Fatigue Damage Accumulation Model Research Articles

Physical description and model validation of welded joint fatigue damage evolution

AbstractFor welded structures, the concept of damage is highly abstract and difficult to describe, leading to a lack of physical foundation and universality for existing fatigue damage accumulation models. A new fatigue damage parameter definition based on remaining bearing capacity is proposed in this paper, which is constructed by the equivalent stress on the remaining bearing surface and the equivalent stress intensity factors along the crack front curve. Tension and three‐point bending fatigue tests under two‐level loading block sequences were conducted, and the real fatigue damage evolution processes were obtained by combining measured crack front information and FEA simulation. Five damage accumulation models were utilized to estimate the fatigue damage evolution processes of the two specimens. Results show that there are differences in describing the damage evolution processes and predicting the early fatigue lives. The Rege model is most consistent with the measured data, demonstrating its applicability and effectiveness.

A new fatigue equation for asphalt mixtures considering loading sequence effects

The fatigue life of asphalt mixture has been found to significantly depend on loading sequences. However, the widely used traditional linear fatigue equations are difficult to determine the fatigue life of asphalt mixture subjected to different loading sequences. This study aims to improve these fatigue equations by establishing a fatigue equation considering loading sequence effects. First, the semi-circular bending (SCB) constant amplitude fatigue tests were conducted under the high loading amplitude (σhigh) and low (σlow) loading amplitude, respectively. Then, two of the loading sequences, namely the low-high stress (σlow-σhigh) and high-low stress (σhigh-σlow), were selected to carry out the SCB variable amplitude fatigue tests. Furthermore, the loading sequence effects on the life fractions and fatigue life of asphalt mixtures were analyzed. Finally, the damage equivalent criterion was successfully applied to establish the nonlinear fatigue damage accumulation model and fatigue equation considering loading sequence effects. It was found that the cumulative life fractions of asphalt mixtures under constant amplitude loading are equal to 1, indicating the linear fatigue damage accumulation. The cumulative life fractions corresponding to the σlow-σhigh and σhigh-σlow are greater than 1 and less than 1, respectively, indicating the nonlinear fatigue damage accumulation. The established nonlinear fatigue damage accumulation model can accurately characterize the dependence of fatigue damage accumulation on loading sequences. The established fatigue equations can improve the traditional linear fatigue equations to some extent and accurately predict the fatigue life of asphalt mixtures corresponding to the loading sequences of the σlow-σhigh and σhigh-σlow.

An enhanced fatigue damage model based on Weibull strength distribution

AbstractConsidering the inherent characteristics of strength degradation, a residual strength model is improved reasonably through the incorporation of the two‐parameter Weibull distribution. Building upon this foundation, an enhanced nonlinear fatigue damage accumulation model that is closer to the actual situation is proposed in view of the randomness of fatigue damage. The model takes into account the effect of load action on fatigue damage. To ascertain the feasibility of the proposed model, the time‐varying reliability of the model is evaluated by applying the probability density evolution method. The model's precision in predicting residual life is corroborated through five experimental data sets under bilevel and multilevel loading conditions. The results demonstrate that the proposed model exhibits excellent applicability and remarkable precision, thereby confirming its potential value in practical applications.

An approach for fatigue life assessment of a road bridge based on measured corrosion and actual traffic loading

Fatigue and corrosion play a significant role in the aging of steel bridges, especially in a marine environment. An absence of fatigue strength curves for details which are exposed to corrosive environments, realistic traffic load models and accurate damage accumulation models increase the susceptibility of fatigue damage of steel bridges. In this paper, remaining fatigue life of a road bridge is assessed based on the measured corrosion wastage and more realis-tic traffic loads. Corrosion fatigue is also studied as it is one of the main factors that reduce the fatigue life and recently proposed fatigue strength curve for structural details exposed to corrosive environments is utilized for this study. A non-linear fatigue damage accumulation model is used for life assessment apart to the conventional damage model, Miner’s rule. The calculated fatigue lives are compared and discussed in quantitative manner to identify the most conservative remaining life and corresponding methods.

A nonlinear fatigue damage accumulation model under variable amplitude loading considering the loading sequence effect

Damage accumulation is nonlinear in the actual fatigue process, and the loading sequence is an important factor under variable amplitude loading. In this paper, a nonlinear fatigue damage accumulation model under variable amplitude loading considering the loading sequence effect is proposed. First, the cumulative rule of fatigue damage under variable amplitude loading is analyzed. It is suggested that the exponential function based on the load cycle ratio can be used to characterize the load sequence effect. Then, a nonlinear fatigue damage evolution equation of materials under constant amplitude load is proposed by taking the static toughness of the material as the damage parameter. Furthermore, the exponent of the load sequence influence parameter is determined as a function of the cycle life and elastic modulus. Then, a fatigue damage accumulation model under variable amplitude loading that considers the effect of the loading sequence is obtained based on the damage equivalence principle. Finally, the model is validated and compared through fatigue test data of five metal materials. It is found that the prediction accuracy of the proposed model is significantly higher than the other two models. In contrast, the difficulty of using the proposed model is lower than that of similar models.

Reliability by Using Weibull Distribution Based on Vibration Fatigue Damage

In this paper, a Weibull probabilistic methodology is proposed with an approach to model vibration fatigue damage accumulation using two parameters: Weibull distribution and a nonlinear fatigue damage accumulation model. The damage is cumulated based on the application of a vibration stress profile and is used to determine both the Weibull β and η parameters, and the corresponding component reliability R(t). The vibration fatigue damage is analyzed to accumulate the damage as a stress function for a fatigue life exponent derived with the assistance of the acceleration’s force response. The steps to determine the Weibull β and η parameters are estimated based only on the principal vibration stresses σ1 and σ2 that allow the reproduction of the vibration fatigue damage. The method’s efficiency is based on the probabilistic approach by using the vibration fatigue damage as the Yi vector that covers the arithmetic mean as well as the β parameter. Finally, the procedure proposed is applied in a practical case where a mechanical component is used as a support for telecommunication connections and is submitted to vibration stress. The results show that using the damage accumulated as the Yi vector to estimate the parameters allows for the analysis of dynamic and individual applications.

Open-Access Experiment Dataset for Fatigue Damage Accumulation and Life Prediction Models

This work addresses the lack of focus on verification and comparison of existing fatigue damage accumulation and life prediction models on the basis of large and well-documented experiment datasets. Sixty-four constant amplitude, 54 two-level block loading, and 27 three-level block loading valid experiments were performed in order to generate an open-access, high-quality dataset that can be used as a benchmark for existing models. In the future, more experiments of various specimen geometries and loading conditions will be added. The obtained dataset was used for a study comparing five (non)linear fatigue damage and life prediction models. It is shown how the performance of several (non)linear damage models is strongly dependent on the considered material dataset and loading sequence. Therefore, it is important to verify models with a broad set of independent datasets, as many existing models show significant bias to certain datasets.

Hysteretic energy damage coupled elastoplastic constitutive model and its application to low-cycle fatigue life prediction of martensitic steel

The microstructure of martensitic steel is analyzed by transmission electron microscopy and X-ray diffraction. The low-cycle fatigue (LCF) test of martensitic steel with different strain amplitudes is carried out by MTS universal hydraulic servo testing machine. The damage accumulation and cyclic elastic-plastic constitutive model of martensitic steel are studied. The influence of tempering on hysteretic loop and fatigue damage is discussed. With the tempering temperature increasing, the area of hysteresis loop increase, the hysteresis energy increases, and the fatigue life decreases. According to the fatigue damage accumulation model of the hysteresis energy method, an improved kinematic and isotropic composite hardening model is proposed in tempering temperature. This model is used to simulate the LCF behavior before fracture under LCF load and to predict the fatigue life with the variation of applied strain amplitude and tempering temperature. The verification results show that the modified model can well describe the phenomenon of acceleration of cyclic softening and great reduction of cyclic stress.

A COMPREHENSIVE STUDY OF FATIGUE CRACK INITIATION AND GROWTH UNDER VERY HIGH CYCLE TORSIONAL FATIGUE LOADING

This paper investigates the fatigue behavior of smooth specimens made of VT3-1 titanium alloy under fully reversed loading conditions. Mathematical modeling results are presented for the fatigue fracture of smooth specimens under high cycle torsional fatigue loading. The fatigue quasi-crack initiation and growth are calculated using a multimode two-parameter model of fatigue damage accumulation. The surface and subsurface quasi-crack initiation under torsional loading is studied. The numerical results are in good agreement with experimental data and can be used to predict the change in crack growth mechanisms under complex multiaxial loadings such as torsion.

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.

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 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.

Train-Induced Dynamic Behavior and Fatigue Analysis of Cable Hangers for a Tied-Arch Bridge Based on Vector Form Intrinsic Finite Element

This paper presents train-induced dynamic response and fatigue damage analyses for the hangers of a tied-arch railway bridge. A train–bridge interaction analysis is carried out using the vector form intrinsic finite element method, through which the inertial force effect of the moving train can be effectively analyzed. The responses of the bridge deck and its hangers are investigated at resonant train speeds. Significantly larger stresses are observed on the shorter hangers near the arch anchorages, which is primarily caused by the first two anti-symmetrical vibration modes. The fatigue damage to the hangers is estimated using the Palmgren-Miner model (PMM) for linear fatigue damage accumulation and the continuum damage mechanics (CDM) method for nonlinear accumulation. The mean stress effect is considered in the S–N curve primarily by Smith–Watson–Topper equation in terms of the effective stress range with a zero-mean stress. Two probability distributions for train speed are considered for the current and future operating conditions with mean speeds of 220 and 300[Formula: see text]km/h, respectively. This study found that the fatigue lives estimated by the nonlinear CDM are significantly shorter than those estimated by the linear PMM. It also found that the shortest hanger reflects the shortest fatigue life at the current operating speed, whereas the longer hanger near the third point of the bridge deck may have the shortest fatigue life at an increased speed in the future.

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.

Modelling of delamination in rolling and sliding contacts

The contact fatigue phenomenon in conditions of cyclic sliding or rolling is studied based on the model of contact fatigue damage accumulation in the subsurface layers of the material. It is assumed that the rate of the damage accumulation depends on the principal shear stress amplitudes. The results of numerical modelling show that the contact fatigue fracture process in the conditions of a constant load, acting on the sliding or rolling body, consists of the following stages: the incubation period, the running-in period with the alternating detachment of material’s fragments of certain thickness (the mechanism of delamination) and the surface wear, and then the steady-state stage, characterizing by the surface wear with a constant rate. The influence of the sliding friction coefficient, the relative slippage and the strength properties of contacting bodies on the evolution of the accumulated damage in the surface layers and on the fatigue wear kinetics in sliding and rolling contacts has been analyzed.

Contact fatigue life prediction of rolling bearing considering machined surface integrity

PurposeRolling bearings often cause engineering accidents due to early fatigue failure. The study of early fatigue failure mechanism and fatigue life prediction does not consider the integrity of the bearing surface. The purpose of this paper is to find new rolling contact fatigue (RCF) life model of rolling bearing.Design/methodology/approachAn elastic-plastic finite element (FE) fatigue damage accumulation model based on continuous damage mechanics is established. Surface roughness, surface residual stress and surface hardness of bearing rollers are considered. The fatigue damage and cumulative plastic strain during RCF process are obtained. Mechanism of early fatigue failure of the bearing is studied. RCF life of the bearing under different surface roughness, hardness and residual stress is predicted.FindingsTo obtain a more accurate calculation result of bearing fatigue life, the bearing surface integrity parameters should be considered and the elastic-plastic FE fatigue damage accumulation model should be used. There exist the optimal surface parameters corresponding to the maximum RCF life.Originality/valueThe elastic-plastic FE fatigue damage accumulation model can be used to obtain the optimized surface integrity parameters in the design stage of bearing and is helpful for promote the development of RCF theory of rolling bearing.

Mathematical modeling of the VHCF resonance loadings with a progressive damage accumulation

One of the most critical in-situ loading modes is resonant. Such loading conditions may lead to premature fatigue damage accumulation and failure. The progressive fatigue damage changes the natural frequency of a structure and causes a permanent modification of loading conditions. This paper considers the model of fatigue damage accumulation regarding its evolution and resonant loading parameters. To describe the evolution of material degradation due to fatigue a complex kinetic model of damage development and numerical algorithm are introduced. The model contains the evolution equation for the damage function depending on stress state. The algorithm is based on a special post proceeding of a numerical solution for an elastic solid mechanics problem that can be also applied for elastic-plastic case. Different loading conditions can be considered by choosing the method of solution for solid mechanics problem. This paper is focused on the comparison between quasi-static and resonant loading conditions used for damage function calculation. It was shown that use of resonant loading solution leads an earlier crack initiation and shorter fatigue life results compared to quasi-static solution. A spatial development of the fatigue damage zone is also different for these two cases. The normal crack opening mechanism is discussing in this paper.

An approach for predicting fatigue life of CFRP retrofitted metallic structural details

This paper presents a new approach to estimate the fatigue life of metallic details retrofitted with bonded CFRP patch. Existing phenomenological and analytical methods to predict the fatigue life of metallic structural details retrofitted with bonded CFRP patch do not consider the cyclic degradation of the composite patch. As for all materials the composite patch (CFRP and adhesive) will experience degradation during fatigue cyclic loading. In this regard, a new approach that takes into account the fatigue cyclic degradation of the composite patch is proposed in this paper by introducing in the fatigue damage accumulation model of the metallic element, a cycle-dependent stiffness degradation parameter of the composite patch. The stiffness degradation parameter is obtained using a fatigue stiffness degradation model calibrated from experimental fatigue data of CFRP adhesively bonded double strap joints. Experimental data available in the literature of central hole aluminium plates bonded with CFRP are utilized for validation of the approach.

Reliability Updating of Offshore Wind Substructures by Use of Digital Twin Information

This paper presents a probabilistic framework for updating the structural reliability of offshore wind turbine substructures based on digital twin information. In particular, the information obtained from digital twins is used to quantify and update the uncertainties associated with the structural dynamics and load modeling parameters in fatigue damage accumulation. The updated uncertainties are included in a probabilistic model for fatigue damage accumulation used to update the structural reliability. The updated reliability can be used as input to optimize decision models for operation and maintenance of existing structures and design of new structures. The framework is exemplified based on two numerical case studies with a representative offshore wind turbine and information acquired from previously established digital twins. In this context, the effect of updating soil stiffness and wave loading, which constitute two highly uncertain and sensitive parameters, is investigated. It is found that updating the soil stiffness significantly affects the reliability of the joints close to the mudline, while updating the wave loading significantly affects the reliability of the joints localized in the splash zone. The increased uncertainty related to virtual sensing, which is employed to update wave loading, reduces structural reliability.