Critical Plane Model Research Articles

Investigation on fatigue parameters in railway wheels using a critical plane model

The contact areas between rail and wheel are critical in determining the performance of rail vehicles. Analyzing the mechanics, materials, tribology, and geometry of the interface is important to understand the contact damage mechanisms, fatigue parameter and fatigue life. Developing a simplified and novel approach to predict crack initiation and fatigue life is key for investigating contact fatigue of rail wheel interaction. This study aims to investigate rolling contact fatigue (RCF) cracks and fatigue life in railroad wheels using Finite Element Model (FEM). Using a proper material model that accounts for plastic shakedown, ratchetting, and cyclic hardening for both the rail and wheel materials, the FEM model is analyzed with the help of Abaqus 2020 tool. The submodelling technique was implemented to reduce computation demand. Stress and strain history outputs extracted from the submodel (at 0 mm, 1.3 mm, 2.6 mm, and 3.6 mm depths) were used to predict critical plane orientation, crack initiation and fatigue life using critical plane models. The orientation of critical (crack) plane was found using a novel MATLAB algorithm by searching for a plane with maximum fatigue parameter (FPmax). The investigation reveals that the location of maximum damage is the subsurface and the crack angles fall within the range of (0°, 40°), (62°, 123°) and (143°, 180°) with a 5 % margin and at a depth of 2.6 mm below the wheel surface. The determined fatigue crack initiation and life at this specific location were 6178 and 7174 cycles, respectively. Predicting the critical zone which is susceptible to shorter crack initiation and fatigue life is a crucial to prevent wheel failure.

Effect of faying surface treatments and bolt tightened levels on fretting fatigue performance of slip critical connections with high strength bolts

The experimental investigation focuses on the fretting fatigue performance of M24 high-strength bolt slip critical connections (SCC) under shear load, taking into account the influence factors of faying surface treatments and bolt tightened levels. A novel extensometer supporting device for measuring micro-displacement between connection plates is proposed. The μ-N curves are obtained. Three-dimensional surface morphology scanning and fracture morphology analysis are conducted on the specimens. The results showed that the SCC contact area can be divided into stick, partial slip, and gross slip, with distribution ranges determined for each zone. Meanwhile the fretting fatigue life decreases with the increase of μ and pre-tension. Finally, a prediction of fretting fatigue life is made based on a multiaxial fatigue critical plane model.

Multiaxial fatigue behavior and life estimation of Al‐Li alloy 2099 under strain‐controlled loading

AbstractAluminum‐lithium alloys are a class of advanced materials designed to reduce weight and improve performance in aerospace and other high‐tech applications. This paper presents a research investigation on the in‐phase and out‐of‐phase multiaxial fatigue behaviors of the third‐generation AW2099‐T83 aluminum‐lithium alloy that have not been addressed before. Additional hardening was observed under nonproportional loading condition at high strain amplitudes. Fatigue lives were estimated using von Mises equivalent strain and two critical plane models: the Fatemi‐Socie (FS) and the Smith‐Watson‐Topper (SWT). In addition, a supervised machine‐learning model (support vector machine—SVM) was employed to predict the fatigue life under the above‐mentioned loading conditions. The FS criterion was found to yield better fatigue life predictions than SWT. The estimations of FS model mostly fall within ±3× scatter bands with some data falling within the conservative and non‐conservative regions. The SVM model resulted in excellent predictions within ±2× scatter bands.

Fatigue performance testing and life prediction of welded fuel pipes

The external piping system which connects power devices, valve control devices, actuators, etc. is an essential system on the aero engine. Under the combined effects of high fluid pressure and external vibration, multiaxial fatigue failure is the main factor that seriously affects the safety of the piping system. The objective of this paper is to establish the multiaxial fatigue life model for the typical welded fuel pipe of the piping system by combining fatigue testing, simulation and theoretical analysis which is of great guiding significance for the engineering application of the piping system. Firstly, the fatigue limits of welded fuel pipes under no and 13.5 MPa internal pressure are obtained by rotational bending fatigue tests using the up-and-down method. Three additional stress levels of rotational bending fatigue tests under no internal pressure are supplemented and then the S-N curve is further obtained by the group method. Since the corresponding fracture surface of the specimens locates at the weld toe near the fixed end, peak stress method is adopted to evaluate the fatigue performance of the weld toe on the pipe specimens. In addition, by comparing the fatigue limit with no and 13.5 MPa internal pressured pipes, it is obvious that the equivalent uniaxial stress corrected by Gerber formula is not applicable for the multiaxial fatigue condition which is caused by the combined effect of fluid pressure and displacement load. The local stress concentration factor caused by the weld toe is determined and based on Findley critical plane model, the multiaxial fatigue life model is established which simultaneously takes the local stress concentration effect, mean stress effect and multiaxial stress effect into consideration. The results of rotational bending fatigue tests under 13.5 MPa internal pressure are within the triple error dispersion band and the accuracy of the proposed life model are verified.

Fretting Fatigue Life Prediction for Aluminum Alloy Based on Particle-Swarm-Optimized Back Propagation Neural Network

Fretting fatigue is a specific fatigue phenomenon. Due to the complex mechanisms and multitude of influencing factors, it is still hard to predict fretting fatigue life accurately, despite there being many works on this topic. This paper developed a particle-swarm-optimized back propagation neural network to predict the fretting fatigue life of aluminum alloys using the test data gathered from the published literature. A commonly used critical plane model, the Smith, Watson, and Topper criterion, was used as a contrast. The analysis result shows that the proposed fretting fatigue life prediction neural network model achieves a higher prediction accuracy compared to the traditional SWT model. Experimental validation demonstrates the effectiveness of the model in improving the accuracy of fretting fatigue life prediction. This research provides a new data-driven methodology for fretting fatigue life prediction.

The strain ratio-dependent multiaxial low cycle fatigue behaviour and life prediction of 316L stainless steel based on critical plane at elevated temperature

The study mainly investigates the effect of strain ratio on the multiaxial low cycle fatigue behaviour of 316L at 550 °C. The evolution of both axial and torsional stress amplitude is observed to go through three stages: cyclic hardening, softening and fracture. What's different is that the torsional loading experiences fewer cyclic hardening cycles compared to the axial loading. Regarding the interaction between axial and torsional stresses, it is observed that as the torsional strain increases, the axial deformation response presents a lower peak stress and a higher softening rate, while the torsional peak stress and softening rate hardly changes with the increase of axial strain amplitude. The fracture pattern is obtained through three-dimensional (3D) depth-of-field observation. It is discovered that as the strain ratio increases, the fracture pattern transits from tensile failure mode to shear failure mode. Furthermore, the orientation angle of the fracture surface increases and lies between the critical plane angle of maximum shear strain and maximum normal strain, indicating a mixed failure mode. Additionally, a comparison of nine representative critical plane models reveals that the energy-based models can better predict the multiaxial fatigue life influenced by the strain ratio. Finally, based on the analysis of deformation and failure mechanisms, a normal damage parameter weakening factor (NDWF) is introduced into the KBM-R model, and an improved normal stress component (INSC) is introduced into the Wu-R model. The two modified models well capture the impact of strain ratio and accurately predict the multiaxial fatigue life of both 316L and P92 steel.

Multiaxial fatigue behavior and crack orientation prediction for steel and cast iron

This study investigates multiaxial fatigue behavior of ductile construction steel S355 and cast iron EN-GJS-500-14. Fatigue lives and crack initiation orientations are measured. Three critical plane models are evaluated for predicting fatigue life and crack initiation angles. While all models achieve decent accuracy in predicting fatigue life, crack initiation angle predictions are less satisfactory. Weak correlation is observed between the quality of fatigue life and crack orientation prediction, particularly for the Smith–Watson–Topper (SWT) and Fatemi-Socie (FS) models. The SWT model performs better in predicting fatigue life and crack angles for cast iron, while the FS model shows higher accuracy for S355. The short-crack model (SC) provides the best overall fatigue life prediction but crack orientation estimation is not superior.

Fatigue life study of Cortical and Cancellous screws: Experimental method and critical plane models

Fatigue life prediction of orthopedic screws against applied impulsive loads during the treatment period is of great importance. In this study, the fatigue bending life of Cortical and Cancellous screws under cyclic bending loads are evaluated by using both experimental tests and numerical simulations. In the experimental tests, various impulsive loads are perpendicularly applied to the screw axis at the middle of threaded area until to observe the crack. Besides, the Fatemi-Socie model is utilized to obtain the life of the screws by using the finite element method. It is observed that the numerical results are in good agreement with those predicted by the experimental tests. Furthermore, the results reveal that the Cortical screws have a longer fatigue life than the Cancellous screws with similar diameters.

Comparison of critical plane models for multiaxial fatigue life prediction

Background. The operation of numerous machines and units takes place under conditions of multi-axial cyclic loading, which, as a rule, is non-proportional. Evaluating the fatigue durability of metal alloys under conditions of multi-axial non-proportional loading is a relevant task in modern engineering. Solving this problem requires fatigue calculation methods that would consider operating conditions and properties of structural materials, including factors such as the type of stress state, loading trajectory, material sensitivity to non-proportional loading, and so on.Objective. To conduct a comparative analysis of a range of fatigue life models based on the concept of the critical plane, including the Fatemi-Socie, Wang-Brown, Smith-Watson-Topper, Liu I, and Liu II approaches, and to identify the limits and peculiarities of their application.Methods. The fatigue lives calculated using the selected models were compared with experimental results obtained for various metal alloys subjected to uniaxial tension-compression, alternating torsion, and proportional and non-proportional multiaxial loading.Results. The applicability limits of fatigue life models based on the critical plane concept were analyzed for different metal alloys under conditions of proportional and non-proportional multiaxial loading.Conclusions. The research results demonstrated that models requiring the use of material constants obtained from tests in both tension-compression and alternating torsion provide reliable fatigue life estimates for various types of metal alloys. Calculations based solely on fatigue curves from alternating torsion better correlate with the results of tests on ductile materials, while calculations based on criteria utilizing fatigue curves from tension-compression align more closely with results from tests on brittle materials.

Comparison of critical plane models based on multiaxial low-cycle fatigue tests of 316L steel

An endurance against multiaxial fatigue of 316L steel is studied. A fatigue life curve of torsional mode is substantially shifted to longer fatigue lives while tension/compression mode causes fracture the earliest. Fatigue life curves of both multiaxial modes are close to axial mode. Fourteen critical plane models for fatigue life predictions were applied and compared. Modified Smith-Watson-Topper models proved to be the most accurate. Criteria proposed by Fatemi and Socie, Li et al., Zhu et al. and by Wang and Brown provided satisfactory results as well. Smith-Watson-Topper model led to the most precise predictions of fatigue crack orientation.

Multiaxial fatigue life estimation based on weight-averaged maximum damage plane under variable amplitude loading

An innovative critical plane determination approach with weight-averaged largest fatigue damage is proposed, in which the material failure modes can be considered. If material exhibits shear cracking behavior, a strain-based critical plane model with shear failure mode is selected to evaluate the weight function. Otherwise, other one with tensile failure mode is adopted. According to the proposed critical plane, a multiaxial fatigue lifetime estimation methodology is established for evaluating fatigue life. And, six kinds of materials are employed to validate the validity of presented methodology. The validation results reveal the presented methodology can estimate the orientation angles of failure plane accurately and supply satisfactory fatigue lifetime estimations for both shear and tensile failure mode materials. Furthermore, the proposed critical plane framework can be extended to be utilized with stress-based fatigue criteria, and prediction results show a good agreement with experimental data by another two materials.

Comparing fatigue life prediction capability of critical plane models using multiaxial test database on 17 materials

AbstractThe present study validates recent as well as extensively used critical plane (CP)‐based fatigue life assessment models for 10 ferrous and 7 non‐ferrous materials. Fourteen CP models, including recently reported in‐house developed model, have been analyzed. These models use resolved stresses, strains, strain energy density, and combinations of stresses and strains to identify critical plane and quantify fatigue damage. The loading conditions cover various proportional and non‐proportional axial‐torsion strain paths with different phase shift angles with (or without) mean stress/strain component(s), loading waveforms, and asynchronous axial‐torsion stain paths. The comparative study brought out the goodness of various models by quantifying the extent of scatter and computational time.Some of the strain energy density‐based models (including in‐house model) have been shortlisted, which produced accurate fatigue life assessments. Among the shortlisted models, in‐house model is free from the calculation subjectivities of resultant shear and performs faster fatigue damage calculations.

Fatigue experiments and life predictions of notched C-Mn steel tubes

Present work is aimed at performing fatigue tests on notched C-Mn steel tubes. Tests were conducted on different sizes of notches under remote axial strain-controlled conditions. Individual effects of peak equivalent strain amplitude and strain gradient are brought out on experimental fatigue life. The localized measured strains are compared with corresponding outcome of FE analyses.Fatigue life for notched specimens was predicted based on peak equivalent strain amplitude/existing critical plane model considering stress/strain information at peak/characteristic distance locations. The characteristic distance location with critical plane model and peak equivalent strain amplitude results in improved fatigue life predictions.

MFLP-PINN: A physics-informed neural network for multiaxial fatigue life prediction

In this study, a physics-informed neural network (MFLP-PINN), combining multiaxial fatigue critical plane model and the neural network, is proposed for life prediction. First, a multiaxial fatigue life prediction model based on the critical plane approach is proposed, which takes the equivalent strain amplitude on the critical plane as the main damage parameter, and considers the normal strain energy on the critical plane. Then, a total of four prediction models including the new critical plane model are integrated into the loss function of a neural network to build the MFLP-PINN. The accuracy of the proposed critical plane criterion and the MFLP-PINN are respectively verified using multiaxial fatigue test data of three materials. Finally, the results show that the prediction model integrated into the loss function has a significant impact on the neural network prediction. For a specific material, integrating a life prediction model with good prediction ability to this material as the loss function into a neural network model is helpful to improve prediction accuracy. Conversely, integrating a life prediction model with poor prediction ability to this material as the loss function into a neural network model will reduce the prediction accuracy.

Multiaxial fatigue of forged Inconel 718 at room and high temperature

This work investigates the effects of high temperature on the fatigue behavior of forged Inconel 718 under axial/torsional loading conditions. To this end, strain-controlled tension, torsion, and proportional fatigue tests were performed at 20 °C and 450 °C on thin-walled tubular specimens extracted from an as-forged turbine disk. All tests were conducted with axial and shear strain ratios equal to zero, and the applied equivalent von Mises strain amplitude was such to result in fatigue lives within the range of 104 to 106 cycles, which is the typical fatigue life of the component of interest in this study. It was observed that for a given loading condition and prescribed equivalent strain amplitude, the fatigue lives of tests at 450 °C were longer than the room temperature tests. Moreover, the longest lives were observed in the torsion tests, followed by the proportional and tension tests in all temperature and prescribed equivalent strain amplitude tested. The capability of the cyclic plasticity model proposed by Chaboche in describing the cyclic response of Inconel 718 was also addressed. This model successfully simulated the stress–strain behavior of this material under all loading conditions, and for both temperatures investigated. In addition, the cracking behavior of the material was examined. For both temperatures, the tension tests failed by Mode I tensile cracks, while Mode II shear cracks were observed in the torsion and proportional tests. After a scanning electron microscope analysis, it was concluded that the transgranular propagation mode was the predominant failure mechanism of all tested conditions. The fatigue life of Inconel 718 was predicted by the Fatemi–Socie (FS) and the multiaxial version of the Smith–Watson–Topper (SWT) fatigue models, resulting in estimations within a factor-of-two and a factor-of-four, respectively. Moreover, crack directions were also determined by the critical plane models and compared with the orientation of the observed cracks. The SWT model correctly predicted the crack direction of the tension tests, while the FS model was more accurate in determining the orientation of the cracks seen in the torsion tests. None of the two models was able to correctly predict the angles of the critical plane in all tested loading conditions.

Study of the notch fatigue behaviour under biaxial conditions of maraging steel produced by selective laser melting

The current work aims to characterise the fatigue behaviour of an additively manufactured maraging steel, AISI 18Ni300. This is a class of high-strength steel widely used in biomedical, aircraft, aerospace, offshore, and military industries thanks to its good performance in terms of strength, toughness, ductility, dimensional stability, and weldability. Laser-beam powder bed fusion (additive manufacturing) is used to fabricate this type of steel and endows it with properties that make it an excellent candidate for producing prosthetic parts, thereby facilitating a reduction in manufacturing material consumption, labour, and machining time. Given the wide range of loads biomedical components are often subjected to, the current study focused on the multiaxial behaviour of this type of steel. To this end, Fatemi–Socie (FS) and Smith–Watson–Topper (SWT) critical plane methods combined with the theory of critical distances were applied to predict the fatigue life and cracking orientation of this material, with and without notches, under three biaxial loading scenarios. Cylindrical specimens were used and these were fabricated on the base plate in the vertical orientation using a linear printing system equipped with a Nd:YAG fibre laser. The building strategy involved the deposition of 40 μm thick layers at a scan speed of 800 mm/s. The two critical plane models returned good results at low life cycle fatigue but the FS model obtained better results at high life cycle fatigue. Regarding the crack angles, SWT model produced the best predictions.

A coupled critical plane-[formula omitted] methodology to estimate fatigue life for an AISI 1045 steel with small artificial defects

The presence of notches, tears, holes, cavities, inclusions, and scratches is common in structural designs and mechanical components, that in the presence of cyclic loading can influence their resistance and fatigue life. The objective of this research is to propose and validate an approach for fatigue life estimation for materials with small defects subjected to combined loading. The approach of the project is formulated based on a calibration strategy for Fatemi-Socie, Smith-Watson-Topper and Susmel and Lazarin critical plane models, using Murakami criteria and notch factor to compute the defect effect. The results predicted by the model were compared and validated with experimental data, showing it to be a promising strategy. For further extension and a more generalized application of the proposed model, it is necessary to perform life prediction comparisons for different materials, loadings, and defect geometries.

Analysis of biaxial fatigue limit models for cases with circular notches

This work shows an analysis of several models of multiaxial fatigue for notches: Navarro-Rios’ model, which analyses the interaction between the crack and its associated plastic zone with the material microstructural barriers, and three models that combine a critical volume method for notches with a critical plane model for multiaxial fatigue in unnotched solids. Specifically, the application of these models for the prediction of the fatigue limit for a plate with a circular hole subjected to axial, shear and in-phase biaxial cyclic loading is studied. The effects of two parameters are analysed: the radius of the hole and the relationship between the torsional and axial fatigue limits. For all the analysed models, cases are observed in which an increase in the hole radius produces an increase in the predicted fatigue limit, that is, the evolution of the fatigue limit with an increasing hole radius is not always monotonically decreasing, as would be expected. These effects, which we have called “humps” because of their appearance on the prediction graphs, mainly occur in shear loading. No humps were observed in the studied experimental results, but the number of available experimental results is too small to assure this tendency. The results shown in the work indicate that a greater knowledge of the physics of multiaxial fatigue in notches is necessary to achieve models that are capable of providing increasingly accurate predictions.

Critical plane based method for multiaxial fatigue analysis of 316 stainless steel

In this work, the fatigue behaviour of 316 stainless steel is studied with different critical plane models. Seven cylindrical samples were used for the study, being subjected to different complex loading paths, generating combined stresses along the axial and transversal sample directions, these being: individual axial stress, individual hoop stress, alternating axial and hoop stress, a proportional combination of axial and hoop stress, and a non-proportional combination of L-shaped and square-shaped axial and hoop stress. The fatigue analysis is performed using five critical plane models; named Fatemi-Socie, Varvani-Farahani, Gan-Wu-Zhong, Liu I and Liu II. The models were assessed based on their fatigue life and crack angle prediction capacity. The Gan-Wu-Zhong recently proposed critical plane model was examined and provided acceptable results for the multiaxial loads tested on 316 steel. Nevertheless, Fatemi-Socie produced the most accurate results in terms of cracking orientation and Liu II gave the best fatigue life predictions.

A deviatoric tensile-based critical plane model to predict peak/mean normal stress effects in multiaxial fatigue

This work aims to improve the modeling of peak/mean normal stress effects on multiaxial fatigue lives, applying a deviatoric strain-life model based on the critical plane approach to predict the initiation of tensile-driven cracks. Based on Kujawski’s deviatoric multiaxial fatigue damage parameter, this model assumes the peak deviatoric stress normal to the crack plane controls these effects. Tensile damage models based on deviatoric parameters can solve the main issue with Smith-Watson-Topper’s pioneer model, which is the prediction of no damage in cyclic compression-compression load histories. A calibration procedure based on Coffin-Manson parameters is presented, without the need for additional data-fitting constants to predict peak/mean stress effects. The calibrated multiaxial model is then compared with other tensile-based models for five structural metallic alloys, involving an extensive dataset with 312 uniaxial, torsion, and tension–torsion tests. It is found that the deviatoric formulation is able to explain the fatigue crack initiation behavior under highly compressive mean stresses, including the challenging case of compression-compression loadings. Under zero or positive mean stresses, this formulation provides similar predictions as the Smith-Watson-Topper model, reproducing the observed peak stress effects. Uniaxial versions of this deviatoric model are also presented and calibrated, showing that the minimum instead of the peak stress controls the damage parameter in uniaxial fatigue tests under highly compressive mean loads.