MODELLING OF STRESS GRADIENT EFFECT ON FATIGUE LIFE USING WEIBULL BASED DISTRIBUTION FUNCTION

In the present paper, a new approach is developed in order to take into account the stress gradient effect on fatigue life of structural components. The proposed approach is based on the weakest link concept in which the shape coefficient of the Weibull distribution becomes a function of a local damage parameter. The function simulates the experimentally observed relationship between the shape of the fatigue life distribution and the stress level. Such an approach allows one to calculate the global probability distribution of the fatigue life for notched structural components in a wide range of fatigue life regime: 104-107 cycles typically. For comparison purposes, the approach is applied to calculate the number of cycles to crack initiation of structural elements under three probability levels: 5%, 63% and 95%. The calculated lifetimes are compared with the lifetimes obtained from experiments performed on notched cruciform specimens and notched round specimens subjected to constant amplitude loading

Estimation of the fatigue strength distribution in high-cycle multiaxial fatigue taking into account the stress–strain gradient effect

Based on the weakest link concept, a probabilistic approach in high-cycle multiaxial fatigue is developed to predict, for a given number of cycles, the probability distribution of the fatigue strength for metallic structural components. A three-parameter Weibull distribution is combined with the energy-based and volumetric high-cycle multiaxial fatigue criterion proposed by Banvillet et al. in 2002 [Banvillet A, Palin-Luc T, Lasserre S. A volumetric energy based high cycle multiaxial fatigue criterion. Int J Fatigue 2003;26(8):755–69; Banvillet A, Palin-Luc T, Lasserre, S, Vittori JF. Energy based high cycle multiaxial fatigue criterion depending on stress–strain distribution. In: Blom AF, editor. Fatigue 2002: Eighth international fatigue congress, vol. 1, EMAS: Stockholm; 2002, p. 283–90]. Whatever the stress state and the loading type are, the corresponding fatigue strength probability distribution can be deduced from three usual experimental fatigue limits. The scale effect is also predicted. Experimental probability distributions and theoretical predictions of the fatigue strength of smooth specimens are in good agreement for the five materials investigated: the 30NiCrMo16 and 35CrMo4 quenched and tempered steels, the C20 annealed steel, the EN-GJS800-2 nodular cast iron and the Ti–6Al–4V titanium alloy

Scaling Invariance of Fatigue Crack Growth in Gigacycle Loading Regime

The role of the collective behavior of defect ensembles at the crack tip and the laws of fatigue crack propagation in R4 high strength steel have been studied under conditions of symmetric tension–compression gigacycle loading at 20 kHz. At every stage of the fatigue crack growth, replicas from the sample side surface were taken and studied by the method of three dimensional relief profilometry (using NewView interferometer profilometer) so as to study the scaling invariant laws of defect related structure evolution.This study was supported in part by the Russian Foundation for Basic Research, Project nos. 08-01-00699, 09-01-92005-NNS_a, and 09-01-92441-KE-

Non-local energy based fatigue life calculation method under multiaxial variable amplitude loadings

Reliable design of industrial components against high cycle multiaxial fatigue requires a model capable of predicting both stress gradient and load type effects. Indeed, taking into account gradient effects is of prior importance for the applicability of fatigue models to real structures. In this paper, a fatigue life assessment method is proposed for proportional and non-proportional multiaxial variable amplitude loadings in the range 104 –107 cycles. This method derives from the fatigue criterion initially proposed by Palin-Luc and Lasserre (1998) [2] and revisited by Banvillet et al. (2003) [16] for multiaxial constant amplitude loading. The new proposal consists of a complete reformulation and extension of the previ- ously cited energy based fatigue strength criteria. It includes two major improvements of the existing criteria. The first one consists in a fatigue criterion for multiaxial variable amplitude loadings while only constant amplitude loadings were considered in the above cited works. The second one is an extension to an incremental fatigue life assessment method for proportional and non-proportional multiaxial variable amplitude loadings. No cycle counting technique is needed whatever the variable amplitude load- ings type considered (uniaxial or multiaxial). The predictions of the method for constant and variable amplitude multiaxial loadings are compared with experimental results on specimens from literature and from new experiments on a ferrito-perlitic steel. The above mentioned method has been implemented as a post-processor of a finite element software. An application to a railway wheel is finally presented.Thèse CIFRE avec la SNCF, contrat direct ARTS / SNC

Elastic–Plastic Transition in Iron: Structural and Thermodynamic Features

The structural and thermodynamic features of the elastic–plastic transition in armco iron and its plastic deformation are studied. Energy storage in iron is shown to have a nonlinear character and be accompanied by wavelike heat dissipation. To describe the energy balance in the plastically deformed metal, a theoretical model is proposed based on a statistical description of the evolution of an ensemble of typical mesodefects (microshears). Moreover, a procedure is developed to experimentally determine the dependence of the potential of the medium on the mesodefect density using infrared scanning data.This work was supported in part by the Russian Foundation for Basic Research, project nos. 05-08- 33652, 07-08-96001, and 07-01-0-96004

The behavior of statically-indeterminate structural members and frames with cracks present

Arts et Métiers ParisTech, invitation en tant que professeur invité de Paul C. Paris au LAMEFIPCrack stability is discussed as affected by their presence in statically-indeterminate beams, frames, rings, etc. loaded into the plastic range. The stability of a crack in a section, which has become plastic, is analyzed with the remainder of the structure elastic and with subsequent additional plastic hinges occurring. The reduction of energy absorption characteristics for large deformations is also discussed. The methods of elastic–plastic tearing instability are incorporated to show that in many cases the fully plastic collapse mechanism must occur for complete failure.The authors acknowledge Arts et Metiers Paris Tech and Foundation Arts et Metiers for the financial support of the Prof. P.C. Paris’ stay at LAMEFIP in 2008 and 2009. The encouragement of Prof. Ivan Iordanoff, Director of LAMEFIP, is also acknowledged with thanks

Microstructure-based study of the crack initiation mechanisms in pure copper under high cycle multiaxial fatigue loading conditions

AbstractThis paper aims to contribute in understanding the fatigue crack initiation mechanisms in metallic materials under high cycle multiaxial fatigue loadings. It addresses proportional and non-proportional multiaxial loading conditions with the analysis and observation of the cyclic plasticity development (mainly persistent slip band) until crack initiation (especially short cracks) on a pure oxygen-free high conductivity (OFHC) polycristalline copper. Observation and analysis techniques are based mainly on optical microscopy and scanning electron microscopy (SEM). It has been observed that the plastic slip multiplicity in grains seems more important for multiaxial loadings at a stress level corresponding to the same median fatigue strength at 106 cycles of the material. A multiaxial loading induces an additional multiplicity of the plastic slip in grains compared to uniaxial loading condition. For all the loading conditions investigated, although most of the grains exhibits single slip activated, analysis of the preferential crack initiation sites and modes show a higher probability of intragranular microcrack initiation in the multiple slip grains (with more than two slip systems activated). Most multiple slip grains and higher probability of crack initiation in these grains were observed especially for non-proportional multiaxial loadings. Finally, the effects of the biaxiality ratio and the phase shift on the fatigue crack initiation was highlighted

Comparative study and link between mesoscopic and energetic approaches in high cycle multiaxial fatigue

Multiaxial fatigue analysis can be categorized into several viewpoints, i.e. empirical formulae, methods based on stress invariants, critical plane approaches, models using averages of stress quantities and energetic considerations. The aim of this paper is not to survey the current state of knowledge concerning multiaxial fatigue but to critically examine two endurance criteria so as to prove that a direct link can be established between them. The first of the two methods, proposed by Papadopoulos, has been built by exploring the fatigue of metals from the mesoscopic scale, that is from the scale of the metal grains of a metallic aggregate. The localized plastic strains developping in some less favourably oriented crystals is considered to be the main cause of fatigue crack nucleation. According to relationships between macroscopic and mesoscopic quantities, this model is finally expressed in terms of the usual macroscopic stresses relative to an elementary material volume. The second approach proposed by Froustey and Lasserre is an energetic based criterion. It has been deduced from experimental observations concerning multiaxial endurance limit and states that crack initiation occurs as soon as the total strain energy density exceeds a critical value. This paper shows that the critical value of the accumulated mesoscopic plastic strain used by Papadopoulos to characterize the endurance limit can be estimated with the global strain energy density at the macroscopic scale. Indeed, it is demonstrated that when dealing with in-phase or out-of-phase synchronous sinusoidal constant amplitude loadings, a single analytical formulation of these criteria can be written either with stress quantities or with energetic ones describing thus the same physical phenomenon. The mean stress influence is discussed; the predictions of the two approaches are similar when the material remains quasi elastic. Another important result concerns the phase difference of the stress tensor components. Very few approaches are able to predict the independence of the fatigue strength on the phase difference between normal and shear stresses. The two proposed criteria reflect this phenomenon which has been experimentally observed for many metals subjected to combined bending-torsion loading. Nevertheless, this independence with regard to the phase shift is no more effective when dealing with some biaxial stress systems with two normal stresses. In this case the two models are consistent with the experimental results since they show a marked influence of the phase difference

Fatigue Life of a SG Cast Iron under Real Loading Spectra: Effect of the Correlation Factor Between Bending and Torsion

This paper deals with the effect on life of the desynchronism between two variable amplitude load sequences in combined bending and torsion. Experiments were carried out on smooth specimens made of the EN-GJS800-2 cast iron. The comparison between experimental lives and predicted ones with the following fatigue life calculation methods is presented: Smith-Watson-Topper, Fatemi and Socie (method proposed by Bannantine), Wang and Brown, Socie's proposal for high cycle fatigue, and Morel. If the scatter of experiments is considered, these experiments show a low effect of the correlation factor on life. All the simulated fatigue life calculation methods give good results for proportional loads, but their predictions are not good for non-proportional loads. Morel’s proposal seems to be the best to predict life of the tested material with our non-proportional fatigue test conditions

The behavior of statically-indeterminate structural members and frames with cracks present

Arts et Métiers ParisTech, invitation en tant que professeur invité de Paul C. Paris au LAMEFIPCrack stability is discussed as affected by their presence in statically-indeterminate beams, frames, rings, etc. loaded into the plastic range. The stability of a crack in a section, which has become plastic, is analyzed with the remainder of the structure elastic and with subsequent additional plastic hinges occurring. The reduction of energy absorption characteristics for large deformations is also discussed. The methods of elastic–plastic tearing instability are incorporated to show that in many cases the fully plastic collapse mechanism must occur for complete failure.The authors acknowledge Arts et Metiers Paris Tech and Foundation Arts et Metiers for the financial support of the Prof. P.C. Paris’ stay at LAMEFIP in 2008 and 2009. The encouragement of Prof. Ivan Iordanoff, Director of LAMEFIP, is also acknowledged with thanks