Statistical evaluation of the critical distance in the finite life fatigue regime

The procedure to evaluate the critical distance with an optimized V-notched specimen is initially reviewed in the paper. This procedure was devised by the authors, and another numerical methodology was recently proposed to evaluate the uncertainty of the critical distance assessment. The input of the analysis is the combination of the statistical distribution of the fatigue properties from which the critical distance is deduced. After assuming the specimen fatigue strengths as Gaussian (normal) distributions, the critical distance turns out to be well represented by a Skew-normal distribution. This statistical assessment is extended to the finite fatigue life, in the present paper, showing experimental results for the aluminium alloy 7075-T6 at two load ratios. The fatigue strength of other specimens are finally evaluated, reconsidering the critical distance deviation, thus providing a complete uncertainty analysis of the critical distance assessment, and a successful comparison with the experimental scatter is obtained

Inverse determination of the fatigue Strain Energy Density control radius for conventionally and additively manufactured rounded V-notches

The Strain Energy Density (SED) fatigue criterion is based on a material control radius. The value of this length is therefore required for an accurate assessment of the fatigue strength of any, especially severely, notched components. The singularity-based control radius is initially obtained by considering the hypothetical perfectly sharp V-notched specimen. The effect of the notch radius on the inverse search is then investigated with numerical simulations, and a new analytical procedure is introduced for the determination of the (actual) control radius. This procedure is applied to the experimental data of three metal alloys with different load ratios and manufacturing conditions

sensibility analysis of the fatigue critical distance values assessed by combining plain and notched cylindrical specimens

Abstract The material critical distance is often deduced from plain and notched specimens, instead of experimentally measuring the (long) crack threshold, which is a challenging task and not adequate in some cases. A dedicated V-notched specimen was proposed along with a dimensionless numerical procedure to derive the critical distance from the fatigue stress concentration factor, by implementing both the line and the point methods. An experimental validation activity is provided here on 42CrMo4+QT steel, focusing on how the critical distance result is sensitive to the actual local radius, the specimen sharpness, and the choice between the line or the point method. The determination of the critical distance with the point method systematically provides higher values than the line method. However, these length discrepancies do not produce large effects in terms of the component strength assessment if the same method for the fatigue limit evaluation is used. By alternatively considering the specimen not involved in the critical distance determination, as a potential design component, the prediction accuracy was evaluated. This analysis confirmed that a small notch radius is recommended for the fatigue strength assessment of larger radius notches or even of a crack, whereas by deducing the critical distance from a blunt notch, a noticeable inaccuracy can be found on smaller radius and crack threshold

optimal notched specimen parameters for accurate fatigue critical distance determination

Abstract The critical distance value should theoretically be determined from the plain specimen fatigue limit and the threshold stress intensity factor, though usually ordinary notch geometries are considered. In this paper, we proposed an optimized sharp notch with the aims of simple and reliable manufacture and, more importantly, a local strong stress gradient able to minimize the sensitivity on the deduced critical distance value. A numerical procedure is proposed to find the critical distance from the fatigue strength of the notched specimen, by implementing the line method with simple formulas based on dimensionless equations and specific coefficients derived from accurate FE analyses. A definition of the boundaries for a valid critical distance evaluation is also introduced and discussed. Finally, an application example is provided on a quenched and tempered steel also comparing the obtained critical distances with the threshold derived values

Statistical significance of notch fatigue prognoses based on the strain-energy-density method: Application to conventionally and additively manufactured materials

The inverse search determination of the strain-energy–density (SED) control radius R1 devised in Benedetti et al. Int J Fatigue 2019;126:306–318 and based on the knowledge of the notch fatigue factor estimated using an optimal V-notch specimen geometry is here reformulated to take into account the statistical properties of the input fatigue properties. It was found that R1 exhibits a non-symmetric probability density function that is well represented by a skew-normal distribution. The uncertainty in R1 can be attributed to the uncertainty in the inverse search procedure and to the material variability in notch sensitivity. By applying the devised procedure to real experimental data, it was found that the former contribution is preponderant in the assessment of very sharp notches, while the latter dictates the fatigue strength of blunt notches, especially in the case of intrinsically flawed materials, such as those additively manufactured

Validation of a strain gauge rosette setup on a cantilever specimen: Application to a calibration bench for residual stresses

It is commonly known that the most difficult part of measuring residual stresses through diffraction or relaxation methods is the high sensitivity of the results to input errors, such as noise in the strain data. Then, quantifying and minimizing stress uncertainties is at least as important as the residual stress results themselves. Results are often validated by leveraging different measurement techniques, although each method is somehow specialized at detecting residual stresses at different locations and length scales. This leads to a fundamental lack of ground truth data and an inherent difficulty in detecting biases. The authors have introduced a calibration bench that facilitates the application of a well-known bending stress distribution on a specimen while conducting residual stress measurements using either the Hole-Drilling Method (HDM) or X-ray Diffraction (XRD). By leveraging Bueckner's superposition principle, the bench allows for determination of both the residual stress distribution and the reference stress distribution through a single experimental setup. This approach not only enables direct evaluation of accuracy but also identification of any procedural systematic errors, as the reference stress distribution is known with a high degree of certainty. In this work, a detailed characterization of the stress and strain fields generated by the externally applied load was pursued. Then, the calibration bench was used to perform a validated characterization of residual stresses produced by two shot peening treatments, through both XRD and HDM. Additionally, both techniques were employed to verify the recognized bending stresses, thereby validating the findings of the residual stress measurements

Determination of the fatigue critical distance according to the Line and the Point Methods with rounded V-notched specimen

The critical distance length should in principle be deduced from the plain specimen fatigue limit and the threshold stress intensity factor range. However, the threshold range is difficult to measure experimentally, hence this length is usually obtained by means of a notched specimen. The critical distance inverse search, both according to the Line and the Point Methods, is presented in this paper referring to a relatively sharp V-notched specimen. Precise indications about the geometry parameters are given along with a complete analytical procedure to easily obtain the critical distance. A sensitivity analysis is discussed, providing evidence of a critical distance range for a well-posed inversion problem

Automated Experimental Modal Analysis of Bladed Wheels with an Anthropomorphic Robotic Station

Experimental modal analysis is challenging when the component has a highly three-dimensional shape, since a great number of measurement points are needed with accurate positioning. An anthropomorphic robotic station is proposed to automate this analysis, specifically on bladed wheels. This provides a reliable control of the spot location and of the beam orientation of a Laser Doppler Vibrometer. The modal frequencies were obtained along with the vibrational shapes and their spatial resolution was managed by exploiting the programming flexibility of the robotic station. The SAFE diagram was easily obtained by measuring a single point for each sector, and an extension of this diagram was demonstrated for the splitter blade wheels. The use of multiple measurement points, for each wheel sector, significantly improved the characterization of the modes having the same number of nodal diameters, hence the same shape coordinate on the SAFE diagram

A fretting fatigue setup for testing shrink-fit connections and experimental evidence of the strength enhancement induced by deep rolling

Fretting tests are usually performed on flat specimens with lateral contacting pads. The shrink-fitted connection, which experiences fretting at the edge of the contact, prompted the alternative use of a round-shaped specimen. This simplified the equipment and provided an accurate alignment between the fretting specimen and the external hub which plays the role of the pad. The deep rolling treatment can also be efficiently applied to a round shape, which would otherwise be difficult on the flat specimen geometry. After introducing this solution for fretting testing, the paper shows an experimental campaign on three shrink-fitted connections with different sizes and material combinations. There was a significant improvement in fretting fatigue strength, induced by the deep rolling, for all three specimen types. Finally, scanning electron microscopic analyses provided insights into the fretting fatigue nucleation mechanisms both for untreated and deep-rolled specimens

Surface and subsurface rolling contact fatigue characteristic depths and proposal of stress indexes

The rolling contact fatigue is distinguished into subsurface initiated (spalling and case crushing) and surface initiated (pitting and micropitting). A characteristic depth was identified for each of these mechanism. The characteristic depth of the case crushing is the hardening depth, while for the spalling it is the maximum cyclic shear stress depth. The pitting depth is the size of the crack for which the mode I stress intensity factor range, due to the fluid pressurization, is higher than the threshold. This depth can be similar to the micropitting depth, in the order of 10 µm, for heavily loaded small radius contacts. Rolling contact fatigue cyclic shear stress indexes are then defined on the basis of the characteristic depths, and they identify the load intensity of each rolling contact fatigue mechanism. The characteristic depths and the stress index approach can be used to relate specific tests to component design, without any size effect misinterpretation