Critical Plane Method Research Articles

A data‐assisted physics‐informed neural network (DA‐PINN) for fretting fatigue lifetime prediction

AbstractIn this study, we present for the first time the application of physics‐informed neural network (PINN) to fretting fatigue problems. Although PINN has recently been applied to pure fatigue lifetime prediction, it has not yet been explored in the case of fretting fatigue. We propose a data‐assisted PINN (DA‐PINN) for predicting fretting fatigue crack initiation lifetime. Unlike traditional PINN that solves partial differential equations for specific problems, DA‐PINN combines experimental or numerical data with physics equations as part of the loss function to enhance prediction accuracy. The DA‐PINN method, employed in this study, consists of two main steps. First, damage parameters are obtained from the finite element method by using critical plane method, which generates a data set used to train an artificial neural network (ANN) for predicting damage parameters in other cases. Second, the predicted damage parameters are combined with the experimental parameters to form the input data set for the DA‐PINN models, which predict fretting fatigue lifetime. The results demonstrate that DA‐PINN outperforms ANN in terms of prediction accuracy and eliminates the need for high computational costs once the damage parameter data set is constructed. Additionally, the choice of loss‐function methods in DA‐PINN models plays a crucial role in determining its performance.

Multiaxial fatigue life assessment of dental implants

As screwed joints, dental restorations may suffer mechanical failures such as screw loosening and implant or prosthetic screw failure due to fatigue. This work is focused on the failure of the implant and develops a numerical methodology to predict its fatigue life under cyclic loading conditions. This methodology is based on the combination of Critical Plane Methods and the Theory of Critical Distances to account for stress multiaxiality and notch effects. The obtained predictions were validated experimentally, which can be used to identify the main geometrical, assembly and operational factors affecting the fatigue behavior of dental implants. As a result, a powerful and efficient design tool for fatigue life prediction of dental implants is presented. This methodology complements a previously presented one focused on the fatigue life prediction of the prosthetic screw, thereby, offering now a complete design tool package regardless the critical component of the dental restoration, predicting accurately the fatigue response of the restoration, with no need for long-term fatigue test campaigns. This is a pioneering work since no other fatigue design methodology for dental implants with such a solid foundation and experimental validation has been published to date.

Research on the Influence of Wheel Tread Defects on Rolling Contact Fatigue

With the rapid development of high-speed trains, local rolling contact fatigue caused by special local defect damage forms has become more prominent. This article takes circular defects as the research object, adopts the Jiang Sehitoglu multi-axis fatigue damage criterion based on the critical plane method, establishes a finite element model of wheel tread circular defects, and studies the influence of wheel tread circular defects on wheel rail rolling contact fatigue. Based on finite element analysis to obtain fatigue damage parameters, an improved PSO-BP neural network was used to establish a neural network prediction model for fatigue damage parameters, and the feasibility of the model was demonstrated. The research results show that the main influencing factors on the rolling contact fatigue life of wheel tread defects are shear stress and shear strain; The fatigue damage parameter is maximum at the edge of the wheel tread defect; As the defect distribution moves from the center to both sides, the contact stress and damage parameters gradually decrease; As the depth of the defect increases to the size of the radius, the contact stress and damage parameters first increase and then decrease; As the diameter of the defect increases, the contact stress and damage parameters increase, but the amplitude change gradually tends to stabilize with the increase of the defect diameter. The neural network prediction results indicate that all predicted samples are within a reasonable range, and this neural network model can provide a reference for predicting fatigue damage of wheel tread.

Fretting fatigue crack initiation and propagation behaviours of Ti6Al4V alloy coated by functionally graded material

Fretting fatigue pertains to the behaviour of engineering components undergoing cyclic loading while in contact with each other. This intricate contact-related phenomenon often results in premature failure compared to conventional fatigue issues. Moreover, when these components operate in high-temperature atmospheres and experience high wear conditions, such as the heat transfer tubes in the nuclear reactor, the application of Functionally Graded Material (FGM) coatings becomes essential. Consequently, it is imperative to investigate how FGM coatings influence the initiation and propagation behaviour of fretting fatigue cracks. This paper employs the Critical Plane (CP) method to calculate the damage parameter. Additionally, Linear Elastic Fracture Mechanics (LEFM), specifically the Extended Maximum Tangential Stress (E-MTS) criterion, is utilized to examine how FGM coatings affect the paths of fatigue crack propagation in the presence of fretting conditions. Meanwhile, due to the unavailability of material properties of FGM coatings, the damage parameter and stress intensity factors are utilized to indirectly assess the effect of FGM coatings on crack initiation and propagation lifetimes. The FGM coating significantly influences tangential stress, thereby affecting the length of the stick zone, while having minimal impact on the distribution of normal stress along the contact surface. Furthermore, it is observed that adjusting the variation in composition of FGM coatings and the elastic modulus of the first FGM coating layer provides a potential technique for enhancing both crack initiation and propagation lifetimes.

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%.

A closed-form solution for evaluating the Findley critical plane factor

The fatigue assessment of structural components is a significant topic investigated both in the academia and industry. Despite the significant progress in comprehension over the past few decades, fatigue damage remains a significant challenge, often leading to unexpected component failures. One commonly used approach for fatigue assessment is the critical plane analysis, which aids in identifying the critical location and early crack propagation direction in a component. However, the conventional method for calculating critical plane factors is computationally demanding and is typically utilized only when the critical regions of the component are already known. In situations where the critical areas are difficult to be identified due to complex geometry, loads, or constraints, a more efficient method is required for evaluating critical plane factors. This research paper introduces an analytical algorithm to efficiently evaluates the widely used Findley critical plane factor. The algorithm operates within the framework of linear-elastic material behavior and proportional loading conditions, relying on tensor invariants and coordinate transformation laws. The algorithm has been tested on different component geometries, including a box-welded joint and a tubular specimen, subjected to proportional loading conditions such as tension, torsion, and a combination of them. The analytical method allowed a significant reduction in computation time while providing the exact solution of critical plane factor and critical plane orientations.

Rapid and accurate semi-analytical method for the fatigue assessment with critical plane methods under non-proportional loading and material plasticity

Despite the substantial progress made over recent decades, fatigue assessment of structural components remains a challenge for designers, often culminating in unforeseen failures. Among the well established methods for evaluating fatigue, critical plane models have the capability of identifying the critical location and the direction of early crack propagation within a component. However, the use of the critical plane concept with the standard plane scanning method results extremely demanding when dealing with real-world scenarios, since, due to complex geometries, loading conditions and constraints, a comprehensive analysis of the part is required. In such situations, a more efficient computational method can be the discriminant to finalize a fatigue assessment. This study introduces a novel semi-analytical algorithm, which efficiently calculates critical plane factors. The algorithm was designed to be implemented alongside finite element analysis which may include elastic–plastic material behavior and non-proportional loading conditions. The method was tested on a notched component subjected to proportional and non-proportional loading conditions. As compared to the plane scanning method, the proposed method offers a time-efficient tool for evaluating critical plane factors and their associated plane orientations, with almost identical results.

Effect of shot peening parameters on fretting fatigue lifetime

Fretting fatigue pertains to the behavior of engineering components subjected to cyclic loading while in contact with each other. This challenging contact-related phenomenon often leads to premature failure compared to typical fatigue issues. To extend the lifespan of components experiencing fretting fatigue, surface strengthening is crucial. One well-established method for enhancing the durability of these components is the application of compressive residual stress to the material's surface, achieved through a process called Shot Peening (SP). Numerous parameters in SP, such as shot speed, ball material, ball diameter, and coverage, must be carefully controlled to make beneficial compressive residual stress. These parameters significantly affect the residual stress distribution, containing the maximum residual stress, the depth of the residual stress area, and the depth of the maximum residual stress. The Critical Plane (CP) approach is used to calculate the damage parameter, and the Theory of Critical Distance (TCD) method is utilized to average the damage parameter due to the stress concentration resulting from the contact problem to investigate the impact of residual stress distribution on crack initiation behavior. Additionally, Linear Elastic Fracture Mechanics (LEFM) criteria, specifically the Extended Maximum Tangential Stress (E-MTS) criterion, are used to study how the residual stress affects crack propagation lifetime under fretting conditions. It is found that the maximum residual stress plays the most important role in improving crack initiation and propagation lifetimes, as well as the depth of the residual stress region. However, an increase in the depth of the maximum residual stress has a negative impact on crack initiation lifetime, and it has little effect on crack propagation lifetime. Furthermore, the enhanced lifetime diminishes as the applied loads increase.

How many critical planes? A perspective insight into structural integrity

The topic of material fatigue is a subject extensively investigated within both scientific and industrial worlds. Fatigue-induced damage remains a critical concern for a variety of components, encompassing both metallic and non-metallic materials, often leading to unexpected failures during their operational lifecycle. In cases necessitating the assessment of multiaxial fatigue, critical plane methodologies have emerged as a valuable approach. These methodologies offer the means to pinpoint the component's critical regions and anticipate early-stage crack propagation. Nevertheless, the conventional technique (i.e., plane scanning method) for computing critical plane factors is a time-intensive process, reliant on nested iterations, predominantly suited for research purposes. In numerous cases, where the critical area within a component is unknown in advance (i.e., primarily due to complex geometries and loading conditions) the method proves impractical. Furthermore, the plane scanning method does not provide a deep comprehension of the critical plane concept; indeed, it is just a numerical artifice for calculating stress and strain quantities on different planes. Recently, the authors introduced an efficient algorithm for evaluating critical plane factors. This algorithm is based on a closed form solution and is applicable to all instances where the maximization of a specific parameter, based on stress or strain components, is required. The methodology relies on tensor invariants and coordinates transformation principles thus enhancing the investigation of various critical plane methods. The paper addresses two formulations of the Fatemi-Socie critical plane factor and discusses how the number of critical planes depend on the loading conditions the component is subjected to. By the use of a closed form solution a deep insight of critical planes orientation can be achieved.

Microstructure evolution, failure mechanism and life prediction of additively manufactured Inconel 625 superalloy with comparable low cycle fatigue performance

During hot end components service, i.e., startup and shutdown processes, the cyclic stress caused by the asymmetry loading conditions is introduced. To study the effect of mean stress on the cyclic response, the low cycle fatigue, failure mechanism and life prediction model of additively manufactured (AMed) Inconel 625 superalloy at room temperature (RT) and service temperature (600°C) with strain ratio R = −1 and 0.1 are conducted. Experimental results indicate that the different cyclic softening and hardening behavior at RT and 600 °C is the result of competition between dislocation slip, back stress hardening and second phase precipitation. According to the evaluation of the internal stress variables, the long-range back stress plays a crucial role to control the cyclic behavior of the alloy. At RT, the heterogeneous grain structure introduced by additive manufacturing causes the back stress hardening, making the material exhibit high fatigue performance. But this hetero-deformation induced (HDI) strengthening is inhibited at high temperatures due to the uniform distribution of dislocations. In addition, a low cycle fatigue life prediction model based on critical plane method is established which presents an easily assess to evaluate the low cyclic fatigue life of an AMed material under various test condition.

Investigation of rail damage considering impact at a welded joint under wet condition

PurposeThe purpose of this study is to develop a transient wheel–rail rolling contact model to primarily investigate the rail damage under wet condition when the train passes through the welded joints.Design/methodology/approachThe impact force induced by welded joints is obtained through vehicle–track coupling dynamics. The normal and tangential wheel–rail contact pressures were solved by elastohydrodynamic lubrication (EHL) theory and simplified third-body layer theory, respectively. Then, the obtained tangential pressure and normal pressure were applied to the finite element model as moving loads, simulating cyclic loading. Finally, the shakedown map and critical plane method were used to predict rolling contact fatigue (RCF) and the initiation of fatigue cracks.FindingsThe results indicate that RCF will occur and fatigue cracks are more prone to appear on the subsurface of the rail, specifically around 2.7 mm below the rail surface in the vicinity of the welded joint and its heat-affected zone.Originality/valueThe cosimulation of numerical model and finite element model was implemented. The influence of surface roughness and fluids was considered. In this model, the normal and tangential wheel–rail contact pressure, the stress and strain and the rail fatigue cracks were obtained under a rail-welded joint excitation.

Fatigue assessment of a FSAE car rear upright by a closed form solution of the critical plane method

Material fatigue is extensively discussed and researched within scientific and industrial communities. Fatigue damage poses a significant challenge for both metallic and non-metallic components, often resulting in unexpected failures of in-service parts. Within multiaxial fatigue assessment, critical plane methods have gained importance due to their ability to characterize a component's critical location and detect early crack propagation. However, the conventional approach to calculate critical plane factors is time-consuming, making it primarily suitable for research purposes or when critical regions are already known. In many real-world scenarios, identifying the critical area of a component is difficult due to complex geometries, varying loads, or time limitations. This challenge becomes particularly crucial after topological optimization of components and in the context of lightweight design. Recently, the authors proposed an efficient method for evaluating critical plane factors in closed form, applicable to all cases that necessitate the maximization of specific parameters based on stress and strain components or their combination. This paper presents and validates the proposed methodology, with reference to a rear upright of a FSAE car, which is characterized by a complex geometry and is subjected to non-proportional loading conditions. The efficient algorithm demonstrated a substantial reduction in computation time compared to the standard plane scanning method, while maintaining solution accuracy.

Fatigue life analysis of spinning bearings for roller-guided bushing special machines considering creep-slip characteristic

In order to ensure the longer working life of rolling guide bushing, this work proposed a fatigue life prediction model of spinning bearings based on the Hertzian contact distribution and creep-slip characteristic. The influence of different parameters on the fatigue life of spinning bearings was analyzed according to the damage parameter theory of the critical plane method and the L-P theory. Finally, the fatigue life prediction model of spinning bearings was verified through the finite element simulation combined with the experiments. The reliability results show that creep-slip characteristic and deformation lead to the contact zone stress of the spinning bearing firstly increases, decreases subsequently to zero and then increases to the peak value. The increase of rotational speed will make the fatigue life of the spinning bearing firstly increases and then decreases. With the increase of friction coefficient, its fatigue life will become smaller and smaller, and the increase of the external load will decrease its fatigue life. Meanwhile, the prediction error rate of the fatigue life prediction model proposed in this study is 4.60%, which is within the error tolerance. This study provides certain methods and ideas for fatigue life prediction of spinning bearings, and lays a theoretical foundation for the design of highly reliable spinning bearings.

Effect of U-shaped stress relief groove on crack initiation life of fretting fatigue

A U-shaped stress relief groove was developed to enhance fretting fatigue strength. The effects of the groove on crack initiation location and life were evaluated using the finite element method and the critical plane method. The results demonstrated that by varying the geometry parameters of the groove, the crack initiation location was altered between the contact zone and the groove. When the damage in both the contact zone and the groove was comparable, the life of fretting crack initiation was increased by up to 3.5 times compared with that of the non-grooved specimen. These findings were expected to propose a potential strategy for enhancing the material's resistance to fretting fatigue by designing a groove near the contact zone and to provide insights into the development of components with improved fatigue resistance.

Fatigue life investigation of rubber bearing for heavy trucks: Optimal design by using finite element method with experimental verification

Rubber bearings consisting of multiple layers of rubber and inlaid steel plates play an important role in cushioning and vibration damping on heavy trucks. In this study, the thermo-mechanical coupling approach together with critical plane analysis theory was utilized to predict fatigue nucleation life of rubber bearing. A new criterion for fatigue life estimation of rubber bearings aiming to eliminate the mesh dependence was proposed, that is, the logarithmic average fatigue life of multiple elements in some local areas with low life (accounting for 0.5% of the total rubber elements) was used instead of the shortest life for a single element. The structure of inlaid steel plates was optimized based on the proposed evaluation criterion for longer service life. The simulation results show that the fatigue life of the optimized rubber bearing is increased by 2.2 times compared with that of the original structure, and the experimental results show that the life of the optimized structure is increased by 2.1 times.

Closed‐form solution for the Fatemi‐Socie extended critical plane parameter in case of linear elasticity and proportional loading

AbstractFatigue damage remains a significant issue for both metallic and non‐metallic components, being the main cause of in‐service failures. Among the different assessment methodologies, critical plane methods have gained significance as they enable identifying the critical location and the early crack propagation orientation. However, the standard plane scanning method used for calculating critical plane factors is computationally intensive, and as a result, it is usually applied only when the component's critical region is known in advance. In the presence of complex geometries, loads, or constraints, a more efficient method would be required. This work presents a closed‐form solution to efficiently evaluate a critical plane factor based on the Fatemi‐Socie criterion, in the case of isotropic linear‐elastic material behavior and proportional loading conditions. The proposed algorithm, based on tensor invariants and coordinate transformation laws, was tested on different case studies under various loading conditions, showing a significant reduction in computation time compared to the standard plane scanning method.

Multiaxial fatigue life predictions of additively manufactured metals using a hybrid of linear elastic fracture mechanics and a critical plane approach

This paper introduces a hybrid approach which leverages Fatemi-Socie critical plane analysis to determine an equivalent-damage uniaxial stress amplitude for various multiaxial loading conditions including uniaxial, torsion, and axial-torsion. Then, mode I crack growth constants along with initial defect information are used to make life predictions for multiaxial loadings as a function of their equivalent-damage uniaxial stress amplitudes. Two different Laser-Powder Bed Fusion metals, Ti-6Al-4V and 17-4 PH stainless steel, in a total of nine different surface and heat treatment conditions are analyzed and life predictions based on initial defect size and mode I crack growth properties from the literature are made using the Hartman-Schijve crack growth equation.

Using the fatigue crack initiation parameter for prediction of the crack location on a curved track by 3D-FE analysis

Dynamic modeling of wheel-rail interaction is significant in accurate fatigue analysis of railways. Both location and magnitude of the contact stresses in the contact area must be evaluated accurately and efficiently via computational tools. In curved railway tracks, the distribution of the force exerted on the wheel is complex as it is multiaxial rather than uniaxial; thus, a more comprehensive computational model is required. In this work, a numerical procedure is developed to investigate the fatigue crack initiation on the curved tracks. The Universal Mechanism software is used to specify the spectrum of axial wheel force as input to a three-dimensional explicit finite element model to obtain the resulting stresses at the wheel-rail contact region. A critical element with the maximum von Mises stress value is treated as the element where the fatigue crack is most probably to be initiated. In this element, the critical plane method is used to determine the orientation of the crack initiation. The effect of the radius and slip ratio on the exact site of fatigue crack initiation is established in this approach, and the contact point influence on the fatigue crack initiation parameter is investigated. The proposed model successfully predicts a practical wheel-rail dynamic response to cyclic loading, applying the geometry of the curved track.

Prediction of the effect of shot peening residual stress on fretting fatigue behaviour

Fretting occurs at two contact bodies, which sustain oscillation loading. The fretting phenomenon decreases the fatigue lifetime dramatically. Shot peening is a commonly used surface treatment to enhance the resistance to damage because the residual stress is introduced to the surface of the material. Some studies showed that residual stress was helpful to improve fatigue lifetime. Under fretting fatigue condition, there are two main stages: crack initiation stage and the crack propagation stage. In this paper, the authors apply the Critical Plane (CP) method combined with the Theory of Critical Distance (TCD) to study the fretting fatigue crack initiation behaviour under the influence of shot peening residual stress, including the crack initiation position, orientation and the crack initiation lifetime. Meanwhile, the Linear Elastic Fracture Mechanics (LEFM) theory and the Extension Maximum Tangential Stress (EMTS) criterion are adopted to study crack propagation behaviour considering shot peening residual stress effect. The results show that the methods applied in this paper can make good predictions of fretting fatigue behaviour, including both initiation and propagation stages. Meanwhile, the influence of residual stress in these two stages are studied as well.

A Critical Plane-Based Multiaxial High-Cycle Fatigue Criterion Considering Mean Stress and Phase Shift Effects for Hard Metals

Abstract Based on the critical plane method, a high-cycle fatigue criterion considering the effects of the phase shift and mean stress on multiaxial fatigue strength is proposed for hard metals. When the materials obey the von Mises criterion and are subjected to proportional loading without the mean stress, the proposed criterion can be reduced to the von Mises criterion. The experimental data conducted under combined bending and torsion loading from some studies were employed to validate the applicability of the proposed criterion. The results demonstrate that the proposed criterion has good agreement with the experimental data under loading conditions with both the mean stress and phase shift effects.