Multiaxial High-cycle Fatigue Criterion Research Articles

Fatigue assessment of notched specimens by means of a critical plane-based criterion and energy concepts

A strain-based multiaxial fatigue criterion previously proposed for fatigue assessment of unnotched specimens is here extended to the case of notched ones. Such a criterion is a reformulation of the stress-based multiaxial High-Cycle Fatigue (HCF) criterion by Carpinteri and Spagnoli. The extension herein presented considers as the critical point, where to perform the fatigue assessment, the material point located at a certain distance from the notch tip, depending such a distance on both the biaxiality ratio (defined as the ratio between the applied shear stress amplitude and the normal stress amplitude) and the control volume radii R1 (related to Mode I) and R3 (related to Mode III). Some multiaxial fatigue data related to specimens made of titanium grade 5 alloy (Ti–6Al–4V) and weakened by sharp notches are examined to validate the extended criterion.

Life estimation by varying the critical plane orientation in the modified Carpinteri-Spagnoli criterion

The modified Carpinteri-Spagnoli (C-S) criterion is a multiaxial high-cycle fatigue criterion based on the critical plane approach. According to such a criterion, the orientation of the critical plane is linked to both the averaged directions of the principal stress axes and the fatigue properties of the material. The latter dependence is taken into account through a rotational angle, ?. Then, the multiaxial fatigue strength estimation is performed by computing an equivalent stress amplitude on the critical plane. In the present paper, some modifications of the original ? expression are implemented in the modified C-S criterion. More precisely, such modified expressions of ? depend on the ratio between the fatigue limit under fully reversed shear stress and that under fully reversed normal stress (in accordance with the original expression), and can be employed for metals ranging from mild to very hard fatigue behaviour. Some experimental data available in the literature are compared with the theoretical results in order to verify if the modified ?expressions are able to improve the fatigue strength estimation capability of the modified C-S criterion.

Defect acceptability under full-scale fretting fatigue tests for railway axles

This paper presents a new approach based on the application of a multiaxial high cycle fatigue criterion together with the use of El-Haddad correction for investigation of fretting fatigue in railway axles. Stress path along the axle–wheel contact, determined by the FE analysis, was implemented into different multiaxial fatigue criteria in order to predict critical sites of nucleation. The equivalent fatigue limit expressed by the applied criterion is compared with the crack size dependent fatigue limit described by El-Haddad correction in order to define a defect size acceptability criterion. Verification of the proposed approach was done by post-test failure investigation of the full-scale axle tests conducted as a part of Euraxles project. Scanning electron microscope (SEM) examination of the failed press-fit sections revealed a critical defect size in the order of 200μm in depth for non-propagating cracks. The obtained results were found to be consistent with the estimations made by the proposed approach.

A critical assessment of methods for the determination of the shear stress amplitude in multiaxial fatigue criteria belonging to critical plane class

Multiaxial high cycle fatigue criteria based on the critical plane approach necessitate unambiguous definitions of the amplitude and mean value of the shear stress (τa and τm) acting on the material planes. Four of the existing definitions relate the values of τa and τm to a geometrical element of the curve described by the tip of the shear stress vector (curve Ψ), respectively, the radius of the Minimum Circumscribed Circle, the Longest Chord, the Longest Projection, the diagonal of the Maximum Rectangular Hull (MRH).In this paper a critical assessment of the above definitions is proposed, focusing on that based on the concept of MRH, which is the most recently developed. The main issues of the comparison are the uniqueness of the solution in the determination of τa and τm, the ability to differentiate proportional and non-proportional stresses, the differences of the values of τa obtained by each of the 4 methods for differently shaped curves Ψ.

A New Multiaxial High-Cycle Fatigue Criterion Based on the Critical Plane for Ductile and Brittle Materials

An improved high-cycle multiaxial fatigue criterion based on the critical plane was proposed in this paper. The critical plane was defined as the plane of maximum shear stress (MSS) in the proposed multiaxial fatigue criterion, which is different from the traditional critical plane based on the MSS amplitude. The proposed criterion was extended as a fatigue life prediction model that can be applicable for ductile and brittle materials. The fatigue life prediction model based on the proposed high-cycle multiaxial fatigue criterion was validated with experimental results obtained from the test of 7075-T651 aluminum alloy and some references.

Estimation of Maximum Fatigue Loads and Bearing Life in Ball Bearings Using Multi-Axial High-Cycle Fatigue Criterion

The methodology of the fatigue load and the bearing life estimation for the ball bearings is presented in the paper. The proposed algorithm is based on the elliptical contact solution and the application of the multi-axial high-cycle fatigue criterion. As the example the radial 6204* and thrust 51104 ball bearings are investigated (SKF). The maximal fatigue loadings are calculated for different geometry (race conformity ratio) and the bearing life of the bearings. The proposed model is also verified with use of the finite element calculations.

Lifetime estimation in the low/medium-cycle regime using the Carpinteri–Spagnoli multiaxial fatigue criterion

A critical plane-based high-cycle multiaxial fatigue criterion, known as the Carpinteri–Spagnoli (C–S) criterion, is here extended to evaluate the fatigue lifetime of plain metallic components under constant amplitude loading in the low/medium-cycle regime. This extended criterion, based on strain components, resolves the strain tensor into the normal and shear components acting on the critical plane, which is determined on the basis of the principal strain courses over the loading cycle. An equivalent normal strain amplitude, computed through a quadratic combinations of strain components in the critical plane, is taken as the fatigue damage parameter. The required input parameters of the criterion are obtained from the classical Manson–Coffin–Basquin law for axial loading. A validation by experimental data pertaining the biaxial fatigue of plain steel specimens under both proportional and non-proportional loadings is performed.

Multiaxial high-cycle fatigue criterion for notches and superficial small holes from considerations of crack initiation and non-propagation

A new criterion is proposed for evaluating the multiaxial high-cycle fatigue limit of components with notches and superficial small holes. Two parameters are specified: (1) one governing crack initiation and (2) the other governing initial crack growth. The new criterion is based on the multiaxial fatigue criterion for smooth components previously proposed by the authors. The accuracies of the proposed and conventional criteria are evaluated using experimentally determined fatigue limit data of notches and superficial small holes under combined bending and torsion stresses and combined axial and torsion stresses. The error of the proposed criterion is approximately 10%.

A Strain-based Multiaxial Fatigue Criterion Connected to the Critical Plane Approach

A critical plane-based high-cycle multiaxial fatigue criterion, known as the Carpinteri-Spagnoli (C-S) criterion, is here extended to evaluate the fatigue lifetime of plain metallic components under constant amplitude loading in the low/medium-cycle regime. An equivalent strain amplitude, computed through a quadratic combinations of strain components in the critical plane, is taken as the fatigue damage parameter. A validation by experimental data pertaining the biaxial fatigue of plain steel specimens under both proportional and non-proportional loadings is performed.

Micromechanical study of the loading path effect in high cycle fatigue

In this work, an analysis of both the mechanical response at the grain scale and high cycle multiaxial fatigue criteria is undertaken using finite element (FE) simulations of polycrystalline aggregates. The metallic material chosen for investigation, a pure copper, has a Face Centred Cubic (FCC) crystalline structure. Two-dimensional polycrystalline aggregates, which are composed of 300 randomly orientated equiaxed grains, are loaded at the median fatigue strength defined at 107cycles. In order to analyse the effect of the loading path on the local mechanical response, combined tension–torsion and biaxial tension loading cases, in-phase and out-of-phase, with different biaxiality ratios, are applied to each polycrystalline aggregate. Three different material constitutive models assigned to the grains are investigated: isotropic elasticity, cubic elasticity and crystal plasticity in addition to the cubic elasticity. First, some aspects of the mechanical response of the grains are highlighted, namely the scatter and the multiaxiality of the mesoscopic responses with respect to an uniaxial macroscopic response. Then, the distributions of relevant mechanical quantities classically used in fatigue criteria are analysed for some loading cases and the role of each source of anisotropy on the mechanical response is evaluated and compared to the isotropic elastic case. In particular, the significant influence of the elastic anisotropy on the mesoscopic mechanical response is highlighted. Finally, an analysis of three different fatigue criteria is conducted, using mechanical quantities computed at the grain scale. More precisely, the predictions provided by these criteria, for each constitutive model studied, are compared with the experimental trends observed in metallic materials for such loading conditions.

Application of Selected Multiaxial High-Cycle Fatigue Criteria to Rolling Contact Problems

The risk of fatigue failure of elements working in rolling contact conditions (such as railway wheels, rolling bearings, etc.) is a significant issue with respect to safety and economy. In this case the complex and non-proportional stress state with pulsating three dimensional compression occurs. Therefore, the analysis of fatigue life of structures working in rolling contact conditions can be performed using recently proposed multiaxial high-cycle fatigue criteria. However, there is no hypothesis that could be universally accepted for calculations of fatigue strength. Furthermore, not all criteria proposed in literature for rolling contact fatigue (RCF) analysis can predict it. In the paper, the most popular criteria based on different theories are investigated in the application to RCF problem. Moreover, modification of the popular Dang Van hypothesis is proposed. The problem of free and tractive rolling contact fatigue is analysed on the example of a cylindrical crane wheel and spherical thrust roller bearing.

Multiaxial high-cycle fatigue criterion considering crack initiation and non-propagation

A new criterion for multiaxial high-cycle fatigue limit is proposed using two parameters: one governing crack initiation and the other governing initial crack growth. The axial fatigue limit and the true fracture strength are used as the material properties required in estimations. The prediction accuracies using conventional criteria and the proposed criterion were compared using known data about fatigue limits under different loading conditions. The comparison was made for the effects of phase difference, mean stress, and the combination of phase difference and mean stress. The estimation error of the proposed criterion was approximately 10%, which is better than that of the other criteria used for comparison.

The effect of geometric features on multi-axial fatigue behaviour of aluminothermic rail welds

Aluminothermic rail welds typically exhibit a variable and often inferior performance when compared with flash butt welds. Fatigue failure as a result of surface defects or harsh geometric features in the presence of high axle loads and tractive forces gives rise to the so-called straight break and horizontal split web fractures. In this study, the reduction of fatigue performance due to geometric irregularities is investigated using a multi-axial high cycle fatigue criterion based on the critical plane concept. A thermo-structural finite element model of a track containing an aluminothermic weld is linked with a developed computer code to perform fatigue crack initiation analysis. Two geometrically different aluminothermic welds, one of which is widely used in Australian heavy haul railways, are investigated in terms of fatigue probability, to facilitate a better insight into the effect of weld collar shape and geometry at the edge of the weld collar on fatigue behaviour. The results confirm that the amount of fatigue damage is critically dependent on the geometric features of the collar edge, especially at the underhead radius which undergoes severe fatigue loading under some operational conditions.

Probabilistic Assessments of the Plate Using Monte Carlo Simulation

This paper presents the probabilistic analysis of the plate with a hole using several multiaxial high cycle fatigue criteria (MHFC). Dang Van, Sines, Crossland criteria were used and von Mises criterion was also considered for comparison purpose. Parametric finite element model of the plate was developed and several important random variable parameters were selected and Latin Hypercube Sampling Monte-Carlo Simulation (LHS-MCS) was used for probabilistic analysis tool. It was found that, different structural reliability and sensitivity factors were obtained using different failure criteria. According to the results multiaxial fatigue criteria are the most significant criteria need to be considered in assessing all the structural behavior especially under complex loadings.

Probabilistic High Cycle Multiaxial Fatigue Analysis Using Finite Element Method

Inhomogeneous materials and manufacturing tolerances occurred in the modern manufacturing and material processing sectors frequently lead to premature failures. During the operation of the components, multiaxial loadings and stresses suffered damage of the structural integrity severely. Therefore, this paper discusses the utilisations of several high cycle multiaxial fatigue criteria in the probabilistic design and analysis. The variations of material and geometrical properties are taken into account in order to study the probability of failure. High cycle multiaxial fatigue criteria are then used to determine the equivalent stress and the deflection. The implementations of these criteria were realised using Ansys Parametric Design Language (APDL) provided in the commercial software ANSYS. From the probabilistic results, von Mises criterion underestimated the probability of failure especially for displacement cases while high cycle multiaxial fatigue criteria, specifically Dang Van and Crossland criteria,...

An improved multiaxial high-cycle fatigue criterion based on critical plane approach

Several groups of fatigue damage parameters are discussed and then an improved multi- axial high-cycle fatigue criterion based on critical plane defined by the plane of maximum shear stress range is presented in this paper. A compromising solution to consider the mean normal stress acting on the critical plane is also proposed. The new fatigue criterion extends the range of metallic materials which is valid for the ratio 1.25 < f −1/t−1 < 2. The predictions based on the presented model show a good agreement with test data.

Effect of retained austenite on high cycle fatigue behavior of carburized 14NiCr11 steel

Two vacuum carburizing treatments were applied to ductile steel 14NiCr11 to obtain equivalent hardened layers with retained austenite contents of 25% and 41%. The properties of the carburized surfaces were examined and characterized before fatigue tests and during cyclic loading. Transformation of retained austenite into martensite during loading, was evaluated by dispersive X-ray diffraction method. The effects of this transformation on the residual stresses have been measured by X ray diffraction in martensite and in retained austenite structures. It was shown that the cyclic retained austenite transformation caused a redistribution of the compressive residual stresses and an increased surface hardness that stabilized after a small number of cycles. The dependence of fatigue behavior on surface properties was determined, and a relationship between the stabilized state and the fatigue limit is suggested. A phenomenological approach is proposed to correlate the influence of surface hardening and the stabilized residual stresses on fatigue limit of carburized specimens. The Crossland, Dang Van and Findley-Matake, multiaxial high cycle fatigue criteria were used in this approach and results have shown a good agreement with experimental data.

Three energy‐based multiaxial HCF criteria for fatigue life determination in components under random non‐proportional stress fields

ABSTRACTThe prominent high cycle fatigue (HCF) criteria have been generally proposed based on definition of an equivalent stress that is mainly a modified version of a static failure criterion or a static yield function. One or more effects including the mean normal and shear stresses, different phase shifts or random frequencies of the stress components, relative instantaneous time variations of the stress components, relative time locations of the extrema of the time histories of the stress components, etc. have not been considered by many of the previously proposed criteria. In the present paper, based on the proposed instantaneous stress amplitude and mean stress concepts, three new energy‐based HCF criteria are proposed to overcome the mentioned shortcomings. A relevant fatigue life assessment algorithm is proposed and results of the prominent criteria are compared with results of the proposed criteria as well as the experimental results prepared by the author. To introduce a comprehensive study, the criteria are examined for components with complicated geometries under proportional, non‐proportional and random loadings. Results confirm the efficiency and accuracy of the proposed criteria. Furthermore, it is deduced that the Liu–Zenner type criteria which include the hydrostatic stress implicitly are more accurate than the Papadopoulos‐type criteria that consider the hydrostatic stress explicitly.

Surface initiated tooth flank damage: Part I: Numerical model

A numerical model for the prediction of surface initiated damage on gear tooth flanks (micropitting and mild wear) is presented. This model hinges on a model of the mixed film lubrication regime and on the application of the Dang Van high-cycle multi-axial fatigue criterion. A simulation of the meshing of spur gears is performed in order to gain some understanding of the events associated with contact fatigue surface damage.

Two New Multiaxial HCF Criteria Based on Virtual Stress Amplitude and Virtual Mean Stress Concepts for Complicated Geometries and Random Nonproportional Loading Conditions

Abstract Almost all of the available multiaxial high cycle fatigue (HCF) criteria are proposed based on definition of an equivalent stress expression that is a modified version of a static equivalent stress definition or a static yield function. All the equivalent stress expressions proposed so far in the fatigue analysis field have been expressed in semistationary forms wherein the global cyclic rather than the instantaneous changes are considered. In the present paper, a new technique for instantaneous fatigue equivalent stress definition is introduced based on new concepts of instantaneous (virtual) stress amplitude and instantaneous (virtual) mean stress. Then, new HCF criteria are proposed using two approaches: (1) polynomial approach and (2) integral approach, to overcome the shortcomings of the available criteria. A relevant fatigue life assessment algorithm is also proposed, and results of the available criteria are compared with results of the proposed criteria as well as the experimental results prepared by the author. To introduce a comprehensive study, the criteria are evaluated for components with complicated geometries under proportional, nonproportional, and random nonproportional loadings. Results reveal that predictions of the proposed approaches are more accurate.