A probabilistic model for quantifying the number of load cycles for crack nucleation at forging flaws in turbine rotor disks has been further developed [1]. This new fracture mechanics-based approach adequately describes the crack nucleation life. The model employs the range of plasticity-corrected stress intensity factor (Delta K-J) as the crack driving force correlating with crack nucleation cycles. Two different approaches for the calculation of Delta K-J are implemented and compared: I) The analytical solution calculates the stress intensity factor (K) and the plastic limit load based on flaw morphologies, types, boundary conditions, and material properties. Here, the failure assessment diagram (FAD) is considered to account for plasticity effects. II) The finite-element method is used to derive Delta K-J from the elastic-plastic J-integral. In the elastic-plastic finite element approach, a mesh convergence study was performed to reduce the effect of the element type and sizes on the numerical solution. As expected, it turns out that the numerical approach improves the accuracy of results due to the limited analytical validity ranges. Subsequently, a fracture mechanics-based crack nucleation model is developed by applying the numerically determined Delta K-J correlating with the experimental crack nucleation cycles. The numerical crack nucleation model shows conservative results compared to the analytical model. Furthermore, a probabilistic framework is proposed for both analytical and numerical crack nucleation models. An approach of integrating the crack nucleation models into the existing crack propagation model under the probabilistic framework is introduced.

The fatigue crack growth rate (FCGR) of austenitic stainless steel 1.4404 was measured in uncharged and in gaseous hydrogen precharged conditions, both as a function of temperature. At room temperature and Delta K < 40 MPa m(0.5), the FCGR of gaseous hydrogen precharged 1.4404 is by a factor of about 5 higher compared to the uncharged condition. FCGR as a function of temperature revealed a broad maximum at temperatures between 293 and 333 K. The temperature of maximum FCGR does not correlate with the temperature of maximum loss of tensile RA, which is about 220 K. A simplistic interpretation based on the respective governing mechanism, HEDE for FCGR tests and HELP for tensile tests, is proposed.

In this paper, experimental and numerical studies are performed to quantify the influence of overloads on the fatigue behaviour of the quenched and tempered steel 42CrMoS4 and the wrought aluminium alloy EN AW-6082 T6. The main objective is to incorporate the influence of overloads in the fatigue assessment. Three series of fatigue tests per material were performed, each under load control conditions, at R ═—1:i) constant amplitude loading (CAL) tests with no overloads; ii) CAL tests after five overload cycles of the magnitude OL 1; iii) CAL tests after five overload cycles of the magnitude OL 2. The respective overload levels are selected to achieve 75 % of the static strength of the test samples either estimated according to the FKM Guideline (2020) for OL 1 or determined directly by specimen testing for OL 2. During the overload cycles, the local notch strains were monitored by means of the digital image correlation (DIC) technique. X-ray diffraction was applied to quantify the residual stresses in the specimens due to manufacturing, after applying overload cycles, as well as after completing tests on runouts. Fatigue test results demonstrate that, depending on the material and the overload level, the fatigue strength can either decrease or increase or, in some cases, be only slightly affected by overloads. To explain the experimental findings, residual stresses determined from both experimental measurements and elastic-plastic finite-element analyses are included in the calculations of the notch stresses and strains and a fatigue damage parameter. The latter is then involved in the damage calculations to quantify the effect of overloads in terms of the magnitude and number of cycles to failure.

The fatigue life of welded joints under cyclic loading is a complex process that can be roughly divided into fatigue crack initiation, crack propagation and final fracture. Usually, these phases are evaluated separately. Several methods are available to estimate the extent of the different phases in welded components, such as stress-based fatigue concepts for crack initiation or linear elastic fracture mechanics for crack propagation; however, distinguishing these phases in welded components is a complex procedure and often relies on assumptions such as transition crack sizes. The objective of this study is to investigate the relationship between fatigue crack initiation and propagation in welded joints using artificially notched specimens with welded joints characteristics of different notch acuity (different radii and opening angle). The experiments show that the investigated relationship basically depends on the notch acuity, the load level and the stress ratio.

In this contribution, the notch strain approach is applied to seam welds including butt welds and filet welds. This allows the fatigue assessment for all regimes of fatigue life, including the low cycle fatigue regime (N > 10). Linear-elastic finite element analyses are used to determine the local stresses. The modeling of the geometry to be assessed is similar to that of the effective notch stress concept. Necessary input values besides linear-elastic stresses are estimated from the hardness of the heat-affected zone. Subsequently, the elastic–plastic stresses and strains are estimated, and a service life calculation is carried out. The used algorithm for the notch strain approach is based on the German FKM-guideline “nonlinear” and includes the influence of stress gradients, highly stressed surfaces, and the influence of surface roughness. Up to now, this FKM-guideline has only been approved for non-welded components. However, this article shows that, with a few modifications, it can also be applied to welds.

This study focuses on predicting the fatigue life of notched specimens with geometries and microstructure representative of welded joints. It employs 26 series of fatigue tests on welded and non-welded specimens containing notches located in different material zones, including the parent material, weld metal, and heat-affected zone. Overall, 351 test samples made of six structural steels are included in the present evaluation. For each individual specimen, the stress concentration factor, as well as the stress distribution in the notched section, was determined for subsequent fracture mechanics calculation. The latter is employed to estimate the fraction of fatigue life associated with crack propagation, starting from a small surface crack until fracture. It was shown that the total fatigue life can be realistically predicted by means of fracture mechanics calculations, whereas estimates of the fatigue life until macroscopic crack initiation are subject to numerous uncertainties. Furthermore, methods of statistical data analyses are applied to explore correlations between the S–N curves and the notch acuity characterized by the notch radius, opening angle, and the stress concentration factor. In particular, a strong correlation is observed between the notch acuity and the slope of the S–N curves.

We present a probabilistic model for quantifying the number of load cycles for nucleation of forging flaws-for a 3.5NiCrMoV high strength low alloy rotor steel-into a crack under gas turbine operating conditions. The model correlates low cycle fatigue data, ultrasonic testing indication data, flaw morphology, and type with the nucleation process. This paper is the third of a series of publications presenting this modeling approach progressively. It focuses on the effect of temperature variation on the nucleation life of forging flaws. We quantified the number of cycles to crack nucleation was for specimens that included forging flaws at elevated temperatures. Flaws of different sizes and shapes are effectively described at respective temperature and stress levels by either an ellipsoidal finite element model or an analytical area-based model. A local probabilistic low-cycle fatigue model analyzes the resulting stress distributions accounting for statistical size effects. Via Maximum Likelihood Estimation of these probabilistic low cycle fatigue results, a probabilistic model for crack nucleation of forging flaws is obtained. This proposed probabilistic model is based on experimental data for realistic heavy duty gas turbine rotor temperature and stress conditions. It can be utilized in the energy sector for component life time quantification. Our suggested approach can support component assessment under flexible gas turbines operation conditions driven by increased availability of intermittent renewable energy sources.

A probabilistic model for quantifying the number of load cycles for nucleation of forging flaws into a crack has been developed. The model correlates low cycle fatigue (LCF) data, ultrasonic testing (UT) indication data, flaw morphology and type with the nucleation process. The nucleation model is based on a probabilistic LCF model applied to finite element analyses (FEA) of flaw geometries. The model includes statistical size and notch effects. In order to calibrate the model, we conducted experiments involving specimens that include forging flaws. The specimens were machined out from heavy duty steel rotor disks for the energy sector. The large disks, including ultrasonic indications on the millimeter scale, were cut into smaller segments in order to efficiently machine specimens including manufacturing related forging flaws. We conducted cyclic loading experiments at a variety of temperatures and high stresses in order to capture realistic engine operating conditions for flaws as they occur in service. This newly developed model can be incorporated into an existing probabilistic fracture mechanics framework and enables a reliable risk quantification allowing to support customer needs for more flexible operational profiles due to the emergence of renewable energy sources.

Small scale fatigue tests aimed at determining the S-N diagram and the Miner Index to be adopted for fatigue damage assessment of railway axles were carried out within the frame of the frame of the research activities of EU funded EURAXLES project. Fatigue tests performed on steel grades EA4T and EA1N adopted by the European EN13103/13104 standards with both constant and variable amplitude loading are reported. The variable amplitude loading fatigue tests were carried out by using loading spectra derived from actual load measurements of fatigue bending moment in railway axles under significant service conditions. The consistent version of Miner's rule (according to the FKM-Guideline) with an allowable damage sum Dcrit = 0.3 adopted in combination with 2.5% percentile (p2.5%) of the S-N curve derived experimentally with small specimens proved to be adequate as design criterion, thus enabling the transferability of small scale fatigue tests to full scale railway axles that would lead to improved fatigue resistance of railway axles with new designs.

In this study, crack initiation and propagation under cyclic loading are first experimentally studied by testing specimens fabricated from a rotor material containing manufacturing defects. The latter represent clusters of non-metallic inclusion which size and location are examined by both ultrasonic testing (UT) and fractographic analyses. Three test specimens were extracted from a material block in such a way that the UT indications were located in the middle part of the cross-section. The specimens were then subjected to cyclic loading, applying tensile stresses with different magnitude and stress ratio. This test procedure produced beach marks on specimen fracture surfaces from which the crack initiation and propagation were backtraced. The experimental results suggest that a considerable number of cycles are required for a crack with a size corresponding to the UT indication to be formed. A numerical approach was then adopted for modeling damage accumulation and crack formation starting from a defect cluster. A material model was first calibrated to describe both the cyclic hardening behavior of the defect-free material and strain controlled low cycle fatigue tests. Subsequently, the model was applied to predict the damage evolution and crack formation at a defect group representative of that in one of the specimens studied.

This paper presents results of a study focusing on the effect of crack-tip constraint on the fracture behaviour of metallic materials. The principal goal is to validate two analytical methods for the consideration of constraint effects in engineering failure assessment – the R6/FITNET approach and the IST methodology. Those methods are briefly reviewed and applied to analyse available experimental data obtained in fracture tests on various cracked geometries and for two materials. Comparing to the conventional route which incorporates fracture toughness values derived in tests on highly constrained standard specimens, both methods provide an improved (less conservative) failure assessment. However, the assessment results from both methods are shown to be strongly dependent on the Weibull exponent which determination requires a certain level of expertise in the field of fracture mechanics. Since non-conservative results are possible when assuming high values, care should be taken to ensure a proper application of the respective assessment methodology.

Предложен способ реализации оптико-электронного контроля цветового отклонения полимерного покрытия оцинкованной полосы на основе нейро-нечеткой модели. Кроме того, определены основные параметры, которые влияют на цветовое отклонение, и предложен способ интеграции разработанной модели в производственную инфраструктуру на базе решений фирмы «Omron». Использование разработанной модели делает возможным прогнозирование полного цветового отклонения полимерного покрытия с ошибкой 4,7 %.

Press-fitted railway axles and wheels are subjected to fretting fatigue loading with a potential hazard of crack initiation in press fits. Typically, the resistance against crack initiation and propagation in press fits is investigated in full-scale tests, which procedure is both costly and time consuming. In this context, combined experimental and numerical approaches are of increasing practical importance, as these may reduce the experimental effort and, moreover, provide a basis for the transferability of experimental results to different axle geometries and materials. This study aims at evaluating stress–strain conditions under which fretting fatigue crack initiation is likely to occur. Experiments on small-scale specimens under varying fretting fatigue load parameters and their finite-element modelling to characterize the resulting stress–strain fields are performed. Subsequently, different multiaxial fatigue parameters are applied to predict crack initiation under fretting fatigue conditions.

This paper focuses on a comparison of different analytical methods for engineering failure assessment of components subjected to high thermal loading. The primary goal is to validate the analysis tools available within the FAD methodology and thus reduce the conservatism of the analytical assessment. Two well-known approaches based on the ρ and V factors, which have been established within the R6 code for taking into account the interaction of the primary and secondary stresses, are considered along with a recently developed Vg procedure. The analytical methods are validated on examples of two-dimensional crack geometries by varying the crack size, material strain hardening, and the ratio of the primary to secondary stresses. The accuracy of the analytical methods is judged by comparing the estimated elastic-plastic crack driving force with results of direct finite-element calculations. The traditional FAD approach incorporating the ρ and V factors is concluded to considerably overestimate the crack driving force, whereas the Vg method is shown to yield most accurate predictions.

Current design rules for railway wheelsets do not directly address issues related to fatigue crack propagation. Nevertheless, the latter topic is a part of the revised safety concept for passenger trains recently adopted in German railway applications. Numerous research activities, including international cooperative projects, have been conducted in the past decade aiming at quantifying fatigue crack growth rates in railway axles and estimating their inspection intervals based on the fracture mechanics methodology. This paper summarizes some experience and findings obtained by the authors within several studies dealing with the assessment of fatigue crack propagation in railway steels. Particular aspects highlighted in the paper include material characterization, effects of the specimen geometry and crack tip constraint on fatigue crack growth rates, stress analyses of axles and wheelsets, the derivation of stress intensity factor solutions applicable to specific conditions achieved in railway axles, considerations of the variability and scatter of geometrical parameters and material data in fatigue crack growth calculations.