Search Results (168)

This paper presents a numerical assessment of bending-fatigue durability in the tooth root region of cylindrical involute gears. Multiple gear pairs were modelled with different numbers of teeth and varying gear rim thicknesses. The generated geometry was implemented in the ANSYS 2025 R2 software suite, where the maximum normal stresses at critical locations in the tooth root region were determined through numerical simulation. A deformation-based method derived from Socie’s models was applied to estimate the duration of the phase leading up to fatigue crack formation in terms of load cycle accumulation. The gear geometry, together with the generated finite element mesh, was transferred to the FRANC2D/L version 4 software suite, where fatigue crack propagation was numerically simulated. Numerical analysis provided effective stress intensity factors, which then enabled an estimation of the number of load cycles required for an initiated crack to grow to the critical length associated with tooth failure. The total fatigue life in the tooth root region was evaluated as the sum of load cycles in the crack initiation phase and the crack propagation phase up to the critical crack length. The results show that all analysed factors exhibit very high resistance to fatigue fractures in the tooth root region. Furthermore, for gears with a rim thickness ratio greater than 0.7, the fatigue crack propagates through the tooth and reaches the fracture toughness limit of the material (K_Ic), whereas for lower rim thickness ratios, crack propagation occurs through the gear rim itself. Full article

This investigation elucidates the elevated-temperature (650 °C) monotonic mechanical response and very-high-cycle fatigue (VHCF) characteristics of Inconel 718 superalloys additively manufactured via selective laser melting (SLM), with a comparative assessment between the as-built and post-process heat-treated states. The results indicate that mechanical performance improves after heat treatment, primarily due to the formation of γ′ and γ″ precipitates, which interact with dislocations to strengthen the alloy. Relative to the as-built specimens, the fatigue strength of the specimen after heat treatment has increased by more than twice. For the as-built specimen, fatigue cracks nucleate at the specimen surface. However, in the high stress range, crack initiation in the heat-treated specimens consistently occurs at the free surface, whereas under low stress conditions, the crack initiation site transitions to the subsurface region encompassing internal defects. Post heat treatment, the fatigue crack trajectory adopts a markedly ductile and tortuous morphology, engendered by the concerted influence of grain-boundary (Laves/δ) precipitates that enforce repeated crack deflection, matrix-strengthening phases that homogenize plastic strain and the attendant reduction in local strain accumulation under the effect of cyclic load. Full article

Cast iron, whose structure simultaneously contains graphite precipitates in various forms, with controlled proportions of individual forms, has been named “Vari-Morph” (VM) cast iron by the authors. The authors have been researching the properties of such cast iron for many years, and the results are being published successively. This new type of cast iron, not included in national (Polish) or European standards, is intended as a material for special-purpose castings. These castings have unique requirements for a set of properties: physical, mechanical, and functional. VM cast iron is characterized by a set of properties that cannot be achieved when the graphite is uniform in shape. The desired properties of VM cast iron are achieved by controlling the morphology of graphite precipitates and the proportion of individual forms in the structure, rather than by changing the matrix. To quantitatively describe graphite precipitates, a proprietary method for determining the graphite shape indicator (f_K) was developed. Graphite precipitate analysis is performed by scanning a microscopic image of the metallographic specimen, and then using Tescan Imaging Software (Tescan ESSENCE™) Unified Control for Imaging and Analysis, each precipitate is described using surface metrology parameters. The final value of the graphite shape indicator (f_K) is calculated as a weighted average of all precipitates present in the analysis field. Empirical relationships between the f_K indicator and a selected group of physical, mechanical, and functional properties of VM cast iron were determined. Studies have demonstrated a very well-correlated relationship between the f_K indicator in VM cast iron and ultrasonic wave velocity (C_L). The relationship C_L = f(f_k) is characterized by a very high correlation coefficient of R > 0.90. In previous publications, the authors presented the relationships between the f_K indicator and physical properties such as thermal conductivity (λ), specific density (ρ), strength (R_m), elongation (A5), index quality (IQ), and functional properties such as low-cycle mechanical fatigue resistance (Z_c), thermal fatigue resistance (N), and cast iron tightness (H) as functions of the f_K index. The study concerned VM cast iron with a ferritic matrix. This work contains new empirical relationships that extend previous studies. The newly developed relationships replace the f_k shape indicator with the velocity of the ultrasonic wave determined in cast iron with a specific f_K indicator value. This resulted in a number of practical dependencies, including: λ = f(C_L); ρ = f(C_L); E_D = f(C_L); R_m = f(C_L); A5 = f(C_L); IQ = f(C_L); N = f(C_L); Z_c = f(C_L); H = f(C_L). These relationships allow us to measure the wave velocity in a Vari Morph iron casting (with various forms of graphite) and determine a number of characteristics and properties of the material/iron from which the casting was made. It is possible to assess the suitability of a casting with a specific structure for operation under selected conditions. Full article

With the height of wind turbine towers increasing, the high-cycle fatigue performance of high-strength concrete has become important for structural design. This study systematically investigates the fatigue life, strain evolution, and stiffness degradation of C80 concrete under constant-amplitude cyclic compressive loading for a maximum stress level ranging from 0.70 to 0.90 and a minimum stress level of 0.10. Based on experimental data, S–N curves are obtained, and a prediction model of fatigue life and stiffness degradation is developed. The results reveal that fatigue strain evolves through three stages and that the second stage accounts for more than 90% of the overall fatigue life, exhibiting linear growth over time. The final strain in the second stage is very close to that in static compression tests, indicating the uniqueness of fatigue strain. In addition, the final strain in the second stage provides a better prediction of fatigue life than an S–N curve and facilitates real-time fatigue life prediction. Meanwhile, the stiffness degradation model more accurately simulates the stiffness degradation process of C80 concrete under fatigue load, laying a foundation for further finite element analysis of fatigue. This study addresses the gap in fatigue life prediction and stiffness degradation modeling for C80 concrete under high-cycle fatigue load, providing a valuable reference for designing safe and durable high-strength concrete structures such as wind turbine towers. Full article

This review presents a comprehensive examination of the total fatigue life behaviour of high-strength steels (HSS) with particular emphasis on fatigue crack initiation in the very high cycle fatigue (VHCF) regime and crack propagation based on fracture mechanics. The discussion draws on recent advances in experimental techniques, microstructural characterisation, and analytical approaches by reviewing studies conducted over the past few years. Key factors influencing fatigue performance, including loading frequency, specimen geometry, microstructure, and environmental conditions, are critically evaluated. The review concludes by highlighting existing knowledge gaps and outlining directions for future research aimed at improving the understanding and optimisation of fatigue performance in current and next-generation HSS. Full article

Very-high-cycle fretting fatigue (VHCFF) behavior at elevated temperatures is critical for the safety and longevity of aerospace components. This study investigates the VHCFF mechanisms of laser-clad IN718/20%WC composite coatings at 650 °C. Fatigue tests were conducted to generate S-N data, and the resulting wear and fracture morphologies were characterized. Crack initiation was found to preferentially occur in grains exhibiting higher Schmid factors, lower elastic moduli, and larger equivalent sizes. To simulate fretting fatigue, a crystal plasticity finite element model (CPFEM) incorporating the actual microstructure was developed. An improved fatigue indicator parameter (FIP) was proposed, which integrates multiple physically significant factors including plastic strain, dislocation density, elastic modulus, and grain size. Life predictions based on a critical FIP value demonstrated high accuracy, with 97.6% of the results falling within a ±3.5 scatter band of the experimental data, confirming the model’s effectiveness in predicting crack initiation life. Full article

Rapid characterization of high-cycle fatigue behaviour is of great interest, since conventional methods for developing S-N curves for longer fatigue lives are both costly in time and financial resources. Ultrasonic fatigue testing offers a promising alternative by enabling S-N curve evaluation in a fraction of the time, often hundreds of times faster, due to its high testing frequencies. Nevertheless, this technique presents specific challenges, including material overheating and limitations in specimens’ geometry. Most ultrasonic fatigue studies employ hourglass specimens; however, this geometry restricts the testing of sheets and thin-walled components, which are increasingly used for their reduced mass and high stiffness-to-mass ratio. To overcome this limitation, the present work introduces a methodology for designing and testing flat specimens and corresponding gripping systems tailored to such components. The procedure is demonstrated for an aluminium alloy (6082), and preliminary experimental fatigue results are presented and compared with literature. Full article

The increased test frequency inherent in Ultrasonic Fatigue Testing (UFT) is commonly observed to result in an increased fatigue resistance for ferritic, low-carbon steels. In this investigation, the fatigue response of S275J2 ferritic structural steel is evaluated at both 20 kHz and 50 Hz. At the ultrasonic frequency, an increase in the fatigue limit of 136 MPa and an increase in the finite life region of 150 MPa was observed, alongside a reduction in the slope of the S-N curve. By combining the S275J2 results with additional data from the literature, generalised versions of previously proposed frequency sensitivity models are produced by evaluating the model coefficients as a function of different combinations of the material properties. Additionally, a new frequency sensitivity model was proposed by evaluating the empirical change in the S-N curve coefficients as a function of these material properties. For all of the models, it was found that the best correlation was against the ferrite content divided by the tensile strength. The generalised forms of these models were rearranged to produce correction factors, which allow the conventional frequency fatigue response to be estimated based on the UFT test. The most reliable correction method was found to be using the empirical change in the S-N curve exponent. Full article

In this paper, very high cycle fatigue (VHCF) strengths are first evaluated for the TC17 titanium alloy and the welding joint of the 6005A-T6 aluminum alloy using the up-and-down method (UDM) and continuous testing method (CTM). Then, the influence of the sample size on the lower limit of the high cycle and VHCF strength (10⁷, 10⁸ and 10⁹ cycles) is investigated based on the experimental data and the previous results for aluminum alloys, steels and titanium alloys. It indicates that, compared to the common size of 15 samples used for the UDM, a sample size of 10~14 can generally give an acceptable evaluation of the lower limit of fatigue strength (LLFS) at 90% and 95% survival probabilities (SPs) and 95% confidence for both the UDM and CTM. The absolute value of the relative difference value of the result of 10~14 samples compared to that of 15 samples is generally within 5%. In addition, the UDM could give very dangerous evaluated results, and it fails to evaluate the LLFS in some cases. The CTM deals with all the testing results and gives a safe evaluation of the LLFS. Ten samples and an LLFS at 90% SP and 95% confidence can be preferred for fatigue strength evaluations using the CTM in a high cycle and VHCF regime. Full article

B is considered a valuable additive for TiAl alloys, because it is believed to improve their properties by refining their microstructures. However, the effects of B on the practical properties of TiAl alloys for jet engine blades and the optimal addition amount for achieving balanced properties remain unclear. Specifically, there have been very few studies to date in which the practical properties of alloys have been evaluated across a wide range of B addition levels. Therefore, we evaluated various reliability, cost, and performance properties of jet engine blade materials using cast Ti-45,47Al-2Nb-2Mn (the same as XD alloys), with varying B addition levels. The results showed that, in some cases, low B addition levels (0.1–0.2 at.%) could enhance the impact resistance and high-cycle fatigue performance. However, even low B addition levels negatively impacted the machinability, castability, and creep strength. Further, adding 0.4 B or more significantly reduced most practical properties. Compared to XD alloys, TiAl4822 exhibited a superior balance, which is attributed to the higher B content (1 at.%) in XD alloys and the greater effectiveness of Cr relative to Mn in improving the alloy’s high-temperature impact resistance. Full article

Understanding the fatigue behavior of materials is essential for designing components capable of enduring prolonged use under varying stress conditions. This study investigates the high-cycle fatigue and fatigue crack growth characteristics of X17CrNi15-2 stainless steel. Very high-cycle fatigue (VHCF) and fatigue crack growth tests were conducted on conventional fatigue and compact tension (CT) specimens fabricated from X17CrNi15-2 stainless steel. The fatigue crack growth behavior of the CT specimens was analyzed using Paris’ law. A revised version of Paris’ law was suggested based on the fatigue crack growth rate plotted against the stress intensity factor range, expanding on prior research utilizing three-point single-edge notch bend specimens. Scanning electron microscopy (SEM) was employed to examine the fracture mechanisms of both fatigue specimen types. The results indicated that the fatigue specimens failed in the VHCF regime under stress amplitudes ranging from 100 to 450 MPa. A power law correlation between stress amplitude and fatigue life was established, with material constants of 7670.3954 and −0.1663. These findings offer valuable insights into the material’s performance and are crucial for enhancing its suitability in engineering applications where high-cycle fatigue is a critical factor. Full article

The mechanical and structural design of railway vehicles is heavily influenced by their lifetime. Because fatigue is a significant factor that impacts the longevity of railway components, it is imperative that the fatigue resistance properties of crucial components, like leaf springs, be thoroughly investigated. This research investigates the fatigue resistance of 51CrV4 steel under bending and axial tension, considering different stress ratios across low-cycle fatigue (LCF), high-cycle fatigue (HCF), and very-high-cycle fatigue (VHCF) regimes, using experimental data collected from this work and prior research. Data included fractographic analyses aiming to help in understanding some of failures for different loads. The presence of geometric discontinuities, such as notches, amplifies stress concentrations, requiring a probabilistic approach to fatigue assessment. To address notch effects, the theory of critical distances (TCD) was employed to evaluate fatigue strength. TCD model was integrated in fatigue statistical models, such as the Walker model (WSN) and the Castillo–Fernández-Cantelli model adapted for mean stress effects (ACFC). Extending the application of the TCD theory, this research provides an improved probabilistic fatigue model that integrates notch sensitivity, mean stress effects, and fatigue regimes, contributing to more reliable design approaches of railway leaf springs or other components produced in 51CrV4 steel. Full article

As high-speed electric multiple units (EMUs) advance in speed and complexity, quasi-static design methods may underestimate the fatigue risks associated with high-frequency dynamic excitations. This study quantifies the contribution of gear meshing-induced vibrations (2512 Hz) to fatigue damage in EMU gearbox housings, revealing resonance amplification of local stresses up to 1.8 MPa at 300 km/h operation. Through integrated field monitoring and bench testing, we demonstrated that gear meshing excites structural modes, generating sustained, very high-cycle stresses (>10⁸ cycles). Crucially, fatigue specimens were directly extracted from in-service gearbox housings—overcoming the limitations of standardized coupons—passing the very high-cycle fatigue (VHCF) test to derive S-N characteristics beyond 10⁸ cycles. Results show a continuous decline in fatigue strength (with no traditional fatigue limit) from 10⁸ to 10⁹ cycles. This work bridges the gap between static design standards (e.g., FKM) and actual dynamic environments, proving that accumulated damage from low-amplitude gear-meshing stresses (3.62 × 10¹¹ cycles over a 12 million km lifespan) contributes to a 16% material utilization ratio. The findings emphasize that even low-magnitude gear-meshing stresses can significantly influence gearbox fatigue life due to their ultra-high frequency, warranting design consideration beyond current standards. Full article

The Ti-6Al-4V alloy is a typical α + β type titanium alloy and is widely used in the manufacture of aero-engine fans, compressor discs and blades. The working life of modern aero-engine components is usually required to reach more than 10⁸ cycles, which makes the infinite life design based on the traditional fatigue limit unsafe. In this study, through symmetrical loading high-cycle fatigue tests on Ti-6Al-4V titanium alloy, a nonlinear cumulative damage life prediction model was established. Further very-high-cycle fatigue tests of titanium alloys were carried out. The variation law of plastic strain energy in the evolution process of very-high-cycle fatigue damage of titanium alloy materials was described by introducing the internal stress parameter. A prediction model for the very-high-cycle fatigue life of titanium alloys was established, and the sensitivity analysis of model parameters was carried out. The results show that the established high-cycle/very-high-cycle fatigue models can fit the test data well. Moreover, based on the optimized model parameters through sensitivity analysis, the average error of the prediction results has decreased from 59% to 38%. The research aims to provide a model or method for predicting the engineering life of titanium alloys in the high-cycle/very-high-cycle range. Full article

This work presents a multiscale, microstructure-aware framework for predicting fatigue strength distributions in additively manufactured (AM) alloys—specifically, laser powder bed fusion (L-PBF) AlSi10Mg and Ti-6Al-4V—by integrating density functional theory (DFT), instrumented indentation, and Bayesian inference. The methodology leverages principles common to all 3D printing (additive manufacturing) processes: layer-wise material deposition, process-induced defect formation (such as porosity and residual stress), and microstructural tailoring through parameter control, which collectively differentiate AM from conventional manufacturing. By linking DFT-derived cohesive energies with indentation-based modulus measurements and a MAP-based statistical model, we quantify the effect of additive-manufactured microstructural heterogeneity on fatigue performance. Quantitative validation demonstrates that the predicted fatigue strength distributions agree with experimental high-cycle and very-high-cycle fatigue (HCF/VHCF) data, with posterior modes and 95 % credible intervals of ${\widehat{\sigma }}_f^{\mathrm{AlSi}10\mathrm{Mg}}={86}_{-7}^{+8}\mathrm{MPa}$ and ${\widehat{\sigma }}_f^{\mathrm{Ti}–6\mathrm{Al}–4\mathrm{V}}={115}_{-9}^{+10}\mathrm{MPa}$, respectively. The resulting Woehler (S–N) curves and Paris crack-growth parameters envelop more than 92 % of the measured coupon data, confirming both accuracy and robustness. Furthermore, global sensitivity analysis reveals that volumetric porosity and residual stress account for over 70 % of the fatigue strength variance, highlighting the central role of process–structure relationships unique to AM. The presented framework thus provides a predictive, physically interpretable, and data-efficient pathway for microstructure-informed fatigue design in additively manufactured metals, and is readily extensible to other AM alloys and process variants. Full article