Multiaxial Fatigue Criterion Research Articles

A review of multiaxial low-cycle fatigue criteria for life prediction of metals

Most of real-world structural components that undergo cyclic loading feature multiaxial fatigue. When the cyclic loading involves also significant plastic deformation, multiaxial low-cycle fatigue takes place. Applications where multiaxial low-cycle fatigue can be observed very often involve metal components. To predict their lives multiple criteria and models have been proposed, but their development has not followed a regular path. Multiple reviews are available in literature. However, many of them are outdated, they often employ different classification methods to categorize available criteria, many focus on specific families of criteria, and others do not include sufficient theoretical background. Moreover, none of the available reviews is based on a systematic literature search method. As a result, approaching the topic can result arduous and chaotic, especially for first timers. This work aims at providing a clear, comprehensive, and definitive review of available criteria for multiaxial low-cycle fatigue. First, the basic theoretical background is explained. Secondly, a systematic approach is described and employed to identify all major currently available criteria. Then, they are classified and commentary about different classification styles that can be found in literature is added. Eventually they are described, together with their latest proposed variations. In this way this review can be employed as a guiding reference, especially for engineers approaching the topic for the first time.

Non-local fatigue criterion based on standard deviation for notches and defects in Ti-6Al-4V

The aim of this study is to propose a non local multiaxial fatigue criterion in order to assess the fatigue limit of stress concentrator such as notches or defects in Ti-6Al-4V. This criterion is based on the standard deviation of the stresses integrated over a given volume around the hot spot point. Up to now, the standard deviation has never been tested as an indicator of stress heterogeneity to assess fatigue life of notch components. Four parameters are necessary to identify the criterion. The criterion is first validated on notched samples based on literature results and shows very good results. A set of experimental tests is conducted on natural and artificial defects including clustering defects and demonstrates the flexibility and accuracy of the criterion.

Prediction of fatigue life of a bolted joint in railway steel arch bridge using multiaxial fatigue criteria

Fatigue represents a critical condition for infrastructure subjected to repeated cyclic loads, such as steel railway bridges. The literature offers several methods to estimate fatigue life, consisting of three main phases: cycle counting, fatigue damage criterion, and damage accumulation criterion. Applying S-N curves might not be conservative in the case of railway bridges subjected to traffic because the stress-time history is complex and cannot be reduced to a sinusoidal history. Additionally, the presence of a multiaxial stress state must be considered. Therefore, this work compares eight multiaxial fatigue damage criteria for evaluating fatigue life in a scenario between high and low-cycle fatigue. Specifically, the authors considered four low-cycle fatigue criteria, namely Smith–Watson–Topper (SWT), Kandil, Brown and Miller (KBM), Glinka, Fatemi and Socie (FS), and four high-cycle fatigue criteria, Crossland, Basquin and the methods recommended by Eurocode 3 and British Standard. The rainflow counting method in ASTM E1049-85 (2011) and Miner’s rule for damage accumulation were used. The Polcevera railway steel bridge was selected as a case study. A 3D numerical model was developed for this purpose using Midas Civil software, taking into account the material non-linearity of the bridge’s elements. Once the area with the highest stress concentration was identified, a detailed analysis was conducted to estimate the stress and strain time histories induced by train traffic. A sensitivity analysis was conducted after critically comparing the eight methods for predicting fatigue life to assess the impact of traffic parameters, train velocity, axle load, and convoy length on fatigue life. It has been found that the criteria considering axial stress tend to overestimate the number of fatigue cycles to failure compared to the criteria, including the effect of shear stress components.

A New Critical Plane Multiaxial Fatigue Criterion with an Exponent to Account for High Mean Stress Effect

The mean stress effect remains a critical aspect in multiaxial fatigue analysis. This work presents a new criterion that, based on the classical Findley criterion, applies a material-dependent exponent to the mean normal stress term and includes the ultimate tensile stress as a fitting parameter. This way of considering the non-linear effect of the mean stress, with a material-dependent rather than a fixed exponent, is totally innovative among the multiaxial fatigue criteria found in the literature. In order to verify its accuracy, the new criterion has been checked against an extended version of the Papuga database of multiaxial experimental tests with 485 results, and compared with the criteria by Findley, Robert, and Papuga. The new criterion provides outstanding results for pure uniaxial cases, with multiaxial performance similar to the Robert criterion with a smaller range of error and a conservative trend, even surpassing the popular Papuga method in several relevant loading scenarios. These features enhance the applicability and versatility of the criterion for its use in the fatigue design of structural components.

Fatigue Life Prediction and Verification of Railway Fastener Clip Based on Critical Plane Method

Accurately predicting the fatigue life of fastener clips is crucial for improving material processing technology, enhancing the anti-fatigue design level, and guiding the maintenance and repair of track structures. Conventional methods that solely evaluate the fatigue life of fastener clips based on the uniaxial stress index under displacement loads may lead to significant errors. In this paper, the stress field of a type-III clip under displacement loading conditions was numerically simulated based on fatigue test standards, and the fatigue life of the clip was analyzed using the Fatemi–Socie (FS) multiaxial fatigue criterion based on the critical plane method. A comparison with standard fatigue test results revealed that, under non-resonance conditions, the predicted position of the fatigue critical plane of the fastener clip coincided with the fracture surface observed at the middle of the measured small arc, with a life prediction error of 7.3%. To further investigate the predictive capability of the FS multiaxial fatigue criterion for the fatigue life of the fastener clip under resonance conditions, the stress levels of the clip under non-resonance and resonance conditions were compared through on-site testing, and the effects of inertial loads caused by vertical and lateral vibration acceleration on the stress field of the clip were analyzed in numerical simulation according to the results of clip acceleration tests; the fastener clip’s resonance fracture position and fatigue life were also predicted based on the aforementioned multiaxial fatigue criterion. To verify the accuracy of the predicted results, a testing method was proposed that equates the high-frequency resonant inertial load of the fastener clip to a low-frequency additional preload under the premise of consistent stress fields. A comparison with the numerical simulation results shows that considering only vertical inertial loads would result in a discrepancy between the measured fracture location and the actual one. Considering both vertical and lateral inertial loads, the fracture location (at the heel of the small arc) under resonance conditions could be accurately determined, with a life prediction error of 13.8%. Compared to the non-resonant displacement loading condition, the inertial loads caused by acceleration under resonance conditions led to a reduction in fatigue life of approximately 77.8%.

Generalizing multiaxial vibration fatigue criteria in the frequency domain: A data-driven approach

Random vibration fatigue of structures is intrinsically multiaxial, driven by complex stress states. Non-proportional multiaxial stresses exacerbate fatigue damage compared to proportional stresses. Frequency domain fatigue analysis is generally more efficient for structures operating near natural frequencies. However, handling non-proportional multiaxial stress effects in the frequency domain remains challenging. This paper introduces a data-driven framework that reformulates time domain multiaxial fatigue failure criteria into their frequency domain counterparts, explicitly addressing non-proportional effects. The method introduces a non-proportional correction factor into the power spectral density of equivalent stress, determined through a data-driven approach, converting various time domain multiaxial fatigue criteria into their frequency domain equivalents. Combined with modal decomposition analysis, this approach efficiently evaluates multiaxial vibration fatigue for engineering structures, effectively accounting for non-proportional stress effects.

Composite effects of residual stress and hardness gradient on contact fatigue performance of rough tooth surfaces and optimization design of detailed characteristic parameters

Residual stress and hardness gradient significantly affect the contact fatigue failure process of rough tooth surfaces, and the meticulous design of their characteristic parameters can help improve the fatigue resistance of gears. In this paper, an efficient computational method for rough tooth surface contact is established based on the reconstruction modeling of asperities and mixed lubrication analysis. By comprehensively considering the effects of residual stress and hardness gradient, the Dangvan multiaxial fatigue criterion is adopted to predict and analyze the contact fatigue life of the gear surface. The correlation between the surface residual stress, maximum residual stress depth, surface hardness, and effective hardening layer depth, among other characteristic parameters, and the contact fatigue performance of tooth surfaces is established. The results show that: (1) Increasing the magnitude of surface residual compressive stress and surface hardness can significantly reduce the risk of fatigue failure in the near-surface layer of the gear. To achieve the same fatigue performance, there is a linear negative correlation between the design values of the two parameters. (2) Affected by the double stress peaks in the rough tooth surface stress field, the maximum residual stress depth significantly affects the depth at which the highest failure risk occurs. With changes in roughness, the optimal design value of the maximum residual compressive stress depth changes from about 0.5 times the Hertzian contact half-width depth in the subsurface layer (Sa < 0.2 μm) to about 15 μm in the near-surface layer (Sa > 0.4 μm). (3) Considering both process cost and gear surface fatigue resistance, the design threshold for the effective hardening layer depth should be greater than the Hertzian contact half-width. This paper establishes a composite correlation between the meticulous characteristic parameters of residual stress, hardness gradient, and the contact fatigue performance of tooth surfaces, providing theoretical support for optimal design of tooth surface anti-fatigue performance.

Effect of non-proportional stress states caused by varying phase shifts on the fatigue life of welded joints

In this paper, the effect of multiaxial non-proportional stress states on the fatigue life of welded joints is investigated. The non-proportional stress states are caused by various phase shifts between the normal and shear stresses. In total 45, welded tube-to-tube specimens are tested under multiaxial proportional and non-proportional loading. The increase in fatigue damage caused by non-proportional stresses, compared to proportional stresses, is quantified by penalty factors. A set of penalty factors are derived from the fatigue experiments for use with the governing multiaxial fatigue criteria by the International Institute of Welding (IIW) and Det Norske Veritas (DNV). The experimental results show that phase shifts decrease the fatigue life. However, this reduction is not to the extend proposed by the governing guidelines. Furthermore, the results indicate that different degrees of phase shift do not induce varying levels of fatigue life degradation.

Study of the Point Method for fretting fatigue life prediction

With the improvement and success of the Theory of Critical Distances (TCD) in notch fatigue problems, the TCD, especially the Point Method (PM), combined with multiaxial fatigue criteria, has been used over the last few years to predict the fretting fatigue life. However, little attention is paid to the effect of different damage mechanisms, especially stress distribution, between the two conditions on the application of the PM. This paper aims to select a suitable path for the PM, considering various stress distributions, for the fretting fatigue life prediction of complete contacts. A new method is developed to select the suitable path of the PM for fretting fatigue life prediction. To validate the analysis, corresponding tests were carried out using an improved proving ring-like rig in a Ti-6Al-4V alloy. Predicted lives on all paths were calculated using the PM combined with different multiaxial fatigue criteria, without incorporating wear effects, and compared with experimental lives using an error bar graph. Results indicate that when the fretting wear is not considered, the minimum predicted life path is more suitable for the PM than the perpendicular and maximum predicted life paths. This suitable path is compared to the path selection in the uniaxial symmetric V-notch fatigue condition. Analysis shows that the conventional path (the notch bisector) of the PM produces the maximum predicted life for the notch fatigue condition. The cause of this different path selection of the PM in the two fatigue conditions is assumed to be the effect of the asymmetric stress distribution and fretting wear damage in the fretting fatigue condition.

Advancements in stress‐based multiaxial fatigue prediction: A data‐driven approach and a new criterion

AbstractA highly accurate iteration of the Liu &amp; Zenner multiaxial fatigue criterion is presented and validated against the FatLim dataset. The proposed criterion modifies the mean stress parameters of the original criterion while keeping the amplitude parameters unchanged. The investigation of the best‐performing stress amplitude parameters revealed that existing multiaxial fatigue criteria that rely on dimensional weight parameters exhibit a notable prediction bias. This bias leads to inaccurate fatigue assessments. The paper sheds light on the extent of this bias and its implications for common engineering practices. By introducing the refined criterion, the study addresses these limitations and provides a more reliable framework for multiaxial fatigue analysis. The comprehensive validation against the FatLim dataset demonstrates the superiority of the proposed criterion in accurately predicting fatigue behavior under diverse loading conditions. The findings underscore the significance of considering both amplitude and mean stress parameters in multiaxial fatigue criteria, offering valuable insights for enhancing the accuracy of fatigue assessments in engineering applications.

Non local multiaxial fatigue modeling of defects : A unified approach to interpret size and shape effects

This paper deals with the effect of defect size and shape under high cycle fatigue for metallic alloys. A large simulation campaign based on a multiaxial fatigue criterion and a non-local approach is presented. A relative defect size based on a ratio between the defect size and a characteristic length introduced by the non-local approach is defined. A normalized Kitagawa–Takahashi diagram is then obtained. A competition between the highly stressed volume size and the local maxima due to the defect is observed and seem dependent on the relative defect size. The effect of the loading mode (uniaxial and pure shear) and of the plasticity are discussed. Finally, a comparison of the simulation results with experimental data on a 316L L-PBF demonstrates the robustness of the proposed approach and explains the negligible effect of the defect morphology compared to its size.

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 generalization capability of artificial neural networks used to estimate fretting fatigue life

This study assesses the generalization capacity of artificial neural networks (ANNs) for predicting fretting fatigue of mechanical contacts using different materials and geometries. These ANN utilize as inputs, material properties and stress quantities that have been physically related to the fatigue crack initiation mechanism under multiaxial loading. Initially trained and validated on aeronautical aluminum alloys data, one tests their generalization performance by applying them to fretting fatigue data for Ti‐6Al‐4V, ASTM A743 CA6NM steel, and Al 7050-T745, employing both cylindrical and spherical pads under various loading conditions, including out-of-phase loading. The ANNs adeptly predict fatigue lives across this extensive dataset, surpassing classical multiaxial fatigue criteria in accuracy. This underscores the effectiveness of ANN-based methodologies in diverse fretting fatigue scenarios.

Numerical and Experimental Analysis of Strength Loss of 1.2709 Maraging Steel Produced by Selective Laser Melting (SLM) under Thermo-Mechanical Fatigue Conditions.

The result of the development of additive manufacturing (AM) methods is the increasing use of the selective laser melting (SLM) method as a technique for producing tooling for injection moulds and die casting pressure moulds from maraging steel powders. The mould components are subjected to varying thermo-mechanical loads during these operations. This paper presents a numerical model that is used to predict the fatigue life of a material that is loaded with a time-varying temperature field according to the classic and modified Coffin test. Using a computational model, the temperature changes in the resistance-heated specimen and the stress and strain fields that are caused by this phenomenon were determined. Using three different multiaxial fatigue criteria, the fatigue life of SLM steel was determined. Numerical calculations were verified using experimental thermal fatigue tests on 1.2709 SLM steel that was aged at 490 °C as well as via metallographic tests. The numerical model was used to predict the durability of the same steel aged at 540 °C. The effect of specimen clamping conditions on the fatigue life of SLM steel was determined numerically. The value of the decrease in strength of SLM steel as a result of the increasing number of cycles of temperature changes was determined experimentally; a great influence of ageing temperature on fatigue life was found. Changes in the structure of steel occurring during cyclic changes in temperature are presented.

Multiaxial fatigue of water pipe grey cast iron

Grey Cast Iron (GCI) water pipes are subjected to multiaxial, cyclic stresses caused by combinations of loads such as internal water pressure and road vehicle weight. However, the multiaxial fatigue performance of this material has not previously been characterised. To address this gap more than 45 fatigue tests, including some under non-proportional tension-torsion loading, were completed using a GCI material very similar to water pipe GCI. Of the four multiaxial fatigue criteria tested, the Smith-Watson-Topper (SWT) criterion provided the best predictions by a narrow margin, supporting the idea that a tensile cracking mode dominates the fatigue life of GCI.

Fatigue life prediction using critical distance on aluminum alloy wire containing indentation produced marks

The present study aims to predict fatigue life in aluminum alloy 6201-T81 wires containing defects produced by hardness indentation procedures. The wires tested were obtained from a 900 MCM All Aluminum Alloy Conductor (AAAC 900 MCM) used in power transmission lines. The stress field in the vicinity of the defect and the determination of the crack initiation site (hotspot) were obtained by applying elastic–plastic simulations via the Finite Element Method (FEM). Such a simulation considered both the indentation process, and the fatigue loading on the wire. The Smith-Watson-Topper multiaxial fatigue criterion applied to an equivalent stress computed by the Volume Method (MV) was used to estimate life. Challenges presented by the incorporation of the residual stress field and the choice of the best calibration procedures were addressed. Comparison between stress gradients in simulations and failures observed in fractographic analyses of specimens subjected to fatigue testing suggested similar potential crack propagation regions. A new and wide experimental campaign showed that presence of indentation defects reduced the fatigue life of the wires. 84% of the lives computed by the proposed methodology were within a factor of 3 compared with tests, being the worst estimate within a factor of 5 .

The influence of load correlation on vibration fatigue damage of symmetrical notched cantilever beam structures

AbstractThis paper aims to develop an innovative multiaxial fatigue criterion based on the stress invariant, in order to perform the fatigue damage analysis of engineering structures subjected to random vibrations. First, the change rule of structural vibration fatigue lifetime under different load correlation conditions is systemically studied by experiments. Then, the finite element analysis of such a structure, including the modal analysis and the spectral analysis, is implemented in order to compute the response stress power spectral density (PSD) functions at the critical fatigue‐prone location under coupled random acceleration base excitations. Finally, the influence rule of load correlation on the vibration fatigue damage of such a symmetrical structure is theoretically illustrated through formula derivation. Moreover, combined with the critical distance theory point method, the proposed time/frequency‐domain multiaxial fatigue criterion is applied for vibration fatigue lifetime evaluation of the structure. The lifetime prediction accuracy of the proposed multiaxial fatigue criterion is verified by comparing with the vibration fatigue test results.

Application of multiaxial fatigue criterion in critical plane to determine lifetime of composite laminates

This paper analyzes the results of fatigue tests of samples made of composite laminate. These samples were cut out from a previously produced laminate with different fiber-orientated layers at different angles. Thus, various variants of the complex stress state were obtained for the material with anisotropic properties. The samples cut out at 0° angle was taken as a reference point for the calculations. In order to perform the calculations, three popular stress criteria used in the case of statics were modified: maximum stress, Azzi-Tsai-Hill and Norris. Then, it was proposed to apply to the analysis of fatigue life of composites the fatigue criteria known from the analysis of isotropic materials, defined in the critical plane. The definition of the critical plane was considered as the plane in which the maximum normal stress or maximum shear stress occurs – obtaining two different versions. As a result of the calculations, it turned out that the best compliance of the calculations with the experiment was obtained using the criterion defined in the critical plane determined by the shear stresses, where the normal and shear stresses were included in it as the sum of their linear combination with weighting factors.

Fatigue crack initiation life prediction using different plasticity models in cold expanded AL-alloy plates utilized in double shear lap joints

Cold expansion of fastener holes is a recognized technique for enhancing the fatigue life of holed plates utilized in detachable joints. This method involves introducing compressive residual stress around the holes, which has proven to be effective in improving the structural integrity and longevity of such components. In this research, the role of using different plasticity models in finite-element simulations of cold expansion (CE) in determining residual stress distribution and predicting the fatigue life of lap joints was investigated. Finite-element simulations were conducted to analyze the distribution of residual stress in cold-expanded Al-alloy 2024-T3 plates utilized in double-shear lap joints. Three time-independent plasticity models, specifically multilinear kinematic hardening, multilinear isotropic hardening (M.L.I.H) based on monotonic tensile tests, and nonlinear combined hardening models derived from saturated hysteresis stress and strain loops, were employed in the simulations. These models allowed for an accurate determination of the residual stress distribution in the plates. In finite-element simulations, two CE sizes of 1.5% and 4.7% were employed to create residual stresses. In the simulations, after creating residual stress by CE, remote sinusoidal loads are applied to the joints corresponding to the previously conducted fatigue tests in order to obtain stress and mechanical strain distributions. In order to predict the fatigue life, four different multiaxial fatigue criteria (Smith–Watson–Topper, Glinka, Kandil–Brown–Miller, and Fatemi–Socie) were employed, using the stress and strain distributions obtained from the finite element simulations with the different plasticity models. The simulations yielded varying stress and strain distribution results for the multilinear kinematic and M.L.I.H models, while the results of the nonlinear combined hardening model fell between the other two models. Notably, the fatigue life prediction based on the nonlinear combined hardening plasticity model closely matched the experimentally observed fatigue lives, with an absolute percentage deviation of 24.8%.

Nonlocal approach to fatigue analysis of a welded bicycle frame joint

AbstractThe paper attempts to predict the probabilistic fatigue strength scatter bands of a welded bicycle frame joint. The experimental data of the base material and the weld material were approximated by a nonlinear probabilistic model of the Weibull distribution. The fatigue strength for the material at the fatigue crack location was estimated considering the mean stress, residual stress, fatigue notch factor, and hardness profile. The output finite element numerical data of the real welded joint were compared with a nonlocal multiaxial fatigue criterion. The implementation of the volumetric method takes into account the stress gradient effect in the three‐dimensional geometry of the weld toe. The comparative localization of the minimum stress and the real crack indicates the validity of the numerical model. The predicted fatigue strength determines the possible failure of a welded joint at 5·105 cycles.