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It is well known that combination of multiaxial cyclic loading and geometrical discontinuities (such as notches and holes) frequently occurs in engineering practice, and different methods are available in the literature for multiaxial notch fatigue analysis. In such a context, a new analytical approach is here proposed in order to assess the fatigue lifetime of notched components. Such an approach consists in the joint application of (i) the multiaxial high-cycle fatigue criterion by Carpinteri et al. (formulated in terms of stresses on the critical plane) and (ii) the Critical Distance Theory by Taylor (in the form of the Line Method). In order to evaluate the accuracy of the proposed approach, experimental data, recently published in the literature and related to severely notched specimens under uniaxial and multiaxial fatigue loading, are examined, being the specimens made of Ti-6Al-4V, material attracting significant interest by leading industries, such as the biomedical one.

Important components such as gears, rollers, or bearings operate in rolling-sliding contact loading conditions. Determination of their fatigue lives remains a challenging task due to complex states of stress and strain in the contact region, as well as complex contact conditions such as variable loading amplitude and complex geometry of contact. A mathematical model of rolling-sliding line contact combined with a multiaxial fatigue life calculation model based on the Fatemi‐Socie critical plane crack initiation criterion is proposed. The developed model was applied to gears' teeth in mesh and compared with fatigue lives of gears reported in the literature. Good agreement was determined confirming the validity of the proposed model. A further advantage is obtaining locations of initiated cracks and the orientation of critical plane(s), which can subsequently be used for the estimation of crack shapes in initial phases of their growth and the damage type that they can be expected to develop into.

This study concerns the multiaxial static and fatigue strength properties. Short-glass-fibre-reinforced phenolic-resin composites (SGP) molded by injection and compression processes were subjected to tensiontorsion combined static and fatigue tests at room temperature under various test conditions. Tension – torsion combined static strength well agreed with Tsai-Hill failure criteria without depending on processes. Relationships between the maximum principal stress, ?p1, max, and the number of fracture cycles, Nf, were approximately linear in the whole range of up to 106 cycles. For a unified evaluation of multiaxial fatigue life for SGP, non-dimensional effective stress, ?*, defined by modifying Tsai-Hill failure criteria was applied. The slopes of ?*- Nf curves according to Baskin’s law were almost identical to the injection (n = 26.3) and compression (n = 26.2). We finally confirmed that the multiaxial fatigue life of SFRP could be predicted by using ?* with a unique Wohler curve without relying on molding processes. KEYWORDS. Short-fibre reinforced plastics; Multiaxial; Fatigue; Tsai-Hill.

Utilizing molecular dynamics (MD) integration model we have investigated some of the relevant physical processes caused by different loading paths at the atomic level in Cu and Al monocrystal specimen. Interactions among the atoms in the bulk are modeled with the standard realistic Embedded Atom Method (EAM) potentials. MD simulation gives us the detailed information about non-equilibrium dynamics including crystal structure defects, vacancies and dislocations. In particular, we have obtained result that indicate increase in the total energy of the crystal during loading (especially cyclic) that provides us direct quantitative evidence of the metal weakening. For the basic response, we have deformed copper and aluminum single crystal according to the simple loading path and a series of multiaxial loading-paths including cyclic repetition. We compute equivalent stress-strain diagrams as well as dislocation total length vs time graphs to describe signatures of the anisotropic response of the crystal.&nbsp

Multiaxial high cycle fatigue is a topic that concerns nearly all industrial domains. In recent years, a great deal of recommendations how to address problems with multiaxial fatigue life time estimation have been made and a huge progress in the field has been achieved. Until now, however, no universal criterion for multiaxial fatigue has been proposed. Addressing this situation, this paper offers a design of a new multiaxial criterion for high cycle fatigue. This criterion is based on critical plane search. Damage parameter consists of a combination of normal and shear stresses on a critical plane (which is a plane with maximal shear stress amplitude). Material parameters used in proposed criterion are obtained from torsion and axial S-N curves. Proposed criterion correctly calculates life time for boundary loading condition (pure torsion and pure axial loading). Application of proposed model is demonstrated on biaxial loading and the results are verified with testing program using specimens made from S355 steel. Fatigue material parameters for proposed criterion and multiple sets of data for different combination of axial and torsional loading have been obtained during the experiment.

This study compares both uniaxial and multiaxial variable amplitude experimental crack growth data for naturally initiated fatigue cracks in tubular specimens of 2024-T3 aluminum alloy to predictions based on two state-of-the-art analysis codes: UniGrow and FASTRAN. For variable amplitude fatigue tests performed under pure axial nominal loading conditions, both UniGrow and FASTRAN analyses were found to produce mostly conservative growth life predictions, despite good agreement with constant amplitude crack growth data. For variable amplitude torsion and combined axial-torsion crack growth analyses, however, the conservatism in growth life predictions was found to reduce. This was attributed to multiaxial nominal stress state effects, such as T-stress and mixed-mode crack growth, which are not accounted for in either UniGrow or FASTRAN, but were found in constant amplitude fatigue tests to increase experimental crack growth rates. Since cracks in this study were initiated naturally, different initial crack geometry assumptions were also investigated in the analyses.

Fatigue damage is a parameter which plays an important role in lifetime and reliability predictions of randomly loaded structures. In this paper, four different forms of the Miner linear accumulation damage rule are examined. They are used to compare observed experimental damage and the results of numerical simulations for both uniaxial and multiaxial fatigue. First, critical fatigue damage values for all forms of the Miner accumulation damage rule are calculated for uniaxial cases. Based on the results presented in this paper, it has been established that for high strength materials the critical damage value is around 0.3. These results are then applied to the multiaxial cases. The multiaxiality is taken into account using either the signed von Mises or critical plane method. Finally, the fatigue fracture surface has been calculated and compared to the experimental pattern of fatigue fracture. The results show that the fatigue fracture surface determined by the numerical simulation is comparable to the fatigue fracture observed experimentally.

Micro electro mechanical systems, coatings, and thin films contain materials that are often subjected to complex loading conditions and high frequencies. Therefore, the implementation of a resonant multiaxial fatigue setup for small-scale samples is of high interest. Finite Element simulations have been used to design small-scale samples which possess very close bending and torsional resonant frequencies. The bending and torsional modes are excited by two piezo actuators working either in or out of phase with one another. The bending and torsional amplitudes are measured independently by a laser and the actuator amplitudes are controlled by a Field Programmable Gate Array. The fatigue setup can be used with a varying range of sample sizes from centimeters down to tens of micrometers. The novel multiaxial resonant micro fatigue setup as well as results (fatigue damage for Ni and lifetime for Cu) from bending small-scale fatigue tests are shown and discussed.

This Special Issue of the International Journal of Fatigue contains selected papers presented at the International Conference on Multiaxial Fatigue and Fracture held in Seville, Spain, on 1–3 June 2016.

In this paper, a methodology has been developed for evaluating the springback of AISI 304 DDQ stainless steel sheet based on a bending under tension test. The main difference of the methodology herein carried out is that tests are made under the multiaxial stresses state that take place in deep drawing processes. This affects to the level of stress value in the test and to the hardening state of the sheet. Springback evaluation has been done in two different areas. Bending area has been evaluated from elastic recovery ratio defined as the ratio between the bending radius after and before bending. Bending and unbending extreme has been studied from the measured curvature radius in this area and taking into account the geometric equivalence of the test with the drawing cups process. Results found allow to state that drawing ratio or deformation ratio have a negligible influence on the springback into the range of values experimented here. Bending radius has hardly influence as well while bending angle is the most significant variable. The results obtained are compared to those measured in deep-drawn cups, finding a great agreement.En este trabajo se presenta una metodología para evaluar la recuperación elástica o springback de chapa de acero inoxidable AISI 304 DDQ basada en la realización de ensayos bajo tensión. A diferencia de los estudios existentes en la literatura, los ensayos realizados son efectuados en condiciones multiaxiales típicas de los procesos de embutición de chapa. Esto afecta fundamentalmente a las tensiones involucradas en el proceso así como al estado de endurecimiento que experimenta el material. La evaluación del springback se ha efectuado en dos áreas diferentes. En la zona de doblado se ha evaluado a partir del factor de recuperación definido como la razón entre el radio de doblado y el radio con el que queda finalmente el material. La zona de doblado y desdoblado se ha evaluado en base a la inversa del radio de curvatura de la chapa en dicha zona y teniendo en cuenta una longitud de arco en función de la relación de deformación practicada en el material. Los resultados encontrados permiten establecer que dentro del rango de valores de ángulo y de radio de doblado experimentados, el springback es independiente de la relación de embutición o de deformación practicada en el material. El radio de doblado tiene poca influencia en el rango de radios ensayados, siendo el ángulo de doblado la variable más significativa. Los resultados obtenidos son contrastados con los medidos en copas embutidas, encontrando un alto grado de concordancia.

Most of the prior studies on the prediction of fatigue lives have been limited to uniaxial loading cases, whereas real world loading scenarios are often multiaxial, and the prediction of fatigue life based upon uniaxial fatigue properties may lead to inaccurate results. A detailed exploration of multiaxial fatigue under constant amplitude loading scenarios for a range of metal alloys has been performed in this study, and a new methodology for the accurate prediction of fatigue damage is proposed. A wide variety of uniaxial, torsional, proportional and non-proportional load-paths has been used to simulate complex, real-world loading scenarios. Test data have been analyzed and a critical-plane based fatigue damage parameter has been developed. This fatigue damage parameter contains stress and strain terms, as well as a term consisting of the maximum value of the product of normal and shear stresses on the critical plane. The shear-dominant crack initiation phenomenon and the combined effect of shear and tensile stresses on micro-crack propagation have been modeled in this work. The proposed formulation eliminates many of the shortcomings of the earlier developed critical-plane fatigue damage models. It is mathematically simple with substantially fewer material dependent constants, and provides design engineers with a tool to predict the fatigue life of machine parts with minimal computational effort. This life prediction methodology is intended for a wide variety of LCF and HCF loadings on machine parts made of metals including advanced alloys. KEYWORDS. Multiaxial; Fatigue Damage Parameter; Non-proportional loading.

Weld start and end points are fatigue failure sensitive locations. Their fatigue behaviour especially in thin sheet structures under multiaxial load conditions is not sufficiently explored so far. Therefore, a research project was initiated to increase the knowledge concerning this topic, which is of special interest in the automotive industry. In the present study, fatigue tests on welded joints were conducted. In the numerical part of the study, notch stresses were calculated with an idealised weld end model. A numerical method which combines the geometrical and statistical size effect to an integrated approach was used, in order to consider the size effects.

Depending on the state of stress, material can fail in a number of different modes during a collision. Three modes are identified here as material separation in the absence of necking, material separation after the onset of necking, and localized buckling/wrinkling. Through a series of case studies, the states of stress present in a collision are analyzed. Of particular interest is leakage in a scaled fuel tank that could not have been predicted by FEA due to resolution and may have been ignored even with sufficient resolution because it was in a region of generally compressive stresses. Following the review of case studies, the aforementioned failure mechanisms are reviewed, and the corresponding states of stress are summarized. It is shown that the current state of technology for failure after the onset of necking is insufficient but quickly improving. Concepts are taken from the sheet metal industry to understand the onset of buckling/wrinkling, but there is little readily available to simulate failure after the initial onset.

Fatigue cracking of longerons manufactured from Al-alloy AVT-1 for helicopter in-service rotor-blades was considered and crack growth period and equivalent of tensile stress for different blade sections were estimated. Complicated case of in-service blades multiaxial cyclically bending-rotating and tension can be considered based on introduced earlier master curve constructed for aluminum alloys in the simple case of uniaxial tension with stress R-ratio near to zero. Calculated equivalent tensile stress was compared for different blade sections and it was shown that in-service blades experienced not principle difference in this value in the crack growth direction by the investigated sections. It is not above the designed equivalent stress level. Crack growth period estimation in longerons based on fatigue striation spacing or meso-beach-marks measurements has shown that monitoring system introduced designer in longerons can be effectively used for in-time crack detecting independently on the failed section when can appeared because of various type of material faults or in-service damages.

This paper describes the methodology developed by Decathlon, through its MKniX Engineering Center, to master the fatigue design of welded aluminium-alloy bicycle frame. The objective is to optimize the design prior to the standard testing by calculating the fatigue reliability of the bicycle frame. The fatigue assessment method is based on the Dang Van multiaxial fatigue criterion combined with a unique S-N design curve independent of the geometry of the welded structure and the loading mode. The design stress is defined through a linear elastic finite element analysis using a specific thin shell meshing method.

Fatigue life formulas are still based on phenomenological models which adopt simple relations directly from experiments for different loading conditions and use fitted material parameters. The combination of enormous complexity of fatigue damage processes and simple, macro appearance of the formulas (usually power laws), are the source of Generic Fatigue Models (GFM). GFMs rely on minimal, but coherent, micro-details which are independent of the specific micro structure. Such a model has been developed, connecting analytically the S-N power law and endurance stress in terms of statistical strength distributions of material microelements and their neighbors. This paper describes two types of generalizations of the basic GFM: a.) Two level (H-L and L-H) loading, in which a history dependent micro-damage evolution law is proposed, and b.) Multiaxial fatigue response by a simple 2D truss. Emphasize is on minimal parameters and capability of analytical predictions, in which every “material constant” has a physical or micro-geometrical meaning. The theoretical generalizations are compared with experimental data from the literature and show that the predictions are coherent with main experimental features.

To assemble pipelines and tubular structures, threaded couplings can be used. In service these couplings are often subjected to dynamic loads. To maintain a secure connection, they are generally preloaded. The combination of preload and external dynamic loads results in a multiaxial stress distribution over the connection, where the coupling’s threads act as stress raisers, initiating fatigue cracks. The fatigue life of the connection depends on its global geometry, local thread geometry, interface and material properties. In this study the fatigue life of standard API Line Pipe couplings and two modified coupling configurations is determined experimentally. The influence of the coupling’s global geometry on the connection’s fatigue life was studied. Threaded pipe samples with a nominal size of 1” were tested on a four-point bending fatigue test setup. A sample was considered to be failed when a through thickness crack appeared. This was detected by pressurizing the tube samples. When a pressure drop was recorded, the test was stopped. The number of elapsed load cycles defines the fatigue life of the connection. Using this methodology, S-N curves were obtained for the standard API Line Pipe connection and two modified coupling configurations. Both configurations exhibited an improved fatigue life relative to the standard connection. In the final part of this paper, these experimental observations are explained by a combination of a damage evolution law and a finite element model.

Multiaxial and uniaxial vibration experiments were conducted in order to study the differences in failure modes and fatigue life for the two types of excitation. An electrodynamic (ED) shaker capable of controlled vibration in six degrees of freedom (DOF) was employed for the experiments. The test specimen consisted of six large inductors insertion mounted on a printed wiring board (PWB). Average damage accumulation rate (DAR) in the inductor leads was measured for random excitations in-plane, out-of-plane, and both directions simultaneously. Under simultaneous multiaxial excitation, the average DAR was found to be 2.2 times greater than the sum of the in-plane and out-of-plane DARs. The conclusion was that multiple-step sequential uniaxial testing may significantly overestimate the durability of large/heavy structures with high center of mass in a multiaxial dynamic environment. Additionally, a test method utilizing uniaxial vibration along a direction other than the principal directions of the structure was examined. This method was found to have significant limitations, but showed better agreement with simultaneous multiaxial vibration experiments.

Multiaxial high cycle fatigue modeling of materials is an issue that concerns many industrial domains (automotive, aerospace, nuclear, etc.) and in which many progress still remains to be achieved. Several approaches exist in the literature: invariants, energy, integral and critical plane approaches all of them having their advantages and drawbacks. These different formulations are usually based on mechanical quantities at the micro or mesoscales using localization schemes and strong assumptions to propose simple analytical forms. This study aims to revisit these formulations using a numerical approach based on crystal plasticity modeling coupled with explicit description of microstructure (morphology and texture) and proposes a statistical procedure for the analyses of numerical results in the HCF context. This work has three steps: First, 2.5D periodic digital microstructures based on a random grain sizes distribution are generated. Second, multiaxial cyclic loading conditions corresponding to the fatigue strength at 106 cycles are applied to these microstructures. Third, the mesoscopic Fatigue Indicator Parameters (FIPs), formulated from the different criteria existing in the literature, are identified using the finite element calculations of the mechanical fields. These mesoscopic FIP show the limits of the original criteria when it comes to applying them at the grain scale. A statistical method based on extreme value probability is used to redefine the thresholds of these criteria. These new thresholds contain the sensitivity of the HCF behavior to microstructure attributes. Finally, the biaxiality and phase shift effects are discussed at the grain scale and the loading paths of some critical grains are analyzed. Financial support of this research by Arts et Métiers Paristech is gratefully acknowledged.

Les auteurs ne possèdent pas le fichier accepté par l'éditeur (à jour) mais non mis en forme ou plus précisément celui dont nous disposons comporte des erreurs de références bibliographiques dues à des problèmes informatiques; International audience; 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 cri- teria. 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 var- iable 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 imple- mented as a post-processor of a finite element software. An application to a railway wheel is finally presented.

International audience; A reliable design of industrial parts against high-cycle multiaxial fatigue requires a fatigue criterion capable of predicting both the stress gradient and the load-type effects. These effects are very important in the transfer of fatigue data from specimen to component. By using the concept of volume influencing fatigue crack initiation proposed by Palin-Luc and Lasserre with an energy based approach, a new criterion is presented. Based on the strain-work density given to the material, this proposal is usable whateverthe constant amplitude loading is: in and out-of-phase combined loadings, with or without mean stress. Its predictions are compared both with a total of 38 experiments on four materials (a mild steel, two high strength steels and a spheroidal graphite cast iron) and with the predictions of local criteria (Crossland, Dang Van, Papadopoulos and Morel). The comparison shows that the predictions of the volumetric proposal are very good and less scattered than those of the local approaches, especially for loadings with mean stresses or under non-proportional loadings.

International audience; 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 anelementary 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 influenceof the phase difference.

International audience; Simulations of the nucleation of dislocations, glide and annihilation ahead of a fatigue crack growing along a localized slip band (a ‘long’ Stage I crack or a Stage II crack with a K value close to the threshold) are performed for the case of push–pull or reversed torsion loadings, ignoring, in a first approach, the effect of grain boundaries. The crack growth rates are deduced from the dislocation flux at the crack tip. An influence of the normal stress on the friction between the crack flanks as well as on the condition for dislocation emission is introduced. A slower Stage I growth rate is then predicted for reversed torsion, consistent with experimental data.

Some mechanical components are subjected to thermo-mechanical fatigue, which occurs when both thermal and mechanical loads vary with time. Due to the complexity of the components geometry, stresses and strains field becomes multiaxial, worsening the fatigue resistance. In this paper several damage models are applied and compared on a case study, an automotive exhaust manifold simulacrum replying the material and the geometrical features of the commercial component. A complete thermo-structural FE analysis has been run and results have been post-processed by means of a numerical code implementing several multiaxial damage models available in literature and based both on a critical plane approach (Kandil-Brown-Miller, Fatemi-Socie) and strain-based models (Von Mises, ASME Code and Sonsino-Grubisic). The model calibration has been carried out by means of literature experimental data referred to commercial exhaust manifolds of similar geometry and material.