Palmgren-Miner Rule Research Articles

Fatigue life prediction under service load considering strengthening effect of loads below fatigue limit

Lightweight design requires an accurate life prediction for structures and components under service loading histories. However, predicted life with the existing methods seems too conservative in some cases, leading to a heavy structure. Because these methods are established on the basis that load cycles would only cause fatigue damage, ignore the strengthening effect of loads. Based on Palmgren-Miner Rule (PMR), this paper introduces a new method for fatigue life prediction under service loadings by taking into account the strengthening effect of loads below the fatigue limit. In this method, the service loadings are classified into three categories: damaging load, strengthening load and none-effect load, and the process for fatigue life prediction is divided into two stages: stage I and stage II, according to the best strengthening number of cycles. During stage I, fatigue damage is calculated considering both the strengthening and damaging effect of load cycles. While during stage II, only the damaging effect is considered. To validate this method, fatigue lives of automobile half shaft and torsion beam rear axle are calculated based on the new method and traditional methods, such as PMR and Modified Miner Rule (MMR), and fatigue tests of the two components are conducted under service loading histories. The tests results show that the percentage errors of the predicted life with the new method to mean life of tests for the two components are −3.78% and −1.76% separately, much lesser than that with PMR and MMR. By considering the strengthening effect of loads below the fatigue limit, the new method can significantly improve the accuracy for fatigue life prediction. Thus lightweight design can be fully realized in the design stage.

Evaluation of fatigue life for titanium alloy TC4 under variable amplitude multiaxial loading

AbstractFatigue tests under variable amplitude multiaxial loading were conducted on titanium alloy TC4 tubular specimens. A method to estimate the fatigue life under variable amplitude multiaxial loading has been proposed. Multiaxial fatigue parameter based on Wu–Hu–Song approach and rainflow cycle counting and Miner–Palmgren rule were applied in this method. The capability of fatigue life prediction for the proposed method was checked against the test data of TC4 alloy under variable amplitude multiaxial loading. The prediction results are all within a factor of two scatter band of the test results.

정상 정규분포 확률과정의 삼봉형 스펙트럼에 대한 피로손상 모델 비교

The riser systems for floating offshore structures are known to experience tri-modal dynamic responses. These are owing to the combined loadings from the low-frequency response due to riser tension behavior, middle-range frequency response coming from winds and waves, and high-frequency response due to vortex induced-vibration. In this study, fatigue damage models were applied to predict the fatigue damages in a well-separated tri-modal spectrum, and the resultant fatigue damages of each model were compared with the most reasonable fatigue damage calculated by the inverse Fourier transform of the spectrum, rain-flow counting method, and Palmgren-Miner rule as a reference. The results show that the fatigue damage models developed for a wide-band spectrum are applicable to the tri-modal spectrum, and both the Benasciutti-Tovo and JB models could most accurately predict the fatigue damages of the tri-modal spectrum responses.

Fatigue damage analysis of the deepwater riser from VIV using pseudo-excitation method

The fatigue damage of a long deepwater riser undergoing in-line and cross-flow vortex-induced vibration (VIV) in deepwater is numerically studied using pseudo-excitation method (PEM) in present paper. For evaluating the fluid–structure interaction problem of vortex-induced vibration of deepwater riser at high Reynolds number, the strip theory is employed in this paper, and the discrete vortex method (DVM) is used to calculate the VIV of each strip to obtain the load spectrum as the pseudo-excitation, while the finite volume method (FVM) is employed to evaluate the structure dynamics of a deepwater riser. The VIV is considered as a stationary random process. The response of riser to vortex induced excitation is calculated using pseudo-excitation method. The DVM model and pseudo-excitation method are both validated by comparing their numerical results with experiments. The fatigue damage of one deepwater riser is evaluated based on the Palmgren–Miner Rule.

Application of nonlinear fatigue damage models in power electronic module wirebond structure under various amplitude loadings

This paper presents mean fatigue lifetime prediction of a wire-bond structure model in power electronic module using a failure physics approach that integrates high fidelity modelling and reduced order modelling. Loading current with variable amplitudes is applied to a finite element model of simplified wirebond structures. The resulting accumulated fatigue damage due to random loads is predicted by using reduced order modelling based on failure physics, a cycle counting algorithm, and various nonlinear fatigue damage models widely used in the literature. The reduced order modelling approach based on failure physics uses prediction data for the electro-thermo-mechanical behaviour of the wire-bond design of a power module obtained through non-linear transient finite element simulations, in particular for the fatigue life-time of the aluminium wire attached to the silicon chip of the wire in the module. The reduced order models that capture the black box function of the accumulated plastic strain are used in predicting the mean fatigue life time of the wire bond structure under random loads. One of the widely used cycle counting algorithms, rainflow counting algorithm, is used to count cycles of the temperature profile at the specific point of the wire bond structure in a power electronic module. The cycle data from the rainflow algorithm mean life time of the wire bond structure are predicted with various cumulative fatigue models. Non-linear cumulative fatigue models such as damage curve approach (DCA), double linear damage rule (DLDR), and double damage curve approach (DDCA), and linear cumulative fatigue damage model such as Palmgren–Miner rule are used to predict the mean fatigue life of the wire bond structure, and the results are compared.

Finite Element Based Vehicle Component Fatigue Life Assessment According to a Customer Usage Profile

Abstract In this study, construction and standardization of a track for performing fatigue and reliability tests of light commercial vehicles are described. Such a test track is necessary for design and manufacturing verification of these vehicles. Fatigue characteristics of Turkish roads were determined by analyzing fifty different roads. This paper focuses on defining the load spectrum and equivalent fatigue damage of the leaf spring resulting from accelerated tests on a route. Fatigue analysis and estimated lifetime of the part were calculated using Finite Element Analyses and verified by the Palmgren-Miner rule. When as customer profile the Turkish automotive user is taken into consideration and accelerated test tracks are designed for the reliability and fatigue tests of the related company, linear FEA of the spring represents a convenient procedure.

Fatigue Life Analysis of Crane K-Type Welded Joints Based on Non-Linear Cumulative Damage Theory

There are large numbers of welds on cranes’ lattice booms. Due to notably complicated force conditions, the fatigue life analysis of the lattice boom is difficult when designing the limit life. The fatigue cycle of the utilization level of a lattice boom crane is in the overlap zone of low-cycle fatigue and high-cycle fatigue. The poor accuracy of measurement of the fatigue life of lattice booms indicates that the calculation dispersion of the linear Palmgren-Miner (PM) rule was high. To obtain real crane stress spectra inexpensively and conveniently, a new stress spectra acquisition method based on the ‘measured & simulated & compared & statistics’ integrated strategy of crane K-type welded joints is proposed. The errors of the maximum stress amplitudes between the measured stress spectra and the simulated stress spectra were less than 10%. The fatigue test results also indicated that errors of the test fatigue life were less than 10% under both the simulated and the measured stress spectra. A new, simplified Huffman non-linear cumulative damage theory is proposed to calculate the fatigue life of crane K-type welded joints based on the notch stress and strain approaches. The calculation results indicated that the accuracy of the non-linear damage accumulation was higher than that of the PM rule, although the calculation result based on the non-linear damage accumulation method was slightly un-conservative when the initial damage was not considered in the calculation. By setting different initial damage conditions, various results were analysed, which revealed that the calculation errors of fatigue life based on the non-linear theory were less than 10% when the initial damage levels were set from 0.02 to 0.04. Such results are appropriate for engineering applications. When the fatigue life calculation needs to be more conservative, the initial damage levels may be set from 0.04 to 0.07; the resulting calculation errors could be less than 25%. As the Huffman non-linear cumulative damage theory requires data from only a few material properties, such as the cyclic stress-strain curve and the constant amplitude strain-life curve, it could therefore be more suitable for engineering applications with higher calculation accuracy and fewer costs.

Effect of whipping stresses on the fatigue damage of ship structures

Fatigue failures in ships are mainly caused by waves. Higher frequent stresses due to vibrations induced by wave impact, called whipping, are typically not considered in design. However, the bow and stern flare of many recently built container vessels has been increased causing higher and more frequent whipping stresses. Full-scale measurements have shown a significant increase of the fatigue damage caused by high-frequent loads if rainflow counting and Palmgren-Miner Rule are assumed. On the other hand, an increased damage rate has not yet been observed so that questions arose if this approach and the neglect of sequence effects of stress cycles are justified for these load processes. Therefore, fatigue tests have been performed with transverse stiffeners on a continuous plate. In a first investigation, low-frequent, constant amplitude loads were superimposed by higher frequent stress cycles. In successive investigations, stress histories extracted from the full-scale measurements on a Panamax containership, containing a typical whipping event, were applied. Fatigue lives obtained from the tests with and without whipping load cycles agree reasonably well with those calculated with the Palmgren-Miner Rule. Finally, a recent proposal of the authors for a simplified consideration of the whipping stresses in fatigue analyses for ships is discussed.

A New Fatigue Life Calculation Method Based on Non-Linear Cumulative Damage Theory

Operating characteristics of small and medium tonnage lattice boom crane which withstand fatigue loads was analyzed in this paper. It showed that the lattice boom crane utilization level is in the overlap zone of low cycle fatigue and high cycle fatigue. There may be some plastic deformation in the structure. So the total damage calculated by the Palmgren-Miner rule had a large scatter. Typical operating conditions was analyzed that K-type welded joints of the boom is under axial load and in-plane bending loads. Several critical areas of K-type welded joints were determined by ANSYS finite element calculation software where the stress amplitude was larger on the single side of the lattice boom. A new stress spectrum acquisition method based on the “measured+statistics+compare+simulation” integrated strategy of crane K-type welded joints was proposed. Based on a simplified Huffman non-linear cumulative damage theory, fatigue life of crane K-type welded Joints were calculated based on the strain parameters. They were compared with Palmgren-Miner rule and together with fracture mechanics method. Results showed that although they were all conservative compared with test results, the new method can be applied easily in for engineering applications because it only need amplitude constant amplitude fatigue strain-life data.

Composite Deck Having Transverse Stiffeners Bonded with a Cementitious Adhesive Subjected to Moving-Wheel Fatigue

This paper presents the behavior of a new composite deck system for twin-girder bridges subjected to moving-wheel fatigue load. The one-half scale system consists of a RC slab with transverse rib stiffeners welded to steel deck plates, which can eliminate the need for posttensioning frequently required for twin-girder bridges. A carbon-fiber-blended cementitious adhesive is used to improve the bond between the concrete slab and the steel deck. The response of the deck system shows a rapid increase in deflection within early fatigue cycles, followed by gradual development when the cycle and loads increase. Energy dissipation of the slab and the level of elastic recovery are discussed. A damage index based on the two-term Weibull function is employed to quantify the degree of fatigue damage. The Weibull damage model reasonably agrees with the simple Palmgren-Miner rule from a practical point of view and supports the adequacy of the proposed system in fatigue configurations. A postfatigue test is conducted to examine the residual capacity of the deck system with emphasis on bond performance of the cementitious adhesive. Bond failure between the concrete and steel deck is not observed, thereby corroborating the effectiveness of such an adhesive on improving the composite behavior of the system.

Application of Kriging and radial basis function in power electronic module wire bond structure reliability under various amplitude loading

This paper discusses life time prediction of wire bond structure in a power electronic module based on computational approach that integrates methods for high fidelity analysis, reduced order modelling, and life time prediction using reduced order model. This methodology is demonstrated for the design of a wire bond structure in a power electronic module with aim of reducing the chance of failure due to the wire bond lift off in power electronic module when a random load is applied to the aluminium wire. In particular, wire bond reliability of the power module related to the thermal fatigue material degradation of aluminium wire is one of the main concerns. In the power electronic module reliability, understanding the performance, reliability and robustness of wire bond is a key factor for the future development and success of the power electronic module technology, because wire bond lift off failure ignites other catastrophic failures.The main focus in this study is on the application of reduced order modelling techniques and the development of the associated models for fast evaluation and analysis. The discussion is on methods for approximate response surface modelling based on interpolation techniques using Kriging and radial basis functions. The reduced order modelling approach uses prediction data for the electro-thermo-mechanical behaviour of the power module wirebond design obtained through non-linear transient finite element simulations, in particular for the fatigue life-time of the aluminium wire attached to the silicon chip of the wire in the module. The reduced order models are used for the analysis of predicting the life time of the wire bond structure under random load. One of the widely used cycle counting algorithm, so called rainflow counting algorithm is utilised to count the cycles of temperature profile at the a specific point of the wire bond structure in a power electronic module. Using the cycle results from rainflow algorithm mean life time of the wire bond structure is predicted by a linear cumulative damage model such as Palmgren–Miner rule. This model is utilised to predict the mean fatigue life of the wire bond structure.

Investigation of a new vortex-induced vibration suppression device in laboratory experiments

In order to mitigate vortex-induced vibration (VIV) of marine risers, especially to eliminate the phenomenon of frequency slock-in’, a new suppression device of crescent-shaped flow spoiler was designed with seven different layout schemes. VIV model tests with six flow levels were conducted in a large wind-wave-current flume. In all cases, vibration responses in both in-line and cross-flow cases were measured. With the installation of suppression devices vibration frequency evolution of a riser was analyzed by Morlet wavelet transform. The principle of VIV suppression was interpreted through vibration characteristics. Fatigue life of the riser was calculated by the Palmgren-Miner rule. Compared with a bare riser, vibration of an outfitted riser with suppression devices disturbed the steady flow, the vibration amplitudes in the two flow directions were reduced, and the riser fatigue life was improved.

Fatigue Reliability Evaluation Model of Drillstring in Bending Section of Horizontal Well

When drillstring rotates through the bending section of horizontal well, the fatigue damage of drillstring will be caused by alternating bending stress. Therefore, a thought to solve the fatigue reliability problem of drillstring in bending section of horizontal well is proposed. The variable amplitude alternating stress is transformed into equivalent fatigue stress, and the fatigue damage of drillstring is analyzed. Considering Palmgren-Miner rule and S-N curve, the fatigue life and reliability evaluation model of drillstring in bending section of horizontal well is established according to the fatigue reliability theory and probabilistic fracture mechanics. This model can calculate the fatigue damage, fatigue life and reliability of drillstring in the process of drilling and the maximum allowable dogleg angle where the drillstring is under compression and tension. And it has the important reference value for the fair use of drillstring and casing program design.

Use of Strain Data to Estimate Remaining Fatigue Life of a Fracture-Critical Bridge

A fracture-critical steel I-girder bridge was instrumented with strain gauges to estimate the remaining design fatigue life. The two girders on the bridge had extensive fatigue cracking. Continuous, dynamic strain data were collected for nearly 2 months to determine an effective stress range and cycle count according to Palmgren–Miner's rule. A simplified rainflow counting algorithm was developed and used to calculate the amplitude of each fatigue cycle. The effective stress range and cycle count were combined with AASHTO's S (stress range)-N (number of cycles to failure) curves to estimate the remaining design fatigue life of certain bridge details. The data revealed that the estimated design fatigue life was exceeded in the east girder (right lane), whereas some life remained in the west girder (left lane). The distribution of observed cracks in the girders was closely correlated with the calculated fatigue life. A method is presented in this paper to index the effective stress range so that strain measurements can be compared over extended periods.

Fatigue at the Molecular Scale

The influence of force on the stability of inter- and intramolecular bonds has been studied in great detail. Experiments, e.g. with AFMs or the Biomembrane Force Probe, have shown that the relationship between the lifetime of biomolecules and applied forces is well described by the Bell equation. However, rather than experiencing a constant (or continuously increasing) force, some biomolecules are subject to repeated force cycles. For instance, myosin motors in muscles experience millions of force cycles over their lifetime. At the macroscopic level, repeated stress cycles can lead to ‘fatigue failure’. Fatigue failure originates in permanent micro-damages and occurs at subcritical stress levels, provided that the number of stress cycles is large enough. Fatigue is a major cause of failure in machinery; however there is no comprehensive theory of fatigue. To design machines, engineers use heuristic methods such as the Palmgren-Miner rule or S-N diagrams. Here, we investigate for the first time a molecular theory of fatigue failure. We aim to provide a theoretical basis for the heuristic methods engineers use to avoid fatigue failure and draw conclusions about the design of molecular machines such as kinesin or myosin motors.

Subsurface rolling contact fatigue damage of railway wheels – A probabilistic analysis

A numerical model for predicting the probability of subsurface initiated rolling contact fatigue failure in railway wheels subjected to operational loading is presented. The loading is evaluated through simulations of dynamic train–track interaction incorporating the influence of, e.g., corrugation. Contact stresses are found from Hertzian theory and the resulting stress field from theory of elasticity. Fatigue damage is evaluated by use of a Wöhler curve where the fatigue strength is decreased due to the influence of material defects, which are presumed to be of random size and occurrence in the stressed volume of the wheel rim. Damage accumulation is performed using the Palmgren–Miner rule, extending the model to cases of variable loading. The results show how a combination of rail corrugation and high train speeds have a significant impact on the probability of fatigue failure. A sensitivity analysis reveals a strong influence of the fatigue strength and the material defect distribution on the probability of fatigue failure.

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.

Combination of Random Waves and Vessel Motions Effects on the Fatigue Damage of Top Tensioned Riser

As one of the main configurations of the riser, top tensioned riser(TTR) encounters harsh environment in its whole service life. In order to ensure that the riser will fulfil its intended functions, a fatigue assessment should be carried out for each representative riser, which is subjected to dynamic fatigue loading. The fatigue life of TTR under the combination excitation of random waves, current and vessel motion is analyzed in this paper. The long-term stress histories of the riser are calculated and the mean stresses, the number of stress cycles and amplitudes are determined by rain flow counting method. The Palmgren-Miner rule for cumulative damage theory with a specified S–N curve is used to estimate the fatigue life of the riser. The corresponding numerical programs which can be used to calculate the response and fatigue life of the riser are compiled. The significant influences of internal flow velocities and low frequency motion of the vessel are analyzed in detail.

Behaviour of hybrid FRP–UHPC beams in flexure under fatigue loading

The fatigue behaviour of innovative hybrid FRP–UHPC beams under flexural loading is investigated in this paper. The beams were made up of a pultruded GFRP hollow box section beam with a cast-in-place UHPC layer on top and either a CFRP or SFRP sheet bonded along the bottom. Four hybrid beams were tested under variable amplitude loading, to determine the effect of cyclic loading on flexural strength and stiffness. Analysis also included the development of a modified S–N curve and evaluation of fatigue damage using the Palmgren–Miner rule. It was found that insignificant loss in strength and stiffness occurred for all beams, where the fatigue damage estimated using the Palmgren–Miner rule overestimated the fatigue life. It was postulated, by comparison, that the hybrid beams reinforced with CFRP sheets may perform better under fatigue loading than the beams reinforced with SFRP sheets.

Sensitivity analysis of fatigue life prediction for deepwater steel lazy wave catenary risers

Steel lazy wave catenary riser (SLWR) has been an attractive choice for deepwater oil field developments. However, fatigue is a critical issue in assessing the feasibility of applying SLWR to large motion vessels such as floating production storage and offloading (FPSO) or semi-submersibles. In this work, the time-domain fatigue analysis of SLWR was adopted for better representing the structural nonlinearity, fluid load nonlinearity and riser-soil nonlinear interaction. The Palmgren-Miner rule was employed for the fatigue life prediction along the riser length. The main purpose of this analysis is to present sensitivity analyses of SLWR fatigue life under various input parameters, which include the structural damping, the hydrodynamic coefficients along the riser, the seabed stiffness, the vessel motions, etc. The analyses indicated the strong dependence of the riser fatigue life on these parameters. The results can help designers to understand the dynamic behavior of the SLWR and provide guidance for selection of some critical parameters that are used in the fatigue design.