Multiaxial Fatigue Criterion Research Articles

Investigation of Contact Performance of Case-Hardened Gears Under Plasto-elastohydrodynamic Lubrication

Case-hardening is widely used to enhance gear loading capacity. Simulation of the material gradient properties and contact characteristics are the key issues in contact fatigue analysis of case-hardened gears. In this work, a plasto-elastohydrodynamic lubrication (PEHL) model incorporating the hardness gradient and surface roughness is developed to investigate the contact performance of case-hardened gears. The generalized Reynolds equation is solved to determine film thickness and contact pressure. The plastic deformation and residual stress are obtained via the half-space eigenstrain problem solving. The Dang Van multiaxial fatigue criterion and the Euler transformation are employed to evaluate the contact fatigue parameter based on the predetermined stress field. The discrete convolution and fast Fourier transform (DC-FFT) algorithm is used for accelerating the computation. The influences of effective case depth, surface hardness and surface roughness on the contact performance are investigated. Numerical results indicate that as the surface hardness increases, the probability of fatigue crack nucleation decreases, and the depth of the crack initiation site increases. For a lower surface roughness case, the maximum von Mises stress and equivalent plastic strain appear at a deeper layer. As the surface roughness increases, the maximum values of pressure and stress increase sharply and move closer to the surface.

Fretting failure of a pressure armour in an unbonded flexible riser

In the present paper, the failure of a pressure armour in a flexible riser under fretting wear loading is analysed. Fretting lifetime is evaluated through the multiaxial fatigue criterion by Carpinteri et al., implementing the critical direction method proposed by Araujo et al. to define the orientation of the critical plane. The fretting map (in terms of number of loading cycles to failure against displacement amplitude) is build starting from the simulation results of some fretting wear tests in partial slip regime. Then, such a map is compared with that determined by means of the results derived through a combined experimental and numerical methodology available in the literature.

Experimental and numerical investigation on compressive fatigue strength of lattice structures of AlSi7Mg manufactured by SLM

Micro-lattice materials represent nowadays a great opportunity for developing new ultra-lightweight materials. Design flexibility and multi-functional properties make them attractive for several applications in automotive, medical, space, aerospace and process industries. Predict fatigue resistance of these micro-structures is a key issue. In this work three different unit cells printed by a Selective Laser Melting process with an AlSi7Mg powder were analysed. Static properties and fatigue strength in compression have been studied by means of different experimental and numerical techniques: experimental tests, Digital Image Correlation, Micro-Computed Tomography and Finite Element analysis. Total fatigue life has been divided in three stages: ratcheting, damage initiation and propagation in one or few struts leading to final failure. The experimental results show that the initial ratcheting strain rate is significantly correlated to the life of each sample. The damage maps show that, even at fatigue limit, crack propagation in one or few struts is expected to occur. The effect of defects and local irregularities on the fatigue strength has been studied by means of finite elements models based on the as-manufactured geometry of the samples and on the definition of an equivalent stress amplitude based on a multiaxial high cycle fatigue criterion. A correlation between broken struts and maximum values of local equivalent fatigue stress amplitude has been demonstrated by post-test tomographies.

A numerical investigation on multiaxial fatigue assessment of Nitinol peripheral endovascular devices with emphasis on load non-proportionality effects

This work first numerically investigates on the effect of the application of cyclic remote loads on the local stress/strain response of a peripheral stent. For this purpose, three stents of identical geometry, but different material properties (linear elastic, elastic-plastic and Nitinol material), were modelled and subjected to uniaxial and multiaxial proportional cyclic loads. The local response under uniaxial loads is non-proportional only for the case of Nitinol stent, while it happens for all the materials when multiaxial loads are applied. This paper also aims to evaluate how the use of different multiaxial fatigue criteria may affect the fatigue assessment for Nitinol peripheral stents. The same stent model was subjected to different proportional and non-proportional multiaxial cyclic loads and the results were interpreted using the standard von Mises and three approaches based on the concept of critical plane. The results showed that the von Mises is the most conservative criterion.

Numerical simulation of competing mechanism between pitting and micro-pitting of a wind turbine gear considering surface roughness

Gear rolling contact fatigue displays itself with many failure modes such as micro-pitting, pitting or tooth flank fracture. Competing mechanism exists between these failure modes. Tooth surface micro-topography plays an important role in contact behavior and contact fatigue performance of gears. In particular, the root of mean square (RMS) of surface roughness is extensively characterized as one of the main parameters influencing the service performance. In this work an elastic-plastic finite element contact fatigue model is proposed in which the surface roughness is explicitly measured through an optical profiler. The relationship between the dimensionless normal loads and the contact area ratio is plotted. The critical planes and the characteristic shear strain amplitudes are captured at each material point within the contact area. Then the Brown-Miller multi-axial fatigue criterion is applied to evaluate the fatigue life of rough surface contacts. Results reveal that the surface roughness significantly influences the contact fatigue life of gears, and the competing mechanism between the micro-pitting from near-surface area and pitting from sub-surface area. When the RMS value of surface roughness is considerably small, the pitting failure risk and the micro-pitting risk coexist since the minimum fatigue life appears both at the near-surface area and the sub-surface area.

Energy Concepts and Critical Plane for Fatigue Assessment of Ti-6Al-4V Notched Specimens

In the present paper, the fatigue life assessment of notched structural components is performed by applying a critical plane-based multiaxial fatigue criterion. Such a criterion is formulated by using the control volume concept related to the strain energy density criterion. The verification point is assumed to be at a given distance from the notch tip. Such a distance is taken as a function of the control volume radii around the notch tip under both Mode I and Mode III loading. The accuracy of the present criterion is evaluated through experimental data available in the literature, concerning titanium alloy notched specimens under uniaxial and multiaxial fatigue loading.

Notch stress to assess multiaxial fatigue of complex welded structures under non-proportional loading

It has been verified that notch stress is effective for stress field and fatigue strength of complex engineering structures, which could consider the influence of welding geometry. However, due to the limitations of applicable conditions of criterion, the results of multiaxial fatigue assessment are not ideal, especially for multiaxial non-proportional loading. Therefore, based on the notch stress approach, several complex fatigue tests are extracted and re-analyzed in six common used multiaxial fatigue criteria. Correspondingly, the fitting notch stress S-N curves are described and analyzed statistically. It is found that the multiaxial non-proportional evaluation results are highly dispersive and unreliable. In order to obtain a more ideal evaluation result, the modified Findley criterion is renewed and re-evaluated based on the correction of stress ratio Kσ and phase difference Kδ.

Wear numerical assessment for partial slip fretting fatigue conditions

Abstract The aim of this work is to evaluate wear effects on life prediction for components subjected to fretting conditions. Therefore, fretting fatigue FE simulations have been carried considering the geometry update due to the material removal and results were compared to both experimental data and FE simulations where wear was neglected. Well known multiaxial fatigue criteria in association with the Theory of Critical Distances (TCD) have been used to estimate life. Results have shown that, for the data assessed, where fretting fatigue tests were conducted on a Ti-6Al-4V alloy under partial slip conditions, considering wear effects might slightly increase the accuracy of life estimates. However, this improvement may not be worth the increase in the computational cost in such analysis.

A fatigue crack initiation and growth life estimation method in single-bolted connections

Fatigue life estimation accuracy of mechanical parts and assemblies has always been the source of concern in different industries. The main contribution of this article lies in a study on the accuracy of different multiaxial fatigue criteria, proposing and investigating the accuracy of four optimized fatigue crack initiation life estimation methods—volume, weighted volume, surface and point, thereby improving the multiaxial fatigue life estimation accuracy. In order to achieve the goal, the fatigue lives of bolt clamped specimens, previously tested under defined experimental conditions, were estimated during fatigue crack initiation and fatigue crack growth and then summed together. In the fatigue crack initiation part, a code was written and used in the MATLAB software environment based on critical plane approach and the different multiaxial fatigue criteria. Besides the AFGROW software was utilized to estimate the crack growth share of fatigue life. Experimental and numerical results showed to be in agreement. Furthermore, detailed study and comparison of the results with the available experimental data showed that a combination of Smith–Watson–Topper approach and volume method results in lower error values, while a combination of Fatemi–Socie criterion and surface or point method presents estimated lives with lower error values. In addition, the numerical proposed procedure resulted in a good prediction of the location of fatigue crack initiation.

Validation of multiaxial fatigue criteria application to lifetime calculation of S355 steel under cyclic bending-torsion loading

The paper presents the validation of two multiaxial fatigue criteria with the implemented concept of life dependent material parameters. The recent research exhibits that an application of damage parameter defined by multiaxial fatigue criterion to lifetime calculation requires substituting material constants with the fatigue characteristic. The damage parameter is compared with the stress amplitude of given fatigue characteristic and in the result, the fatigue life is calculated. Since the introduced fatigue characteristics are also the function of a number of cycles to failure the calculation process of the final lifetime becomes complex. This life depended material parameter concept was successfully implemented into a few well-known fatigue criteria. The main aim of the paper is the validation of two multiaxial fatigue criteria under high cycle fatigue regime with the application of the life dependent material parameters.

Taking into account the non-proportional loading effect on high cycle fatigue life predictions obtained by invariant-based approaches

Industrial structures are often subjected to multiaxial fatigue loadings. If the multiple stress signals are not synced the loading is said to be non-proportional. Most of the multiaxial fatigue criteria give highly inaccurate lifetime predictions when used in the case of such loadings. The scalar equivalent stress defined by the criteria does not take into account the non-proportional nature of the multiaxial loading and leads to non-conservative predictions. Moreover a multiaxial fatigue criterion can only be applied on a stress cycle which has no clear definition when multiple unsynced signals are to be considered. This study addresses these issues by proposing a correction of an invariant based multiaxial fatigue criterion through the definition of a non-proportional degree indicator. A definition of multiaxial cycle is also given based on the Wang-Brown method. Finally a complete chain of invariant based lifetime prediction for non-proportional multiaxial fatigue is validated.

Recent progress in the application of multiaxial fatigue criteria to lifetime calculations

This paper presents the concept of life-dependent material parameters applied to multiaxial fatigue damage models. Every multiaxial fatigue limit criterion based on the history of the stress tensor components is defined by a scalar parameter that is compared with the fatigue limit. The defined damage parameter is usually also a function of some characteristic material parameters. These material parameters are usually derived from fatigue limits obtained under uniaxial and torsion loading. Attempts to extend this classic form of the damage parameter beyond the fatigue limit domain, i.e. to lifetime calculations, fail even within the high cycle fatigue domain. The aim of this paper is to demonstrate that the material parameters derived from fatigue limits should not be applied in multiaxial fatigue criteria for lifetime calculations. A definition of these material parameters based on applying fatigue uniaxial and torsion characteristics instead of fatigue limits implies that the resulting parameters are functions of the fatigue life. Applying a life-dependent material parameter to the Matake multiaxial fatigue criterion leads to a remarkable improvement in the fatigue life prediction for 2124-T851 aluminium alloy.

Multiaxial fatigue criteria applied to motor crankshaft in thermoelectric power plants

Fatigue failures of motor crankshafts operating in thermoelectric power plants have recently been reported. Stress fields provided by finite element calculations at critical points of a crankshaft that failed in service are used to test the structural integrity of the component. Taking into account the fact that the stresses acting at a given point are most likely out of phase, multiaxial fatigue criteria based on the von Mises stress are considered to be most suitable for predicting the fatigue behavior of the crankshaft. Using the von Mises stress, it was also possible to apply octahedral shear stress-based criteria and the results obtained have indicated that the crankshaft made of DIN 34CrNiMo6 steel should not suffer fatigue failure under the action of the stress fields in question. However, such failures have been occurring and this apparent discrepancy is presented and briefly discussed in the present study.

Bolt fatigue parametric study of a bolted assembly

Structural integrity of aircraft, nuclear power plants, space rockets, ships, automotive structures, biomedical devices, and many other applications, is a major design purpose and concerns various components subjected to cyclic loads for which fatigue is generally the dominant factor leading to its failure. The fatigue damage cumulation phenomenon is a process which may lead to cracks initiation and possibly to the structure failure under the action of variables stresses cycles. The mechanical components are generally subjected to multiaxial stress states. Taking into account this stress states triaxiality generally deals with multiaxial fatigue criteria. They are suitable tools for assessing the material fatigue resistance against periodical stress states, especially when they are multiaxial. The study carried out in this paper aims to analyze the fatigue behaviour of pre-stressed bolts involved in a so-called tee-stub bolted assembly that is subjected to variable loads. A multiaxial fatigue post-processing tool using two multiaxial fatigue approaches (integral approach and critical plan approach) is developed and implemented on Matlab software in order to assess the bolt fatigue damage and then its fatigue life through an iterative process. The tool is validated by fatigue test results on bolted assemblies found in the literature, which are additionally compared with those obtained by standards (Eurocode, VDI). A parametric study on the tee-stub is then performed.

ОЦЕНКА УСТАЛОСТНОЙ ДОЛГОВЕЧНОСТИ И ОПРЕДЕЛЕНИЕ КРИТИЧЕСКОЙ ПЛОСКОСТИ ПРИ МНОГООСНОМ ЦИКЛИЧЕСКОМ НАГРУЖЕНИИ С ПРОИЗВОЛЬНЫМ СДВИГОМ ФАЗ

The real experience of different structural elements shows that cyclic loading conditions and stress strain state are often quite different from laboratory test conditions such as axial tension-compression, bending or pure torsion. As a rule, the structural elements are subjected to complex (multiaxial) loading conditions during service, that is why multiaxial fatigue criteria should be used for durability estimation of such elements. A present multiaxial criterion allows us to estimate the number of cycles to fracture for specimens or structural element (fatigue life) with an influence of the orientation of the so-call critical plane of fatigue damage accumulation. Analytical solutions were obtained for the present fatigue criterion to determine the orientation of the critical plane of the fatigue damage development under cyclic loading for multiaxial stress states. Cyclic loading with arbitrary shifts of phases for the classical fatigue range (low-cycle and high-cycle fatigue) was considered. Several common cases of the three dimensional cyclic loading, i.e. tension-compression and bending-torsion, are studied. It is shown that at certain values of phase shifts the fatigue durability can be very low even under stress amplitudes that do not lead to fracture in the case of sine phase loading. The comparison with the experimental data and numerical calculations based on the other criterion is made. A disc of a low-pressure stage of a gas-turbine engine subjected to cyclic loading due to centrifugal forces was considered. By using a simplified stress distribution, as well as a stress distribution calculated by the finite element method, the areas of stress concentration and orientation of the critical plane in these zones are determine and the durability of the disk operating was estimated.

General Procedure for Formulation of Multiaxial Fatigue Failure Criteria in Frequency Domain

Fatigue life assessment under multiaxial loading conditions needs the use of multiaxial fatigue failure criteria. There are many formulations of such criteria which are usually divided in the groups of critical plane criteria and invariants based criteria. Other classifications refer to the parameter that determines fatigue, and these are stress, strain and energy criteria. Recently, the development of computational techniques for fatigue analysis in the frequency domain have been noticed. Analyzing the literature, it can be noted that these criteria are mainly created by the new formulation of them in the new domain. There is therefore a need to develop a general approach to the problem of formulating criteria in the frequency domain on the basis of existing proposals for the time domain. The paper presents the manner in which the values appearing in the criteria in the frequency domain can be determined. In particular, the process of formulating criteria of multiaxial random fatigue, using the critical plane approach proposed by Macha was presented. During the formation the linearity of such criteria was successfully used. Situations that indicate the correctness of transformations are also presented.

Mean stress effects on Low-Cycle Fatigue behaviour of Inconel 718 alloy

Uniaxial and biaxial fatigue test results related to Inconel 718 specimens are analysed by using the critical plane-based multiaxial fatigue criterion by Carpinteri et al., formulated in terms of strain, in conjunction with a model similar to that by Smith-Watson-Topper (SWT). More precisely, both smooth solid specimens and thin-walled tubular specimens subjected to proportional and non-proportional loading consisting of tension, torsion, and combined tension and torsion loading under strain control are examined, for strain ratio equal to 0 or -1. Fatigue life is then analytically computed through the above procedure and compared with the experimental one, in terms of number of loading cycles needed to form a surface crack whose length is equal to 1 mm.

Including the normal to shear stresses ratio in fatigue life estimation for cyclic loadings

The paper presents the estimation of the fatigue life under multiaxial cyclic loading of two construction materials. The main aim of this paper is to present a new method which allows evaluation of fatigue life during the design and construction phase of machine elements. In paper three well known multiaxial fatigue criteria based on the critical plane approach verified. This paper contains a proposition to define a new way of determining an orientation angle of the critical plane. The comparison between experimental and theoretical results varying the critical plane orientation appears to be satisfactory.

Influence of critical plane definition on fatigue lifetime estimation under variable amplitude nonproportional multiaxial loading.

In real operation, most of load bearing parts are commonly loaded with multiaxial variable amplitude loading. Fatigue lifetime estimation of such a component consists of multiple tasks. One of the most important problem to solve is how to handle multiaxiality of loading signal. Nowadays, the most commonly used way is use of multiaxial fatigue criterion based on critical plane theory. These criterions are based on assumption that fatigue lifetime of a component is determined by combination of shear and normal stresses (strains) in particular plane (critical plane). The definition of such a plane varies depending on different used criterions. While fatigue lifetime of component loaded with proportional loading signal can be estimated based on damage accumulated in critical plane, during the fatigue lifetime estimation under variable amplitude nonproportional loading the damage in noncritical plane has to be considered as well. This, however, leads to inaccuracy of the final results as multiaxial criterions often incorrectly calculate damage in noncritical plane. The aim of this paper is to discuss the influence of critical plane definition on fatigue lifetime estimation under variable amplitude nonproportional multiaxial loading. The results from fatigue lifetime estimations of component loaded by modeled signal using multiple different multiaxial criterions (with different critical plane definition) are presented and critically discussed.

An alternative approach to calibrate multiaxial fatigue models of steels with small defects

In this work the authors propose a new methodology to estimate threshold loading conditions for naturally defective steels under complex stress states. In this setting, multiaxial fatigue models based on the critical plane approach and in the stress invariant approach are adapted to assess the effect of non-metallic inclusions in the material. In order to do so, it will be used a method that relates the √area parameter of a small defect and the Vickers hardness of the material Hν) with the nominal fatigue limit for this material either under uniaxial (σw) or under torsional (τw) loading. Therefore, uniaxial and torsional fatigue limits usually required to calibrate the multiaxial criteria will be calculated by the √area parameter. With this methodology the multiaxial fatigue criteria utilized are not changed. However, calibrating them is considerably cheaper and faster compared to traditional methods. To assess the new methodology, combined axial-torsional multiaxial fatigue data in DIN 42CrMo6 steel generated by the authors will be used. The proposed methodology is compared to the experiments and agreement within 5% error bands were obtained.