Multiaxial High-cycle Fatigue Research Articles

A continuum approach to multiaxial high-cycle fatigue modeling for ductile metallic materials

In this work we propose a generalization of the endurance function employed in the continuum approach to high-cycle fatigue modeling by Ottosen et al. (2008). The von Mises-type backstress-modified effective stress term of the original formulation is replaced by the non-quadratic Hershey-Hosford function, which introduces flexibility with respect to the predicted fatigue limit in pure shear. While the original model assumes a fixed ratio between the fatigue limits in fully reversed torsion and fully reversed bending of 0.5774 for all materials, the modification enables the ratio to take on values on the interval from 0.5 to 0.5852 by calibration to experimental data that is readily available in the literature. Like the original formulation simplifies to the invariant-based Mises-Sines fatigue limit criterion for proportional stress histories, the current proposal can be written as a Hershey-Hosford-Sines criterion. A systematic validation to experimental multiaxial infinite fatigue life data from eight different mild and semi-hard metals with fully reversed torsion and bending fatigue limit ratios lower than 0.6 demonstrates that the proposed modification increases the accuracy and reduces the number of non-conservative predictions.

Stress-Based Model for Calculating the Opening Angle of Notch Cracks in a Magnesium Alloy under Multiaxial Fatigue

This paper presents a model to calculate the opening angle of crack initiation in notched fractures subjected to multiaxial loading. To validate the proposed model, a study was performed on polished AZ31B-F magnesium alloy specimens under multiaxial high-cycle fatigue loading. The specimens exhibited a notch in the smaller cross-sectional area, which was created with a special drilling jig to promote the formation of fatigue cracks in this localized area of the specimen. The load paths used in the experiments and numerical analyses were proportional and non-proportional, resulting in different stress states in the crack front opening, which were determined by finite element analysis to validate the proposed model. To obtain more accurate numerical results for these estimates, these finite element analyses were performed using the nonlinear Chaboche plasticity model of ABAQUS® 2021 software. A sensitivity analysis was also performed to determine which load component—axial or torsional—has a greater influence on the fatigue strength and contributes significantly to the crack opening process. The results show that the type of load path and the stress level of each load component—axial and torsional—has a strong influence on the opening angle of the notch crack and the fatigue lifetime of the specimen. This result is confirmed not only by the experimentally determined fatigue strength, but also by a fractographic analysis performed on the surface of the specimens for both load paths. Moreover, the results show an acceptable correlation between the experimental results and the estimates obtained with the proposed model and the stresses obtained with the finite element analysis.

Multiscale-based multiaxial fatigue model of short fiber reinforced polymer composites under high-cycle proportional loading

Due to the inhomogeneity and anisotropy of short fiber-reinforced polymers (SFRP), even uniaxial loading can induce multiaxial stress states inside them, which significantly increases the difficulty of grasping their fatigue behavior. To efficiently predict the fatigue life of SFRP under proportional multiaxial stress, a multiaxial high-cycle fatigue model is proposed, relying upon the multiscale modeling strategy capable of integrating the influence of fiber microstructure. Taking the fiber-matrix interface stress at the critical region as the internal driving factor of fatigue fracture is the core assumption verified by microscopic observations. Off-axial fatigue tests with different orientations and stress ratios are performed to validate the fatigue model. Results show that the prediction accuracy has reached an acceptable level, and the quadratic polynomial surface can well represent the relationship between fatigue life and multiaxial stresses. This work provides an efficient tool for multiaxial fatigue life prediction and expounds the failure behavior of SFRP from multiscale perspectives.

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

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

Multiaxial high-cycle fatigue failure and life prediction based on critical plane method

Multiaxial high-cycle fatigue failure criterion and life prediction is important for structural components under complex low stress. A new multiaxial high-cycle fatigue damage parameter based on the plane of maximum shear stress is proposed, which includes the maximum shear stress amplitude, normal stress amplitude and maximum equivalent normal stress. The maximum equivalent normal stress is defined in the form of SWT stress function considering the influence of mean stress. The feasibility of the proposed failure criterion and life prediction model is verified by test data of different materials. The predicted results show that the life prediction error of the proposed fatigue model is basically within three times by comparing with McDiarmid, Matake, Crossland and Papadopoulos fatigue models.

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.

Multiaxial high cycle fatigue of 304L stainless steel with a small defect

The influence of a small defect on the multiaxial fatigue strength of 304L stainless steel was experimentally investigated. The fatigue tests were carried out on specimens containing a cylindrical defect with area = 400 µm. Five fully reversed loading paths were employed: tension-compression, torsion, in-phase, 90° out-of-phase, and square shape. Crack orientation in the vicinity of the defect was examined at and just above 2 × 106 cycles (run-out condition). The fatigue limits and crack angles measured were used to evaluate a tensile-based critical plane criterion for small defects. Predicted and measured results were in good agreement, indicating a tensile-dominated failure mechanism in the range of experimental conditions studied.

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.

Lifetime Assessment for Multiaxial High-Cycle Fatigue Using Twin-Shear Unified Yield Criteria

In this paper, a life prediction model associated with maximum principal stress and equivalent shear amplitude based on twin-shear unified yield criterion for multiaxial high-cycle fatigue is proposed. The equivalent shear amplitude is the normalized format of the equivalent shear amplitude based on clusters of yield criteria embodying Tresca and the linearization of Huber-von Mises, extending the application to metallic materials. Simultaneously, the effect of mean stress on multiaxial high-cycle fatigue is considered in the proposed model. As an assessment of the new prediction model, the criterion is compared with experimental data of aluminum alloy LY12CZ and carbon structural steel SM45C published in the relevant literature, which shows that most of the data are located within an error range of less than two times the data and are in good agreement with the experiment. Moreover, the proposed model is also compared with other models, such as McDiarmid, Liu, and Freitas, to validate its competitiveness.

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.

A modification of Matake criterion for considering the effect of mean shear stress under high cycle fatigue loading

AbstractIn the present paper, a brief review for some existing critical plane‐based life prediction models is presented, and limitations of these models in reflecting the influence of mean stress on fatigue life are discussed. It is found that the effect of mean normal stress on fatigue damage has been well taken into account for most of the critical plane‐based fatigue life prediction models, while mean shear stress effect is not well considered in these models. Therefore, a new critical plane‐based multiaxial high cycle fatigue life prediction model is proposed in this paper to account for the effects of both mean shear and normal stresses. The shear Walker factor and mean normal stress sensitivity index are introduced in the developed criterion to consider the effects of mean shear and normal stresses, respectively. Procedures to determine the damage parameters acting on the critical plane and to calculate the material constants contained in the proposed model are all presented. Experimental validations by using six different materials show that most of the predictions are within a factor of 3 in fatigue life.

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.

Leading edge erosion of wind turbine blades: Multiaxial critical plane fatigue model of coating degradation under random liquid impacts

AbstractA computational model of rain erosion of wind turbine blades is presented. The model is based on the transient fluid–solid coupled finite element (FE) analysis of rain droplet/coating interaction and fatigue degradation analysis. The fatigue analysis of the surface degradation is based on multiaxial fatigue model and critical plane theory. The random rain fields are constructed computationally, and the estimated droplet sizes are included in FE model to acquire a library of load histories. Subsequently, the resulted nonproportional multiaxial high cycle fatigue problem is solved to assess the damage and lifetimes of the coatings. The approach can be used to design new coating systems withstanding longer service times.

An experimental and numerical study of the high cycle multiaxial fatigue strength of titanium lattice structures produced by Selective Laser Melting (SLM)

A numerical approach is proposed to assess the high cycle fatigue (HCF) strength of periodic cellular structures produced by Selective Laser Melting under multiaxial loads. The model is based on a general numerical homogenisation scheme and an explicit description of the Elementary Cell (EC) combined to an extreme values analysis making use of a fatigue indicator parameter based on Crossland’s criterion. This method is applied to 33 EC topologies.In addition, geometric discrepancy and surface roughness are experimentally characterised and considered in the numerical model using three methods which are compared to the experimental HCF strength.

Surface roughness effect of SLM and EBM Ti-6Al-4V on multiaxial high cycle fatigue

As built Ti-6Al-4V parts obtained by SLM and EBM, often stress-released and HIP-treated, show a very rough surface which affects the fatigue properties. In many cases of complex geometries, surface treatments can not be achieved so that the use of such parts for structural applications requires to understand and to quantify the effect of roughness on fatigue strength. This study presents an experimental and numerical approach to take into account the role of roughness on the high cycle fatigue strength of additively manufactured parts. The specific roughness of “as-built” surfaces was evaluated by several acquisition methods(2D and 3D profilometry, tomography) on “as-built” surfaces and different surface finish (machining and chemical polishing). Fatigue strength of SLM and EBM specimens with an “as built”, machined or chemically polished surface were evaluated under fully reverse tension (Rσ = 1) and torsion (Rτ = 1). Fractography analyses were performed in order to identify defects at the origin of fatigue crack initiation. Finally, a numerical approach based on finite element (FE) computation of real surface topologies was proposed to quantify the effect of the surface roughness on fatigue strength. The surface roughness was modelled from 2D and 3D profilometry and the FE computations were conducted in elasticity and elastoplasticity. The proposed numerical approach combines a non local fatigue indicator parameter (FIP) integrating the high stress gradients at notch root and a statistical description of potential initiation sites by extreme value statistics.

Generalized 3D high cycle fatigue criteria for multiscale bridging‐based progressive damage analysis of multilayer composite parts under random loads and material deterioration

AbstractTwo frameworks are employed to develop two distinct categories of multiaxial high cycle fatigue life assessment models for composite components experiencing general and random loading conditions. In this regard, the decay in the material properties with cycles is also taken into account. It is obvious that in multilayer components, the fatigue failure is a progressive process that may be accompanied by gradual or sudden changes in the material properties and, consequently, the resulting stresses. In addition to using the traditional progressive damage analyses, a new concept is proposed for tracing of the localized fatigue failures more accurately. It is postulated that generally, the stress components have distinct frequencies, phase shifts, and mean values that all vary with time in a random manner. The proposed fatigue criteria, especially, the equivalent‐stress–based ones, are capable of predicting various fatigue failure modes, such as the fibre breakage, matrix cracking, and interfacial debonding. A special and comprehensive fatigue failure tracking and cycle counting algorithms that are capable of handling the mentioned general peculiarities are proposed. The proposed HCF criteria and the relevant fatigue life assessment algorithm are then implemented on a composite multilayer mono‐leaf spring of a realistic vehicle under a random field‐measured loading condition, as a typical component, and the results are compared and the experimental results conducted by the authors, for accuracy investigations. The considered stochastic road inputs have been chosen on the basis of the consumption times and field measurements.

Bending and Torsion Fatigue-Testing Machine Developed for Multiaxial Non-Proportional Loading

A new fatigue-testing machine was developed to perform high-cycle multiaxial fatigue tests at 50 Hz, in order to reduce testing time. The developed machine can combine bending and torsion loading and perform fatigue tests at a high frequency, under proportional and non-proportional loading conditions, where the principal stress direction changes during a cycle. The proportional loading is cyclic bending loading, and the non-proportional loading is cyclic, combining bending and reversed torsion loading. In this study, the effectiveness of the testing machine was verified by conducting tests under these loading conditions, using specimens of type 490A hot-rolled steel and type 304 stainless steel. The fatigue life linked to bending loading obtained using the new testing machine was slightly extended compared with that obtained using the conventional fatigue-testing machine. The fatigue life derived as a result of a combination of bending and torsion was comparable to that obtained using the conventional fatigue-testing machine, although a fatigue limit reduction of 100 MPa was observed compared to the former study. The feasibility of tests using the developed multiaxial fatigue-testing machine was confirmed.