Load Spectrum Research Articles

Fatigue life prediction of metal materials under random loads based on load spectrum extrapolation

The impact of random loading on the fatigue life of mechanical components contains numerous uncertainties. This study aims to enhance the precision of life prediction by developing mean and amplitude distribution models based on the road load spectrum and extrapolating the operational load beyond the threshold value in the time domain. Additionally, it considers the influence of high cycle fatigue (HCF) and low cycle fatigue (LCF) loads on the initiation life of metal cracks. To address this, a load correction factor is introduced, and critical stresses for high and low cycle loads are proposed. Furthermore, a two-dimensional programmed load spectrum is prepared, taking into account the mean and amplitude. The accuracy and rationality of the fatigue life model are validated through examples using 45# steel and 316L, while experiments on engine support are conducted to confirm the effectiveness and accuracy of the over-threshold extrapolation life prediction method under random loading.

Experimental investigation of bending fatigue behaviors for T-shaped welded joint

A fatigue test was conducted on a T-shaped welded joint under three-point bending conditions. Prior to the test, the geometry of the weld toe on both sides of the specimen was observed and measured. The locations of Fiber Bragg Gratings (FBG) strain gauges were determined based on the weld toe’s geometric features. During the experiment, a 2-level load spectrum block of cyclic loading was applied, resulting in distinct beach marks on the fatigue fracture surface. The stress-time history of the weld toe’s geometric features was monitored. After the test, the fatigue fracture was observed and measured, the influence of the crack path on the crack propagation rate was analyzed, and the influence of the crack propagation pattern on the stress evolution in the nearby area was studied. The experimental results show that the multiple cracks initiation positions have strong relationship with the characteristic points of weld toe morphology. Based on the Linear Elastic Fracture Mechanics (LEFM) theory and the concept of varying remote stress, four crack propagation simulation patterns were constructed and carried out. The results show that the varying remote stress has an more important influence on life prediction of welded joints, while the threshold mainly affect the life prediction of the early stage.

Characterization of Magnetorheological Impact Foams in Compression.

This study focuses on the development and compressive characteristics of magnetorheological elastomeric foam (MREF) as an adaptive cushioning material designed to protect payloads from a broader spectrum of impact loads. The MREF exhibits softness and flexibility under light compressive loads and low strains, yet it becomes rigid in response to higher impact loads and elevated strains. The synthesis of MREF involved suspending micron-sized carbonyl Fe particles in an uncured silicone elastomeric foam. A catalyzed addition crosslinking reaction, facilitated by platinum compounds, was employed to create the rapidly setting silicone foam at room temperature, simplifying the synthesis process. Isotropic MREF samples with varying Fe particle volume fractions (0%, 2.5%, 5%, 7.5%, and 10%) were prepared to assess the effect of particle concentrations. Quasi-static and dynamic compressive stress tests on the MREF samples placed between two multipole flexible strip magnets were conducted using an Instron servo-hydraulic test machine. The tests provided measurements of magnetic field-sensitive compressive properties, including compression stress, energy absorption capability, complex modulus, and equivalent viscous damping. Furthermore, the experimental investigation also explored the influence of magnet placement directions (0° and 90°) on the compressive properties of the MREFs.

Experimental investigation on the fatigue life and damage mechanism of plain weave composites under biaxial tension–torsion combined fatigue loading

In this paper, the fatigue life and damage mechanism of plain weave composites under biaxial tension–torsion combined fatigue loading (TTF) are experimentally investigated. A biaxial TTF loading spectrum is designed to consider different fatigue frequencies and amplitudes, and an automated multi-module loading method with synchronized acquisition of the digital image correlation (DIC) and the testing machine is proposed. A comprehensive analysis of the experimental results, including fatigue lives, strain distribution, temperature variation, stiffness degradation, and typical damage morphologies at different fatigue cycles, has been conducted by utilizing DIC, infrared thermography (IRT) and computed tomography (CT). It is observed that the superimposed torsional fatigue load results in a rapid reduction in fatigue lives of plain weave composites, accompanied by more significant residual strain, energy dissipation, temperature rise and stiffness degradation. Particularly, the superimposed torsional fatigue loads mainly promote matrix cracking and debonding around the fiber/matrix interfaces, which then accelerates the damage initiations and accumulations of fiber yarns, ultimately leading to a rapid reduction in TTF fatigue lives. This study can provide valuable references for the design and safe application of plain weave composites under TTF loading.

An approach to interpreting metastable austenitic material sensors for fatigue analysis

The transformation of metastable austenite to martensite under mechanical loading can be harnessed to create a material sensor which records a measure of the load history without the need for electrical energy and can be read out at arbitrary intervals via eddy current probing, thus leading to an ultra-low-power sensing solution. This paper presents possibilities of processing this load amplitude-dependent evolution of martensite content loading for component fatigue analysis. The general method is based on using a theoretical material model typically used in finite element analyses which includes hardening plasticity and phase transformation to precompute tables of stress amplitude or cumulative damage corresponding to different sensor readings which can be stored on a low power processing system onboard the component for energy-efficient lookup. At nominal single amplitude loading, the sensor can be used as a load cycle counter for known loads or as an overload detection device upon divergent martensite content rise. Interpretation of block program loading is less practical due to resolution issues. Under random loading, sequence effects get averaged out; interpretation is easiest with narrow load spectra, but information can be gained from very wide spectra as well. Multiple sensors at different locations can aid interpretation. Uncertainty due to necessary assumptions and untreated influences of temperature and loading rate is discussed.

Fatigue Analysis of Composite Bolted Joints under Random and Constant Amplitude Fatigue Loadings.

This paper attempts to analyze the random fatigue life and failure modes of joints using two calculation methods. Three kinds of tests were carried out, which were the static test, constant amplitude fatigue test and the random fatigue test, and four kinds of joints were designed. After the static test, the joint was subjected to a constant amplitude fatigue test by selecting different percentages of load according to the static strength. In order to predict the random fatigue life more precisely, two calculation methods were carried out, which were the linear cumulative damage method and the equivalent loading finite element method. Based on the linear cumulative damage hypothesis, the fatigue life of the joint was established as a function of the load amplitude, and then, the random life prediction was calculated by the amplitude distribution of the random loading. Another method was the equivalent loading method, which was to obtain the equivalent constant amplitude fatigue loading of the random loading spectrum. The finite element model was established based on the stiffness and strength degradation rule. The equivalent random life and fatigue failure modes of the joint were modeled. The two life prediction methods show good agreement with the fatigue experimental result, and all prediction results were included in a scatter band of the factor of 2.

Establishment and Analysis of Load Spectrum for Bogie Frame of High-Speed Train at 400 km/h Speed Level

The bogie frame, as one of the most critical load-bearing structures of the Electric Multiple Unit (EMU), is responsible for bearing and transmitting various loads from the car body, wheelsets, and its own installation components. With the increasing operating speed of high-speed EMUs, especially when the design and operational speeds exceed 400 km/h, the applicability of current international standards is uncertain. The load spectrum serves as the foundation for structural reliability design and fatigue evaluation. In this paper, the measured loads of the bogie frame of a CR400AF high-speed train on the Beijing–Shanghai high-speed railway are obtained, and the time-domain characteristic of the measured loads is analyzed under different operating conditions. Then, through the Weibull distribution of three parameters, the Weibull parameters at the 450 km/h speed level are fitted, and the maximum load and cumulative frequency under the speed level are derived. Finally, the load spectrum of the bogie frame at the 450 km/h speed level is established, which provides a more realistic load condition for accurately evaluating the fatigue strength of bogie frames at higher speed levels.

Large-eddy simulation study on wave-wake interactions past an offshore wind turbine

Large-eddy simulations (LES) of the flow past an offshore wind turbine under different underlying wave fields have been performed. A one-way coupling between the air and water flows has been realized through a hybrid immersed-boundary/level-set method. The velocity in the water domain is forced with the potential flow solution, while the response of the atmospheric boundary layer to the changes in the sea-surface height (tracked by the level-set equation) is simulated with a LES approach coupled to a rotating actuator disk model to mimic the effect of the wind turbine. A parametric study has been performed varying the wave period and wavelength while keeping the amplitude constant, resulting in different wave age parameters ranging from young developing waves to old swell waves. The wave field has a significant effect on the lower region of the atmospheric boundary layer, slowing down the wind field in proximity of the air-water interface and considerably increasing the local turbulence kinetic energy (TKE). The interaction between the wave evolution and the TKE results in a non-monotonic trend of the wake recovery rate with the wave age, when compared to the baseline value in the wake of a turbine over a flat wall. Both developed waves results in a lower recovery rate, whereas intermediate-age waves present a larger value than the baseline. The increased TKE in the lower layers of the rotor revolution induces an increased fluctuating component in the power production and blade loads. Nevertheless, for the parameters considered in this study, the spectra of the blade loads do not show a clear signature at the wave frequency, but the increased fluctuating component occurs over a broad range of frequencies.

Evaluation of soil accelerated corrosion of typical grounding materials used for electrical equipment

Abstract At present, research methods for soil corrosion include sample weight loss methods, physical and chemical properties research, electrochemical research, indoor accelerated corrosion tests, etc. However, most existing soil corrosion evaluation methods have many drawbacks, such as high research costs, long experimental cycles, long results transformation cycles, and significant environmental limitations. In this paper, based on the electrochemical test results of environmental corrosion factors using typical grounding materials, a corrosion simulation solution load spectrum and an accelerated corrosion experimental system corresponding to the soil corrosion environment level were established. The accelerated corrosion samples were thoroughly studied and analyzed using macroscopic morphology observation, microscopic morphology analysis, and energy spectrum analysis. The results show that the soil accelerated corrosion method has strong stability and small deviation, which applies to the study of accelerated corrosion in the soil environment of grounding materials.

Investigating the properties of mixed finite elements

The paper considers quadrature-cubic interpolation in problems of restoration of functions of two arguments. The properties of the most common finite elements Q12 (Lagrange version) and Q10 (Serendipity version) are investigated as finite elements. For more than fifty years, researchers of the finite element method have known the procedure of converting the Lagrangian model to the serendipity model. But, as is known, not all results when using this procedure satisfy users, especially proponents of physical interpretation. We are talking about the magnitude of the nodal loads of the uniform mass force of the serendipity finite element. Thus, if we consider the finite element Q10, it receives the physical inadequacy of the "spectrum" as an inheritance from the "parent" pair of Lagrangian finite elements Q8 and Q12. In Pascal's scheme, there is also a hidden connection between the finite element Q10 and the finite element Lagrangian Q12. The analysis of the inherited properties suggests that it is fundamentally possible for a Q10 substitute-base to exist in nature with the same local and integral characteristics. It turns out that the search for such a base goes beyond the capabilities of traditional modeling methods. An alternative substitute-basis Q10 was found by nonmatrix condensation of the prototype of element Q10, i.e., by using the Lagrangian model Q12. The universal nature of the non-matrix transformation of Q12 into Q10 opens up the possibility of designing a model series of mixed finite elements with physically adequate spectra of nodal loads.

Fatigue Damage Assessment of Turbine Runner Blades Considering Sediment Wear

The wear phenomenon that occurs on the blades during operation has a significant impact on the fatigue life of the blades. To address the issue of fatigue life assessment for turbine runner blades subjected to increased dynamic stress due to sediment wear, taking a specific high-head hydropower unit’s mixed-flow turbine as the research subject, a hydraulic model of the turbine was established. The wear zones of the runner blades are determined based on the distribution of the flow field’s velocity and the sediment volume fraction. According to the wear rate formula for runner blade material, the amount of wear on the blades is determined, and the dynamic stress data for the dangerous areas of the blades under different degrees of wear are calculated using a unidirectional fluid–structure coupling method. The load spectrum of the time–stress history data for the dangerous area at different levels of wear was compiled using the rain-flow counting statistical method. The operating time ratios for the flood season and the non-flood season are combined. Based on the fatigue cumulative damage theory, the total fatigue damage at the maximum stress part of the runner blade was calculated for different stages of wear, providing a reference for the life calculation of mixed-flow hydraulic turbines.

Impact of Environmental Conditions on Predicting Condition Rating of Concrete Bridge Decks

Highway agencies prioritize maintaining bridge infrastructure through bridge management systems amid budget constraints. The premature deterioration of reinforced concrete (RC) bridge decks caused by more frequent and increasingly heavy truck load spectra coupled with aggressive environmental conditions has become a critical concern. Despite the prevalence of conventional models and the emerging popularity of machine learning (ML) models in bridge deterioration predictions, they fall short in feature selection and handling of climate conditions, leading to suboptimal accuracy. To address these gaps, this study presents a data-driven framework utilizing ML-based techniques to predict the condition rating of RC bridge decks with a focus on identifying the influencing factors that affect the deck condition. The framework employs the XGBoost algorithm for model development, encompassing comprehensive datasets that include structural, geographical, and climate variables from across the U.S. Furthermore, the Shapley additive explanations approach is applied to identify the explanatory variables with the most impact. Age emerged as the most crucial factor, followed by freeze-thaw cycles and truck traffic, as indicated by the average daily truck traffic. Rainfall also plays a substantial role in deck deterioration. Based on feature importance and monotonicity, this study recommends a series of bridge classifications for transportation agencies to incorporate into their deterioration models. Overall, this research enhances understanding of the primary causes of bridge deck deterioration, enabling more informed decisions about funding allocation and bolstering bridge performance against environmental challenges.

Crack propagation simulation and overload fatigue life prediction via enhanced physics-informed neural networks

The fatigue crack growth simulation and life prediction of structures are implemented in this paper based on the physics-informed neural networks (PINNs). Firstly, the enhanced PINNs are proposed by introducing the crack tip asymptotic displacement fields, so that the crack tip stress intensity factors can be calculated accurately even when the number of collocation points is small and the distribution grid is regular. The enhanced PINNs essentially transform the solution of elastic body containing crack into the optimization of minimizing the constructed loss functions, and can invert the fracture parameters. Then, an automatic crack propagation simulation method is developed based on the enhanced PINNs. The network architecture and the overall node distribution can be unchanged during the crack propagation process, and only new crack surfaces need to be processed and corresponding loss functions need to be modified. Because the nodal refinement around crack-tip is not required, this simulation method is convenient and can accurately predict the mixed-mode crack propagation path. Finally, the fatigue crack growth life algorithm considering overload is developed, where the effect of each overload can be captured by the cycle-by-cycle method. Based on this algorithm, the retardation behavior can be characterized and the fatigue life of structure under the load spectrum with periodic overloads can be accurately predicted. The sufficient examples are given to verify the feasibility and accuracy of the method proposed in this paper.

Mapping the defect acceptance for dynamically loaded components by exploiting DIC-based full-field receptances

Potential defect acceptance can be seen dependable upon the mapping of effective strains on the whole surface, due to dynamic loading of the components as they are mounted. With proper constitutive models and loading spectra, the experiment-based mapping of the equivalent stresses can be achieved from optical full-field receptances in an extremely dense grid, also for lightweight parts, without inertia distortions thanks to contactless measurements. Fatigue spectral methods turn this mapping into components’ life distributions, for a clear assessment of the material’s utilisation: a risk grading mapping for potential defects can be formulated in the area of inquiry in order to discriminate between safe and dangerous locations. By following this experiment-based approach, potential defects in exercise and production might be tolerated in safer locations, under the chosen dynamic task, with great savings in costs and maintenance. Among the image-based full-field measurement techniques, Hi-Speed DIC has proved to work in many environments, to be able to estimate full-field receptances of real components in their effective assembling and loading conditions, in different cases of industrial interest. The quality achieved by DIC in the receptance maps helps in numerically deriving the strain FRFs on the sensed surface. Extended scenarios – with newly modelled coloured noises for an advanced excitation definition from two shakers – and a vibrating rectangular plate, as real mounted component, are highlighted in details to prove the effectiveness of DIC-based risk index mapping under defect acceptance criteria.

Fatigue life analysis of scraper conveyor chain ring under different chain speeds and loads

This study aims to explore how different chain speeds and loads impact the fatigue life of the scraper conveyor chain ring. To achieve this, the study validates the reliability of a coupled simulation involving multi-body dynamics and the discrete element method. It also acquires time-varying tension load spectra under various operational conditions. The research evaluates the effects of distinct chain speeds and loads on parameters such as chain tension, vibration acceleration in the Y and Z-directions of the chain ring. Furthermore, finite element simulation is employed to examine stress distribution changes and fatigue life trends within the three-chain ring structure. The findings demonstrate that Y and Z-direction vibration accelerations of the chain ring correlate positively with the load. Additionally, the vibration acceleration in the Y-direction correlates positively with the chain speed. Across different chain speeds and loads, the maximum equivalent stress in the chain ring exhibits dynamic variations mirroring the load spectrum. Within the elastic deformation range of the chain ring, the highest stress within the transition region correlates linearly with chain tension. Load has a greater effect on the fatigue life of chain rings than chain speed. The fatigue life within the transition region of the chain ring decreases exponentially with increasing load at a constant chain speed. Conversely, at a constant load, chain ring life correlates positively with chain speed. Specifically, the fatigue life of the chain ring in LS 22 amounts to 32.64 days. When both chain speed and load are adjusted by 25%, the chain ring's lifespan reduces by 51.66% during simultaneous increments and increases by 39.26% with concurrent reductions in speed and load.

A method for the fatigue-life assessment of subsea wellhead connectors considering riser wave-induced vibration

During drilling operations, strong non-linear environmental loads are applied to the riser, which can generate powerful fatigue loads, resulting in safety hazards. This paper deals with the problem of the 330 m subsea wellhead connector in the Liu-hua 11–1, which is subjected to long-term non-linear fatigue loading in drilling conditions. Examining the fatigue response law of the subsea wellhead connector ensures the safe operation of offshore oil and gas wells. First, fatigue tests were performed on key components to obtain the stress-fatigue life curve. The F22 strain fatigue life curve was constructed based on the Neuber stress-strain relationship theory and Manson-Coffin strain-life equation. Then, the overall drilling platform - riser - subsea wellhead - soil model was established, and the bending moment-stress data of the subsea wellhead connector was obtained via finite element analysis. Then, the fatigue load spectrum was determined via the MATLAB program using the rainflow counting theory. The response characteristics of the wellhead connector fatigue damage were also compared based on four fatigue damage accumulation theories. A set of fatigue calculation and analysis methods for subsea wellhead connectors was finally developed. This method can provide reference and guidance for subsequent studies.

Durability analysis of large and medium-sized unmanned aerial vehicles based on load spectrum and probabilistic fracture mechanics

The analysis of unmanned aerial vehicle (UAV) durability is crucial for cost-effective repair and maintenance. Assessing the degree of damage and predicting the economic lifespan of a UAV is a critical component of its design and use. To evaluate the durability of large and medium-sized UAVs, data is gathered, and simulations are performed under real-world working conditions. The analysis includes creating a crack growth model for small cracks and determining the distribution of crack sizes, estimating the distribution of Time to Crack Initiation (TTCI), and calculating the general Equivalent Initial Flaw Size (EIFS) distribution. The results obtained from these analyses meet the UAV’s flight hour requirements and help to predict its economic life. This prediction is also beneficial for managing and maintaining the UAV’s life cycle.

Redundant Non-Serial Implicit Manipulator Kinematics and Dynamics

Abstract Redundant non-serial manipulators that include a spectrum of parallel and non-parallel heavy load bearing construction and material handling equipment are treated, using foundations of differential geometry. Kinematics of this category of manipulator are defined in manipulator configuration space by algebraic equations in input and output coordinates that cannot be explicitly solved for either as a function of the other. New sets called assembly components of manipulator configuration space are defined that partition the space into maximal, path-connected, disjoint, topological components. All configurations within an assembly component can be connected by one or more continuous paths within that component, but configurations in different assembly components cannot be connected by continuous paths. Forward and inverse kinematically singular configurations are characterized by criteria that partition each assembly component into path-connected, singularity-free assembly components in which equations of kinematics and dynamics are well behaved. It is shown that a generalized inverse velocity-based kinematic formulation that is problematic for serial manipulators is likewise plagued with problems for non-serial implicit manipulators that can be avoided using the methods presented. Singularity-free differentiable manipulator configuration space components are defined and parameterized by both input and operational coordinates, leading to well-posed ordinary differential equations of manipulator dynamics in both input and operational coordinates. Three typical applications and associated model problems are studied throughout the paper to illustrate the methods and results presented.

Stability and Failure of Thin-Walled Composite Plate Elements with Asymmetric Configurations.

In the present study, the stability and failure phenomena of thin-walled constructions subjected to axial compression, featuring a central cut-out, and constructed from composite materials were explored. These constructions were fabricated from a carbon-epoxy composite using the autoclave method. The research encompassed experimental assessments on actual specimens alongside numerical analyses employing the finite element approach within the ABAQUS® software. The investigation spanned the entire load spectrum up to the point of structural failure, incorporating both practical trials and simulation analysis. During the practical assessments, the study monitored the post-buckling response and captured acoustic emissions to thoroughly evaluate the composite's failure mechanisms. Additionally, the ARAMIS system's non-invasive three-dimensional scanning was employed to assess deformations. Theoretical simulations utilized a step-by-step failure analysis, initiating with failure onset as per Hashin's theory and proceeding to failure progression based on an energy criterion. The simulation outcomes, particularly concerning the critical and post-critical phases, were juxtaposed with empirical data to identify the composite's vulnerability zones. The comparison underscored a significant concordance between the simulation predictions and the empirical findings.

An improved methodology for thermal calculation and design optimization of a thermosiphon waste heat boiler for CCPP

The study is dedicated to enhancing design and computational methodologies for thermosiphon waste heat boilers (WHB) within combined cycle power plants (CCPP). The optimized WHB design and an improved thermal calculation approach are shown. The efficiency of the proposed WHB has been improved by optimizing the area and arrangement of the surface. The novel method incorporates considerations for the internal thermal resistance within thermosyphons and the graded velocity of natural circulation within the evaporation circuit. To refine the calculation method, empirical and experimental data concerning internal temperature gradient in thermosiphon functioning within a heat load spectrum of up to 17 kW/m2, were used. Important findings include three categories. Firstly, increasing the number of sections will slightly increase capital costs and decrease WHB gas temperature, which could be neglected by the unification of thermosiphon sections. Secondly, by applying this modified methodology to a power plant facility featuring a 6700 kW gas turbine engine (GTE), notable adjustments in thermal power were realized, amounting to 157 kW (approximately 6 %), along with corresponding electrical power adjustments of 149 kW (approximately 2 %). Third, the new method is limited to a GTE power of up to 10 MW due to the experimental data used for validation.