Nonlinear Fatigue Damage Accumulation Model Research Articles

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.

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 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.

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.

A Modified Model for Nonlinear Fatigue Damage Accumulation of Turbine Disc Considering the Load Interaction Effect

Fatigue damage accumulation theory is one of the core contents in structure fatigue strength design and life prediction. Among them, the nonlinear damage model can overcome the shortcomings of the linear damage model, which takes the loading sequence effect into account. Besides, the loading interaction cannot be ignored for its profound influence in damage accumulation behavior. In the paper, some commonly-used methods of the linear and nonlinear fatigue damage accumulation theory are investigated. In particular, a modified nonlinear fatigue damage accumulation model which considers the effects of loading sequences as well as loading interactions on fatigue life is developed, and a load interaction parameter is obtained by analyzing damage models which assumes that the load logarithm ratio between adjacent stress levels can characterize this phenomenon. Finally, the modified model is employed to predict the fatigue life of high pressure turbine disc. Moreover, comparison is made between the experimental data as well as the predicted lives using the Miner’s rule, the Ye’s model, and the modified model.

Nonlinear fatigue damage accumulation: Isodamage curve-based model and life prediction aspects

Cumulative fatigue damage analysis and life prediction of engineering structures/components is vital for ensuring their structural integrity and operational reliability under variable amplitude loadings. In this regard, a new nonlinear fatigue damage accumulation model is proposed by introducing a damage function related to the isodamage curves and remaining life aspects. Specifically, its damage exponent is refined by considering effects of loading history. Experimental data from tests available in literature are utilized for model validation and comparison. Compared with four existing models, the proposed model shows higher precision for cumulative damage modelling and fatigue life prediction than others. Moreover, it improves the deficiencies inherent in other rules under the promise of maintaining its simplicity in practice.

RETRACTED: Reliability analysis of mechanical components based on a nonlinear fatigue damage accumulation model

The dynamic reliability models of mechanical components with the failure mode of fatigue are mainly based on the linear damage accumulation theory, which is also called the Miner’s rule. But the Mi...

Nonlinear fatigue damage accumulation and life prediction of metals: A comparative study

AbstractFatigue damage modelling and life prediction of engineering components under variable amplitude loadings are critical for ensuring their operational reliability and structural integrity. In this paper, five typical nonlinear fatigue damage accumulation models are evaluated and compared by considering the influence of load sequence and interaction on fatigue life of P355NL1 steels. Moreover, a new nonlinear fatigue damage accumulation model is proposed to account for these two effects. Experimental datasets of pressure vessel steel P355NL1 and four other materials under two‐block loadings are used for model comparative study. Results indicate that the proposed model yields more accurate fatigue life predictions for the five materials than the other models.

A new fatigue damage accumulation model considering loading history and loading sequence based on damage equivalence

In this study, a new nonlinear fatigue damage accumulation model is proposed to consider the effects of loading history and loading sequence under multi-level stress loading based on the Miner–Palmgren rule and S-N curve. By using damage equivalence, the new model is simplified and another form of the model is given. This model improves the application of the traditional Miner–Palmgren rule, by considering not only the loading sequence effect but also the loading history effect. The methods for calculating the degree of safety of specimens and cumulative damage of low-amplitude loads are also presented. Applicability of the new model is validated by predicting the fatigue life of 16Mn and 45 steel specimens under two-level stress loading. Further validation is carried out for the case of 41Cr4 and Aluminum alloys 6082 T6 under multi-level stress loading, and the strengthening and damaging effect of low-amplitude loads is considered. Comparing with the Miner–Palmgren rule and some new models, this new model gives more accurate and reliable prediction.

Residual life prediction based on nonlinear fatigue damage accumulation model

When a nonlinear fatigue damage accumulation model based on damage curve approach is used to get better residual life prediction results, it is necessary to solve the problem caused by the uncertain exponent of the model. Considering the effects of load interaction, the assumption that there is a linear dependence between the exponent ratio and the loading ratio is established to predict fatigue residual life of materials. Three experimental data sets are used to validate the rightness of the proposition. The comparisons of experimental data and predictions show that the predictions based on the proposed proposition are in good accordance with the experimental results as long as the parameters that represent the linear correlativity are set an appropriate value. Meanwhile, the accuracy of the proposition is approximated to that of an existing model. Therefore, the proposition proposed in this paper is reasonable for residual life prediction.