Multiaxial Fatigue Damage Parameter Research Articles

Static axial tension or compression stress effects on shear cracks initiating under cyclic torsion loads in multiaxial fatigue tests

This work proposes models that can better fit and explain apparently contradictory mean stress effects observed when superimposing axial tension or compression loads on cyclic torsion fatigue tests. It introduces new shear-based multiaxial fatigue damage models, modifying the classic Fatemi-Socie equation to consider the peak deviatoric stress normal to the initiating shear crack as the actual driving force for the peak or mean effects of the normal stresses. This deviatoric hypothesis can quantify the odd detrimental effects of static axial compression observed on axial shear cracks tested under cyclic torsion. Additionally, applying the peak deviatoric correction term only to the elastic component of the shear strain range allows an even better description of the increasing mean normal stress effects in high-cycle fatigue, eliminating the need for a variable normal stress sensitivity coefficient in the multiaxial fatigue damage parameter. To evaluate the proposed shear-based models, their life and crack initiation direction predictions are compared for cyclic torsion experiments both with and without superimposed static axial stresses for steels and aluminum alloys, including both literature and original data. The experiments show that axial compression can be detrimental to fatigue crack initiation lives, depending on the cracking mode and on the presence of bifurcations, which effects could be explained from the proposed deviatoric damage parameters.

A novel machine learning method for multiaxial fatigue life prediction: Improved adaptive neuro-fuzzy inference system

In this study, a neuro-fuzzy-based machine learning method is developed to predict the multiaxial fatigue life of various metallic materials. First, the fuzzy inference system and neural network are combined to identify and capture the nonlinear mapping relationship between multiaxial fatigue damage parameters and fatigue life. Non-proportionality and phase differences are introduced to characterize different loading paths. Next, the Adam algorithm is employed to update the premise parameters of the original model to achieve fast and accurate convergence. Then, subtractive clustering is applied to extract fuzzy rules between input variables and output for more efficient prediction. Moreover, the hyperparameters in the proposed model are automatically optimized by the adaptive opposition slime mould algorithm to obtain the optimal model. The predictive performance of the proposed model is verified by fatigue experimental data for six materials in published literature, which indicates that the proposed model can effectively predict the fatigue life of various materials under different loading paths. Meanwhile, compared with six classical machine learning models, it is found that the proposed model has better predictive performance and extrapolation capability.

Very high cycle fretting fatigue behavior of IN718 reinforced by IN625/20 % WC laser cladding

The objective of this study is to evaluate the very high cycle fretting fatigue (VHCFF) behavior of laser cladding (LC) Inconel 718 (IN718) metal matrix composites reinforced with IN625/20 % WC. Experiments and simulations were conducted to analyze the fretting fatigue behavior of the cladding layer. The wear and fracture morphologies were obtained by using a confocal laser scanning microscope (CLSM) and a scanning electron microscope (SEM). The multiaxial fatigue damage parameters of the FS and SWT models were used to predict fatigue life through the fitting curve, and the critical plane method was adopted to predict the crack initiation and propagation path. Results indicate that the predicted crack corresponds well with the real crack of the specimen. WC particles can improve the anti-fatigue performance of the contact surface, which is proportional to the contact area between the WC and fretting pad.

Component Tests and Numerical Investigations to Determine the Lifetime and Failure Behavior of End Stage Blades

Abstract The paper focuses on experimental and numerical fatigue assessment procedures to evaluate the influence of multi-axial stress state caused by high centrifugal forces superimposed with bending loads due to blade vibrations on the lifetime of end stage blades from steam turbines. The experimental investigations on original-sized end stage blades were carried out on a test rig specially developed for high forces and multicomponent force application. This was based on detailed numerical simulations by the MPA University of Stuttgart. During the fractographic postexaminations of the tested blades using magnetic particle inspection, light and scanning electron microscopes, two competing damage mechanisms were identified that occurred at different locations. Numerical investigations by means of elastic–plastic finite element analyses were carried out to estimate the local stress conditions acting in the blade root. The local stresses and strains were postprocessed using the critical plane approach and advanced multi-axial fatigue damage parameters. Due to the high stress gradients at the edge of contact, over-conservative predictions may result if their effects are not taken into account. Based on the critical plane method in conjunction with fatigue damage parameters, an approach taking the stress gradient into consideration was developed to predict the fatigue life of the end stage blades. The approach is verified by the component tests on original-sized blades.

Multiaxial fatigue life prediction by equivalent energy‐based critical plane damage parameter under variable amplitude loading

AbstractA new path‐independent multiaxial fatigue damage parameter , which is defined as the largest normal stress range between adjacent turning points of the maximum shear stress on the critical plane, is proposed to describe multiaxial fatigue damage. By combining the maximum normal stress or the largest normal stress range with the maximum shear stress range on the critical plane, two axial equivalent stress modification factors, and , are proposed, which can account for the influence of non‐proportional additional hardening. The sensitivity of the proposed axial equivalent stress modification factors to multiaxial variable amplitude loading sequences is analyzed. Furthermore, two new multiaxial fatigue damage models based on the axial equivalent stress modification factors are proposed to estimate fatigue life. The applicability of the presented methodology was verified by the experimental data of En15R steel and 7050‐T7451 aluminum alloy, and the results showed that the predicted fatigue lifetimes agree well with the experimental data under variable amplitude multiaxial loading.

Multiaxial fatigue damage parameters and life prediction for adhesively bonded butt-joint based on the stress-based approach

The fatigue life evaluation of adhesively bonded joints has attracted more and more attention with its extensive application. Here, the fatigue experiments under various loading conditions were carried out to understand the stress amplitude, mean stress, cycle period, and loading path related to the fatigue life of the adhesively bonded tubular butt-joints. The experimental results showed that the fatigue life of the adhesively bonded butt-joint decreased with the increase of stress amplitude and mean stress, and the influence of cycle period on the fatigue life was more obvious since the mechanical property of the selected adhesive was rate dependent. Meanwhile, the fatigue life of the adhesively bonded butt-joint was influenced by the loading path under multiaxial loading conditions. In addition, the relationship between the damage parameters and fatigue life was characterized based on the experimental observations. Accordingly, a stress-based fatigue life prediction model was developed which can simultaneously consider multiple damage parameters related to fatigue life of the adhesively bonded joint. The predicted results indicated that the predicted life correlated well with the experimental data of the adhesively bonded joints.

A damage-based method to predict crack initiation lifetime of high-strength steel under proportional bending-torsional loadings

The fatigue life of specimen consists of crack initiation and crack propagation life. As the fracture toughness of high strength steel is low, the specimen will fail soon once crack appears. Therefore, the crack initiation life of high strength steel is considered to be its whole life. Based on the evolution of material fatigue damage and the critical plane method commonly used in multiaxial fatigue strength theory, a crack initiation life prediction method for multiaxial specimens is proposed in this paper. Firstly, a uniaxial nonlinear fatigue damage evolution equation is proposed based on the principles of thermodynamics and continuous damage mechanics. Then, a theoretical calculation method for determining the critical plane under multiaxial load is proposed, and the specific calculation process is given. After the critical plane is determined, the multiaxial fatigue damage parameter is constructed from the normal strain amplitude and shear strain amplitude on the critical plane, and a multiaxial nonlinear fatigue damage evolution equation is proposed by replacing the uniaxial damage parameter using the multiaxial damage parameter. Finally, the crack initiation life of fatigue specimens is predicted by using the proposed multiaxial nonlinear fatigue damage evolution equation, and the multiaxial fatigue tests of Q690D steel under different bending-torsion ratios and different amplitudes are validated. The comparison results show that the prediction error of the proposed method is within the two-fold dispersion band and better than that of Manson-Coffin method.

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.

A fast method to estimate the multiaxial non-proportional elastic–plastic stress–strain in rail rolling contact fatigue problems

This paper aims to propose a new and fast method to estimate the multiaxial non-proportional elastic–plastic stress and strain time histories developed in rails due to rolling contact and evaluate its accuracy for fatigue analysis. The method has the pseudo-elastic stress time history as input, which is obtained by a coupled analytical and numerical method. Therefore, a method originally proposed for notch-root elastic–plastic stress–strain analysis was extended to the Rolling Contact Problem (RCF). The problem is solved incrementally and is established considering a set of equations composed by constitutive and multiaxial notch correction equations. Additionally, a kinematic cyclic plasticity model was included. An equivalent model based on the Finite Element Method was used for comparison purposes. The comparison was made in terms of multiaxial fatigue damage parameters in critical planes, according to fatigue analysis models developed by Matake and Brown & Miller. The more relevant advantage of the method over the non-linear FEM analysis is the possibility to readily obtain long elastic–plastic stress and strain histories and to perform material parameter and load case studies. The method proposed agrees with the equivalent FEM and proved to be a powerful tool for fast wheel-rail failure analysis, especially in RCF problems.

A stress gradient-based fatigue life prediction method for multiaxial notched specimen considering additional hardening effect

In this paper, the damage parameter considering stress field distribution near the notch root is employed to overcome the deficiency of the equivalent stress method (ESM) ignoring the influence of stress gradient, and a new multiaxial fatigue life prediction method is then developed taking into account stress gradient effects and additional hardening effects. Firstly, the equivalent stress distribution on the critical plane is analyzed using the finite element method (FEM), and the equivalent stress field intensity of fatigue damage affected area is defined as the multiaxial fatigue damage parameter to estimate the fatigue life of notched specimens. Secondly, a new non-proportional additional hardening coefficient is defined to consider the influence of phase difference and material characteristics on multiaxial fatigue life. Finally, in order to verify the reliability of the proposed model, the estimated lives using the proposed method and the equivalent stress method are compared with the test life, and the comparison results show that the accuracy of the proposed method considering stress gradient effect and additional hardening effect is higher than that of the equivalent stress method under proportional and non-proportional loading.

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.

A multiaxial fatigue life prediction method for metallic material under combined random vibration loading and mean stress loading in the frequency domain

A spectral method for the determination of the critical plane is proposed for metallic material under random vibration loadings based on the criterion of maximum shear stress amplitude, where the direction of critical plane is obtained by solving the maximum value of a function using mathematical optimization method and the fatigue critical location of the structure can be determined. A multiaxial fatigue damage parameter is proposed for combined random vibration loading and mean stress loading cases based on Susmel’s criterion, which is a Power Spectral Density (PSD) of the equivalent shear stress and can be adopted for fatigue life evaluation. The fatigue life estimation of structures under multiaxial random vibration loadings with mean stresses in the frequency domain could be carried out based on this damage parameter constructed at the fatigue critical location with the spectral method for random vibration fatigue life. The multiaxial random vibration fatigue experiment with mean stress loadings is conducted on the notched plate specimens made of 2297-T87 aviation grade aluminum alloy, and the initiation sites of the fatigue cracks as well as the experimental fatigue lives are compared with those calculated by the proposed models, where satisfactory prediction capabilities on both the fatigue crack initiation locations and fatigue lives of the models are demonstrated.

A topologized resolved shear stress method for the life prediction of nickel-base single crystal superalloys

Fifteen multiaxial critical-plane fatigue damage parameters of isotropic metal materials are applied to the life evaluation of nickel-base single crystal superalloys. These parameters are classified into stress-, strain- and strain-energy parameters, and their predictive abilities are evaluated by 12 groups of single crystal fatigue data obtained from mainly an intermediate temperature range (500–760 °C) where the slip deformation is the main damage mode. The results show that the strain energy group exhibits the best fitting characteristics with correlation coefficients. A topologized resolved shear stress method (TRSS) considering the interaction of main slip systems is further proposed. The dispersion degree of resolved shear stress among the main slip systems is quantified by a dispersion factor, and the real driving capacity of resolved shear stress is amended according to the topology of driving force. The obtained results show that the proposed method has achieved an improvement of correlation ability.

Equivalent energy-based critical plane fatigue damage parameter for multiaxial LCF under variable amplitude loading

Combining the concept of energy on the critical plane, a multiaxial fatigue damage parameter without any weight coefficient was proposed and the effects of non-proportional additional hardening and mean stress on fatigue damage can be reflected more perfectly using an equivalent form of shear strain energy. Furthermore, two sets of experimental data are employed to verify the proposed method, and the sensitiveness to fatigue life of the proposed equivalent stress correction factor is discussed as well. The results show that satisfactory and conservative assessments can be obtained by the proposed method, especially under multiaxial irregular loading with great randomness.

Very high cycle fretting fatigue damage and crack path investigation of Nimonic 80A at elevated temperature

Fretting fatigue failure generally appears in turbine blades and disk tenon joint position subjected to high frequency vibration loads at elevated temperature. To study the fretting resistance of Nickel-based super alloy at high temperature, a set of fretting rig with a special heater was integrated with ultrasonic fatigue testing machine. Fretting tests with the developed apparatus were performed in very high cycle fatigue regime at elevated temperature. The initiation site and path of the cracks were analyzed via laser confocal microscope and scanning electron microscope. The cracks have a high proportion to initiate at the trailing edge of the wear zone and tend to extend to one side of the wear zone. Critical plane method with multiaxial fatigue damage parameters was used to predict the main propagation path of fatigue cracks.

A new critical plane-energy model for multiaxial fatigue life prediction of turbine disc alloys

Abstract For engine components under complex loadings, multiaxial fatigue life prediction is critical for ensuring their structural integrity and reliability. Combining the critical plane method with the virtual strain energy concept, a new multiaxial fatigue damage parameter is proposed to characterize the influence of both shear/normal mean stress and non-proportional hardening on fatigue life. Particularly, no extra material constants are needed for model application. Experimental data of TC4 and GH4169 alloys under various loading paths are utilized to evaluate and validate the proposed damage parameter as well as four other models. Results show that the proposed damage parameter yields a higher accuracy on multiaxial fatigue life prediction than others.

A damage model based on the critical plane to estimate fatigue life under multi-axial random loading

A multi-axial random vibration fatigue damage parameter was proposed based on a critical plane damage parameter for multi-axial high cycle fatigue, which is an equivalent stress power spectral density (PSD). The fatigue life calculation under multi-axial random loading could be conducted based on the equivalent stress PSD, combined with the spectral method under uniaxial random loading. The multi-axial random vibration fatigue experiment was conducted on the thin-walled circular tube with slots on the side. The fatigue life results obtained from the experiment were compared with the ones calculated from the proposed model, which indicated that the proposed parameter did a good job in predicting the multi-axial random vibration fatigue life.

A New Approach to the Fatigue Life Prediction for Notched Components Under Multiaxial Cyclic Loading

A new fatigue life prediction approach for notched components is proposed under multiaxial cycle loading. Firstly, the pseudo equivalent strain-real equivalent stress relationship is determined by utilizing the Neuber’s rule and the material stress-strain relation under proportional loading. Secondly, the pseudo elastic strain histories at the notch need to be solved for the investigated notched components under multiaxial cyclic loading. Thirdly, for the pseudo elastic strain histories, it is proposed that the Shang–Wang multiaxial fatigue damage parameter can be used to substitute the equivalent strain under proportional loading to take account of the additional hardening due to the non-proportionality of external loadings. Meanwhile, the real equivalent stress amplitude at the notch can be solved. Fourthly, based on the real equivalent stress amplitude at the notch integrated with the Neuber’s rule, the real equivalent strain amplitude can be determined. Finally, the real equivalent strain amplitude is utilized to predict the fatigue crack initiation lifetime of notched components. The proposed method is verified by the experimental data of SAE 1045 notched shaft specimens under proportional and non-proportional cyclic loading. The results showed the prediction errors are mostly within a factor of 2.

Multiaxial Fatigue Damage Parameter and Life Prediction without Any Additional Material Constants

Based on the critical plane approach, a simple and efficient multiaxial fatigue damage parameter with no additional material constants is proposed for life prediction under uniaxial/multiaxial proportional and/or non-proportional loadings for titanium alloy TC4 and nickel-based superalloy GH4169. Moreover, two modified Ince-Glinka fatigue damage parameters are put forward and evaluated under different load paths. Results show that the generalized strain amplitude model provides less accurate life predictions in the high cycle life regime and is better for life prediction in the low cycle life regime; however, the generalized strain energy model is relatively better for high cycle life prediction and is conservative for low cycle life prediction under multiaxial loadings. In addition, the Fatemi–Socie model is introduced for model comparison and its additional material parameter k is found to not be a constant and its usage is discussed. Finally, model comparison and prediction error analysis are used to illustrate the superiority of the proposed damage parameter in multiaxial fatigue life prediction of the two aviation alloys under various loadings.

A survey on multiaxial fatigue damage parameters under non‐proportional loadings

AbstractIn this paper, several multiaxial fatigue damage parameters taking into account nonproportional additional hardening are reviewed. According to the way nonproportional additional hardening is considered in the model, the damage parameters are classified into 2 categories: (1) equivalent damage parameters and (2) direct damage parameters. The equivalent damage parameters usually define a nonproportional coefficient to consider nonproportional additional cyclic hardening, and make a combination of this nonproportional coefficient with stress and/or strain quantities to calculate the equivalent damage parameters. In contrast, the direct damage parameters are directly estimated from the stress and strain quantities of interest. The accuracy of 4 multiaxial fatigue damage parameters in predicting fatigue lifetime is checked against about 150 groups of experimental data for 10 different metallic materials under multiaxial fatigue loading. The results revealed that both Itoh's model, one of equivalent damage parameters, and Susmel's model, which belong to direct damage parameters, could provide a better correlation with the experimental results than others assessed in this paper. So direct damage parameters are not better than the equivalent damage parameters in predicting fatigue lifetime.