Linear Damage Accumulation Rule Research Articles

An approach for fatigue damage estimation under broadband non-Gaussian random loadings based on the Johnson transformation model

Estimating fatigue damage of marine structures using spectral methods under broadband random loadings is a complex and challenging task. In the presence of non-Gaussian loading, the spectral method typically employs the Hermite polynomial model (HPM) to address the non-Gaussianity. However, the applicability of HPM is limited in certain non-Gaussian cases due to the requirement of monotonicity. This paper adopts the Johnson transformation model (JTM) instead of HPM and integrates it with the non-Gaussian TB method (Ding and Chen, 2015) to overcome the constraints in broadband non-Gaussian fatigue estimation. To verify the performance of the new approach, this paper analyses the transformation accuracy of the two models. Additionally, taking the time-domain fatigue damage obtained by the rainflow counting method and the linear damage accumulation rule as a benchmark, this paper compares the fatigue damage estimates obtained from the spectral methods. The comparative assessment encompasses various spectra, S-N curves, and non-Gaussian characteristics. The results indicate the performance of JTM within the non-Gaussian TB method is comparable to HPM in most cases and even surpasses it in hardening non-Gaussian cases. Given the broader applicability of JTM across ranges of skewness and kurtosis, it emerges a superior option for the non-Gaussian TB method in estimating broadband non-Gaussian fatigue damage. Furthermore, the limitations of the proposed approach are discussed.

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

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

Constitutive modelling and damage prediction of AlSi10Mg alloy manufactured by SLM technology with emphasis on ratcheting in LCF regime

The present work has been aimed at developing an improved cyclic plasticity model in the framework of Ohno-Wang kinematic hardening formulation and evaluating the performance of the model with reference to the critical experimental investigation. LCF test specimens of the AlSi10Mg aluminium alloy have been fabricated through selective laser melting technology. The material shows strain-range dependent variation of modulus of elasticity under symmetric strain-controlled loading. The modulus of elasticity decreases with increasing strain amplitude. Stress–strain responses have been critically examined under multistep uniaxial ratcheting in the LCF regime with incremental mean stress and stress amplitude. Damage calculation considering ratcheting and LCF mechanisms as independent gives unconservative predictions. The linear damage accumulation rule taking the largest contribution of both is bringing much more accurate estimates. The proposed model incorporates effects of mean stress and stress amplitude under uniaxial multistep ratcheting in the LCF regime. All fatigue tests in the LCF regime have been simulated using the proposed improved model. Evolution of strain-range dependent elastic modulus has been incorporated in the formulation of the improved model through the memory history dependent parameter. The ratcheting parameter is newly formulated in this present work to account for the effects of accumulated mean plastic strain on the opening of stress strain hysteresis loops that results in a better prediction of the behaviour of cyclic plastic deformation. The proposed model has been validated by comparing simulated results with experimental observations and reference published simulation results.

Influence of Power Cycling Test Methodology on the Applicability of the Linear Damage Accumulation Rule for the Lifetime Estimation in Power Devices

The lifetime of power semiconductor devices, operating under a given mission profile and subjected to power cycling stress, is conventionally estimated under the assumption of linear damage accumulation rule, that is the application of the Miner's rule. To this purpose, lifetime models must be properly defined allowing to take into account for the relevant parameters of power cycling stress. This work shows how to estimate a cumulative distribution function in the case of an arbitrary temperature swing profile, starting from the statistical distribution at constant power cycling conditions. It is found that the accuracy of the linear damage accumulation rule is related to the experimental methodology adopted for power cycling tests. A detailed experimental activity is carried out on packaged IGBT devices, providing useful guidelines for the definition of lifetime models to be adopted in the Miner's rule.

Fatigue life prediction considering temperature effect for carbon fibre reinforced composites under variable amplitude loading

Fatigue life prediction method based on stress normalization was proposed to reduce the influence of material property dispersion on life for CFRC (carbon fibre reinforced composites). In order to consider the effect of temperature on fatigue damage, a temperature influence factor was introduced into the fatigue limit equation and the life prediction method under variable amplitude loading at high temperature. Combined with the rainflow cycle counting and Miner linear damage accumulation rule, the proposed fatigue life prediction method was verified by the experimental results of composite multidirectional laminates under constant amplitude and variable amplitude loadings at various temperatures, and the prediction errors are within a factor of 5.

Comparison of some selected time-domain fatigue failure criteria dedicated for multi input random non-proportional loading conditions in industrial components

This paper presents time-domain procedure to evaluate High-Cycle Fatigue (HCF) life of industrial components with complicated geometries and subjected to multi-input random loading conditions. To this end, the authors discuss some well-known equivalent stress criteria which can consider the orientation of critical plane changes with the time in non-proportional loading conditions to estimate the time history of equivalent stress. This task is successfully accomplished by knowing time histories of local stress tensor components in a critical area of the part that is prone to failure. Next, two different categories were used to predict fatigue life of component: 1- Linear Damage Accumulation (LDA) rule by employing Rain-flow cycle counting and 2- probabilistic approach by utilizing level crossing counting method. To apply these methodologies and awareness of their challenges, a case study was performed on the automotive steering knuckle. Finally, the predicted lives were compared to experimental results, and the accuracies of different fatigue life assessment techniques were reported. The obtained results show that combination of Rain-flow cycle counting with the Liu-Zenner criterion and especially, with the Energy-based instant fatigue damage tracing proposed by Shariyat lead to the highest accuracies. However, using the probabilistic approach, we will get the response in a much shorter time compared to another category. Therefore, the choice which method to use also depends on the parameters of the research situation, and the interaction of the two factors of prediction accuracy and prediction time in the industry.

Study on Creep-Fatigue Mechanical Behavior and Life Prediction of Ti2AlNb-Based Alloy.

Low-cycle fatigue, creep and creep-fatigue tests of Ti2AlNb-based alloy were carried out at 550 °C. Compared with low-cycle fatigue, a creep-fatigue hysteresis loop has larger area and smaller average stress. The introduction of creep damage will greatly reduce the cycle life, and change the fatigue crack initiation point and failure mechanism. Based on the linear damage accumulation rule, the fatigue damage and creep damage were described by the life fraction method and the time fraction method, respectively, and the creep-fatigue life of the Ti2AlNb-based alloy is predicted within an error band of ±2 times.

Crack initiation and evolution in glass/epoxy laminates under two-stage block loadings

In this work, the transverse crack initiation, propagation, and the crack density evolution in cross-ply laminates are analysed under two-stage block loadings. A theoretical formulation for the cracking probability under variable amplitude blocks is obtained based on the linear damage accumulation rule, often adopted in crack density prediction models from the literature. The comparison between the experimental results and the predictions for the cracking probability and the crack density evolution validate, from the phenomenological point of view, the adequacy of the linear damage accumulation rule for crack initiation under block loadings. Investigations of the damage evolution at the micro-scale are also presented, providing a mechanistic support to this approach.

Evaluation of uncoupled ductile damage models for fracture prediction in incremental sheet metal forming

The formability limit in a typical incremental sheet forming (ISF) far exceeds the conventional estimate assuming necking failure. The material subjected to incremental forming fails by fracture. Although damage models have been used to correlate the failure in incremental forming, a detailed understanding of the failure mechanism spanning strain paths is not clear yet. In this work, three parts with varied shapes (hybrid five lobe, pyramid and variable wall angle conical frustum (VWACF)) were developed using ISF to cover a range of possible strain paths. The failure is predicted using established uncoupled phenomenological damage models. Damage models were calibrated for AA1050 aluminium sheet by the method of inverse approach using carefully designed tensile tests and FE simulations. Three different damage models were implemented as user subroutine in commercial software code, ABAQUS/Explicit and the results predicted were compared. The linear damage accumulation used to develop fracture locus under monotonic loading could not predict the failure limit in a benchmark single groove test. Therefore a non linear damage accumulation rule (NLDA) is implemented to simulate ISF. The parameters of the NLDA were calibrated from the single groove test. The fracture forming limits during ISF was established using circular grid analysis near the failure zone of the formed part. A good agreement can be found between the experimental observations and numerical predictions for fracture location and part height. It was observed that the overall predictive capability of Hosford Coulomb (HC) damage model is better among three damage models investigated for the given range of loading conditions. However all the three models under-predicted the experimental fracture strain measured in ISF. The possible explanation for the discrepancy is explored.

Fatigue life prediction of needled ceramic matrix composite under variable amplitude loading

The fatigue loading parameter-life (S-N) curve of the needled composite was proposed by constant amplitude fatigue tests first, and then the variable amplitude fatigue tests of needled C/SiC ceramic matrix composite were completed. Combined with the rainflow counting method, the Goodman line, the constant amplitude S-N curve and the linear damage accumulation rule, the fatigue life of the needled C/SiC composite was predicted under tensile variable amplitude block loading. According to the ratio of the width containing needled fiber bundle to the specimen width, the influence of needled fiber bundle on the fatigue life dispersion was quantitatively analyzed for the specimens with different fatigue lives.

A PFA methodology to investigate UD composites in fatigue comprising a KTF-based model for matrix damage and stochastic fiber failure prediction

A physics-based, multiscale, progressive fatigue damage analysis methodology for continuous fiber-reinforced polymer composites was further developed and applied to the problem of fatigue damage prediction in open hole tension (OHT) coupons comprised of multidirectional laminates undergoing tension–tension loading. Based off lamina level calibration data, cumulative damage analysis of matrix and fiber constituents under cyclic loading condition was implemented with the objectives to: (i) predict the onset and the progression of subcritical matrix failures as well as the ultimate failure due to fiber fracture, and (ii) observe the effects of damage mode interactions on the progressive failure process. A kinetic theory of fracture (KTF) based durability prediction methodology was utilized to keep track of the matrix damage transpiring in the intra- and inter-laminar layers of the laminate. Tensile strengths were randomly assigned to the fibers using two-parameter Weibull statistics, while the maximum stress theory in tandem with the linear damage accumulation rule was applied to capture the tensile rupture of the reinforcements. Progressive fatigue damage prediction of OHT coupons consisting of the unidirectional composite IM7/977-3 and layup schedules of [0/45/90/−45]2S and [60/0/−60]3S were carried out and benchmarked against available experimental data. It was observed that the KTF-based fatigue model captured the damage state at individual layers, overall loss of mechanical performance, and stochastic nature of the ultimate failure well. The effects of interactions among the damage modes, namely matrix cracking, delamination, and fiber rupture were also investigated and it was recognized that such interactions are a critical feature of the progressive failure process in composite structures.

SHEAR BEHAVIOR AND MECHANICAL MODEL FOR SELF-DRILLING SCREW CONNECTIONS BETWEEN THIN STEEL SHEETS

Self-drilling screw connections between thin steel sheets were tested under shearing forces, and the impacts of the sheet thickness and the screw diameter on the shear behavior of the connections were investigated. It has been indicated that: the obtained three typical failure modes including bearing failure of steel sheets, pull-out failure and shear failure of screw, depend on the ratio between the screw diameter and the thickness of the sheet adjacent to the screw head. The shear resistance of each connection is positively correlated with the sheet thickness and the screw diameter, and the initial stiffness and the ductility of the connections are also related to these two parameters. Elaborated finite element (FE) models for the self-drilling screw connections were developed by introducing the Johnson-Cook damage constitutive model and the linear damage accumulation rule, and by considering the geometric characteristics of screw threads. The developed FE models were validated against the obtained test results, which provide accurate simulations of shear behavior of self-drilling screw connections. By using the calculation formulas for the shear resistance of self-drilling screw connections in the Chinese code GB 50018−2002, a new three-stage simplified mechanical model was proposed herein by considering the impacts of the compressive stiffness of steel sheets and of the shear stiffness of screw, as well as of the multi-screws effect, which has been further verified for accurately predicting the shear force versus deformation relationships of self-drilling screw connections.

Influence of Load Interaction between Creep and TMF on the Life of Single Crystal Nickel-based Superalloy

Experimental investigation on the influence of load interaction on the life of Single Crystal Nickel-based Superalloy is conducted. Three kinds of load spectrums considering single and coupled failure mode are designed. Life tests are carried out under creep, thermo-mechanical fatigue (TMF), and creep-TMF interaction loading. The test results show that test lives, under the creep-TMF interaction loading, are lower than the life predictions given by the linear damage accumulation (LDA) rule, indicating that the load coupling can accelerate the damage evolution process. The microstructure of fractured specimens shows that under the creep-TMF interaction loading, rafting cause more dislocations to accumulate in the at γ/γ′ phase boundary, which could be the evidence of life decrease.

Multiaxial fatigue tests under variable strain paths and asynchronous loading and assessment of fatigue life using critical plane models

In the present work, axial-torsion fatigue tests were performed under two loading categories, (i) variable strain paths sequential loading and (ii) asynchronous (different loading frequencies) conditions on low C-Mn steel. Variable strain paths tests brought out that saturated cyclic stress-strain behaviour under a given strain path, is insignificantly affected by loading history. However, transient material behaviour is history dependent.Three different critical plane models, Fatemi-Socie (FS), Smith-Watson-Topper (SWT) and Arora et al. (bi-axial SWT) along with linear damage accumulation rule were used to predict fatigue life. FS and Arora et al. model resulted in accurate assessments under both loading categories.

Fatigue performance of an innovative shallow-buried modular bridge expansion joint

Bridge expansion joint can accommodate the deformation under the effects of vehicle load and temperature. Fatigue damage readily occurs because it is directly subjected to repeated load. In this paper, fatigue and static loading tests were conducted on modular bridge expansion joint (MBEJ). This is an innovative type of shallow-buried modular bridge expansion joint, and the anchoring depth is reduced by 40%-50% compared with traditional ones. The reduced overall height can well adapt to the slide shutter rapid construction method in practical engineering. A loading device was designed to simulate vertical and horizontal load. The load-deflection relationship after fatigue loading were discussed. The fatigue crack types, crack initiation locations, failure criteria, and fatigue failure modes of MBEJs were also studied. Following that, a finite element model was established to calculate the internal force of welded connections. Structural analysis on MBEJs was used to calculate the stress range within center beam and support bars under the test conditions. A theoretical fatigue performance assessment method on MBEJs was introduced, which is based on the nominal stress method and a linear Miner damage accumulation rule. The theoretical prediction agreed well with the experimental observations.

Improving accuracy of dual-axial resonance fatigue testing for wind turbine blades by using predicted equivalent test loads caused by combined loading

The dual-axial resonance fatigue test provides for accurate and efficient testing of wind turbine blades through optimizations. However, the existing dual-axial test optimization does not yield an accurate test design because it compares the test loads that correspond to the mode shapes with the target loads that are aligned to the local chord axes. Therefore, this paper proposes equivalent applied loads to predict the flatwise and edgewise test loads by transferring the mode shapes to the local chord axes and using the linear damage accumulation rule. The application of the equivalent applied loads helps the dual-axial test optimization yield satisfactory test schemes without much additional computing time.

Effects of Damaged Fiber Ropes on the Performance of a Hybrid Taut-Wire Mooring System

Abstract In this study, effects of damage levels of fiber ropes on the performance of a hybrid taut-wire mooring system are investigated. The analysis is performed using a numerical floating production storage and offloading (FPSO) model with a hybrid mooring system installed in 3000 m of water depth. An in-depth study was conducted using the numerical model, the dynamic stiffness equation of damaged fiber ropes, the time-domain dynamic theory, the rainflow cycle counting method, and the linear damage accumulation rule of Palmgren-Miner. Results indicate that, in a mooring line with an increasing damage level, the maximum tension decreases, while the offset of the FPSO increases. Particularly, when a windward mooring line failure occurs, in addition to the significant increase in the offset of the FPSO, the maximum tension, tension range, and annual fatigue damage levels of the remaining lines adjacent to the failed also increase significantly. The present work can be of great benefit to the evaluation of the offset of the floating platform, the tension response, and the service life of the hybrid mooring systems.

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.

Lifetime extension through Tj equalisation by use of intelligent gate driver with multi-chip power module

Typical high-current power modules used in traction and wind generation contain several dies in parallel. Non-ideal geometries and electrical parameter variations cause an unequal aging of each die which limits the effectiveness of using parallel devices. This paper presents an intelligent power module with a TSEP-based junction temperature measurement and internal temperature equalisation for extending its operational lifetime. As the magnitude and number of junction temperature cycles strongly dictate the power module lifetime, this paper focuses on the quantification of the lifetime gain via the application of common automotive drive cycles. Thus, a general thermal model is first deduced from the experimental results. The lifetime is then estimated using a stress-counting rainflow algorithm, a pre-determined damage law and a linear damage accumulation rule. Finally, in order to illustrate the lifetime extension, 160 drive cycles, including the legislatives drive cycles, are simulated. A lifetime gain of up to two times can be expected with the temperature equalisation method. Therefore, the initial investment on the developed intelligent power module is justified by the benefit of the large gain in lifetime and of the end-of life indication functions.

Fatigue life assessment of welded joints made of the stainless steel X6CrNiNb18‐10 for thermomechanical and variable amplitude loading

AbstractThe aim of the presented work is to develop improved concepts for the prediction of fatigue lifetime under variable amplitude loading including plastic deformation and thermomechanical fatigue of welded joints made of the austenitic stainless steel 1.4550. Local strain amplitudes are located in the regime of low cycle fatigue, which is dominated by short crack growth. This can best be described by nonlinear fracture mechanics. To develop a fracture mechanics based lifetime model, different experiment types are carried out to estimate the influence of loading history, thermal cycling, and mean stresses. For the evaluation, different estimation concepts based on Palmgren‐Miner's classic linear damage accumulation rule are used: solely calculated by strain ranges, damage parameter established by Smith, Watson and Topper, and a damage parameter based on the cyclic effective J‐integral. The differences in the concepts are highlighted and used for further considerations on how to improve the lifetime prediction models.