Random Fatigue Research Articles

Experimental validation of an ANN model for random loading fatigue analysis

The use of artificial intelligence especially based on artificial neural networks (ANN) is now prevalent in many fields of data analysis and interpretation. There have been a number of papers published in the literature on the use of ANN for fatigue characterisation. Most of these have however been developed for rather focussed application with limited capability for fatigue life prediction for a broad scope of material and loading conditions. The authors recently presented a uniquely generalised ANN model that is capable of making fatigue life prediction for a broad range of material fatigue properties and loading spectral forms. The model was developed using simulated data albeit subject to conceivable constraints between possible materials properties and load forms. This paper presents a validation of the ANN model using a Society of Automotive Engineers (SAE) random fatigue loading experimental test data. The capabilities and potentials of the model are demonstrated by comparison with the SAE random load fatigue test results and with results obtained from other predictive methods. The performance of the ANN is highly encouraging as a general tool for random loading fatigue analysis.

Theoretical and numerical investigation of stress mode shapes in multi-axial random fatigue

Abstract Random fatigue is inherently multi-axial due to the complex stress state in real vibrating structures. This paper investigates the role of Stress Modal Analysis (SMA) in multi-axial random fatigue. Predicting hotspots of multi-axial random fatigue by Stress Mode Shapes (SMSs) was theoretically demonstrated. An improved approach was proposed to exploit SMSs in random fatigue with a multi-axial criterion. First, SMA is conducted to locate the multi-axial fatigue hotspots in a vibrating structure. Second, the frequency-domain approach for random fatigue is performed at the identified hotspots. The capability of SMSs in locating multi-axial fatigue hotspots was verified by numerical investigation. The finite element (FE) model of an L-shaped thin-walled structure containing geometry changes was constructed for case study. Local regions were identified as hotspots by SMSs information. Then, random response and multi-axial fatigue damage of the whole structure were evaluated for verification. Damage map indicates that the critical positions predicted by SMSs have good accuracy. Results show the improved approach with SMA can ensure both accuracy and efficiency for multi-axial random fatigue.

A frequency domain approach in residual stiffness estimation of composite thin-wall structures under random fatigue loadings

Based on the constant-amplitude fatigue experiment, a new residual stiffness model combining with power spectral density is proposed to adapt random stress states. The random loading process can be divided into multi-level variable amplitude loadings. All stiffness degradation increments can be integrated to obtain the stiffness degradation by using a numerical integral method. Fatigue damage accumulation of composite thin-wall structures subjected to random cyclic loadings is investigated by using the proposed method, which is also verified by random vibration tests with limited-bandwidth excitation. The influence of local stiffness damage on the fundamental frequency of the experiment specimen is calculated by using finite element method, which is in good agreement with the experimental results. The life predictions based on the proposed residual stiffness model are more conservative in comparison of that with linear damage accumulation rule.

Damage evaluation under complex fatigue loading conditions

Fatigue damage and life assessment of multiaxial loadings is still an issue yet to resolve. Many methods have been proposed with promising agreements with the experimental results. However, the performance of such methods is, more than often, purely based on fatigue tests with simple loading conditions. In this work the stress scale factor (SSF) criterion and the virtual cycle counting (vcc) method are used to estimate fatigue life and damage accumulation with two damage accumulation rules. Fatigue tests were carried out with three different variable amplitude random loadings, applied to several specimens made from a 42CrMo4 high-strength steel. Fatigue crack plane measurements were compared with predictions from several critical plane models. The applied methods provided very acceptable results making the SSF package (SSF equivalent stress and virtual cycle counting method) a good method to estimate fatigue life and assessment of the damage accumulation in random fatigue loadings.

Improved density peak clustering-based adaptive Gaussian mixture model for damage monitoring in aircraft structures under time-varying conditions

Abstract For the reliable damage monitoring of aircraft structures under Time-Varying Conditions (TVCs), Gaussian Mixture Model (GMM)-based damage monitoring methods combined with Guided Wave (GW) have been studied increasingly frequently in recent years. In this paper, to enhance the performance of the GMM-based damage monitoring method, an Improved Density Peaks Clustering (IDPC)-based Expectation Maximization (EM) algorithm is proposed to improve the constructing algorithm of the GMM. In the algorithm, the unique initial value of the GMM parameters is obtained based on an adaptive searching strategy of the probability density peaks of GW Damage Features (DFs) first. Next, the GMM is constructed simply and efficiently by the EM algorithm based on the initial parameters. The IDPC-EM algorithm can stably construct the GMM with fewer experience-dependent initialization parameters while promising the probability modelling accuracy and maintaining high computational efficiency. Based on the IDPC-EM algorithm, a new adaptive GMM-based damage monitoring method combined with the GW is established. The method is simple, stable, highly computationally efficient and less experience-dependent due to the adaptive GMM. In this method, two GMMs of the DFs obtained in the healthy state and the damage monitoring state of an aircraft structure are constructed, respectively. By measuring the similarity of the two GMMs, the variation trend of the probability distributions of the DFs between the two states is obtained to detect the damage. Finally, the method is validated in a full-scale aircraft fatigue test which is close to an in-flight load test on the ground. The cracks of the right landing gear spar and the left wing panel are monitored reliably and stably under random fatigue load conditions.

Stochastic analysis of fatigue of concrete bridges

A novel method is proposed in this work for the assessment of the remaining fatigue life and fatigue reliability of concrete bridges subjected to random loads. The fatigue reliability of a bridge is a function of the fatigue damage accumulation; a stochastic fatigue damage model (SFDM) with physical mechanism is introduced for deriving the fatigue damage process. In order to implement the probabilistic analysis, based on the probability density evolution method (PDEM), the generalised density evolution equation (GDEE) for the remaining fatigue life is developed. Finally, a prestressed concrete continuous beam bridge located in China is illustrated. The random fatigue load acting on the bridge is modelled as the compound Poisson process, and the simulation of the random load uses the stochastic harmonic function (SHF) method. To simplify the reliability analysis, an equivalent constant-amplitude (ECA) load process is introduced based on energy equivalence. By employing SFDM, the finite element analysis of the bridge under the fatigue loading is performed. Then, the fatigue damage accumulation process of the bridge under the fatigue loading is obtained. Through solving the probability density evolution equation for the remaining fatigue life, the probability density functions (PDFs) of the remaining fatigue life evolving with time is obtained. The fatigue reliability is then calculated by integrating the PDF of the corresponding remaining life.

Random fatigue damage accumulation analysis of composite thin-wall structures based on residual stiffness method

The damage accumulation and life prediction for C/SiC composite panels subjected to random vibration loading was studied by using the residual stiffness model in combination with critical failure stiffness ratios in the different stress levels. According to the results of stiffness degradation and material S-N curves for constant-amplitude fatigue loadings, a new residual stiffness model was established and extended to adapt random stress states by using an equivalent damage ratio algorithm in time domain. The stiffness degradation and material S-N curves were obtained by using constant amplitude fatigue experiments. Random vibration tests with limited-bandwidth excitation were conducted to verify the prediction model. Good agreement is observed compared with the results of 2D plain-woven C/SiC composite panel subjected to random vibration loadings.

A universal, damage-criterion-independent cycle counting method for multiaxial and variable amplitude fatigue

None of the procedures for cycle-counting defined in the ASTM document with designation E1049-85 (Reapproved 2017) [1] are generally applicable to non-proportional, multi-axial Fatigue. In addition, as the concepts of amplitude and mean stress are defined per cycle, their values are dependent (or co-define) the cycle counting method. This poses an obvious problem to the analysis of non-proportional, multi-axial fatigue damage, as lifetime is, not in all but in many cases, an amplitude and mean stress dependent material property. Most of the newer cycle counting methods developed till date are at least inspired by the works of Wang & Brown [2] and of Bannantine & Socie [3], both of which are themselves still frequently used. Being built inspired by counting methods developed for uniaxial cycling, all of the approaches to date known to this author are limited in a way that is very well phrased by Anes et al [4], whom, on page 79 of their article, write that (quote): The damage criterion is the base stone to set up random fatigue. The damage parameter must capture the fatigue damage behavior to allow set up a cycle counting method and an accumulation model. Challenging this statement, a new cycle counting procedure is presented that is completely independent of the damage criterion, and universally works from the simplest uniaxial experiment, to the most complex, variable amplitude and frequency, non-proportional multiaxial fatigue loading. The definition of this new cycle counting concept is surprisingly simple. Despite of its simplicity, the new cycle counting procedure has different advantages when compared to the procedures known to date. Its standalone definition, allows it to be combined with any damage criterion. It does not require periodicity of the loading cycle, and can therefore be straightforwardly used to analyze variable frequency and amplitude, multiaxial fatigue loading.

Random Loading Fatigue Life of Injection Molded Short Carbon Fiber Reinforced Composite and Its Prediction

Random Loading Fatigue Life of Injection Molded Short Carbon Fiber Reinforced Composite and Its Prediction

General Procedure for Formulation of Multiaxial Fatigue Failure Criteria in Frequency Domain

Fatigue life assessment under multiaxial loading conditions needs the use of multiaxial fatigue failure criteria. There are many formulations of such criteria which are usually divided in the groups of critical plane criteria and invariants based criteria. Other classifications refer to the parameter that determines fatigue, and these are stress, strain and energy criteria. Recently, the development of computational techniques for fatigue analysis in the frequency domain have been noticed. Analyzing the literature, it can be noted that these criteria are mainly created by the new formulation of them in the new domain. There is therefore a need to develop a general approach to the problem of formulating criteria in the frequency domain on the basis of existing proposals for the time domain. The paper presents the manner in which the values appearing in the criteria in the frequency domain can be determined. In particular, the process of formulating criteria of multiaxial random fatigue, using the critical plane approach proposed by Macha was presented. During the formation the linearity of such criteria was successfully used. Situations that indicate the correctness of transformations are also presented.

The generalized criterion of multiaxial random fatigue based on conception proposed by prof. Macha

This criterion has been repeatedly verified, analyzed and special cases of this criterion reducing complex stress to equivalent uniaxial were taken into account. Since both normal and shear stress are vectors, we encounter the mathematical problem of adding these vectors, and the question arises how to understand the obtained equivalent stress, because two perpendicular vectors are added with weighting factors. Therefore, in this work it was proposed to adopt a system of complex numbers. Normal stress was defined as the real part and shear stress as imaginary part. As a result, on the basis of the defined complex number and basing on pure bending and pure torsion after transformations, the expression for equivalent stress was identical to the previously proposed criteria defined on the basis of the concept of prof. Macha.

Random fatigue of plane frames via lumped damage mechanics

Fatigue of metal structures has long been recognized as a random process, subject to significant uncertainties. To avoid excessive conservativeness, design and maintenance of such structures require explicit consideration of uncertainties in material properties and loading. This can severely impact computation times, when numerical models are employed in the analysis. In this context, this paper presents a novel application of Lumped Damage Mechanics (LDM) to the random fatigue analysis of plane frames subject to cyclic loading. The method is based on the observation that, in plane frames subject to dynamic loading, fatigue damage concentrates at the joints. Parameters of the proposed lumped damage model are obtained from parameters of linear elastic fracture mechanics. These parameters are calibrated in a cantilever beam problem, for which S-N data is given in building codes. Efficiency of the method is then demonstrated in application to 6 and 25-element plane frames. The proposed method has obvious applications to the reliability-based design and maintenance scheduling of frame structures subject to random wind and wave loadings.

Fatigue Life and Strength Analysis of a Main Shaft-to-Hub Bolted Connection in a Wind Turbine

High-strength bolts are widely used in wind turbines and play a significant role in their operation. In this paper, in order to study the ultimate strength of high-strength bolts in the connection between the hub and main shaft in a 2.5 MW wind turbine with pretension effects, two kinds of finite element models are presented: a solid bolt model and a simplified bolt model. Theoretical calculation was used to compare these models with the results of finite element methods. The ultimate strength analysis results showed that the simplified bolt model was the most efficient and useful in terms of computational time and memory usage. Based on this study, the simplified bolt model was used in the fatigue calculation considering multiple random fatigue loads, and the fatigue life of high-strength bolts was determined by combining the S–N curve of the bolt, based on the Palmgren–Miner Linear damage accumulation hypothesis.

An investigation on residual strength and failure probability prediction for plain weave composite under random fatigue loading

The residual strength and the failure probability of the plain weave carbon-fiber reinforced epoxy composite subjected to random fatigue loading are investigated. According to the constant amplitude residual model and the experimental S-N curves, a new model is proposed, in which both the probability density function of stress peaks and the power spectrum density of stochastic processes are employed. The degradation of residual strength (dSr) in a time increment (dt) is calculated via an integration of the decrease of residual strength due to the stress peaks (dSrp) in the definitional domain of the peak probability density function. A linear damage accumulation of residual strength is used in this time increment. The evolutions of the residual strength with time are determined via a double integral method. The new model’s prediction results are in good agreement with the experiment results and it can give the curves of the variation of fatigue life with failure probability.

Experimental Validation of Fatigue Life of CCGA 624 Package with Initial Contact Pressure of Thermal Gap Pads under Random Vibration Excitation

Thermal gap pads are widely used for effective heat transfer from high-heat-dissipating components to a heat sink. The initial contact pressure of thermal pads is an important parameter for enhancing the heat transfer capability of thermal design during the assembly process of the heat sink. However, this causes stress on the solder joint of the component as a result of the pad’s inherent resistance to deformation. In this study, we investigated the effect of thermal pad on the fatigue life of the solder joint of CCGA 624 package for space usage. A random vibration fatigue test for several specimen assembly sets with various pressurization levels of thermal gap pads was performed, and their fatigue lives were compared with that of the package without the initial pressure of thermal gap pads.

A new frequency domain method for random fatigue life estimation in a wide‐band stationary Gaussian random process

AbstractA new frequency domain method for random fatigue life estimation in a wide‐band stationary Gaussian random process was proposed for application in fatigue analysis. Simulations of the power spectral densities of different types were firstly performed; the simulated results showed that the accuracy and applicability for the current frequency domain methods are not only related to the spectral type but also associated with the types of the analysed materials. Compared with the current methods, the proposed method, in which the rain‐flow amplitude obeys Nakagami distribution, has better universality and could significantly reduce the error for the random fatigue life estimation with simulated and actual spectra. Verified application in cast‐steel fatigue life analysis were performed between random fatigue life and constant amplitude fatigue life. It is shown that the fatigue life analysis under random load cannot be ignored and the proposed new method can serve as a recommended method.

Study of random fatigue behavior of C/SiC composite thin-wall plates

As an alternative method of acoustic experiment, vibration tests of C/SiC thin-wall plates were conducted to study the random fatigue behavior. The vibration specimen was clamped with cantilever boundary and subjected to limited-bandwidth vibration excitation. The strain history and fundamental frequency of the specimens were monitored during the vibration test. It was found that the measured strain value and strain amplitude value accorded with Gauss and Rayleigh distribution, respectively. The fundamental frequency decreased greatly when the vibration specimen failed, which could be recognized as failure criterion for the specimen under random loading. The microscopic fracture morphologies showed that the majority failure mode of fibers in the longitudinal and transverse directions were fiber pull-out and fiber splitting, respectively. The tensile force induced by reversed bending load is the main driving force for damage in specimen.

Failure detection technique under random fatigue loading by machine learning and dual sensing on symmetric structure

To avoid the sudden failure of mechanical structures under repeated loading and to supplement conventional methods of managing life time, we propose a failure detection technique under random fatigue loading using machine learning and dual sensing on a symmetric structure. The state of a shackle, which is used to connect the cargo to the hoist efficiently, under fatigue loading was collected using two strain sensors of a dual system. The strains were preprocessed and labeled as normal or abnormal. Logistic regression machine learning was employed to determine the decision boundary line. Then, we gathered the decision boundary lines of each experiment for determining the time of failure, and we verified every experiment with the most conservative decision boundary line. The results indicate that failure was detected before the crack occurred and the time to notice maintenance could be controlled.

Influence of random fatigue loading non-proportionality on damage

The aim of the present paper is to evaluate the effect of the loading non-proportionality on damage accumulation. Such an analysis is performed at material macro-level by means of numerical simulations concerning random bending-torsion loading. A wide group of random bending and torsion input signals is generated by varying (a) the spectral content and variance of the above signals, and (b) the value of the cross correlation coefficient. The spectral criterion by Carpinteri et al. is applied to compute the expected damage. A linear relationship between damage ratio and cross correlation coefficient is proposed for signals characterised by variance ratio equal to 1.0.

Crystal orientation effect and multi-fidelity optimization of a solid single crystal superalloy turbine blade

Single crystal (SC) turbine blade adopts directional solidification casting, traditional design approach requires the [0 0 1] crystal orientation coincide with the blade stacking axis, and the principal deviation angle is less than 10 deg, the other crystal orientation is random. This design philosophy result in random fatigue life of the formed blade even in the same service environment. Crystal orientation effect on mechanical response of a SC turbine blade is investigated using finite element calculation, then presents a multi-fidelity optimization procedure for crystal orientation optimizations of the blade. A nonlinear turbine blade FEM model with orientation dependent crystal plastic theory and coupled temperature conversion provides the high-fidelity model, the low-fidelity model involves a surrogate model technique. Through the multi-fidelity optimization of crystal orientation design, taking into account the efficiency and accuracy to reduce the maximum resolved shear stress (Rss) at the dangerous position of solid turbine blade and effectively improve the fatigue life of the blades. The results demonstrate that crystal orientation have an appreciable variation on Rss in the dangerous position of solid turbine blade. The influence of temperature and structure must be taken into consideration, especially the maximum Rss has the significant effect on evaluating the fatigue life of turbine blade. The optimization model based on the approximation theory can accurately describe the response between the design variables and optimization targets. The optimization reduces the Rss and deformation by 28% and 17%, respectively. The multi-fidelity optimization strategy can effectively optimizes the crystal orientation of the blade and improves the blade life.