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Nowadays, the estimation of fatigue life under multiaxial random loading is still an extremely complex task. In this paper, a comprehensive review of the multiaxial random fatigue criteria available in the literature is presented. Such a review is mainly devoted to stress-based criteria for the evaluation of fatigue life in high-cycle regime. Time...
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... Further, on the basis of PSD-based characterizations a variety of analytical and empirical models have been introduced which estimate peak amplitude distributions for narrowband processes [1], expected peak amplitudes [2,3], and rainflow-counting collectives for broadband processes [4,5]. Also a series of multiaxial fatigue criteria have been adjusted to run on PSD-based statistical characterizations [6,7,8,9]. These methodologies provide the foundation for a statistical-based approach to a fatigue assessment -closely linking statistical characterizations with structural dynamics, providing significantly faster and in principle more robust results. ...
In various technical applications, assessing the impact of non-Gaussian processes on responses of dynamic systems is crucial. While simulating time-domain realizations offers an efficient solution for linear dynamic systems, this method proves time-consuming for finite element (FE) models, which may contain thousands to millions of degrees-of-freedom (DOF). Given the central role of kurtosis in describing non-Gaussianity - owing to its concise, parametric-free and easily interpretable nature - this paper introduces a highly efficient approach for deriving response kurtosis and other related statistical descriptions. This approach makes use of the modal solution of dynamic systems, which allows to reduce DOFs and responses analysis to a minimum number in the modal domain. This computational advantage enables fast assessments of non-Gaussian effects for entire FE models. Our approach is illustrated using a simple FE model that has found regular use in the field of random vibration fatigue.
... The equivalent uniaxial stress approach converts multiaxial stress components into an equivalent uniaxial stress parameter [25], typically based on static strength criteria such as the Tresca or von-Mises criteria [26]. Although this method is straightforward, it cannot capture damage caused by non-proportional loading and may result in unconservative fatigue life estimates. ...
... (24) In the equation, is the time period of which the excitation signal is collected. The fatigue life can be estimated by the following equation: (25) In Eq. (24) and (25), is the time period of which the excitation signal is collected. ...
... Remarkably, our investigation indicates that within the specific case under examination, slight variations in the non-proportional correction factor Φ, derived from three distinct data-driven methods, lead to minor discrepancies in the PDF distribution of . Utilizing the PDF distribution, we estimated fatigue life through Eq. (24)- (25), as shown in Fig. 21. It is essential to highlight that the slight discrepancies in Φ values across the three different datadriven models result in only marginal variations in the estimated final fatigue life. ...
... Structural components usually face different cyclic or varying load conditions over their service life. As highlighted in a literature review from 2017 [1], while specimens typically undergo constant amplitude (CA) loading conditions during fatigue testing, practical applications introduce greater complexity, leading to load spectra characterized by patterns like variable amplitude (VA) and stress/strain features referred to as gradients. In the 2000s, several studies explored fatigue damage accumulation [2][3][4][5], using the Palmgren-Miner linear cumulative damage rule (Miner's rule) for its simplicity. ...
The objective of the current work is to study the mean stress effect of variable amplitude (VA) loading on the fatigue strength of load-carrying fillet-welded joints (LCFWJs). Experimental fatigue tests were carried out on LCFWJs made of S700 high-strength steel, considering constant amplitude (CA) and VA loads. In the case of VA loads, a Gaussian load spectrum shape with both constant minimum and maximum stress levels was considered to study varying mean stress conditions. Numerical analyses were conducted to determine the effective stresses at the weld root. The fatigue behavior of LCFWJs was evaluated using the 4R method, which takes into account the local stress ratio (R local, i), material ultimate strength (R m), residual stress (σ res), and weld toe radius (r). Lower fatigue strength was found for the VA tests with the constant maximum stress tests compared to the CA tests when using damage parameter of D = 1.00, while the VA tests with the constant minimum stress tests showed higher fatigue performance. Nonetheless, employing damage parameters of D = 0.2 and D = 0.5 for variable amplitude loads with and without fluctuating mean stress conditions, respectively, provided conservative assessments compared to the design standards. By employing the 4R method, the precision of the assessments could be significantly improved, and the CA and VA fatigue test results fit into a single scatter band with scatter index of T σ = 1.06 with damage sum of D = 1.00.
... Due to geometric irregularities of the wheel structure, multiaxial stress-strain states are found in most area of the automotive wheel in service loads [44]. Comparing with uniaxial fatigue models, multiaxial fatigue models are more suitable for real complex loading conditions [45]. Some studies have considered multiaxial fatigue damage criteria in automotive wheel fatigue prediction, but these criteria show discrepancy in different loading cases [46][47][48]. ...
A R T I C L E I N F O Keywords: Biaxial wheel fatigue test Tire-rim interface forces Reduced order model Proper orthogonal decomposition Radial basis function A B S T R A C T This paper presents a rapid method for predicting the biaxial fatigue life of automotive wheels using a combination of proper orthogonal decomposition and radial basis function algorithm. Currently, numerical simulations of biaxial fatigue tests are being developed to evaluate wheel performance. However, these simulations are computationally expensive due to the need to simulate multiple discrete loading cases within a given biaxial spectrum. To address this issue, we propose a novel approach that utilizes proper orthogonal decomposition and radial basis function algorithm to improve computational efficiency. By leveraging high-fidelity simulation results from a small number of loading cases, a reduced order model is constructed to accurately predict the tire-rim interface force fields required for wheel strength calculations. The reduced order model significantly reduces the computational time by 65.4% for simulating all loading cases, while maintaining a maximum predicted error of less than 2% compared to the high-fidelity model. Subsequently, the predicted interface forces are mapped onto the rim surface for strength calculation, and the wheel fatigue life is determined using the Brown-Miller multiaxial damage criterion. Comparative analysis with experimental results demonstrates the desirable accuracy of our method in simulating the stress-strain history, crack initiation position, and minimum fatigue life of the wheel. Overall, the proposed method offers a powerful tool for the rapid fatigue analysis of spectrum-loaded wheels, providing an efficient and accurate means of predicting biaxial fatigue life.
... Cyclic loads and fatigue of mechanical components can be found in various industries, such as plant engineering, automotive and railway engineering. [1] Compared to the constant amplitude load conditions usually applied in component testing, real engineering applications are often more complex and there are usually several situations in which variable amplitude (VA) load conditions can be observed [2]. These stress ranges might also include individual high peak loads that have a notably higher value than traditional in-service cyclic loads [1]. ...
Different load spectra and individual load peaks might substantially relax high residual stresses as well as induce compressive residual stresses in welded components and, consequently, affect the fatigue performance of these joints. Consideration of peak loads and resulting relaxation of residual stresses in fatigue analyses can substantially enhance the accuracy of life prediction. The aim of the current study is to experimentally investigate the fatigue strength of welded joints subjected to different levels of overloads and variable amplitude (VA) loads and to develop local fatigue assessment method to account for the relaxation of residual stresses via a mean stress correction using the 4R method. The 4R method applies a local stress ratio for the mean stress correction considering material strength, residual stresses, applied stress ratio of external loading and local weld geometry in elastic–plastic material behaviour. Fatigue tests were carried out on fillet-welded longitudinal gusset joints made of S700 high-strength steels under applied stress ratio R = 0–0.1. A mild strength steel (S355) and ultra-high-strength steel (S1100) were selected as reference steel grades for the fatigue testing to study the material strength effects. Numerical analyses were conducted to evaluate the fatigue notch factors using the effective notch stress concept with the reference radius of r ref = 1.0 mm and theory of critical distance (TCD) using the point method. The experimental results indicated that a substantial improvement in the fatigue strength capacity can be claimed in the joints subjected to tensile overloads, particularly in the studied S700 and S1100 steels. The higher-level overload (0.8 f y ), corresponding to the nominal cross-sectional area, improved the mean fatigue strength of the welded joints manufactured of high-strength S700 steel by approximately 60%, while the lower overload (0.6 f y ) improved the mean fatigue strength by 20%. In addition, a use of equivalent nominal stresses for the joints subjected to VA loads resulted in conservative assessments when employing S–N curves obtained for the CA loading. The 4R method, via the local mean stress correction for individual cycles, provided higher accuracy for the fatigue assessments.
... In many cases, these loads can also be considered as non-proportional, causing different principal stress axis or a rotation of the principal stress directions, resulting in a challenging fatigue calculation. Relevant examples of multiaxial loads can usually be found at components in aerospace, railway, naval or automotive industry [1]. An emerging product that also falls into this category is the eBike drive unit (DU), which is affected by highly variable user and situation-dependent load spectra coupled with internal loads of the engine [2]. ...
... Typically, the application of these two categories depends on the variability of the loading situation, where random loads are usually considered in a statistical and spectral calculation in the frequency domain. Deterministic loads with constant or variable amplitude are calculated in the time domain [1]. Although frequency domain analysis has been established for uniaxial variable loads, the application of a frequency-based method for multiaxial non-proportional loads is still a point of current research. ...
In this paper, a method is developed to consider multiaxial load spectra and their variation in a computationally efficient local fatigue calculation procedure. This method is based on an FE data-based surrogate model and is intended to support the simulation-based product design process. To demonstrate their application and necessity, a case study on the design of eBike drive units is presented. For this purpose, the general requirements for the design of eBike drive units as well as the fundamentals of multiaxial fatigue analysis and surrogate modeling are outlined. In addition, a validation process of the surrogate model and its use for fatigue calculation is presented and discussed.
... Carpinteri et al. (2016) evolved the frequency-domain formula for critical-plane criterion in order to achieve more accuracy in terms of fatigue life estimation for smooth metallic structural components under multiaxial random loading. A review of multiaxial fatigue criteria for random variable amplitude loads is shown in Carpinteri, Spagnoli, and Vantadori (2017) where time and frequency domain approaches are tested. Also, some discussions about the recent developments in multi-axial spectral methods are done in Benasciutti, Sherratt, and Cristofori (2016). ...
The aim of this paper is to determine the fatigue damage of structures subject to random vibrations generated by Qualmark chamber. In real life, structures are generally subjected to complex multiaxial random load. To determine their fatigue life, many criteria have been elaborated, mostly in time domain. To minimize the computing time, the fatigue damage analysis should be done in the frequency domain. Tests that lead to the failure of the structures are commonly used to determine their weakness. But these tests are sometimes costly. To this end, in this paper an original new numerical model of the Qualmark chamber that leads us to determine the generated excitation at each point of its table is proposed. This model is validated using experimental measurement where adjustment process is proposed. Then, we develop a numerical strategy that leads to determine the multiaxial fatigue damage of structure under random vibrations using Matsubara’s criterion developed in the frequency domain of structures tested with Qualmark chamber. A numerical application of a PCB tested with Qualmark chamber is presented at the end of this paper where fatigue damage is determined at each point using the developed strategy. Boundaries condition of the PCB is then determined using the proposed Qualmark table model.
... Due to geometric irregularities of the wheel structure, multiaxial stress-strain states are found in most area of the automotive wheel in service loads [44]. Comparing with uniaxial fatigue models, multiaxial fatigue models are more suitable for real complex loading conditions [45]. Some studies have considered multiaxial fatigue damage criteria in automotive wheel fatigue prediction, but these criteria show discrepancy in different loading cases [46][47][48]. ...
This paper presents a rapid method for predicting the biaxial fatigue life of automotive wheels using a combination of proper orthogonal decomposition and radial basis function algorithm. Currently, numerical simulations of biaxial fatigue tests are being developed to evaluate wheel performance. However, these simulations are computationally expensive due to the need to simulate multiple discrete loading cases within a given biaxial spectrum. To address this issue, we propose a novel approach that utilizes proper orthogonal decomposition and radial basis function algorithm to improve computational efficiency. By leveraging high-fidelity simulation results from a small number of loading cases, a reduced order model is constructed to accurately predict the tire-rim interface force fields required for wheel strength calculations. The reduced order model significantly reduces the computational time by 65.4% for simulating all loading cases, while maintaining a maximum predicted error of less than 2% compared to the high-fidelity model. Subsequently, the predicted interface forces are mapped onto the rim surface for strength calculation, and the wheel fatigue life is determined using the Brown-Miller multiaxial damage criterion. Comparative analysis with experimental results demonstrates the desirable accuracy of our method in simulating the stress-strain history, crack initiation position, and minimum fatigue life of the wheel. Overall, the proposed method offers a powerful tool for the rapid fatigue analysis of spectrum-loaded wheels, providing an efficient and accurate means of predicting biaxial fatigue life.
... Multiaxial fatigue damage and life assessment is still a challenging and important subject, both theoretically and experimentally, even after decades of intensive research [1][2][3][4]. More than a decade ago, the first two authors of this paper had developed the path-dependent maximum range (PDMR) multiaxial fatigue damage and life assessment method [5][6][7][8], which consists of both multiaxial fatigue cycle counting and the identification of damage parameters for a given cycle or half cycle, specifically for welded structures, which often have clearly predefined critical planes or cracking surfaces. ...
... It should be noted that several papers by Stefanov published in the 80s and 90s provided similar concepts on incremental path length and its moments [50][51][52][53]. With these ideas, it is possible to integrate damage continuously as the loading is applied, therefore, cycle identification and cycle counting is not required, especially for multiaxial fatigue, in which any multiaxial cycle counting is believed to be ill-defined for non-proportional loading [4,14,47,48]. Such incremental fatigue damage (IFD) models have been explored for a long time [4], for example, Wetzel and Topper proposed the first uniaxial model in 1970 [54]. ...
... With these ideas, it is possible to integrate damage continuously as the loading is applied, therefore, cycle identification and cycle counting is not required, especially for multiaxial fatigue, in which any multiaxial cycle counting is believed to be ill-defined for non-proportional loading [4,14,47,48]. Such incremental fatigue damage (IFD) models have been explored for a long time [4], for example, Wetzel and Topper proposed the first uniaxial model in 1970 [54]. Chu [55] outlined the generalization of Wetzel's model to multiaxial non-proportional loadings, however, indirectly requiring cycle detection, thus limiting its advantages [4]. ...
... Stress life fatigue using High Cycle Fatigue (HCF) parameters is generally the standard approach in the research literature for spectral fatigue (e.g., [3,4,5]); in particular, R XX , S XX , G XX Auto-correlation function, two-sided PSD, and onesided PSD associated with input time signal X(t). ...
Frequency-domain fatigue damage prediction based on spectral moments provides a framework in which anticipated life calculated over an entire structure subject to vibratory random loading (typically in the high cycle fatigue regime) can be rapidly obtained. However, the basis of the methods of spectral fatigue assume stationary, Gaussian, zero-mean, narrow-band (single dominant frequency) input, without the presence of overloads (stresses that exceed the initial yield stress), a significant set of restrictions. Given the importance of overloads in determining fatigue lifeI, we propose a novel “bilinear” formulation of spectral fatigue equations, that separates damage due to small and large strain amplitudes, is developed that matches or significantly outperforms existing stress-based HCF approaches (including for multiaxial elastoplastic loading) while avoiding non-conservative predictions suffered by an existing strain-based implicit formulation when the power spectral density include excursions into plastic loading due to the presence of overloads. Comparisons with synthetic and experimental data sets demonstrate the efficacy of the approach in a variety of different loading conditions.
