Multiaxial High-cycle Fatigue Criterion Research Articles

Fatigue life prediction of the nitrided steel by multiaxial high cycle fatigue criteria

The present study aims to predict the fatigue strength of ion-nitrided 42CrMo4 steel, using multiaxial high cycle fatigue (HCF) criteria and considering the effects of stabilized residual stresses and surface hardening. The predicted fatigue strength was compared to experimental data obtained after three-points bending fatigue tests at two stress ratios (0.1 and 0.5) and for notched (Kt = 1.6) nitrided and untreated specimens. A 3D finite element (FE) model of a three-point bending fatigue test was developed under ABAQUS software in order to determine the actual applied cyclic stress state at the notch. The results show that ion-nitriding treatment led to 32% improvement in the fatigue strength at 106 cycles compared to the untreated material. This improvement is explained by the advantageous effect of ion-nitriding treatment in terms of compressive residual stresses and surface layer hardening. Both stabilized residual stress state and hardening effects were successfully implemented into various multi-axial HCF criteria, including Sines, Crossland, Dang Van and Matake criteria. A sensitivity analysis has shown that Crossland criterion has permitted to predict the fatigue limits in accordance with the experimental results.

On the predictive capability of stress-based multiaxial high-cycle fatigue criteria

On the predictive capability of stress-based multiaxial high-cycle fatigue criteria

Assessment of multiaxial fatigue of crankshafts subjected to both designed and theoretically critical loadings

Fatigue failures of motor crankshafts operating in thermoelectric power plants are recently being reported. Since crankshafts are subjected to non-trivial stress states throughout their operation, multiaxial fatigue theory is required. A previously carried-out finite element analysis (FEM) that determined the stress states of critical points within the crankshaft’s was used as input. Biaxial stress states were extracted from the FEM analysis and submitted to multiaxial fatigue testing. The fatigue behaviour of the given loading conditions was assessed by using seven multiaxial high-cycle fatigue criteria, namely Findley (F), Matake (M), McDiarmid (McD), Susmel & Lazzarin (S&L), Carpinteri & Spagnoli (C&S), Liu & Mahadevan (L&M) and Papadopoulos (P). An additional set of critical loading conditions was also considered and submitted to both fatigue testing and theoretical predictions. By using experimentally observed fatigue resistance limits, the predictions deliver a slight tendency to fatigue failure in their prediction, in contrast to experimental observations. The results were used to compare the prediction capability of the selected criteria, where all presented reasonably fair agreement. Within the present study’s context, Papadopoulos’ model was the one that presented the least spread in fatigue predictions while also presenting the closest to ideal average behaviour, with the convenient feature of being slightly conservative.

Numerical and Experimental Investigation of Cumulative Fatigue Damage under Random Dynamic Cyclic Loads of Lattice Structures Manufactured by Laser Powder Bed Fusion

Lattice structures are lightweight engineering components suitable for a great variety of applications, including those in which the structural integrity under vibration fatigue is of paramount importance. In this work, we experimentally and numerically investigate the dynamic response of two distinct lattice configurations, in terms of fatigue damage and life. Specifically, Face-Centered-Cubic (FCC) and Diamond lattice-based structures are numerically studied and experimentally tested under resonant conditions and random vibrations, until their failure. To this end, Finite Element (FE) models are employed to match the dynamic behavior of the system in the neighborhood of the first natural frequency. The FE models are employed to estimate the structural integrity by way of frequency and tip acceleration drops, which allow for the identification of the failure time and a corresponding number of cycles to failure. Fatigue life under resonant conditions is well predicted by the application of conventional multiaxial high cycle fatigue criteria to the local state of stress. The same approach, combined with the Rainflow algorithm and Miner’s rule, provides good results in predicting fatigue damage under random vibrations.

Gear Root Bending Strength: A Comparison Between Single Tooth Bending Fatigue Tests and Meshing Gears

Abstract Gear tooth breakage due to bending fatigue is one of the most dangerous failure modes of gears. Therefore, the precise definition of tooth bending strength is of utmost importance in gear design. Single tooth bending fatigue (STBF) tests are usually used to study this failure mode since they allow to test gears, realized and finished with the actual industrial processes. Nevertheless, STBF tests do not reproduce exactly the loading conditions of meshing gears. The load is applied in a predetermined position, while in meshing gears, it moves along the active flank; all the teeth can be tested and have the same importance, while the actual strength of a meshing gear, practically, is strongly influenced by the strength of the weakest tooth of the gear. These differences have to be (and obviously are) taken into account when using the results of STBF tests to design gear sets. The aim of this article is to investigate in detail the first aspect, i.e. the role of the differences between two tooth root stress histories. In particular, this article presents a methodology based on high-cycle multi-axial fatigue criteria to translate STBF test data to the real working condition; residual stresses are also taken into account.

Validating the Methods to Process the Stress Path in Multiaxial High-Cycle Fatigue Criteria.

The paper discusses one of the key features in the multiaxial fatigue strength evaluation—the procedure in which the stress path is analyzed to provide relevant measures of parameters required by multiaxial criteria. The selection of this procedure affects the complete equivalent stress derived for any multiaxial load combinations. Three major concepts—the minimum circumscribed circle, minimum circumscribed ellipse, and moment of inertia methods—are described. Analytical solutions of their evaluation for multiaxial stress state with components described by harmonic functions are provided. The concepts are validated on available experimental data when included into six different multiaxial fatigue strength criteria. The results show that the moment of inertia results in too conservative results. Differences between both methods of circumscribed entities are much smaller. There are indications however that the minimum circumscribed ellipse solution works better for critical plane criteria and for the criteria based on stress tensor transformation into the Ilyushin deviatoric space. On the other hand, the minimum circumscribed ellipse solution tends to shift integral criteria to the conservative side.

On the Influence of Mean Shear Stress on Multiaxial High Cycle Fatigue of Metallic Materials

A study has been made of the influence of a superimposed mean shear stress on the capability of some multiaxial high cycle fatigue criteria to predicting fatigue behavior of 42CrMo4 and 34Cr4 alloy steels. Five selected critical plane-based criteria, namely Matake (M), Susmel & Lazzarin (S&L), Findley (F), Carpinteri & Spagnoli (C&S) and Liu & Mahadevan (L&M), were applied to a number of published experimental fatigue resistance limit tests, involving synchronous sinusoidal in-phase and out-of-phase bending and torsion. Applying to the same loading conditions a mesoscopic scale-based criterion proposed by Papadopoulos (P), one could verify that predictive capability of such an approach is almost invariably superior to those associated with the M, S&L, F, C&S and L&M models. As the Papadopoulos criterion is independent of mean shear stress, it seems appropriate to conclude that the inclusion of such a stress as loading parameter in the critical plane-based models does, in fact, exert a negative influence on their predictive capability. Finally, it is worth mentioning that, except for the Matake, S&L and L&M criteria, the other critical plane-based criteria exhibit a dependence of the fatigue resistance in pure torsion with respect to a superimposed mean shear stress, in disagreement with well-established experimental observations.

Notch fatigue life estimation of Ti-6Al-4V

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-4 V, material attracting significant interest by leading industries, such as the biomedical one.

Evaluation of multiaxial high-cycle fatigue criteria under proportional loading for S355 steel

Multiaxial stresses are usually present in engineering structures and are often associated to multiaxial fatigue failures. However, multiaxial fatigue is an open topic, full of questions and different points of view. Therefore, an experimental campaign of uniaxial and multiaxial fatigue tests under proportional loading was conducted aiming at evaluating the multiaxial fatigue behaviour of S355 structural steel in the high-cycle fatigue regime. Five different multiaxial models were used and evaluated, namely the Sines, Findley, McDiarmid, Dang Van and Susmel-MWCM. Each of them was applied to experimental data and the mean fatigue curves obtained from it were evaluated and compared. The coefficients present in each model definition were studied and determined through different methods. The Dang Van’s multiscale approach and Susmel model showed great accuracy in the description of the fatigue behaviour of the S355 steel, providing the best correlation of the uniaxial and multiaxial experimental data.

Multiaxial High Cycle Fatigue Criteria Based on Fracture Plane Identification: Applicability to Metallic Materials

Two multiaxial high cycle fatigue criteria pertaining to the critical plane-based approach are reviewed. The models were proposed by Carpinteri and Spagnoli (C&S) and Liu and Mahadevan (L&M), and unlike other models based on the same approach, they have the critical plane directly correlated with the fatigue fracture plane. As the aim of this study is mainly to compare their capability to predict fatigue failure, the two models were applied to a number of published experimental fatigue tests, involving synchronous sinusoidal in-phase and out-of-phase bending and torsion. The results indicate that both models possess good predictive capability under fully reversed stresses, with the L&M model being on the average slightly more conservative. Applying, to the same loading conditions, a mesoscopic scale-based approach proposed by Papadopoulos, one can verify that its predictive capability is as good as those corresponding to the C&S and L&M criteria. However, in the presence of superimposed mean stresses, the capability of these two models to predict fatigue behavior is seen to be considerably lower than that detected for Papadopoulos’.

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.

Corrected stress field intensity approach based on averaging superior limit of intrinsic damage dissipation work

Corrected stress field intensity obtained by averaging the superior limit of intrinsic damage dissipation work in critical domain, which considers thoroughly thermodynamic consistency within irreversible thermodynamic framework, was proposed for predictions of high-cycle fatigue endurance limits. Simultaneously, the effects of mean stress, additional hardening behavior related to non-proportional loading paths and stress gradients on multiaxial high-cycle fatigue are taken into account in the proposed approach. The approach is an extension of the general stress field intensity. For a better comparison, existing multiaxial high-cycle fatigue criteria were employed to predict the endurance limits of different metallic materials subjected to different multiaxial loading paths, and it is shown that present proposal performs better from statistical value of error indexes, which make the proposed approach of corrected stress field intensity and its associated concepts provide a new conception to predict endurance limits of multiaxial high-cycle fatigue with high accuracy.

Fatigue reliability prediction of defective materials based on a useful equivalent Wöhler curve

The purpose of this manuscript consists in suggesting an approach able to predict the reliability of the fatigue behavior devoted to defective material. A multiaxial high cycle fatigue criterion is adopted and improved by taking into account the 3D stress gradient effect around a defect. An equivalent multiaxial stress is figured out and reported in a useful SN curve. The proposed approach gives a more secure prediction of polycyclic fatigue behavior by coupling FE analysis and Monte Carlo reliability from which practical Iso-probabilistic SN curves are deduced. An application has been made with defective C35 steel. It has been noted that the findings are in good accord with the experimental investigation and leads to a greater reliable high cycle fatigue forecasting compared to the deterministic results. This method has also been used to analyze and discuss the impact of the defect on the fatigue behavior of the structure. This coupling Fatigue reliability gives an attractive and a strong engineering fatigue forecasting for design office.

Mode I+II Fatigue Crack Growth Delay by Stop-Holes

The technique of retarding the growth of fatigue cracks by drilling holes on the crack tip is well known. Most of the research works on this subject are limited to fatigue cracks subjected to mode I loading conditions. In the present work the fatigue crack growth retardation by stop-holes of cracks under mode I+II loading is investigated. The proposed approximate solution is based on the implementation of a mixed-mode fatigue crack growth model and a multiaxial high cycle fatigue criterion. Numerical results for mode I+II fatigue crack growth retardation on Al-2024 thin plate are derived and the effect of the crack inclination angle, as well as the diameter of the stop-hole, are discussed and commented.

An efficient algorithm for the solution of min-max problems in multiaxial fatigue

Numerous fatigue criteria require the evaluation of critical quantities to estimate fatigue damage. The approach based on the construction of the minimum circle or hypersphere is often employed in multiaxial high-cycle fatigue criteria to compute critical quantities as the amplitude and mean value of the shear stress. Such a construction can be mathematically formulated as a min-max optimization problem for which efficient numerical strategies are of utmost importance. The present paper proposes a novel algorithm for solving such an optimization problem. The algorithm is based on the alternating direction method of multipliers (ADMM) and is very simple to implement. A wide range of fatigue loading paths, formulated in the two-dimensional and deviatoric spaces, are considered for numerical testing. Comparisons with reference solutions and with two alternative optimization approaches demonstrate the accuracy as well as the high efficiency of the proposed ADMM-based algorithm. A discussion on the adopted stopping criterion and on algorithm parameters is also addressed.

On the applicability of multiaxial high cycle fatigue criteria to metallic materials

A comparative study is made of the applicability of critical plane based multiaxial high cycle fatigue models to predicting the fatigue behavior of metallic materials. A number of models, namely Matake, McDiarmid, Carpinteri and Spagnoli, Liu and Mahadevan and Papadopoulos, were applied to fatigue limit states, involving synchronous fully reversed in-phase sinusoidal bend and torsion loading. The results obtained indicated a good predictive capability of the models with an average error index situated approximately between -5,5% and 4,5%. However, this average was limited to less than 3% for the latter three models. Finally, the critical plane orientation, which, for a given material, is characteristic of the proper model, is compared with that of the fracture plane, exclusively determined by the ratio between the shear stress and normal stress amplitudes.

Numerical assessment of fatigue load capacity of cylindrical crane wheel using multiaxial high-cycle fatigue criteria

The application of multiaxial high-cycle fatigue criteria to the analysis of the subsurface rolling contact fatigue of structures working in contact conditions is discussed. In such objects, an increase in compressive and shear stresses is strongly non-proportional. Therefore, the first part of the paper is devoted to the comparison of the results of six recently used high-cycle fatigue criteria estimating the effort for both different multiaxial proportional and non-proportional loads. In the second part of the paper, the issue of frictionless and tractive rolling contact fatigue is discussed. The fatigue load capacity of a crane wheel has been estimated using recently popular criteria. The orientation of critical planes and location of dangerous points are determined and discussed in detail. It has been found that the Dang Van criterion, which is often proposed in rolling contact fatigue analysis, underestimates the equivalent fatigue stress for such type of loads. Comparison of the results obtained using different multiaxial criteria with the results of the experimental tests enables a selection of criteria suitable for fatigue assessment of machine parts working in cycling rolling contact conditions.

Size optimization of rectangular cross section members subject to fatigue constraints

Although in the scientific literature there are studies regarding optimization of structural members subject to static loads or even cyclic in-phase loads, the optimization of structures subject to cyclic, out-of-phase multiaxial loads is still an unexplored issue. In this paper, we present an approach to the problem of size optimization of rectangular cross-section members subject to multiaxial in-phase and out-of-phase cyclic loads. The objective of the optimization is to minimize the cross sectional area of such elements while retaining their fatigue endurance. Under the proposed methodology, optimum values of the area are achieved for six loading cases and for three values of the height to width ratio of the cross section, and these values are reported. The novelty of the approach lies in the inclusion of two multiaxial high cycle fatigue criteria, i.e., Dang Van and Vu-Halm-Nadot ones, as constraints for size optimization problems, fully integrated within an in-house developed tool, capable of handling non-proportional stresses. A plot of the feasible solution space for this optimization problem is also obtained.

Multiaxial high-cycle fatigue life prediction model based on the critical plane approach considering mean stress effects

The aim of this paper is to propose a modified multiaxial high-cycle fatigue criterion based on the critical plane approach. The proposed criterion contains three parameters, that is, shear stress amplitude, normal stress amplitude and mean normal stress. In order to take into account the mean shear stress effects, the critical plane is determined by the maximum shear stress. In the proposed multiaxial fatigue criterion, the influence of mean normal stress on fatigue damage is also considered. Based on the proposed criterion, the multiaxial fatigue life is predicted, and the results showed a good agreement with experimental data obtained from some literatures.

Multiaxial high-cycle fatigue criteria and life prediction: Application to gas turbine blade

A recent work conducted by the authors (Maktouf and Saï, 2015) demonstrated that the root cause of the premature blade failure was caused by high-cycle fatigue (HCF) mechanism initiated at a localized carbon-rich area inducing grain boundary brittleness. The blade was subject to multiaxial cyclic loadings during its service life and any attempt to assess component fatigue strength leads to the question of choosing an appropriate fatigue design criterion. In this paper several multiaxial fatigue models are applied as post-processing step of the Finite Element Analysis (FEA) output results and the estimated fatigue lifetimes were assessed under different loading conditions. The material fatigue parameters, required as an input to the selected fatigue models were determined through a series of bending and torsion tests on specimens made of aged Inconel 718. A numerical post-processing algorithm was developed for Fatemi-Socie fatigue criterion and included as additional post-computation model in the used computer aided fatigue damage evaluation tool. The authors point out that the majority of the multiaxial fatigue studies available in the literature are conducted mainly for correlating the experimental laboratory results on specimens while they have been used in the frame of this study to investigate their application to an industrial case.