A probabilistic model for multiaxial high cycle fatigue

A probabilistic framework developed to model multiaxial high cycle fatigue tests is proposed. Up to now, with a probabilistic point of view (i.e., Weibull law), models account for the stress heterogeneity effect by introducing the concept of effective volume. It is proposed to extend this concept to multiaxial load histories. It consists in introducing a factor representing the distribution of activated slip directions. The non‐proportionality effect is taken into account with no additional parameter with respect to traditional (i.e., Weibull) probabilistic approaches. The proposed model is validated on a large experimental data base and compared with other models.     

A high-cycle fatigue life model for variable amplitude multiaxial loading

A high‐cycle fatigue life model for structures subjected to variable amplitude multiaxial loading is presented in this paper. It treats any kind of repeated blocks of variable amplitude multiaxial loading without using a cycle counting method. This model based on a mesoscopic approach is characterized by the following features: (i) the choice of a damage factor related to the accumulated mesoscopic plastic strain per stabilised cycle; (ii) the use of a mesoscopic mechanical behaviour taking into account the fatigue mechanisms such as plasticity and void growth. This behaviour is a von Mises elastoplastic model with linear kinematic hardening and hydrostatic stress dependent yield stress. The fatigue life model has six parameters identified with one SN curve and two fatigue limits. In‐phase and out‐of‐phase experimental tests from the literature are simulated. The predicted fatigue lives are compared to experimental ones.     

A multiaxial high-cycle fatigue life evaluation model for notched structural components

A model for multiaxial high-cycle fatigue life evaluation of notched structural components is proposed, which considers the impact of the stress field on fatigue life by utilizing the Theory of Critical Distances (TCD) and Finite Element Method (FEM). The maximum shear stress range plane is defined as the critical plane, and the damage parameters are the maximum effective shear stress amplitude and the maximum effective normal stress, which are obtained by averaging the stress in the hemisphere volume around the maximum stress point. To validate the accuracy of the model, multiaxial fatigue tests are carried out for both smooth and notched specimens of Aluminum–Silicon alloy. The results indicate that the evaluated life and experimental life have a good agreement.     

A stochastic damage accumulation model for crack initiation in high-cycle fatigue

A stochastic damage accumulation model for crack initiation in high-cycle fatigue is proposed. It is assumed that the fatigue damage is accumulated in the form of dislocations under the repeated stress and that the slip band crack is initiated when the strain energy due to a local pile-up of dislocations exceeds a critical value. The size of an initiating crack is the cell size, derived from a probabilistic argument and its depth is determined in relation to the stored dislocation energy. Our theoretical results are compared with the experimental data from a low-carbon steel S20C in order to examine the consistency of our model.     

A high-cycle fatigue apparatus at 20 kHz for low-cycle fatigue/high-cycle fatigue interaction testing

High-cycle fatigue (HCF) failures in aircraft engines are attributed to material damage states, created during processing or by in-service loading and environmental conditions, and then propagated to failure by HCF loading. The loading configuration experienced by aircraft engine turbine blades consists of an axial load caused by the centrifugal acceleration during rotation combined with the tensile and compressive loads caused by the natural vibrations of the blades themselves. To simulate these loading conditions a new testing apparatus was developed that is capable of providing interactive low-cycle fatigue/high-cycle fatigue (LCF/HCF) loading, in ratios (of magnitude and frequency) that give a realistic simulation of the actual flight loads experienced by engine components. This testing apparatus is based on a HCF cell operating at 20  kHz. The cell can also be integrated to a servo-hydraulic load frame, which provides a second fatigue cycle. The objective of this study was to demonstrate the capabilities of the new HCF apparatus via thermographic measurements and by performing LCF/HCF interaction tests.     

A high-cycle fatigue accumulation model based on electrical resistance for structural steels

For high-cycle fatigue of metals, the DC electrical resistance is a more sensitive parameter to the initiation of micro-cracks during the irreversible fatigue damage accumulation process. This implies that the electrical resistance is a suitable parameter that can be consistent with the fatigue damage physical mechanism. The relation between the ratio of electrical resistance changes and the cyclic fraction of the fatigue specimen may reasonably represent deterioration in mechanical properties of structural steels during the high-cycle fatigue process. The high-cycle fatigue damage accumulation model based on electrical resistance for structural steels was proposed. The model was verified by some experimental data for three structural steels; normalized 45C steel, 20 Mn steel and 16 Mn steel, and good agreement was obtained. The corresponding fatigue lifetime on the basis of the electrical resistance model was also performed. The results show that the approach to fatigue lifetime prediction and failure based on the electrical resistance is a good non-destructive technique.     

Probabilistic model for length effect on fatigue life of longitudinal elements

This paper studies the length effect on fatigue life of longitudinal element at the macroscale. An asymptotic weakest‐link Weibull phenomenological model that incorporates a statistical length effect for the fatigue life of longitudinal element is proposed in this research. In the proposed model, the weakest‐link effect gradually becomes dominant and causes a decrease in fatigue life that increases along , the normalized length of the longitudinal element. To this end, the fatigue life under a specified stress range is divided into 3 zones according to the normalized length : (1) is the zone where length effects can be ignored, and the fatigue life can be treated as a random variable; (2) is the zone where the fatigue life is length dependent; and (3) is the zone where the fatigue life follows asymptotic length dependence. The asymptotic threshold normalized length, , can be evaluated by the asymptotic weakest‐link Weibull model. To validate the proposed model, 3 previously published datasets are used: (1) the fatigue data of Picciotto yarn, (2) hipo‐eutectoid steel wire with different lengths, and (3) the fatigue data of high‐strength steel wire with different lengths and different constant stress ranges. Finally, the results obtained by the proposed model are compared with those from the literature and discussed in detail. The analytical solutions obtained using the proposed model allows for assessment of the fatigue life of certain components and structures that are beyond current testing capabilities. In particular, the length effects on the fatigue life of the high‐strength steel wire in stay cables are investigated to gain insight into issues regarding safe designs.     

Probabilistic approach in high-cycle multiaxial fatigue: volume and surface effects

The stress gradient and the size of a component are known to influence the fatigue strength of metallic components. Indeed, in high‐cycle fatigue, experiments prove that the stress distribution as well as the size of the loaded specimen can be responsible for changes in the fatigue limit (for instance, the fatigue limits in tension and bending are different, and decrease with the size of the specimen). When dealing with multiaxial load conditions, those effects still act but a relevant criterion must be used to account for the complex state of stress. The weakest‐link concept together with a multiaxial endurance criterion based on a microplasticity analysis are then combined to describe the fatigue limit distribution of different metallic materials. Several load conditions are analysed: tension–compression, torsion, rotating bending and plane bending. By means of the proposed model, all the known effects on fatigue strength can be reflected. First, the endurance probability can be adequately predicted for any complex load conditions knowing some reference data from uniaxial fatigue tests. It can be linked to the probability of finding a defect with a critical size. The weakest‐link theory also accounts for the decrease of multiaxial fatigue limit with the stressed volume. For the same load condition (i.e. for the same stress distribution in the volume), the probability of finding a critical defect increases with the component size and then according to the weakest‐link theory the fatigue strength drops. A second model, based only on the damage developed at the surface, is also proposed. While the original Weibull theory makes no distinction between potential initiation sites at the free surface and in the volume and can lead to unsatisfactory predictions when applied to materials containing defects such as nodular cast iron, the new surface approach distinguishes between surface and volume effects.     

A probabilistic approach for thermal shock fatigue life of glass

This paper presents a probabilistic approach for predicting fatigue life of glass subjected to near‐ΔT_C (critical temperature difference) thermal shock which exhibits little subcritical crack extension. First, thermal shock fatigue life N_f was derived as a function of temperature difference ΔT, fracture probability F and Biot's modulus β from the slow crack growth concept in conjunction with the Weibull distribution model. Next, thermal shock fatigue tests as well as flexural tests were performed for borosilicate glass to measure ΔT_C and N_f versus ΔT. The parameters associated with slow crack growth were then determined from the experimental results while the heat transfer coefficient h or β was obtained with the aid of finite element analysis. Thirdly, the thermal shock fatigue diagram (ΔT?N_f curves) was depicted for various values of β. Finally, crack length was simulated on the basis of the present approach.     

A new damage parameter for fatigue life predictions under local strain analysis

A new damage parameter is proposed for fatigue life prediction using a local stress-strain approach. This parameter has a physical energy basis, and makes it possible to obtain the same accuracy as, and better life assessments than, the well-known Smith et al parameter using significantly less calculation time for load history treatment. Comparisons of life predictions obtained using the proposed parameter with experimental results and other predictions are presented.     

A unified statistical model for S‐N fatigue curves: probabilistic definition

In recent years, experimental tests exploring the gigacycle fatigue properties of materials suggest the introduction of modifications in well‐known statistical fatigue life models. Usual fatigue life models, characterized by a single failure mechanism and by the presence of the fatigue limit, have been integrated by models that can take into account the occurrence of two failure mechanisms and do not consider the presence of the fatigue limit. The general case, in which more than two failure mechanisms coexist with the fatigue limit, has not been proposed yet. The paper presents a unified statistical model which can take into account any number of failure mechanisms and the possible presence of the fatigue limit. The case of S‐N curves with different fatigue life distributions coexisting for the entire stress range covered by fatigue tests is also considered. The adaptability of the statistical model to the S‐N curves proposed in the open literature is demonstrated by qualitative numerical examples.     

An invariant-based approach for high-cycle fatigue calculation

Fatigue failures of in-service components are frequently due to multiaxial loadings; therefore, damage quantification in such conditions is important to many industrial applications. In this work a multiaxial criterion suitable for high-cycle fatigue assessment is formalized. It makes use of hydrostatic stress component and deviatoric stress component to estimate fatigue damage. A new formulation for the equivalent amplitude of the deviatoric component is formalized and compared with definitions proposed by Deperrois and Li and De Freitas. Damage evaluation procedure is discussed for deterministic loads and explicit analytical formulation is presented for sinusoidal loadings. Fatigue criterion is applied to experimental data taken from literature, related to several materials subjected to either in-phase or out-of-phase loads. It is shown that the new approach gives good predictions for both smooth and notched specimens. A similar comparison between experimental and theoretical results is also presented for other common criteria. It appears that the quality of the fatigue assessments obtained with the present criterion is better or, at most, similar to that of the other criteria analysed.     

A probabilistic approach to predict the very high-cycle fatigue behaviour of spheroidal graphite cast iron structures

A new probabilistic approach is developed to study structures made of spheroidal graphite cast iron and subjected to very high-cycle fatigue. Until now, the probabilistic approach was based on S–N curves obtained from experiments carried out only until 10⁷ cycles. To validate this approach, failure predictions relating to the safety of components are computed and compared to experimental results. In addition to this development, an extension is proposed in order to improve the very long life assessment of complex structures. An extrapolation of the previous fatigue results to 10⁹–10¹¹ cycles illustrates the error made on cumulative failure probabilities. Finally, the respective influence of the casting flaw distribution, volume and stress field heterogeneity within specimens and industrial components is studied.     

A fracture plane approach in multiaxial high-cycle fatigue of metals

The high-cycle fatigue behaviour of metals under multiaxial loading is examined. By employing the weight function method, the authors propose to correlate the fatigue fracture plane orientation with the averaged principal stress directions. The results derived by applying such an approach are compared with the experimental data collected from the relevant literature, concerning different types of metals under in-phase or out-of-phase sinusoidal biaxial normal and shear stress states. Theoretical results determined by McDiarmid are also reported.     

Effect of zirconia addition on the fatigue behaviour of fine grained alumina

The fatigue behaviour of fine grained Al₂O₃ and ZrO₂ toughened Al₂O₃ (ZTA) compositions with 15 vol% ZrO₂ (3 mol% Y₂O₃ stabilized: 3Y-TZP) have been investigated by using three different techniques. Primarily 4-point bending load was employed to generate tension-tension fatigue data under both static and cyclic conditions. The results clearly showed that the materials were susceptible to both the static and cyclic fatigue and the time to failure under cyclic loading was considerably shorter than the equivalent static loads. The repeated indentations at the same spot with varying loads showed a typical fatigue behaviour. In addition, both the materials were subjected to the repeated impact cycles at varying subcritical loads simulating impact fatigue. In all the cases typical fatigue curves were obtained having a progressive endurance at subcritical loads having an endurance limit. The fatigue behaviour of Al₂O₃ was much improved by the addition of 15 vol% 3Y-TZP, having micro-plasticity contributing towards the cyclic fatigue phenomena of these materials.     

Statistical properties of the model parameters in the continuum approach to high-cycle fatigue

This paper is a sequel to papers studying the continuum approach to the high-cycle fatigue model of Ottosen et al. First, we study the estimation of fatigue limit and statistical characteristics of the estimates. We have two cases. Either the fatigue limit is a material constant or it is a random variable. Finally, we derive approximate distributions for the parameter estimators of the fatigue model due to Ottosen et al.     

A method for modelling of fatigue life for rubbers and rubber isolators

A method for modelling fatigue life of rubbers and rubber isolators is presented in this paper. Firstly, a fatigue experiment is carried out for a rubber dumbbell cylindrical specimen and a rubber isolator. Based on the finite element analysis, the damage parameters including the strain energy density, the maximum principal Green–Lagrange strain and the effective stress are calculated and discussed. Secondly, three fatigue life prediction models are established by using the three damage parameters and using the relation between the measured fatigue life of a dumbbell cylindrical specimen and the computed value of the damage parameters. Thirdly, three proposed prediction models are used to investigate which one can be best used to predicting fatigue life of rubber isolators, taking a typical powertrain rubber isolator as studying example. The fatigue lives of the rubber isolator predicted by the three models are compared with the experimental life. The results demonstrate that the predicted fatigue lives of the rubber isolator using the three fatigue models agree well with the experimental fatigue life within a factor of four, and the model using the effective stress as the damage parameter can predict the fatigue life within a factor of two, which has the best accuracy among the three models.