Palmgren-Miner Rule Research Articles

Fatigue Performance of RC Beams Strengthened with CFRP under Overloads with a Ladder Spectrum.

Vehicle overload is detrimental to bridges and traffic safety. This paper presents a study on the fatigue performance of typical reinforced concrete (RC) beams of highway bridges under vehicle overload. A definition method of vehicle overload and a construction method of overload ladder spectrum were first proposed based on traffic data acquisition, statistical analysis and structural calculation of the highway bridges in Guangzhou. A fatigue experimental method was also proposed with the three-ladder vehicle overload spectrum, and the fatigue tests of 15 RC beams strengthened with carbon fiber reinforced polymer (CFRP) under three loading levels were then carried out. The fatigue performance and the failure mechanism of the strengthened beams were presented and discussed, and two fatigue life prediction methods were proposed with the established modified Palmgren-Miner rule and the loading level equivalent method respectively. The results showed that the fatigue performance of the strengthened RC beams was severely degraded under overload ladder spectrum compared with that under constant amplitude cyclic load, and the life prediction methods were proved effective.

Impact of meteorological variations on the lifetime of grid-connected PV inverters

In this paper a grid-connected single-phase PV inverter is employed as a study case in order to investigate the effects of different meteorological conditions on the reliability analysis. The lifetime evaluation of the power modules consisting of the PV inverter is evaluated, taking into account variations on the solar irradiance and ambient temperature but also including the PV panel thermal dynamics (i.e., thermal capacitance). The mission profiles are used as the input and then translated into the thermal loading of the power switch. The Bayerer's model and Palmgren-Miner's rule are used to calculate the life consumption (LC) and B10 lifetime. The results show that the increase in irradiance generates more energy. However it strongly reduces the system lifetime. Also, the thermal dynamic of the PV panel has important impact on the lifetime prediction.

Protecting Museum Collections from Vibrations Due to Construction: Vibration Statistics, Limits, Flexibility and Cooperation

ABSTRACT Vibrations due to heavy construction work continue to be a major concern for museums. Although there has been an increase in research on the effect of vibrations on objects of cultural heritage in recent years, selecting measures to protect collections and remain open during construction work continues to be difficult because of a lack of data on what objects can actually withstand, the complexity of vibration loads, and the uniqueness of each situation. The major renovation of the Central Library in Liverpool, UK, which shared walls with the World Museum and Walker Art Gallery, both of which belong within National Museums Liverpool, showed how museums and other institutions can successfully deal with such situations. An integral approach was taken, beginning with an extensive risk analysis to determine which objects could remain on display, which needed extra protection and regular condition monitoring, and which had to be removed. The museums then negotiated a vibration protocol and action plan with the contractors, including continuous monitoring, and trigger levels requiring consultation or work stoppage. Vibration data were also stored and used for later analysis. This integral approach was successful in protecting the collections on exhibition, with only two incidents of reported damage directly related to vibrations. A combination of museum staff experience, excellent communications with the contractors, and some flexibility in defining vibration limits provided a successful recipe for both museums. The analysis of the vibration data using the basic engineering concept of the Palmgren-Miner rule, supports a more flexible approach to setting vibration limits based on recently published guidelines.

The fatigue life of a friction stir welded 19501 aluminium alloy T-joint

AbstractFriction stir welding (FSW) is a solid-state joining which reduces the structural weight significantly and hence it has received worldwide attention for the joining of aluminium alloys. In this paper, fatigue tests and finite element analysis were employed to study the mechanical and fatigue properties of a friction stir welded T-joint of 19501 aluminium alloy. An LS-2 FSW machine with 100 kN capacity was used to fabricate the T and butt joints. The tensile properties of the friction stir welded joint show that there is a marginal reduction of about 5% in strength and ductility as compared to an un-welded 19501 aluminium alloy. S-N test results of theT-joint specimen at two stress ratios of 0 and −1 showed that there was a reduction of 15% in the fatigue strength due to the change of stress ratio from 0 to −1. The effect of mean stress can be well approximated using Goodman’s criterion as compared to Gerber’s or Soderberg’s criteria. The predicted fatigue lives from the proposed model using the Palmgren-Miner rule (PMR) were found to be within reasonable accuracy. Micrographs shown for the fracture surfaces of the retreating side, mid-weld zone and the advancing side of the T-joint indicate that fracture surfaces are a mixture of dimple and cleavage features.

A modified accumulation damage algorithm for predicting corrosion fatigue life by considering load interaction for aluminum alloys

Fatigue tests were conducted on centrally notched aluminum alloys 2524-T3 and 7050-T7451 under constant-amplitude and actual random spectrum loading in dry air and in 3.5% NaCl sodium chloride solution, and fatigue damage mechanisms under the load interaction and the corrosion effect on fatigue crack initiation and propagation were deduced from fractographic analysis. Pure and corrosion fatigue lives under actual random spectrum load history were modelled based on a modified accumulation damage algorithm accounting for the load interaction. More reasonable predictions were achieved from the modified algorithm proposed in the paper than from the Palmgren–Miner rule.

Fatigue Life Prediction for Warship Operation in Indonesian Water

The fatigue life of a corvette ship structural detail was predicted by using a spectral fatique analysis. The fluctuated wave load act to the ship’s structure in regular wave was estimated by using Diffraction Theory. The stress spectrum was defined using analytical approach consider to the design constructions of ship. The operational routes of a corvette ship were determined in Indonesian water condition for a year period of ship’s mission. The sea condition was ilustrated in term of wave spectrum which was developed using the ITTC formula. The spectral response of stress bending moment was calculated by multiplication of wave spectrum and stress bending moment in regular wave for certain life time. Furthermore, the estimation of the fatigue life was performed by using Palmgren-Miner rule during its life time of operation. Finally, the fatigue life of a corvette ship was predicted about 84 years based on the mission and water condition of Indonesia.

Wheel life prediction model – an alternative to the FASTSIM algorithm for RCF

ABSTRACTIn this article, a wheel life prediction model considering wear and rolling contact fatigue (RCF) is developed and applied to a heavy-haul locomotive. For wear calculations, a methodology based on Archard's wear calculation theory is used. The simulated wear depth is compared with profile measurements within 100,000 km. For RCF, a shakedown-based theory is applied locally, using the FaStrip algorithm to estimate the tangential stresses instead of FASTSIM. The differences between the two algorithms on damage prediction models are studied. The running distance between the two reprofiling due to RCF is estimated based on a Wöhler-like relationship developed from laboratory test results from the literature and the Palmgren-Miner rule. The simulated crack locations and their angles are compared with a five-year field study. Calculations to study the effects of electro-dynamic braking, track gauge, harder wheel material and the increase of axle load on the wheel life are also carried out.

Evaluation of Fatigue Life for TC4 Notched Components Under Variable Amplitude Multiaxial Loading

Fatigue tests under variable amplitude multiaxial loading were conducted on notched specimens of titanium alloy TC4. The key issues of fatigue life estimation under variable amplitude multiaxial loading for notched components have been researched. Multiaxial fatigue critical area of notched specimen was determined first. Then, fatigue damage control parameter based on Wu–Hu–Song model and rainflow cycle counting as well as Miner–Palmgren rule was applied in prediction approach. The proposed prediction procedures were checked against the test data of TC4 notched specimens under variable amplitude multiaxial loading. The prediction results are all within a factor of two scatter band of the test results.

Fatigue life resolution of the steering wheel tie rod of a LCV with FEA

In this study, an accelerated test track construction necessary during research and development phase of Light Commercial vehicles (LCV) is described. By the questionnaire method, the Turkish customer automotive usages are defined. This paper focuses on defining load spectrum affected by steering wheel tie rod axial force derived during maneuvers. Finite Element Analyses (FEA) is used for fatigue analysis and it is verified by the Palmgren-Miner rule. As a result, lifetime of the part is calculated. An accelerated test tracks is designed for reliability and fatigue tests of the related company and linear FEA of the steering wheel tie rod represents a convenient procedure.DOI: http://dx.doi.org/10.5755/j01.mech.23.5.16078

A plain linear rule for fatigue analysis under natural loading considering the sequence effect

Fatigue under variable amplitude loading is currently assessed with the Palmgren-Miner rule in structural standards, ignoring the order of loading, which would require non-linear or mixed rules, especially for the random loading sequences applied to certain structures. Therefore, the goal is to develop a practical and simple correction factor ensuring the linear summation of damage is conservative, so as to take the sequence effect into account in random loading from natural sources. The theoretical consistency of this approach is demonstrated and a case study is developed to test the feasibility of the new rule and its simplicity.

Statistical evaluation of fatigue strength of double shear riveted connections and crack growth rates of materials from old bridges

The maintenance of old riveted bridges has become a major concern for railroad managers across Europe. These metallic structures, built on their majority on the second half of the 19th century, are indeed submitted to ever increasing traffic loads (augmentation in weight and speed of rolling stock).To assess the remaining life of these metallic bridges, some critical structural details have been identified and associated to S-N curves to be used in damage estimation (using Palmgren-Miner's rule for cumulative damage, for example). These constructional details are often described in construction standards, such as the EN 1993-1-9, the BS 5400 and the AASHTO standards. The particularity of older hot-riveted bridges is that their numerous geometric configurations are often under-represented, thus, limiting the accuracy of damage estimation.To compensate the absence of hot riveted assemblies in the standards, numerous research groups have performed extensive experimental campaigns. However, the heterogeneity and rarity of the material (no longer produced nowadays), as well as the very diverse geometrical configurations used at the time of the construction of the bridges (given the novelty proposed by the introduction of metal as a new material in monumental construction), makes difficult the comparison of experimental data.In order to facilitate interpretation and differentiation of fatigue data of a particular type of constructional detail, experimental data from double shear assemblies manufactured from three different metallic ancient bridges is considered (French and Portuguese puddled iron bridges). Then, through statistical analysis (linearized boundaries and the Fernández-Canteli model), the S-N curves corresponding to their structural configuration are identified. Comparisons to the EN 1993-1-9, the BS 5400 and the AASHTO standards are also proposed.The combination of the S-N curves and Fracture Mechanics approaches can be used to evaluate the residual life of the old riveted metallic bridges. Thus, a statistical analysis and discussion of experimental fatigue crack propagation data available for materials from the ancient riveted metallic bridges are made. This analysis is important for the application of the Fracture Mechanics approaches to predict the residual life of structural details.

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.

Fatigue life prediction of Package-on-Package stacking assembly under random vibration loading

This paper presents a general methodology to predict the fatigue life of the Package-on-Package (PoP) under random vibration loading by means of vibration tests and finite element (FE) simulation. The behavior of the critical solder joints of the PoP under vibration loading was accurately described by FE model using ANSYS software and confirmed by modal analysis and linear sweep tests. The stress-life (S-N) curve of the PoP solder joints was obtained by the sinusoidal fatigue vibration tests and FE simulations to characterize the fatigue properties of the PoP under vibration. The comparison of the S-N curves of the SAC305 solder joints in different structures indicates the S-N curve of the SAC305 solder joints depends on the package structure. With the same fatigue cycles, the stress levels for the current 3D package is the smallest compared with the other 2D package due to the stacked structure of the PoP. Spectrum analysis for the random vibration tests was performed by the FE simulations to acquire the stress response power spectral density (PSD) of the critical solder joint. A specific frequency domain approach based on the Palmgren-Miner's rule was established to predict the fatigue life of the PoP under random vibration. Results show that simulated fatigue life matches well with the random vibration test results, which implies that this approach could be a potential method for the predication of fatigue life of the 3D packaging under random vibration.

Evaluation of corrosion fatigue and life prediction of lower arm for automotive suspension component

Lower arm is one of the suspension components of automobile. It is suffered from driving vibration and corrosive environment, namely corrosion fatigue. In this study, corrosion fatigue property of lower arm was investigated, and a modified model based on Palmgren-Miner rule was developed to predict the lifetimes of corrosion fatigue. The corrosion fatigue life of lower arm was about 1/6 times shorter than fatigue life. Based on the results of corrosion fatigue tests and meteorological data in Seoul and Halifax, the corrosion fatigue life of lower arm was predicted. The satisfaction of 10-year and 300,000 km warranty was dominated by the climate of automobile driving. This prediction indicates that the weather condition or driving condition influences the life of automotive parts. Therefore, to determine the warranty of automotive parts, the driving condition has to be carefully considered.

Computational Framework for Online Estimation of Fatigue Damage using Vibration Measurements from a Limited Number of Sensors

This study proposes a computational framework for the online estimation of fatigue damage using operational vibration measurements from a limited number of sensors. To infer the stress response time histories required for fatigue prediction, the measured structural response is driven to a high fidelity finite element (FE) model, which is reconciled using appropriate model updating techniques that minimize the discrepancy between the experimental and analytical frequency response functions (FRFs). Fatigue is accordingly estimated via the Palmgren-Miner rule, while the available FE model allows for stress estimation at unmeasured spots. The method is successfully validated and assessed through an experimental study that pertains to a linear steel substructure supporting the entire body of a pre-beater assembly at a PPC power plant.

Evaluating fatigue life of materials and structures under low-cycle loading

The problem of evaluating strength and fatigue life of critical engineering objects, the operational properties of which are characterized by multi-parametric nonstationary thermal-mechanical effects, is discussed. The main degradation mechanisms of structural materials (metals and their alloys) characteristic of such objects are considered. The main requirements for mathematical models of fatigue damage accumulation are formulated. To evaluate the stress-strained state (SSS) and fatigue life of critical engineering facilities (CEF) in the framework of modern achievements of mechanics of damaged media (MDM), a mathematical model is developed which describes the processes of cyclic thermal-plastic deformation and fatigue damage accumulation in structural alloys subject to multiaxial non-proportional paths of combined thermal-mechanical loading. The MDM model consists of three interconnected parts: thermal plasticity constitutive equations, accounting for their dependence on the failure process; an evolution equation of damage accumulation and a strength criterion of a damaged material. To qualitatively and quantitatively assess the constitutive relations of MDM for low-cycle modes of thermal-cyclic loading, the numerical and experimental results for the fatigue life of a notched compact sample in a non-uniaxial stress state under block modes of thermal-cyclic loading were compared, which supported the validity of the constitutive relations of the MDM model for thermal fatigue. An approach based on the Palmgren-Miner rule of linear summation of damage, when used for evaluating the fatigue life of structural elements, may result in both conservative and non-conservative estimates. This conclusion is confirmed by the experimental and theoretical studies of foreign and domestic authors. The results of numerical modeling of the fatigue durability of a compact specimen with an obtuse notch are presented for two loading histories. It is shown that several cycles of more intensive loading at the beginning of the strain history are the reason why the rule of linear summation of damage can overestimate or underestimate the value.

Mitigation of Fatigue Damage and Vibration Severity of Electric Drivetrains by Systematic Selection of Motion Profiles

The offshore drilling industry is among the most demanding markets for electrical equipment. Heave motion, irregular cyclic loads, harsh weather conditions, and vibrations are causing accelerated deterioration of drilling equipment. One of the most common solutions to these problems is to design actuation systems of such machinery overly conservative to gain additional safety, which results in too high initial investment and maintenance costs. To mitigate the fatigue damage and vibration severity of rotating elements of electric drivetrains operating offshore, this paper presents a comparative analysis of four popular input functions used in motion control of industrial systems. We evaluate them not only by using well-known performance indicators, such as maximum load or velocity, but also by assessing their influence on fatigue life and vibration severity of electric drivetrains. The rainflow counting algorithm is used to assign amplitudes and mean values of distinguished cycles from random loading history. Then, the Palmgren–Miner rule together with S–N curves are applied to determine the total damage for cycles with varying amplitudes. In addition, we quantify the cumulative effect of vibrations and jerk on machine damage by using the metric based on the jerk energy. The importance of this study is illustrated on a full-scale offshore pipe handling machine by benchmarking simulation results with the field data. The outcomes demonstrate not only a serious decrease in damage caused by vibrations for smooth motion profiles, but also provide a basis to formulate rules of thumb for selection of the most suitable motion profile for certain applications.

New models for depicting corrosion fatigue behaviour and calendar life of metallic structural component

New [Formula: see text] surface model is proposed for depicting corrosion fatigue behaviour and novel formulae are derived to estimate the parameters of proposed model by best fitting from a minimal experimental dataset of corrosion fatigue tests. From the Palmgren–Miner rule, a cumulative damage model for the alternation between corrosion and fatigue is developed to evaluate calendar life of metallic structural component. Corrosion tests are conducted on unnotched and notched specimens from LD10CS aluminium alloy and 15CrMnMoVA alloy steel in artificial corrosion environments. Fatigue tests are also performed on corroded specimens subjected to constant amplitude loading and the interaction mechanisms between corrosion and fatigue are deduced from fractographic studies. The applicability of the new models has been shown for experimental datasets for depicting corrosion fatigue behaviour and for evaluating calendar life of motor brace rod in helicopter.

Damage accumulation of bovine bone under variable amplitude loads

Stress fractures, a painful injury, are caused by excessive fatigue in bone. This study on damage accumulation in bone sought to determine if the Palmgren-Miner rule (PMR), a well-known linear damage accumulation hypothesis, is predictive of fatigue failure in bone. An electromagnetic shaker apparatus was constructed to conduct cyclic and variable amplitude tests on bovine bone specimens. Three distinct damage regimes were observed following fracture. Fractures due to a low cyclic amplitude loading appeared ductile (4000μϵ), brittle due to high cyclic amplitude loading (>9000μϵ), and a combination of ductile and brittle from mid-range cyclic amplitude loading (6500 –6750μϵ). Brittle and ductile fracture mechanisms were isolated and mixed, in a controlled way, into variable amplitude loading tests. PMR predictions of cycles to failure consistently over-predicted fatigue life when mixing isolated fracture mechanisms. However, PMR was not proven ineffective when used with a single damage mechanism.

Probabilistic Palmgren–Miner rule, with application to solder materials experiencing elastic deformations

It has been recently shown that there are effective ways not only to reduce the interfacial stresses in electronic packaging assemblies with solder joint arrays as the second level of interconnections, but to do that to an extent that inelastic strains in the peripheral joints, where the induced thermal stresses and strains are the highest, are avoided. While various and numerous modifications of the empirical Coffin–Manson relationship are used to predict the fatigue life of solder materials experiencing inelastic strains and operated in low cycle fatigue conditions, the Palmgren–Miner rule of the linear accumulation of fatigue damages, although suggested many decades ago, is still viewed by many material scientists and reliability physicists as a suitable model that enables one to quantify the cumulative fatigue damage in metals experiencing elastic strains. In this analysis the Palmgren–Miner rule is extended for the case of random loading, and a simple formalism is suggested for the evaluation of the remaining useful lifetime for a solder material subjected to random loading and experiencing elastic thermally induced shearing deformations. Special highly focused and highly cost effective accelerated tests have to be conducted, of course, to establish the S–N curve for the given solder material. In the future work we intend to extend the suggested methodology to take into account various aspects of the physics-of-failure: the role of the growth kinetics of intermetallic compound layers; the random number, size and orientation of grains in the joints; position of the joint with respect to the mid-cross-section of the assembly (peripheral joints are more prone to elevated interfacial stresses); assembly size, etc. All this effort, important as it is, is, however, beyond the scope of this analysis, which is aimed at the extension of the classical Palmgren–Miner rule for the case of random loading.