response, thus highlighting the importance of testing large risk volumes for a reliable assessment of VHCF behavior. The average value of the VHCF strength is close to that of the hourglass specimen tested in the literature. The variability of the VHCF strength is instead significantly larger, due to the scattered size distribution of the defects located near the specimen surface, which is the most critical region for crack initiation.

The research on the size-effects in Very-High-Cycle Fatigue (VHCF) has recently drawn the attention of several scholars. The fatigue cracks in VHCF originate from the largest defect present within the loaded material volume (risk-volume) and the larger the risk-volume, the larger the probability of critical defects affecting the VHCF response (size-effect). Many models have been proposed in the literature to deal with size-effects in VHCF. However, the proposed models cannot be validated on full-scale components, since VHCF tests are typically carried out with ultrasonic fatigue testing machines. The authors have proposed a specimen geometry, the so-called Gaussian specimens, to enlarge as much as possible the risk-volume in ultrasonic VHCF tests. In this study, fully reversed tension–compression ultrasonic VHCF tests up to 10⁹ cycles were carried out on AISI H13 steel Gaussian specimens with a risk-volume of 5000 mm³, two times larger than the largest tested in the literature. The stress distribution and the absence of bending loads were verified with strain gages, proving that VHCF tests on risk-volumes of 5000 mm³ can be reliably carried out. Ultrasonic VHCF tests were also carried out on small hourglass specimens, confirming that larger risk-volumes allow for a more reliable design against VHCF failures.

Modern structures are designed to withstand in-service loads over a broad frequency spectrum. Nonetheless, mechanical properties in numerical codes are assumed to be frequency-independent to simplify calculations or due to a lack of experimental data, and this approach could lead to overdesign or failures. This study aims to quantify the frequency effects in the fatigue applications of a bi-material adhesive joint through analytical, numerical, and experimental procedures. Analytical and finite element models allowed the specimen design, whereas the frequency effects were investigated through a conventional servo-hydraulic apparatus at 5, 25, and 50 Hz and with an ultrasonic fatigue testing machine at 20 kHz. Experimentally, the fatigue life increases with the applied test frequency. Run-out stress data at 10⁹ cycles follow the same trend: at 25 Hz and 50 Hz, the run-out data were found at 10 MPa, increasing to 15 MPa at 20 kHz. The P–S–N curves showed that frequency effects have a minor impact on the experimental variability and that standard deviation values lie in the range of 0.3038–0.7691 between 5 Hz and 20 kHz. Finally, the trend of fatigue strengths at 2·10⁶ cycles with the applied loading frequency for selected probability levels was estimated.