Nonlinear Fatigue Damage Research Articles

Combined high and low cycle fatigue life prediction model based on damage curve method considering loading interaction effect

Through analyzing the characteristics of the Miner’s rule and the Manson-Halford (M-H) model, a nonlinear fatigue damage accumulation model is established based on the damage curve method under combined high and low cycle fatigue loading. In this model, an interaction factor related to the maximum stress and high cycle stress range is proposed to consider the loading interaction effect. Furthermore, the proposed model does not require any additional material parameters except for the S-N curve parameters. The experimental data of five materials, including TC11 alloy, 2024-T3 aluminum alloy, 45 steel, LY12-CZ aluminum alloy, and GH4033 Ni-based alloy, are introduced to verify the proposed model. Compared with the Miner’s rule and the M-H model, most of the prediction results by the proposed model are within the life factor range of 2, implying the established model has higher prediction accuracy.

A non-linear cohesive zone model for low-cycle fatigue of quasi-brittle materials

The low-cycle fatigue behaviour of quasi-brittle materials (e.g., concrete and rock) that is characterized by fatigue induced inelastic deformation significantly affects the integrity and serviceability of engineering structures. However, the low-cycle fatigue mechanism and fatigue-controlled fracture process of quasi-brittle materials is not clear. This paper develops a new cyclic cohesive zone model (CZM) for low-cycle fatigue of quasi-brittle materials. Based on in-situ stress and damage state, a nonlinear fatigue damage model is proposed and implemented into the cyclic CZM. The fatigue parameters are determined based on S–N curve. A worked example for monotonic and cyclic loading of concrete beam under three-point bending is presented to demonstrate the application of the developed numerical model. After validation against experimental data, the fatigue crack mechanisms are discussed and a comprehensive parametric study is carried out to investigate the effects of fatigue parameters, stress levels and loading sequences on the fatigue failure. It has been found that there are three stages for the development of crack mouth of displacement, i.e., crack initiation, stable growth and rapid fracture which are caused by combined static and fatigue damage, fatigue damage, and combined static and fatigue damage dominated by static damage, respectively. The developed cyclic CZM is practically significant and its parameters are easy to be determined based on S–N curve. It provides a new and useful tool for low-cycle fatigue crack modelling of quasi-brittle materials.

Characterization of strength, modulus, and fatigue damage properties of cement stabilized macadam based on the double modulus theory

• Flexural tensile strengths calculated with tensile and compressive differences are reduced by nearly 20 % when compared to those calculated without tensile and compressive differences. • A power function decay model of the tension–compression moduli of cement stabilized macadam was established in the four-point bending fatigue test. • The fatigue damage model of cement stabilized macadam was established and its accuracy was verified. Cement stabilized macadam (CSM) is a mixture created by combining cement as a binding material, water, and various particle sizes of minerals. The cement stabilized macadam material exhibits different moduli in tension and compression due to both its mechanical properties and the mechanical response in the asphalt pavement structure. To explore the strength, modulus and fatigue damage characteristics of CSM under different tensile and compressive modulus, this paper carried out the research. The calculation formulas for flexural tensile strength and tension–compression modulus were derived based on the difference in tension–compression modulus. A four-point bending strength test of CSM was carried out. Four-point bending fatigue tests with varying stress ratios were performed. It reveals deterioration laws of tension–compression modulus during fatigue process. The double logarithmic fatigue equation of CSM, as well as its nonlinear fatigue damage evolution equation, are established based on fatigue life results. The results of an analytical solution for fatigue life of rectangular section beams based on damage mechanics were obtained and compared to the results of four-point bending fatigue tests. The results reveal that the modulus of CSM differs in tension and compression. The calculated flexural tensile strength with the tension and compression difference is nearly 20 % lower than without the difference. The calculation approach that does not account for the difference in tension and compression overestimates the flexural tensile strength of CSM. The tension–compression moduli of CSM exhibit a power function decay law in the four-point bending fatigue processes. In the first stage, the dynamic modulus decays at a steady rate, accounting for 90 % of total fatigue life. The second stage in the life ratio of 0.9 occurs when the decay rate of the modulus rapidly increases and enters the stage of sharp decay. Based on the results of the four-point bending test, the modulus decay model was created. The decay parameter m has an exponential relationship with the stress ratio. The relative errors between the mean values of fatigue life tests and the predicted values of the analytical solutions range from 10.8 to 30.6 percent. The established fatigue damage equation for CSM can better reflect its fatigue damage evolution law. The research findings have great significance to solve the determination of pavement materials parameters based on the difference in tension and compression modulus. It also has a specific reference value for asphalt pavement design theory and calculation method when the varied modulus of tension and compression are considered.

Method for statistical evaluation of cumulative damage models applied to block loading

AbstractThere is an abundance of nonlinear fatigue damage accumulation models but a lack of verification and comparison to experimental datasets. First, an extensive two‐level block loading experimental fatigue dataset is reprocessed according to current standard practice. Next, four nonlinear damage accumulation models and the Palmgren–Miner linear damage rule are critically compared using a range of statistical metrics. For the considered dataset, the Palmgren–Miner rule consistently performs worst and the damage curve approach is found to perform significantly better than the other nonlinear models. This study shows that the current practice of performance verification of new fatigue damage accumulation models in literature is too limited which enables cherry‐picking of verification datasets to improve perceived performance. Future fatigue damage accumulation models should be verified much more rigorously to both readily available and new experimental datasets.

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.

A nonlinear uniaxial fatigue damage accumulation model based on the theory of material configurational forces

AbstractTo ensure the integrity and reliability of structures, it is of great importance to understand the fatigue damage mechanism of materials under different amplitude loading conditions. For this purpose, a nonlinear fatigue damage accumulation model based on material configurational forces is developed in this paper. Specially, since the material configurational force is defined on the material space point and directly associated with the evolution of material configuration, it is introduced as an internal variable to describe fatigue damage accumulation. Additionally, the corresponding relation between configurational force and stress state is presented. Meanwhile, the damage increasing among every loading cycle, that is, the damage rate, is dependent on the stress state and damage state variable. Therefore, the formulation of damage rate is proposed by a function of material configurational force and damage state variable. Further, numerical implementation of this proposed nonlinear fatigue damage accumulation model has been carried out through two notched structures to describe the fatigue damage evolution and predict the fatigue life of materials. The results indicate that the numerical results are consistent with previous experimental data.

Markov chain based non-linear fatigue damage accumulation model

Methodology to model fatigue damage accumulation of Fiber-Reinforced Plastics (FRP) composite laminates subjected to variable amplitude spectrum loading is proposed in this paper. Markov chain based Probability Transition Matrices (PTM) are modeled for each of the different block load levels, applying matrix multiplication to combine the PTM’s, resulting in a single probability mass function for the full variable amplitude load spectrum. Variable amplitude block load experimental data was used to demonstrate and validate the methodology and compare against other for Fiber-Reinforced Plastics commonly applied linear and non-linear damage accumulation and strength degradation based fatigue damage accumulation models. PTM’s modeled directly from experimental data for the different variable amplitude load levels were obtained to calculate the probability of failure for the full load spectrum. When applying Markov chain based probability transition matrices together with matrix multiplications, both load sequence effects as well as non-linear fatigue damage growth behavior can be accurately modeled, resulting that the model predicts failure probabilities very close to the actual experimental results.

A modified nonlinear fatigue damage accumulation model for life prediction of rolling bearing under variable loading conditions

AbstractDuring the use of rolling bearings in wind turbines, aero engines, and other equipment, they often operate under variable operating and loading conditions. The practice has shown that the sequence of these loads and their interaction has a significant impact on the fatigue life of rolling bearings. In order to better understand this issue, a modified nonlinear fatigue damage accumulation model, which considers the influences of both load sequence and load interaction, is proposed in this paper and verified using the fatigue testing data for six materials. Then, the verified model was applied to evaluate the fatigue damage accumulation and fatigue life of a rolling bearing. The results have shown that, compared with the existing models, the proposed model can more accurately predict the damage accumulation and fatigue life of the rolling bearing under variable loading conditions.

Numerical Study on Vibration Response and Fatigue Damage of Axial Compressor Blade Considering Aerodynamic Excitation

Axial compressor blades with a deformed initial torsion angle caused by aerodynamic excitation resonated at the working speed and changed the rule of fatigue damage accumulation. The fatigue life of a blade has a prediction error, even causing serious flight accidents if the effect of torque causing damage deterioration of the blade fatigue life is neglected. Therefore, in this paper, a uniaxial non-linear fatigue damage model was modified using the equivalent stress with torsional shear stress, and the proposed fatigue model including the torsional moment was used to study the compressor blade fatigue life. Then, the blade numerical simulation model was established to calculate the vibration characteristics under complex loads of airflow excitation and a rotating centrifugal force. Finally, the blade fatigue life under actual working conditions was predicted using the modified fatigue model. The results show that the interaction between centrifugal and aerodynamic loads affects the natural frequency, as the frequencies in modes dominated by bending deformation decreased whereas those dominated by torsional deformation increased. Furthermore, the blade root of the suction surface showed stress concentration, but there is an obvious difference of stress distribution and amplitude between the normal stress and the equivalent stress including torsional shear stress. The additional consideration of the torsional shear stress decreased the predicted fatigue life by 4.5%. The damage accumulation rate changes with the loading cycle, and it accelerates fast for the last 25% of the cycle, when the blade fracture may occur at any time. Thus, the aerodynamic excitation increased the safety factor of blade fatigue life prediction.

Multiaxial fatigue damage and reliability assessment of aero-engine compressor blades made of TC4 titanium alloy

This paper discusses the multiaxial fatigue damage and reliability evaluation of aero-engine compressor blades using an improved strength degeneration scheme based on Chaboche damage model combined with stress-strength interference (SSI) approach. Firstly, the multiaxial proportion and non-proportion fatigue tests of TC4 (Ti-6Al-4V) alloy under a series of loading paths are carried out. The nonlinear fatigue damage calculation and life prediction of TC4 alloy is described by combining the Chaboche nonlinear damage criterion and critical plane method with proposed damage control parameter. Secondly, a nonlinear strength degradation model based on accumulative damage is further developed, and it is proved that the model can get greater precision under different loading conditions. Finally, a revised time-varying reliability model is established by viewing mechanical characteristic of compressor blade set as interconnected system with variant load component on each blade. According to the results of Monte Carlo simulation, the proposed revised model has a better prediction precision, with the error controlled less than 5%.

An improved manson-halford model for multi-level nonlinear fatigue life prediction

The Manson-Halford (M−H) nonlinear fatigue damage model is widely used for fatigue damage analysis. It, however, does not consider the load interaction effect. This paper presents an improved M−H model with a load interaction factor defined as the ratio of the first and second stress levels. The characteristic exponent of the M−H model is modified by multiplying the load interaction factor and fatigue life ratio. The characteristic exponent can consider the load interaction effect and the load sequence effect under multi-level loading. Experimental data from five materials under two-level and multi-level stress loadings verify the accuracy of the proposed model.

On the prediction of fatigue life subjected to variable loading sequence

AbstractMiner's rule is one of the most widely used cumulative damage equations for evaluating useful fatigue life. However, it often yields unsatisfactory predictions due to its linearity of the damage accumulation. In this paper, a new nonlinear fatigue damage accumulation model is developed that treats loading sequence effect and, also, enables one to predict the rate of damage by introducing a loading sequence parameter. This parameter is defined using the loading sequence ratio, which depends on material properties. Applicability of the proposed model is validated using the results of nine sets of independent experimental measurements of fatigue life under multiple loading sequences. It is shown that the predictions are in agreement with measured results and that the model provides a reliable estimation of fatigue life.

New Nonlinear Cumulative Fatigue Damage Model Based on Ecological Quality Dissipation of Materials

The failure of many aircraft structures and materials is caused by the accumulation of fatigue damage under variable-amplitude cyclic loading wherein the damage evolution of materials is complicated. Therefore, to study the cumulative fatigue damage of materials under variable-amplitude cyclic loading, a new nonlinear fatigue damage accumulation model is proposed based on the ecological quality dissipation of materials by considering the effects of load interaction and sequence. The proposed new model is validated by the test data obtained for three kinds of material under multilevel fatigue loading. Compared with the Miner model and Kwofie model, the proposed model can more effectively analyse the accumulative damage and predict fatigue life of different materials under variable-amplitude cyclic loading than others. The study provides a basis for predicting fatigue life accurately and determining reasonable maintenance periods of aircraft structures.

Novel nonlinear time-varying fatigue reliability analysis based on the probability density evolution method

The evolution of fatigue damage in materials of structures under cyclic loading is a time-varying cumulative process. Method on time-varying fatigue reliability analysis is scarce due to the popular use of Miner’s rule in defining the fatigue damage which does not consider the influence of the load sequence. A novel nonlinear time-varying fatigue reliability analysis method is presented to improve the accuracy and efficiency of time-varying reliability analysis. A nonlinear fatigue damage index is defined based on the toughness exhaustion of material, and the fatigue damage limit state function is then derived. This state function is then analyzed with the probability density evolution method (PDEM), and the generalized density evolution equation is solved numerically. The complete process of the time-varying fatigue reliability analysis is presented. Two sets of experimental results are employed to validate the proposed method. Results show that the accuracy and efficiency of time-varying fatigue reliability can be improved with the proposed method considering the effects of nonlinearity of the fatigue damage and loading sequence.

Fatigue life prediction for orthotropic steel deck details with a nonlinear accumulative damage model under pavement temperature and traffic loading

Taking into account uncertainties in the nonlinear process of fatigue damage accumulation for the fatigue life prediction of the structural details in orthotropic steel decks, a novel fatigue damage regression analysis model and a new fatigue reliability assessment method based on the nonlinear fatigue model are developed and then used with reliability profiles to predict the fatigue life of details in the orthotropic steel deck. In the regression analysis model, both the long-term moving vehicle loads and the asphalt concrete (AC) pavement temperature work as the main factors. The monitored data of the long-term moving vehicle loads and AC pavement temperatures from the structural health monitoring systems installed on a Yangtze River cable-stayed bridge are first used to construct the prediction models of the vehicle loads and the AC pavement temperatures. An exponential model is then developed based on the strain measurements to quantify the relationship between daily averaged pavement temperatures, moving vehicle loads (the annual average hourly aggregated traffic volumes (AAHTV) or the annual average hourly aggregated traffic weight (AAHTW)) and the unit vehicle load induced fatigue, which is derived from a nonlinear fatigue damage accumulative model. Further, a limit equation based on the aforementioned exponential regression model and the nonlinear fatigue damage accumulative model for the fatigue life prediction, which takes into account both the traffic conditions and pavement temperature, is developed. Finally, this methodology is employed to predict the fatigue life of the structural details in orthotropic steel decks under different vehicle load growth patterns in a cable-stayed bridge.

Residual bearing capacity of steel-concrete composite beams under fatigue loading

This study was conducted to investigate the residual bearing capacity of steel-concrete composite beams under highcycle fatigue loading through experiments and theoretical analysis. Six test beams with stud connectors were designed and fabricated for static, complete fatigue, and partial fatigue tests. The failure modes and the degradation of several mechanical performance indicators of the composite beams under high-cycle fatigue loading were analyzed. A calculation method for the residual bearing capacity of the composite beams after certain quantities of cyclic loading cycles was established by introducing nonlinear fatigue damage models for concrete, steel beam, and shear connectors beginning with the material residual strength attenuation process. The results show that the failure mode of the composite beams under the given fatigue load appears to be primarily affected by the number of cycles. As the number of fatigue loadings increases, the failure mode transforms from midspan concrete crushing to stud cutting. The bearing capacity of a 3.0-m span composite beam after two million fatigue cycles is degraded by 30.7% due to premature failure of the stud. The calculated values of the residual bearing capacity method of the composite beam established in this paper agree well with the test values, which indicates that the model is feasibly applicable.

Nonlinear fatigue life prediction model based on material memory

New nonlinear fatigue damage accumulation model is established on the basis of material memory theory and fatigue driving energy damage parameters to evaluate high-cycle fatigue life under multilevel variable amplitude loading. The loading interaction factor is constructed on the basis of damage degree and then the model is modified to consider the effect of loading interaction on fatigue damage accumulation. The two proposed models are convenient for calculation and have only two parameters that can be easily identified through experiments. In accordance with the test data of aluminum alloy Al-2024-T42, titanium alloy Ti-6Al-4V, nodular cast iron GS61, Q235B welded joint, and hot-rolled 16Mn steel, the two models developed in this study have been verified to predict fatigue life effectively. For multilevel loading, the modified model achieves higher prediction accuracy and its results are closer to the actual test data compared with those of the other models.

Isodamage curve-based fatigue damage accumulation model considering the exhaustion of static toughness

Cumulative fatigue damage is a continuous and irreversible process that refers to the degradation of the component mechanical properties under cyclic loadings. In this work, using the concept of isodamage curves, a new non-linear fatigue damage accumulation model is proposed to account for fatigue damage evolution under multiple load levels. In particular, a computational process is established in which the isodamage curves converge into one point due to the exhaustion of static toughness. Experimental data of five materials are used for model validation and comparison. Results indicate that the proposed model provides better life predictions than the other four models.

A new multiaxial fatigue life prediction model considering additional hardening effect

The established linear fatigue life prediction model based on the Miner rule has been widely applied to fatigue life prediction under constant amplitude uniaxial and multiaxial loading. Considering the physical significance of crack formation and propagation, a multiaxial equivalent linear fatigue life prediction model is put forward based on Miner rule and critical plane method under constant amplitude loading. The essence of this approach is that the equivalent strain, which consists of the shear strain and normal strain on the critical plane, replaces the relevant parameter of uniaxial nonlinear fatigue damage model. The principal axes of stress/strain rotate under non-proportional loading. Meanwhile, the microstructure of material and slip systems change, which lead to additional hardening effect. The ratio of cyclic yield stress to static yield stress is used to represent the cyclic hardening capacity of material, and the influence of phase difference and loading condition on the non-proportional hardening effect is considered. The multiaxial fatigue life is predicted using equivalent stain approach, maximum shear stain amplitude model, CXH model, and equivalent multiaxial liner model under proportional and/or non-proportional loading. The smooth and notched fatigue specimens of four kinds of materials (Q235B steel, titanium alloy TC4, Haynes 188, and Mod.9Cr-1Mo steel) are used in the multiaxial fatigue experiments to verify the proposed model. The predicted results of these materials are compared with the test results, and the results show that these four models can achieve good effect under proportional loading, but the proposed model performs better than the other three models under non-proportional loading. Meanwhile, it also verifies that the proposed enhancement factor can reflect the influence of phase difference and material properties on additional hardening.

Models of Nonlinear Fatigue Damage Accumulation Under Cyclic Block Loadings of Layered Composites

Considered are two types of multistage cyclic block loading rather common in the practice of fatigue tests and fatigue life predictions for layered polymer composite materials: block loading by four-stage cyclic regular zero-tension loads and block loading by multistage (8-10 levels) asymmetric cyclic loads. In order to improve the prediction accuracy for the fatigue life of carbon-fiber-reinforced plastics under such loadings, special nonlinear fatigue damage accumulation models are proposed. Elaborated are methods for predicting the fatigue life of carbon-fiber-reinforced plastics by the models proposed. The prediction methods are verified by the example of T800/5245 and AS4/3501-6 carbon-fiber-reinforced laminates. A relatively high accuracy of fatigue life predictions for the laminates was obtained as compared with that given by prediction methods using the Palmgren–Miner rule.