Uncertainty in fatigue loading: Consequences on statistical evaluation of reliability in service

A design-by-reliability approach is ever more required and accurate design inputs are needed to meet reliability targets while reducing costs. Different models have been proposed in the literature to describe fatigue life variation with respect to the applied stress by assuming the applied stress as a deterministic independent variable and the fatigue life as a dependent random variable. In the paper also the applied stress is considered as a random variable with its own uncertainty and the procedure to valuate the error on the estimation of parameters usually adopted in service reliability assessment of structural components is shown. Exact equations are proposed for some special cases and an illustrative example showing the reliability errors originated by applying the ASTM recommendations is give

VHCF strength decrement in large H13 steel specimens subjected to ESR process

Failures at very high number of cycles (Very-High-Cycle Fatigue, VHCF) generally originate from inclusions or defects present within the material. VHCF response of materials is therefore strongly affected by the defect population and, in particular, by the characteristic defect size, which statistically increases with the material volume. According to this well-known dependency, Size Effects were found to significantly affect the VHCF strength of high-strength steels. The paper aims at assessing the influence of Size Effects on the VHCF response of a high performance AISI H13 steel subjected to Electro Slag Remelting (ESR) refinement process. Ultrasonic VHCF tests were carried on specimens characterized by different loaded volumes (hourglass and Gaussian specimens). Experimental results showed that Size Effects strongly influences the VHCF response of the investigated high performance steel, even if it is characterized by a high degree of purity and by a population of inclusions with limited size

Effect of defect size on P-S-N curves in Very-High-Cycle Fatigue

It is well-known that internal defects play a key role in the Very-High-Cycle Fatigue (VHCF) response of metallic materials. VHCF failures generally nucleate from internal defects, whose size strongly affects the material strength and life. Therefore, S-N curves in the VHCF regime are defect size dependent and the scatter of fatigue data is significantly influenced by the statistical distribution of the defect size within the material. The present paper proposes an innovative approach for the statistical modeling of Probabilistic-S-N (P-S-N) curves in the VHCF regime. The proposed model considers conditional P-S-N curves that depend on a specific value of the initial defect size. From the statistical distribution of the initial defect size, marginal P-S-N curves are estimated and the effect of the risk-volume on the VHCF response is also modeled. Finally, the paper reports a numerical example that quantitatively illustrates the concepts of conditional and marginal P-S-N curves and that shows the effect of the risk-volume on the VHCF response

A general model for crack growth from initial defect in Very-High-Cycle Fatigue

It is well-known in the literature that internal defects play a major role in the Very-High-Cycle Fatigue (VHCF) response of metallic materials. Generally, VHCF failures nucleate from internal defects characterized by a limited size. Unexpectedly, it has been found that cracks can grow from the initial defect even if the Stress Intensity Factor (SIF) is quite below the characteristic threshold for crack growth. Even though researchers unanimously accept this singular experimental evidence, they still dispute about its physical justification. Different micromechanical explanations have been proposed in the literature: local grain refinement, carbide decohesion, matrix fragmentation, hydrogen embrittlement, numerous cyclic pressure and formation of persistent slip bands are the most famous proposals. Regardless of the specific micromechanical explanation, it is generally acknowledged that a weakening mechanism occurs around the initial defect, thus permitting crack growth below the SIF threshold. The present paper proposes an innovative approach for the quantitative modeling of the weakening process around the initial defect. The proposed model considers an additional SIF that reduces the SIF threshold of the material. Starting from a very general formulation for the additional SIF, possible scenarios for crack growth from the initial defect are also identified and described. It is theoretically demonstrated that, depending on the scenario, a VHCF limit may also be present and its final formulation recalls the well-known expression previously proposed by Murakami

Gaussian Specimens for Gigacycle Fatigue Tests: Damping Effects

Experimental tests investigating the gigacycle fatigue properties of materials are commonly performed with ultrasonic testing procedures, which allow for a significant reduction of testing time but induce a significant temperature increment in specimens. In order to evaluate the significance of size effects on the fatigue strength of materials, the Authors recently proposed to adopt Gaussian specimens for gigacycle tests. Fatigue specimens were designed without taking into account the hysteretic damping and its effects both on the stress distribution and on the heat power dissipation. However, in order to evaluate the temperature increment and the feasibility of ultrasonic fatigue tests with Gaussian specimens, the total dissipated heat power as well as the distribution of the dissipated heat power density along the specimen must be taken into account. The present paper proposes an analytical model validated through a finite element analysis, which permits to evaluate the effects of the hysteretic damping on the stress distribution, on the dissipated heat power density distribution and on the total dissipated heat power in Gaussian specimens

Crack growth from internal defects and related size-effect in VHCF

It is well-known in the literature that fatigue cracks in VHCF originate from small internal defects. More than 95% of the total VHCF life is consumed in originating the so-called Fine Granular Area (FGA) around the small initial defect. Within the FGA, crack growth takes place even if the Stress Intensity Factor (SIF) is smaller than the threshold value for crack growth. Researchers proposed different explanations for this unexpected phenomenon but they unanimously accept that a weakening mechanism occurs around the initial defect, which permits crack growth below the SIF threshold. In the present paper, crack growth in the VHCF regime is innovatively modeled and a general expression for the fatigue limit is then obtained. The statistical distribution of the fatigue limit is also defined and a model for the fatigue limit as a function of the risk-volume is proposed. Finally, the proposed model is successfully applied to an experimental dataset

Prediction of cyclic fatigue life of NiTi rotary files by Virtual Modeling and Finite Elements Analysis

Introduction: The finite element method (FEM) has been proposed as a method to analyze stress distribution in nickel-titanium (NiTi) rotary instruments but has not been assessed as a method of predicting the number of cycles to failure (NCF). The objective of this study was to predict NCF and failure location of NiTi rotary instruments by FEM virtual simulation of an experimental nonstatic fatigue test. Methods: ProTaper Next (PTN) X1, X2, and X3 files (DentsplyMaillefer, Baillagues, Switzerland (n = 20 each) were tested to failure using a customized fatigue testing device. The device and file geometries were replicated with computer-aided design software. Computer-aided design geometries (geometric model) were imported and discretized (numeric model). The typical material model of an M-Wire alloy was applied. The numeric model of the device and file geometries were exported for finite element analysis (FEA). Multiaxial random fatigue methodology was used to analyze stress history and predict instrument life. Experimental data from PTN X2 and X3 were used for virtual model tuning through a reverse engineering approach to optimize material mechanical properties. Tuned material parameters were used to predict the average NCF and failure locations of PTN X1 by FEA; t tests were used to compare FEA and experimental findings (P < .05). Results: Experimental NCF and failure locations did not differ from those predicted with FEA (P = .098). Conclusions: File NCF and failure location may be predicted by FEA. Virtual design, testing, and analysis of file geometries could save considerable time and resources during instrument development