An Improved Nonlinear Cumulative Damage Model Considering the Influence of Load Sequence and Its Experimental Verification

According to the change characteristics in the toughness of the metal material during the fatigue damage process, the fatigue tests were carried out with the standard 18CrNiMo7-6 material. Scanning the fracture with an electron microscope explains the lack of linear cumulative damage in the mechanism. According to the obtained results, a nonlinear damage accumulation model which considered the loading sequence state under the toughness dissipation model was established. The recursive formula was devised under two-level. The fatigue test data verification of three metal materials showed that using this model to predict fatigue life is satisfactory and suitable for engineering applications.

Continuum Damage Mechanics Approach for Modeling Cumulative-Damage Model

In this study, we propose a novel cumulative-damage model based on continuum damage mechanics under situations where the mechanical components are subjected to variable loading. The equivalent completely reversed stress amplitude accounting for the effect of mean stress, stress gradients, loading history, and additional hardening behavior related to nonproportional loading paths on high-cycle fatigue under variable loading is elaborated. The effect of mean stress, stress gradients, loading history, and additional hardening behavior related to nonproportional loading paths is considered by averaging the superior limit of the intrinsic damage dissipation work in the critical domain. We developed a novel cumulative-damage model by introducing the equivalent completely reversed stress amplitude into the damage-evolution model. For better comparison, existing cumulative-damage models, including the Palmgren–Miner law, corrected Palmgren–Miner law, Morrow’s plastic work interaction rule, and Wang’s rule, were employed to predict the fatigue life under variable loading. The proposed model performed better, considering the error scatter band obtained by plotting the predicted and experimental fatigue life on the same coordinate system. The model precisely predicts fatigue life under variable loading and easily identifies its material constants.

On classes of life distributions based on the mean time to failure function

The performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.

Optimal replacement policy under cumulative damage model and strength degradation with applications

In many real-life scenarios, system failure depends on dynamic stress-strength interference, where strength degrades and stress accumulates concurrently over time. In this paper, we consider the problem of finding an optimal replacement strategy that balances the cost of replacement with the cost of failure and results in the minimum expected cost per unit time under cumulative damage model with strength degradation. In the most general setting, we propose to find optimal choices of three thresholds on operation time, number of arriving shocks and amount of cumulative damage such that replacement of the system due to failure or reaching any of the three thresholds, whichever occurs first, results in the minimum expected cost per unit time. The existing recommendations are applicable only under the assumption of Exponential damage distribution including Poisson arrival of shocks and/or with fixed strength. As theoretical evaluation of the expected cost per unit time turns out to be very complicated, a simulation-based algorithm is proposed to evaluate the expected cost rate and find the optimal replacement strategy. The proposed method is easy to implement having wider domain of application including non-Poisson arrival of shocks and non-Exponential damage distributions. For illustration, the proposed method is applied to real case studies on mailbox and cell-phone battery experiments.

A Novel Probabilistic Fatigue Life Prediction Method for Welded Structures Based on gPC

The traditional fatigue life prediction methods based on the S-N curve all believe that the parameters in the model are deterministic constants and can be categorized to the deterministic life prediction. However, in practice, it is difficult to carry out a large number of experiments due to the limitation of time or the possible shortage of funds. In addition, the specimens used in the experiments are not exactly the same, and the test operations and data reading depend on the accuracy of the test equipment as well as the subjective judgment of the testers, which result to the uncertainty of the S-N curve. Therefore, the uncertainty should be considered in order to improve the accuracy of the fatigue life prediction. In this paper, the uncertain factors affecting the fatigue life of welded joints are summarized, and the generalized polynomial chaos (gPC) is introduced into fatigue life prediction. A novel probabilistic fatigue life prediction method combined with the nonlinear cumulative damage model considering the uncertainty of the S-N curve is constructed. An illustrative example is presented to demonstrate the advantages of the proposed approach.

An improved nonlinear cumulative damage model for strength degradation considering loading sequence

In order to determine the effect of different loads on fatigue damage, a strength degradation model is proposed according to the law of residual strength degradation of metal materials. The model is verified with the strength degradation test data, and the results show that the model can describe the strength degradation process of general metal materials well. Combined with the strength degradation model, an improved equivalent damage model for different loading sequences is proposed. On this basis, a nonlinear fatigue cumulative damage model based on strength degradation is derived. The cumulative damage model is applied to the estimation of fatigue residual life under two-, three-, and four-stage loads to investigate the effects of different loading sequence on fatigue damage under various loading conditions. Combining with experimental data, it is verified that the cumulative damage model can accurately estimate the fatigue life under two-, three-, and four-stage loads.