Palmgren-Miner Rule Research Articles

Numerical Simulation for Durability of a Viscoelastic Polymer Material Subjected to Variable Loadings Fatigue Based on Entropy Damage Criterion.

This study aims to explore the impact of load history on the premature failure of the viscoelastic polymer matrix in carbon-fiber-reinforced plastics (CFRPs) using a method based on the concept of fracture fatigue entropy (FFE). A user-defined subroutine (UMAT) developed by the authors in previous studies was incorporated to apply the FFE damage criterion using ABAQUS software. Several variable-amplitude load modes, including frequent load amplitude changes and intermittent interruptions, were designed based on the conventional linear damage accumulation method (Palmgren-Miner rule), and the fatigue life under these loadings was obtained via numerical simulations. The results show that both frequent amplitude changes and even brief pauses in loading can accelerate damage accumulation, leading to premature failure of the polymer matrix. In these scenarios, the fatigue life ranged from 33.6% to 91.9% of the predictions made using the Palmgren-Miner rule, which shows significant variation and highlights cases in which the predicted fatigue life falls far short of expectations. This study offers a more practical and reliable approach for predicting fatigue life under complex loading conditions. Since the accuracy of the FFE criterion has been comprehensively validated in previous studies, this research focuses on its application to predict failure under variable loading conditions.

A numerical procedure for calculating ice-induced fatigue damage for ship hulls in level ice

Ship hulls advancing in level ice are exposed to considerable cyclic ice loadings, which might cause fatigue damage, threatening the structural integrity and endangering the crews’ lives. Ice-induced fatigue problem is of significance to ice-going ships. In this paper, a fatigue analysis for ship structures in level ice is performed based on a dedicated 6-degree-of-freedom (6-DOF) numerical model of ice-ship interaction, founded on a circumferential crack assumption. The numerical procedure considers the time-varying instantaneous waterline and the couplings between ship motions and external forces. The local ice loads used for fatigue assessment can be obtained from numerical simulations, and the random load peaks are represented by Weibull distribution. A case study of fatigue calculation for designated transverse frames is carried out, of which the applied stress is converted from ice loads by means of structural beam theory. Eventually, according to a proper S-N curve, the fatigue damages are evaluated on the basis of Palmgren–Miner rule, respectively under the operational scenarios of laterally symmetrical and asymmetrical initial ice edges.

Application of a new method for probabilistic fatigue analysis from strain measurements on bridges

Increasing loads, ageing of materials as well as environmental change make the issue of fatigue damage critical on bridges, especially in the case of old steel or iron structures. The assessment of the fatigue loads on specific elements of these assets can be carried out from on-field strain measurements with the application of classical methods involving rainflow cycle counting and the use of Palmgren-Miner's rule. However, such a fatigue assessment suffers of significant uncertainties about the real fatigue damage ratio and the consecutive residual fatigue life. A new probabilistic method for the fatigue assessment is proposed, as the result of a joint research by OSMOS Group and the Ecole des Ponts. The theoretical background of the method is described, involving a probabilistic formulation of Miner's rule and the use of a Weibull-Basquin model to describe the health of structural elements. Real field case studies are presented, on two historical iron truss road bridges in France, with a dataset of more than 18 months of continuous strain measurements used for the fitting of the probabilistic model of fatigue loads. The incidence of the quantity of data and of the number of sensors used for the analysis is discussed, along with the conclusive results concerning the probabilistic description of the residual fatigue life.

Fatigue Damage Analysis of Steel Truss Suspension Bridge Under Non-Stationary and Non-Gaussian Buffeting

The wind field environment in mountainous zones is complex. If the wind field characteristics are regarded as stationary and Gaussian, the inaccurate response results of the structure will be obtained. In this paper, a fatigue evaluation method of steel truss suspension bridge members under non-stationary and non-Gaussian buffeting is proposed. This approach can solve the fatigue evaluation problem of steel truss suspension bridge members under mountain wind. Firstly, the normal wind speed (stationary and Gaussian) is obtained by the harmonic wave synthesis method. The wind speed considering non-stationary characteristics is obtained by adopting time-varying power spectrum. Secondly, through non-linear translation, the wind speed considering non-stationary characteristics is transformed into wind speed considering both non-Gaussian and non-stationary characteristics. Finally, combined with the Palmgren–Miner rule, the effects of three different buffeting responses on fatigue damage of suspension bridge members are studied. They are traditional buffeting response, buffeting response considering non-stationary characteristics and buffeting response considering both non-stationary and non-Gaussian characteristics. The results indicate that the fatigue damage of the main cable of the suspension bridge is the biggest at the mid-span. Under the same wind speed, considering two characteristics, the component fatigue damage will further increase.

Neural network based fatigue lifetime prediction of metals subjected to block loading

Fatigue lifetime predictions for variable amplitude loading are primarily based on the linear damage accumulation rule of Palmgren–Miner, which does not account for load sequence effects. Various nonlinear models have been developed, but their generalization capability is limited. Although neural network models have been used for prediction of the lifetime of metals subjected to constant amplitude loading, random loading and two-level block loading sequences before, they have never been used for multi-level block loading to the authors knowledge. The primary goal of this study is the development of neural network models for fatigue life estimation of metals subjected to block loading. To achieve this, a sufficient amount of qualitative data is required. Therefore a large number of rotating bending fatigue experiments with constant amplitude and block loading sequences are carried out. This new data is combined with data gathered from literature, leading to the most extensive open-access collection of variable amplitude fatigue data published to date. Neural network models are trained with the developed dataset and compared to four cumulative damage models including the linear Palmgren–Miner rule and three non-linear models. It is concluded that the neural network model for multi-level block loading outperforms all of the considered analytical models.

Analyzing Safety Factors and Predicting Fatigue Life of Weak Points in an Electrically Driven, Multi-Purpose Cultivation Tractor

The advancement of agriculture and a shortage of labor have led to an increased use of agricultural machinery. However, the resulting environmental issues have prompted a shift from internal combustion engines to electric drivetrains. The electric drivetrain includes the installation of batteries, which can lead to decreased energy efficiency and significant loads on the vehicle due to their heavy weight. Consequently, the importance of ensuring the safety of agricultural machinery is being increasingly emphasized. The load on the frame of agricultural machinery is not consistent during off-road driving, and the accumulation of load cycles can lead to the destruction and failure of components. Therefore, it is necessary to ensure a level of safety and to predict the fatigue life. In this study, we estimate the safety factor and predict the fatigue life of weak points in an electrically driven, multi-purpose cultivation tractor based on working conditions (width, soil, and drive). Strain gauges were attached to these weak points to measure the strain, which was then converted to von Mises stress. Fatigue life was predicted using the rainflow counting method and the Palmgren–Miner rule. The results showed that the safety factor measured under various working conditions was greater than 1. The estimated minimum fatigue life was 124,176 years. Considering that the cultivator is used for 29.7 h annually and has a durability lifespan of 5 years, it is expected to be safely usable throughout its service life.

Fatigue strength assessment of aluminium welded joints under variable amplitude loading using the Peak Stress Method

One of the simplest and most efficient ways to design lightweight structural components is the combination of welding and aluminum alloys. However, welded joints are extremely sensitive to fatigue failure and making accurate lifetime predictions is still challenging when Variable Amplitude (VA) loading conditions are involved. Among all design criteria available in the literature, the present investigation focuses on the Peak Stress Method (PSM), an engineering finite element (FE)-based approach to rapidly assess the fatigue strength of welded joints. In more detail, the PSM suggests modelling both weld toe and weld root as sharp V-notches having null tip radius and correlates their fatigue strength using the intensity of the local linear elastic asymptotic stress distributions described by the Notch Stress Intensity Factors (NSIFs). The theoretical formulation of the PSM for the fatigue strength assessment of welded joints subjected to VA loadings has been recently proposed by combining its Constant Amplitude (CA) formulation with the Palmgren-Miner's cumulative linear damage rule. Such VA formulation has been successfully validated against a large bulk of experimental fatigue results generated by testing welded joints made of structural steels under uniaxial as well as multiaxial loadings. In the present investigation, the VA formulation of the PSM has been further validated against experimental data relevant to welded joints made of aluminium alloy under VA loadings.

Predicting the Remaining Useful Life of Light Aircraft Structural Parts: An Expert System Approach

This paper introduces an expert system approach for predicting the remaining useful life (RUL) of light aircraft structural components by analyzing operational and maintenance records. The expert system consists of four modules: knowledge acquisition, knowledge base, inference, and explanation. The knowledge acquisition module retrieves data from mandatory records, such as aircraft logbooks and mass and balance sheets. The knowledge base stores specific remaining useful lives (SRULs) for different load profiles that are determined using numerical strength analysis. The inference module utilizes the Palmgren-Miner rule to estimate the accumulated fatigue damage of the structural component based on the input data and the knowledge base. Lastly, the explanation module links the accumulated damage to the maintenance program and suggests the appropriate maintenance action. The Cessna 172R main landing gear leg is utilized as a case study, demonstrating the variance of RUL depending on the operating conditions. The objective of this approach is to enhance light aircraft maintenance decision making and advance operational safety.

Structural durability proof of aluminium safety components substituting steel safety components – criteria regarding testing time by the example of commercial vehicle wheels

AbstractThe experimental structural durability proof bases on a damage equivalent shortening of the design spectrum into a test spectrum with reduced length taking statistics founded safety factors into account. Historically, test spectra were first derived for steel parts using Woehler‐lines for steel; the damage equivalence was calculated by applying the Palmgren–Miner rule with the modification according to Haibach. When aluminium parts were introduced later, the question arose, whether test spectra developed for steel parts could be applied without modifications for their durability proof. Caused by different slopes of aluminium before and after the knee‐point, the test spectra derived for steel wheels result for aluminium components a lower cumulated damage in comparison to the design spectra. This fact requires a longer test duration for aluminium components when test spectra or proving grounds developed for steel components are used.By the example of steel and aluminium wheels for commercial vehicles with comparable highly stressed areas, the material dependent features regarding the required test life for the structural durability proof of aluminium parts are demonstrated.

Fatigue Safety Assessment of Concrete Continuous Rigid Frame Bridge Based on Rain Flow Counting Method and Health Monitoring Data

The fatigue of concrete structures will gradually appear after being subjected to alternating loads for a long time, and the accidents caused by fatigue failure of bridge structures also appear from time to time. Aiming at the problem of degradation of long-span continuous rigid frame bridges due to fatigue and environmental effects, this paper suggests a method to analyze the fatigue degradation mechanism of this type of bridge, which combines long-term in-site monitoring data collected by the health monitoring system (HMS) and fatigue theory. In the paper, the authors mainly carry out the research work in the following aspects: First of all, a long-span continuous rigid frame bridge installed with HMS is used as an example, and a large amount of health monitoring data have been acquired, which can provide efficient information for fatigue in terms of equivalent stress range and cumulative number of stress cycles; next, for calculating the cumulative fatigue damage of the bridge structure, fatigue stress spectrum got by rain flow counting method, S-N curves and damage criteria are used for fatigue damage analysis. Moreover, it was considered a linear accumulation damage through the Palmgren-Miner rule for the counting of stress cycles. The health monitoring data are adopted to obtain fatigue stress data and the rain flow counting method is used to count the amplitude varying fatigue stress. The proposed fatigue reliability approach in the paper can estimate the fatigue damage degree and its evolution law of bridge structures well, and also can help bridge engineers do the assessment of future service duration.

Investigating the Ice-Induced Fatigue Damage of Offshore Structures by Field Observations

The oil and natural gas resources of the Bohai Sea are mainly marginal oil fields, and there are currently a large number of structures that are approaching or have reached the end of their service life called aging structures. The interactions between ice and offshore structures could lead to significant ice-induced vibration. Ice-induced vibrations may evoke fatigue damage in tubular joints, which results in severe dangers for offshore platforms in the Bohai Sea. Dynamic ice force models and sea ice fatigue environmental parameters have not been well developed in the current design codes. It is not accurate to evaluate the fatigue damage of structures only with numerical simulation. In this paper, a faster method for evaluating fatigue damage on aging structures is proposed. Firstly, the approximate linear relationship between the fatigue hot spot stress and the vibration response of the deck structure has been discovered using dynamic analysis for jacket platform of Bohai Sea. Then, the procedure of the fatigue damage evaluation of the aging structures in the Bohai Sea is established. Finally, the numerical simulation of the structure is carried out considering ice thickness, ice velocity, ice direction, and action height of sea ice. Fatigue damage is calculated by the fatigue hot spot stress and the Palmgren–Miner rule. The measured data on the platform in the Bohai Sea are selected to obtain the fatigue hot spot stress using a mathematical model. The fatigue damage results considering the actual ice conditions of a jacket structure in the Bohai Sea are compared using the proposed method and finite element analysis. The comparison of the results verifies the rationality of the method proposed in this work.

Theory and methods of constructing equations for the evolutionary damageability of materials

The theory and methods for constructing equations (functions) of evolutionary damage and rupture of materials in the Kachanov model (creep rupture and fatigue rupture) are presented. In general, it is proved that the factorized Kachanov model is identical to the Palmgren-Miner rule, which is often not confirmed experimentally. To construct damageability functions adequate to the experimental data, new mathematical objects (potential and normalized potential) are introduced. If the entire history of changes in the damage variable is known in experiments, then the use of the potential makes it possible to construct a damageability function of any complexity without integrating the evolutionary equation (explicit method). For cases where only rupture moments are recorded in experiments, a criterion for the adequacy of the normalized potential is formulated and an implicit method for its construction is developed. It is supplemented with a recursive algorithm that generates an unlimited number of such potentials. The implicit method is illustrated by examples, following which the reader can construct a damageability equation for his material without a thorough study of the theory.

Study on the safety performance of large offshore wind turbine coupling

An offshore wind turbine coupling (OWTC) safety performance assessment method for torque transfer and overload protection of the main drive train of offshore wind turbine is proposed in the paper. First, the local mechanical model and the overall finite element model of the OWTC are established, and the fatigue life assessment method of the OWTC is given. Then, the effectiveness of the proposed method was verified by experiments and finite elements. The structural strength under different working conditions of the OWTC and the influence of the bolt tightening torque on the OWTC slip torque are studied, and the torque transfer efficiency is evaluated. Finally, the stress response of the OWTC was obtained by the finite element method considering the time-series torque load, the fatigue life of the OWTC was evaluated by combining the S/N curve parameters and the Palmgren-Miner rule. The results show that the proposed method for assessing the safety performance of the OWTC is reliable and valid. The calculated results of the local mechanical model are in good agreement with the test and simulation results, and the connecting rods and bolts of the OWTC are highly susceptible to damage under fatigue loading and should be of particular concern.

Fatigue damage calculation of ship hulls caused by ice loads in broken ice fields

ABSTRACT Fatigue damage induced by ice loads is a key concern as ships operates in broken ice fields where a sea route is normally developed. This paper proposes a method for calculating fatigue damage of a ship structure advancing in broken ice, on the basis of numerical simulations. A random broken ice domain with polygon-shaped ice floes is generated using Centroidal Voronoi Tessellation (CVT) algorithm. A discrete element method (DEM) is employed to imitate ice-ice and ice-structure interactions, and produce the required ice loads data for fatigue assessment. A Weibull model is used to describe the probability distribution of ice load peaks. The fatigue stress is determined using structural beam theory. Finally, the fatigue damage is estimated based on the Palmgren–Miner rule. An example of fatigue calculation is presented with hypothetical scenarios in broken ice fields, and comparisons of the proposed method are made against the ShipRight FDA ICE procedure.

A wind turbine blade leading edge rain erosion computational framework

Blades are one of the most important components, in terms of capital and operational costs, of wind turbines. The experienced acquired by the industry in the latest decades has shown that leading edge erosion is a problem of concern that impacts the reliability of the blade and the power production of the turbine, among others. This study provides a framework to estimate leading edge erosion evolution and energy production degradation throughout time to apply in operation and maintenance decision making. It is based on the generation of synthetic wind and rain data based on observations from the site and ERA5 reanalysis data, whirling arm test data of erosion protection coatings, along with aerodynamic polar curves for clean and eroded airfoils of the blade. Rain erosion is calculated based on impingement, and assumed to be linearly accumulated using the Palmgren–Miner rule. Synthetic wind and rain time series are used to evaluate 25-year erosion degradation and energy production scenarios. A case study using the 5MW NREL’s wind turbine located in the North Sea has been analysed with the proposed framework showing maximum annual energy production losses in the range of 1.6–1.75% and first erosion failure between years 2 and 6.

Automation of Aircraft Fatigue Life Estimation

Abstract The fatigue is an important factor in aircraft operation. A correct estimation of structure fatigue life is crucial for user and payload safety. However, due to high amount of data gathered during a typical recording of load spectra for different types of flights, the overall results become prone to human error. The paper describes development of a software able to perform an automated, in-depth analysis of data recorded with onboard accelerometers. Using the Rainflow Cycle Counting method, it transforms received data points into a Markov matrix. The prepared array is then recalculated into a half-cycle matrix, which can be collapsed into scalar value of fatigue level using the Palmgren-Miner rule. The method was tested with loads recorded during a typical flight conducted according to the Polish NSTS-06 flight scenario and simulated camera mounting fixed to a multirotor.

Time-domain fatigue assessment for blade root bolts of floating offshore wind turbine (FOWT)

A methodology for time-domain fatigue assessment for preloaded blade root bolts floating offshore wind turbine (FOWT) is proposed in the paper. The stress responses of the blade root bolts are calculated by finite element (FE) method in terms of the time history of environmental loading on the blade root joint where the wind, wave, and current are taken into account. Stress ranges on blade root bolts and the corresponding cycles are achieved by the rain-flow counting method. Fatigue life prediction for blade root bolts is then conducted with use of S–N curves and Palmgren-Miner's (PM) rule. During the fatigue assessment, the mean stress effects and the influence of different design and installation factors on fatigue strength of blade root bolts are considered. A fatigue assessment for blade root bolts of a NERL 5 MW Spar type FOWT is performed to demonstrate the capability of the proposed methodology. Fatigue lives of the blade root bolts with different design and installation factors are predicted and the impact of bolt preload, bolt size and thickness of connecting flange on the fatigue strength of blade root bolts is discussed.

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.

Accumulated fatigue damage assessment of side structural details in a double hull tanker based on spectral fatigue analysis approach

The fatigue life of structural details in the double side of a tanker ship was investigated, employing the spectral fatigue analysis approach. The stochastic environmental loads were derived by seakeeping software based on the 3D diffraction theory, in the frequency domain, and then mapped on a structural finite element model for the ship hull. The stress response at the considered details was extracted from the finite element analysis and the accumulated damage was estimated by Palmgren-Miner's rule. The reduction of the hull girder section modulus and the deterioration of fatigue strength due to corrosion were taken into account. The influences of different wave scatter diagrams, reduction of hull girder section modulus, stress concentration factor, free corrosion S–N curve, wave direction, wave spectrum and operational profile on the accumulated fatigue damage were investigated.

Experimental field test on a multipiece steel wheel and influence of the material properties on its fatigue life evaluation

Wheels are important components for the general vehicle reliability. Their design validation is usually based on fatigue tests conducted in laboratory under constant amplitude load conditions, according to industrial standards. In the off-highway industry, the variety of applications and machines often makes it difficult to complete standard tests, due to the high load capacity requirements or to lack of information about specific applications. Therefore, strain data acquisition during field test on real machines can be a useful tool to understand actual load conditions. In this paper, a fatigue life assessment based on field test is applied to a multipiece wheel that experienced an unexpected crack development in a critical section. The local strain approach is used, together with rainflow counting method and Palmgren-Miner rule for the total damage evaluation. Mean stress influence is considered through the Smith-Watson-Topper method. The fatigue life estimation is completed for structural steel S355J2. The influence of extremely hard working conditions is also investigated and assessed to be the root cause of the failure. Finally, a possible design improvement regarding the use of a higher base material grade S690 is evaluated and proposed.