Cycle Counting Method Research Articles

Comparison of HCF life prediction methods based on different critical planes under multiaxial variable amplitude loading

AbstractHigh‐cycle fatigue life prediction methods based on different critical planes, including the maximum shear stress (MSS) plane, the weighted average shear stress plane and the Maximum Variance shear stress plane, are compared by two multiaxial cycle counting methods, i.e. the main and auxiliary channels (MAC) counting and the relative equivalent stress counting. A modified damage model is used to calculate the multiaxial fatigue damage. Compared with the experimental lives for 7075‐T651 aluminium alloy, the predicted results show that the MSS method together with MAC counting is suitable for the multiaxial fatigue life prediction.

Modelling Mechanical Degradation in Lithium-Ion Batteries during Cycling

Understanding the ageing phenomena in the Li-ion batteries is of great importance nowadays for their successful commercialization. Li-ion degradation under storage conditions has been widely studied and the causes are well established. However, ageing during cycling remains still unsolved nowadays. Mechanical degradation is recognized as the main ageing mechanism of the battery due to volume changes of the electrodes during the cycling process. So far, many investigations have been published where the stresses on single particles have been analyzed [1]. Others, in more recent publications, have modelled the propagation of the fracture surface and combined it with the chemical degradation in order to explain the break and repair effect [2] and the electrical isolation of the active material [3].In this research, S-N curve fatigue approach has been followed to describe the fracture of the active material. By means of this method, gradual decrease of the particle size has been reproduced. Furthermore, a parametric analysis has been carried in order to clarify the role of the stress factors (i.e. DOD, Crate, SOCmean, etc…) as well as the design parameters on the cycling ageing mechanisms. The coupled mechanical-physicochemical model The mechanical degradation model has been integrated in a one dimensional physicochemical model of a Li-ion battery [4], all implemented in Matlab/Simulink®. Figure 1 shows the scheme of the mechanical model.The stresses are calculated based on the diffusion induced stress phenomenon (DIS) [1]. Due to the cyclic nature of the stress profile, during the cycling of the battery, a fatigue approach is employed to predict the fracture of the active material. The stress profile is first processed using a rain flow cycle counting method. Subsequently, a probabilistic S-N curve [5] is applied, which describes the relationship between the stress and the number of cycles to failure. Finally, damage accumulation is computed using Palmgren-Miners’ rule [5] to estimate the fracture of the active material particle.The model shows that most of the mechanical degradation takes place in the first cycles, later the effect becomes smaller and smaller, a fact that has been verified experimentally by other authors [6]. Using the simulation model, this behavior has been identified to be due to the initial larger particle size which produces larger stresses. As particle size decreases due to particle fracture the induced stress decreases (see Figure 2).The use of the mechanical degradation model is a big advantage as it enables to analyze the fracture and the mechanical degradation of the electrode under different working conditions.This work is an attempt to qualitatively study the mechanical degradation and its effect on the performance degradation of Li-ion batteries. Figure 1: Flow chart of the mechanical degradation model. Figure 2: The stresses in the graphite in the area close to the separator versus cycle number. The evolution of the particle size is shown in the graph. Smaller particles produce smaller stresses. Acknowledgments: The project upon which this publication is based is funded by the Impuls- und Vernetzungsfond der Helmholtz-Gemeinschaft e.V. through the framework of the research initiative HGF Energie Allianz.

Analysis of crosswind fatigue of wind-excited structures with nonlinear aerodynamic damping

This study addresses crosswind fatigue analysis of wind-excited flexible structures at the vicinity of vortex lock-in speed where the nonlinear aerodynamic damping effect is significant. The nonlinear aerodynamic damping is modeled as a polynomial function of time-varying displacement or velocity of vibration. The crosswind response is a narrow-band hardening non-Gaussian process with a reduced peak factor and having a distribution of vibration amplitude different from Rayleigh distribution. Analytical solutions of cycle number and fatigue damage are derived and their accuracy is validated through comparison with rainflow cycle counting method using simulated response time histories. A correction factor as a function of response kurtosis is also introduced that facilitates the calculation of non-Gaussian fatigue damage from the Gaussian fatigue prediction. The effectiveness and accuracy of the proposed framework are illustrated by crosswind responses of a squared tall building and a two-dimensional structural section model, and by full-scale vibration measurement data of a traffic-signal-support-structure. This study provides an improved estimation of crosswind fatigue of wind-excited flexible structures with a consideration of hardening non-Gaussian response character.

New cycle counting method for multiaxial fatigue

Multiaxial fatigue is a very important physical phenomenon in several mechanical components. Fatigue life study under cyclic stresses is of utmost importance to avoid unexpected failure of equipments, vehicles or structures. Among several fatigue characterization tools, a correct definition of a loading cycle under multiaxial fatigue loading conditions shows to be crucial to estimate multiaxial fatigue life.The aim of this work is to achieve a correct definition for a multiaxial fatigue loading cycle and accomplish a multiaxial fatigue model to estimate block’s fatigue life under multiaxial loading conditions. To reach this goal, several loading paths were carried out using the 42CrMo4 low alloy steel under different loading conditions. Sequential, proportional, non-proportional and asynchronous loading effects were modulated through eleven loading blocks. Furthermore, two models were proposed: a cycle counting method and a fatigue life evaluation criterion. The results from the proposed models were correlated with the fatigue data and compared with two well known cycle counting models: the Bannantine and Socie and the Wang and Brown criteria. The proposed models were successfully validated by experimental data. Results show that the new proposals lead to an improved multiaxial fatigue characterization under complex loading conditions.

Performance study of the simplified theory of plastic zones and the Twice-Yield method for the fatigue check

As elastic–plastic fatigue analyses are still time consuming the simplified elastic–plastic analysis (e.g. ASME Section III, NB 3228.5, the French RCC-M code, paragraphs B 3234.3, B 3234.5 and B3234.6 and the German KTA rule 3201.2, paragraph 7.8.4) is often applied. Besides linearly elastic analyses and factorial plasticity correction (Ke factors) direct methods are an option. In fact, calculation effort and accuracy of results are growing in the following graded scheme: a) linearly elastic analysis along with Ke correction, b) direct methods for the determination of stabilized elastic–plastic strain ranges and c) incremental elastic–plastic methods for the determination of stabilized elastic–plastic strain ranges.The paper concentrates on option b) by substantiating the practical applicability of the simplified theory of plastic zones STPZ (based on Zarka's method) and – for comparison – the established Twice-Yield method. The Twice-Yield method is explicitly addressed in ASME Code, Section VIII, Div. 2. Application relevant aspects are particularly addressed. Furthermore, the applicability of the STPZ for arbitrary load time histories in connection with an appropriate cycle counting method is discussed.Note, that the STPZ is applicable both for the determination of (fatigue relevant) elastic–plastic strain ranges and (ratcheting relevant) locally accumulated strains. This paper concentrates on the performance of the method in terms of the determination of elastic–plastic strain ranges and fatigue usage factors. The additional performance in terms of locally accumulated strains and ratcheting will be discussed in a future publication.

폴리에틸렌 보트의 내구성 평가에 관한 연구

선체 내구성은 기존 선급 규격에 의하여 구조 치수를 결정한 후 이러한 치수의 선체구조에 대하여 스펙트랄과 결정론적 및 간이 방법에 의하여 평가되고 있다. 이러한 방법은 선체재료를 선급 규격에서 제안하고 있는 재료로 구성하는 경우에는 적용할 수 있으나 선체 재료를 신소재로 구성하는 경우에는 적용할 수 없다. 따라서 본 연구에서는 폴리에틸렌 보트 선체에 대한 피로 손상을 평가하기 위하여 선체에 부하되는 단기간 선체 가속도를 직접 측정하고 이러한 데이터를 기초로 구조설계와 피로수명평가방법이 확립되지 못한 소형 선박의 선체 내구성을 선형누적손상 법칙으로 평가하는 방법을 제안하였다. 개발된 폴리에틸렌 보트의 경우 최대 가속도 상태에서 보트에 부하되는 최대 Von-Mises 응력은 1.8MPa로서 $1{\times}10^9$ 사이클 피로강도 5.9MPa 아래에 있고 유한피로수명개념을 적용한 폴리에틸렌 보트의 내구수명은 415년으로 평가되어져 거의 무한수명을 가지고 있다. 【Endurance of ship hull can be estimated by existing regulations and fatigue estimation methods. These can be applied to the hull materials that are recommended by ship regulations but can't be applied to new materials. In this study, structural force in the worst sailing condition is obtained by the acceleration measurement test of small polyethylene boat and the endurance of small polyethylene hull is estimated by rainflow cycle counting method and linear cumulative damage rule. Maximum Von-Mises stress on the polyethylene boat is 1.8MPa and much lower than the fatigue strength of at least 5.9MPa for the fatigue life of $1{\times}10^9$ cycles. Fatigue life of the polyethylene boat hull is estimated to be 6,229 years.】

A generalized cycle counting criterion for arbitrary multi-axial fatigue loading conditions

In this article, a generalized cycle counting criterion applicable for both uniaxial and arbitrary multi-axial loading conditions is presented. This criterion consists of two parts: (1) an effective fatigue damage parameter definition in either stress or strain space and (2) a fatigue cycle definition corresponding to maximum damage possibly attained by the fatigue damage parameter within a given loading history. After discussing its mathematical and mechanics basis, we first provide a rigorous proof that the proposed generalized cycle counting criterion yields exactly the same results as the rainflow counting method under uniaxial variable amplitude loading conditions. Then, its applications in multi-axial fatigue are demonstrated by presenting a series of closed-form solutions of both the fatigue damage parameter and number of cycles for a general harmonic loading history of three independent traction stress components on a crack plane. The validity of the new generalized cycle counting criterion is demonstrated by its ability to correlate available fatigue test data in the literature. These new developments also provide a more refined physical and mechanics basis for the recently proposed path length–based cycle counting method developed by the same authors for performing cycle counting of variable amplitude multi-axial loading histories.

Static and Fatigue Behaviour of the Main Section of a Fast Patrol Boat

This paper analyses the static resistance, as well as the fatigue resistance, of the main section of a fast patrol boat designed and manufactured in Portugal. The ship under study is a high-speed lightweight craft that was mainly fabricated with two types of aluminium series alloys, namely the 5083-H111 and the 6082-T6 alloys, which are commonly used in shipbuilding. The structural response of the critical section of the ship was obtained using the Finite Element Method (FEM), when the structure was submitted to different loading conditions, such as the hydrodynamic and hydrostatic sea loads, the longitudinal sagging or hogging, or the loads on fuel oil tanks. Results obtained for the load cases considered showed that the Von Mises equivalent stresses do not exceed the Yield Strength of the aluminium alloys used in the manufacturing of the ship. In addition, strain gages were placed on the main ship's bulkhead, near a structural detail in its bottom, and real-time acquisition strain data was collected using a computer code routine written in LabView. The Rainflow cycle counting method was applied to load spectrum gathered in order to obtain the Rainflow matrix and to predict the fatigue life of the critical main section of the ship.

부유식 복합 재생에너지 플랫폼 계류선의 효과적 배치에 관한 연구

This paper presents the conceptual design procedure for the taut-leg mooring lines of a floating-type combined renewable energy platform. The basic configuration of the platform is determined based on an understanding of floating offshore plants. The main dimensions and mass distribution are determined based on a hydrostatic calculation. To identify the motion history of the floating platform and the tension history of the mooring lines, a hydrodynamic analysis is executed using Ansys.Aqwa. This helps in the selection of the best configuration for the mooring system such as the number of mooring lines, wire types, anchored positions, etc. In addition, the fatigue life of the mooring lines can be predicted from the tension history using the rain -flow cycle counting method.

Protocol for testing of cold-formed steel wall in regions of low-moderate seismicity

Loading protocols have been developed for quasi-static cyclic testing of structures and components. However, it is uncertain if protocols developed for conditions of intense ground shaking in regions of high seismicity would also be applicable to regions of low-moderate seismicity that are remote from the tectonic plate boundaries. This study presents a methodology for developing a quasi-static cyclic displacement loading protocol for experimental bracing evaluation of cold-formed steel stud shear walls. Simulations presented in the paper were based on conditions of moderate ground shaking (in Australia). The methodologies presented are generic in nature and can be applied to other regions of similar seismicity conditions (which include many parts of China, Korea, India and Malaysia). Numerous response time histories including both linear and nonlinear analyses have been generated for selected earthquake scenarios and site classes. Rain-flow cycle counting method has been used for determining the number of cycles at various ranges of normalized displacement amplitude. It is found that the number of displacement cycles of the loading protocol increases with increasing intensity of ground shaking (associated with a longer return period).

Multiaxial fatigue and life prediction of elastomeric components

Elastomeric components have wide usage in many industries. The typical service loading for most of these components is variable amplitude and multiaxial. In this study a general methodology for life prediction of elastomeric components under these typical loading conditions was developed and illustrated for a passenger vehicle cradle mount. Crack initiation life prediction was performed using different damage criteria. The methodology was validated with component testing under different loading conditions including constant and variable amplitude in-phase and out-of-phase axial–torsion experiments. The optimum method for crack initiation life prediction for complex multiaxial variable amplitude loading was found to be a critical plane approach based on maximum normal strain plane and damage quantification by cracking energy density on that plane. Rainflow cycle counting method and Miner’s linear damage rule were used for predicting fatigue life under variable amplitude loadings. The fracture mechanics approach was used for total fatigue life prediction of the component based on specimen crack growth data and FE simulation results. Total fatigue life prediction results showed good agreement with experiments for all of the loading conditions considered.

An Efficient Implementation of the Rainflow Counting Algorithm for Life Consumption Estimation

In many reliability design and model-based health management applications where load profiles are variable and unpredictable, it is desirable to have efficient cycle counting methods to identify equivalent full and half cycles within the irregular load profile. Conventional cycle-based lifetime models can then be applied directly to provide information about the life consumption of the products. The use of an off-line rainflow algorithm is a common solution for arbitrary loads, but it cannot be applied in real time in its original form. This paper presents an in-line coding algorithm which uses a stack-based implementation, and a recursive algorithm to pick out the equivalent full and half cycles of the irregular load profile. The method can be integrated easily within time-domain or serial data applications to generate equivalent full and half cycles as they occur. Thus it is of particular significance for life estimation in real-time applications where use of the traditional implementations of the counting algorithm is impractical. In comparison with the off-line traditional rainflow method, the on-line method doesn't require any knowledge of the time history of the load profile because it processes each minimum or maximum when it occurs. Therefore, it provides a more efficient cycle counting method using less memory storage, and making more efficient use of computational resources within the real-time environment.

Comparison of multiaxial fatigue damage models under variable amplitude loading

Based on the cycle counting method of Wang and Brown and on the linear accumulation damage rule of Miner, four multiaxial fatigue damage models without any weight factors proposed by Pan et al., Varvani-Farahani, Shang and Wang, and Shang et al. are used to compute fatigue damage. The procedure is evaluated using the low cycle fatigue experimental data of 7050-T7451 aluminum alloy and En15R steel under tension/torsion variable amplitude loading. The results reveal that the procedure is convenient for engineering design and application, and that the four multiaxial fatigue damage models provide good life estimates.

Stochastic dynamics and fatigue analysis of large-scale mechanical models using multilevel substructuring

An efficient methodology is presented for predicting dynamic response and fatigue life of large-scale nonlinear mechanical models, subjected to random excitation. The methodology developed is based on a combination of techniques leading to a fast and accurate determination of the dynamic response with a method related to an efficient prediction of fatigue life. Specifically, the first step involves application of an appropriate coordinate transformation, causing a drastic reduction in the degrees of freedom. This opens the way to the application of another numerical method, leading to direct determination of periodic steady-state response of nonlinear systems under periodic forcing. This approach provides a solid foundation for the subsequent application of a rainflow stress cycle counting method, leading to prediction of fatigue failure. The computational accuracy and effectiveness of the methodology is illustrated by a quite involved example model, representing a city bus subjected to road excitation. Typical results are presented for both the stochastic response and the fatigue life by considering excitation arising from selected road profiles with known statistical properties. Special attention is paid to assessing the effect of the nonlinearity, by considering profiles of different quality. Moreover, a critical comparison is performed on results referring to the expected fatigue lifetime, obtained by applying methods in both the frequency and the time domain. In this way, the applicability of classical spectral methods in nonlinear models is also investigated.

A rapid path‐length searching procedure for multi‐axial fatigue cycle counting

ABSTRACTIn this paper, a series of advanced searching algorithms have been examined and implemented for accelerating multi‐axial fatigue cycle counting efforts when dealing with large time histories. In a computerized calculation of the path‐length dependent cycle counting method, most of the central processor unit's (CPU) time is spent on searching for the maximum range or distance in a stress or strain space. A brute‐force search is the simplest to implement, and will always find a solution if it exists. However, its cost, in many practical problems, tends to grow exponentially as the size of the loading spectrum increases with a search time measured in the order of O(n2), where n is the number of spectrum data points. In contrast, a form of Andrew's monotone chain algorithm, as demonstrated in this paper, can remarkably reduce the solution time to the order of O(n log n). The effectiveness of the new path‐length searching procedure is demonstrated by a series of worked examples with a varying degree of non‐proportionality in multi‐axial loading history.

A Theoretical Approach to Predict the Fatigue Life of Flexible Pipes

This paper focuses on a theoretical approach to access the fatigue life of flexible pipes. This methodology employs functions that convert forces and moments obtained in time‐domain global analyses into stresses in their tensile armors. The stresses are then processed by well‐known cycle counting methods, and S-N curves are used to evaluate the fatigue damage at several points in the pipe’s cross‐section. Finally, Palmgren‐Miner linear damage hypothesis is assumed in order to calculate the accumulated fatigue damage. A study on the fatigue life of a flexible pipe employing this methodology is presented. The main points addressed in the study are the influence of friction between layers, the effect of the annulus conditions, the importance of evaluating the fatigue life in various points of the pipe’s cross‐section, and the effect of mean stresses. The results obtained suggest that the friction between layers and the annulus conditions strongly influences the fatigue life of flexible pipes. Moreover, mean stress effects are also significant, and at least half of the wires in each analyzed section of the pipe must be considered in a typical fatigue analysis.

Development of a Phenomenological Method for Description of Crack Initiation Behavior under Thermo-Mechanical Fatigue Loading

Description of crack initiation behavior under thermo-mechanical fatigue (TMF) of modern high chromium steel is prerequisite for design optimization of steam turbine components. In this paper a phenomenological method which envelopes the synthesis of stress-strain hysteresis loops according to cycle counting methods and the individual assessment of creep fatigue damage is extended to TMF with superimposed creep. Recalculation of such service-type experiments on specimen of rotor steel 10CrMoWVNbN shows acceptable results for deformation description and lifetime estimation.

Fatigue Design of Mooring Lines of Floating Type Combined Renewable Energy Platforms

This paper presents the concept design procedure of a floating-type combined renewable energy platform based on hydrodynamic analyses and is focused on the fatigue design of taut-type mooring lines of the platform. Two types of combined renewable energy platforms are considered: a combination of wind turbine, wave turbine and photovoltaic energy plant and a combination of wind turbine, current turbine and photovoltaic energy plant. The basic configurations are conceptually determined from the understanding of floating offshore plants, while the main dimensions have been determined based on a hydrostatic calculation. Fully coupled hydrodynamic analyses have been carried out to identify the motion characteristics of the floating body and the tension histories of the mooring lines. The tension history is used for the fatigue life prediction based on the rain-flow cycle counting method. For the fatigue life prediction, tension life curves from API and the Palmgren-Miner rule are employed.

Development of a design verification methodology including strength and fatigue life prediction for agricultural tractors

During the operations of an agricultural tractor, front axle and front axle support encounter the worst load conditions of the whole tractor. If the design of these components is not verified by systematic engineering approach, the operators of the tractor may face with sudden failures. This paper aims to develop a verification method, which involves testing an agricultural tractor on a special test track and agricultural field and together with the computer aided engineering analysis, in order to prevent such failures in the lifetime of the agricultural tractor. For this purpose, a strain gage data acquisition system has been designed to measure the strain values on the component in order to determine maximum principle stresses for the calculation of overload safety on the agricultural field and stress data for the prediction of fatigue life on a radial washboard test track. The cycle number of these stress data for the fatigue analysis has been established by rainflow cycle counting method. Total fatigue damage for the front axle support has been calculated considering damage accumulation hypothesis defined by Miner.

Fatigue analysis of the taut-wire mooring system applied for deep waters

Precisely predicting the fatigue life of taut-wire mooring systems has become an interesting and important problem for scientists and engineers since there are still difficulties in the inspection and maintenance of mooring lines in a rough sea environment especially in deep waters. In this paper, a comprehensive fatigue analysis is performed for a polyester taut-wire mooring system of an FPSO based on the time domain dynamic theory, rainflow cycle counting method and linear damage accumulation rule of Palmgren-Miner. Three influential factors in the fatigue analysis including the pre-tension, dynamic stiffness and T-N curve are investigated in detail. Two polyester T-N curves, one is from the DNV-OS-E301 and the other is from the API-RP-2SM, are adopted in the calculation. The fatigue analysis of the mooring system after one-line failure is also carried out. The calculation results indicate that the fatigue life is significantly affected by the T-N curve. The fatigue life decreases with increasing pre-tension, and is largely reduced if taking into account the dynamic stiffness caused by cyclic loading. The analysis also proves that one-line failure has remarkable effects on the fatigue lives of other mooring lines. The present parametric and comparative study is believed to be meaningful to further understanding of the taut-wire mooring system for deepwater applications.