Nonlinear Fatigue Damage Accumulation Research Articles

Fatigue damage assessment of a large rail-cum-road steel truss-arch bridge using structural health monitoring dynamic data

Structural health monitoring (SHM) system provides valuable information for the fatigue assessment of existing rail-cum-road bridges. This paper aims to develop an effective fatigue assessment approach for the rail-cum-road bridge, Jiujiang Yangtze River Bridge, by utilising the SHM data, focusing on dynamic modal analysis, finite element model updating and fatigue assessment. First, the traffic load spectrum and modal characteristics of the bridge are investigated from the SHM data. A three-dimensional finite element model is constructed and then updated by using the measured modal data through the proposed regularised model updating method. Then, the updated numerical model is verified with the measured dynamic response data, which can be utilised for calculating stress response at critical structural components of the rail-cum-road bridge. Finally, an improved Corten-Dolan’s model is proposed to analyse the fatigue damage and structural reliability of the critical structural components of the bridge, taking into account the combined effects of train and highway vehicle loads. The results demonstrate that the proposed fatigue assessment method provides more reliable results for the rail-cum-road bridge by considering the combined effect of multi-level traffic loads and the non-linear fatigue damage accumulation. It is concluded that the short H-shaped suspender is identified as the most vulnerable structural member of the rail-cum-road bridge, and the remaining fatigue service life of the typical components of the bridge should meet the design requirement.

A Novel Multi-Objective Dynamic Reliability Optimization Approach for a Planetary Gear Transmission Mechanism

Planetary gear transmission mechanisms (PGTMs) are widely used in mechanical transmission systems due to their compact structure and high transmission efficiency. To implement the reliability design and optimization of a PGTM, a novel multi-objective dynamic reliability optimization approach is proposed. First, a multi-objective reliability optimization model is established. Furthermore, considering the strength degradation of gears during service, a dynamic reliability analysis is conducted based on the theory of nonlinear fatigue damage accumulation. In addition, to improve computing efficiency, a random forest surrogate model based on the particle swarm optimization algorithm is proposed. Finally, an adaptive multi-objective evolutionary algorithm based on decomposition (AMOEA/D) is designed to optimize the mechanism, along with an adaptive neighborhood updating strategy and a hybrid crossover operator. The feasibility and superiority of the proposed approach are verified through an NGW planetary gear reducer. The results show that the proposed surrogate model can reduce the calculation cost and has high accuracy. The AMOEA/D algorithm can improve transmission efficiency, reduce gear volume and ensure reliability at the same time. It can provide guidance for actual gear production.

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.

Prediction model of rail head check initiation considering wear and nonlinear fatigue damage accumulation

AbstractWear and rolling contact fatigue (RCF) cracks are the key defects affecting the service life of heavy‐haul railways in China. In this study, based on the influences of the loading sequence and the interaction between adjacent loads, a modified nonlinear fatigue damage accumulation model under the steady‐state wheel–rail contact was developed to predict the coexistence of wear growth and head check (HC) initiation. A twin‐roller fatigue test was designed and performed, and the testing data were compared with the predicted data to verify the established model. Compared with the linear model, the nonlinear model yielded the faster fatigue damage with an HC initiation life of 2.58 × 105 wheel cycles, which was 24.34% less than that of the linear model. In addition, the HC initiation lives obtained from the nonlinear and linear models were close to the median and upper limits observed in the field, respectively. The results of the linear and nonlinear models were respectively 41.3% and 22.5% higher than the two‐round test results. The result of the nonlinear model was closer to the two‐round test result of 2 × 105.

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.

Effects of traffic load amplitude sequence on the cracking performance of asphalt pavement with a semi-rigid base

ABSTRACT The propagation of cracks in in-service asphalt pavements is closely related to the complicated traffic loading patterns over time. However, typical traffic-related variables capture only the overall traffic level without being able to account for the load-time history. Therefore, this study aims to investigate the effects of traffic load sequence on the cracking performance of asphalt pavement from both field and laboratory perspectives. A load amplitude sequence (LAS) index was developed to characterize the traffic loading sequence in the field. Two machine learning (ML) algorithms, namely artificial neural network (ANN) and random forest regression (RFR), were applied to correlate the LAS index with field pavement cracking performance. The two-block semi-circular bending (SCB) test was developed to characterize the non-linear fatigue damage accumulation of asphalt mixtures. It was found that heavier traffic loads in early stages are detrimental to the long-term pavement cracking performance. The LAS index plays a crucial role in the prediction and development of pavement cracks. The laboratory test results reveal that a loading sequence starting with a higher stress may shorten the fatigue life and vice versa. The outcomes of this study may contribute to a better understanding of the traffic loading characterization of in-service asphalt pavements.

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.

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.

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.

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.

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.

Residual fatigue life prediction based on a novel damage accumulation model considering loading history

AbstractThe influence of prior low‐cycle fatigue (LCF) on the residual fatigue life was investigated experimentally. A Ni‐based alloy was cyclically loaded under stress‐controlled low‐high (LH) block loading. In the first loading step, low‐amplitude loading was performed with the stress amplitude of 283.5MPa at 710°C. Different cycles of preloading were performed, varying from 100 to 10 000. Subsequently, high‐amplitude fatigue loading was carried out with the stress amplitude of 315MPa at 800°C. Experimental results show that the previous loading was beneficial to the residual fatigue life when the consumed life fraction is below 0.2 and detrimental when the consumed life fraction is larger than 0.2. A novel nonlinear fatigue damage accumulation model was proposed to estimate the residual LCF life under LH loading path considering the effects of load sequence and preloading cycles. The proposed model provided a better life prediction than some existing models, such as Kwofie‐Rahbar model, Miner' rule, Peng model, and Ye‐Wang model. Lastly, this model was further validated using various materials under LH and high‐low block loadings.