Linear Damage Research Articles

Estimating the optimal duration of random loading as part of machine part durability research

Aim. Making an informed decision regarding the durability of machine parts requires information on the operational load that needs to be measured on a representative section of the track. It should not be too long as well. Thus, it is required to determine the optimal duration of implementation. The duration of implementation that is optimal in terms of the reliability of load registration is defined for a process that is stationary in a special sense. Stationarity in a special sense is defined specifically for the task of assessing the durability of a specific part. Methods. The use of spectral theory for the study of random processes is probably not the best way of examining non-stationary loading processes in the context of durability assessment. We believe it would be optimal to use a cycle counting procedure (rain flow method) with subsequent calculation of durability. A lemma and a theorem were formulated on the sufficient duration of implementation for a process that is stationary in a special sense. A sufficient duration of implementation is defined as a limit past which its increase will not lead to a noticeable change in the calculated durability. Results. The matters of stationarity of a process in a narrow sense and the required duration of implementation will help in planning operational tests to measure and record random processes of machine part loading. Both matters were examined in terms of fatigue damage accumulation using Miner linear damage rule, as well as the adjusted linear damage summation hypothesis taking into account the fatigue curve slope parameter m. Some practical engineering problems were examined, including the problem of the optimal duration of implementation of a mining machine whose loading process is characterized by a high degree of irregularity and the problem of finding the required duration of implementation of load recording in a rolling stock component. Conclusion. A theorem on the required and sufficient duration of implementation was formulated. In order to test the method, Markov transition matrix-based model processes were used. In addition, the method and theorem were tested using examples of some experimental processes obtained from operational tests of vehicles and production machines.

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.

Sequence effects on the life estimation of welded tubular structures made of S355J2H under uniaxial fatigue loading

The use of hollow sections to form lightweight structures is widespread in common steel processing industries such as crane, commercial vehicle, steel bridge and agricultural machinery construction. The hollow sections are mainly designed as truss or frame structures, in some cases using high-strength and higher-strength steels in order to achieve optimum utilization of the component and material. A new collection of fatigue life data covering sequence effects and the accuracy of the linear damage accumulation is presented. Effects of the shape of the applied load spectra and sequence effects of different amplitudes have been investigated. This document covers tubes of 4 to 8 mm thickness made by low-carbon or mild steel S355J2H. In general, it was found that the spectrum shape and the loading sequence have an influence on the service life. Depending on the shape of the spectrum, random tests tended to lead to shorter service lives than tests with block-loading sequences. An influence of overloads was also found for the tests with interspersed overloads. Typical maximum linear damage sums taken from recommendations and codes of 0.2 or sometimes 0.5 are exceeded for all spectra investigated and in some of the cases even significantly above 1.0. Transferability of the recommendations to component-type structures like tubular joints needs revision to lift its lightweight potential. Using stress concentration factors (SCF) from finite element analysis, typical strength values for the structural and effective notch stress concepts are checked. All joints investigated show a significantly higher strength compared to the IIW recommendations using the structural stress approach or compared to the DVS 0905 with the effective notch stress approach.

Applicability evaluation of damage evolution models in simulating repeated low-velocity impact behavior of composite laminates

This study aims to provide a valuable reference for selecting appropriate damage evolution models (DEMs) when simulating the behavior of repeated low-velocity impacts (LVIs). Four DEMs are systematically evaluated in simulating mechanical response, dissipated energy, damage evolution, and accumulation under three repeated impacts. 3D Puck failure criteria and various DEMs combined with element characteristic lengths associated with physical fracture modes are used to predict repeated LVI damage behavior. Delamination behavior is simulated by zero-thickness cohesive elements. Two damage indexes are proposed to quantify and compare the damage distribution and accumulation. The post-peak softening and LVI behavior predicted by four DEMs are compared and verified through representative volume elements simulation and LVI experiments. The findings reveal that DEMs have varying degrees of influence on the mechanical response, damage evolution, damage distribution, and accumulation under repeated impacts. The exponential models proposed by P. Maimı et al. and Matzenmiller et al. are more suitable to simulate mechanical response or damage accumulation behavior under repeated impacts than the linear damage evolution model due to their non-linear post-peak softening characteristics. In contrast, Linde model shows brittle behavior due to the rapid damage accumulation during repeated impacts, rendering it unsuitable for repeated impact simulation.

Discrete wavelet transform assisted convolutional neural network equalizer for PAM VLC system.

With the deepening of research and the further differentiation of damage types, and to compensate for both linear and nonlinear damage in visible light communication systems (VLCs), we propose a novel discrete wavelet transform-assisted convolutional neural network (DWTCNN) equalizer that combines the advantages of wavelet transform and deep learning methods. More specifically, wavelet transform is used in DWTCNN to decompose the signal into diverse coefficient series and employ an adaptive soft-threshold method to eliminate redundant information in the signal. The coefficients are then reconstructed to achieve complete signal compensation. The experimental results show that the proposed DWTCNN equalizer can significantly reduce nonlinear impairment and improve system performance with the bit error rate (BER) under the 7% hard-decision forward error correction (HD-FEC) limit of 3.8 × 10-3. We also experimentally compared DWTCNN with the Long Short-Term Memory (LSTM) and entity extraction neural network (EXNN) equalizer, the Q factor has been improved by 0.76 and 0.53 dB, and the operating ranges of the direct current (DC) bias have increased by 4.76% and 23.5%, respectively.

Creep-fatigue life estimation of circumferential welds in thermal high energy piping systems

ABSTRACT To prevent accidents in high energy piping systems of thermal power plants, it may be important to accurately estimate the creep-fatigue life of circumferential piping welds. The main failure mode in the damage cases was Type IV damage which was creep-dominated damage occured at the fine-grained HAZ(FGHAZ). The damege mode is considered to change from longitudinal failure at the base metal to circumferential Type IV failure when the ratio of axial stress to hoop stress exceeds a certain value. The allowable thermal expansion stress in the design, the stress relaxation property of the material, and the creep rupture strength of welded joints are investigated, as factors affecting creep damage of circumferential piping welds. Fundamental creep-fatigue tests were perfomed using cross-weld specimens and their lives were estimated by a linear damage summation rule. In the life estimation, it seems necessary to consider elastic follow-up phenomena where strain transfers to the HAZ.

Probabilistic modeling of double linear damage accumulation and its application in fatigue reliability analysis

AbstractIn this paper, a probabilistic double linear damage accumulation model is proposed to characterize the uncertainty of damage accumulation using the statistics of material fatigue life. The probabilistic modeling framework is performed under normal distribution assumption of fatigue life. By applying a one‐to‐one probability density function transformation method, the probability distribution of critical damage and cumulative damage can be extracted and derived. The proposed probabilistic damage accumulation model is then used for fatigue reliability analysis by building the reliability formulas with respect to the cumulative damage and the critical damage under both constant and variable amplitude loadings. It treats the mean and variance of cumulative damage as time‐dependent values that dynamically vary with increase in usage life. The reliability can be easily calculated by limited data necessary from fatigue life samples. The applicability of the proposed method is demonstrated using the experimental data of two metallic materials under constant amplitude and two‐block loadings. The results show that the model predictions are in good agreement with the experimental observations under constant amplitude loading and L‐H loading sequence. In addition, the proposed method provides better predictive ability than the Miner rule under constant amplitude loading and H‐L loading sequence. Moreover, the predicted reliability plots can typically present a two‐stage fatigue characteristic during crack initiation and crack propagation periods.

Interpreting and reporting fission-track chronological data

Abstract Fission-track dating is based on the analysis of tracks—linear damage trails—produced by the spontaneous fission of 238U in a range of natural accessory minerals and glasses. The retention of tracks is sensitive to elevated temperatures, and the data serve principally as a tool for recording thermal histories of rocks, potentially over the range of ~20–350 °C, depending on the specific minerals studied. As such, in most cases, fission-track data generally bear little or no direct relationship to the original formation age of the material studied. The age range of fission-track dating is related to the product of age and uranium content, and ages from several tens of years to older than 1 Ga are reported. Fission-track analysis led to the development of powerful modeling techniques. When used with appropriate geological constraints, these modeling techniques allow important geological processes to be addressed in a broad range of upper crustal settings. Since early attempts to standardize the treatment of fission-track data and system calibration over more than 30 years ago, major advancements were made in the methodology, necessitating the development of new, updated data reporting requirements. Inconsistencies in reporting impede public data transparency, accessibility and reuse, Big Data regional syntheses, and interlaboratory analytical comparisons. This paper briefly reviews the fundamentals of fission-track dating and applications to provide context for recommended guidelines for reporting and supporting essential meta fission-track data for publication and methodological archiving in structured formats that conform with FAIR (Findable, Accessible, Interoperable, and Reusable) data principles. Adopting such practices will ensure that data can be readily accessed, interrogated, and reused, allowing for further integration with other numerical geoscience techniques.

Rate dependent cohesive zone model for fatigue crack growth

Experimental observations indicate that the frequency of cyclic loads can influence fatigue crack growth. To address this phenomenon in simulation modelling, this study introduces a rate-dependent cohesive zone model designed for analysing fatigue crack growth under arbitrary cyclic loading conditions. The model operates in the time domain, where both critical traction and fracture toughness are modelled as functions of the separation rate, thereby considering the rate dependency of material damage and cracking. Unlike conventional models, this approach does not rely directly on loading frequency, suggesting its capability to address fatigue crack growth under non-periodic loading or repeated impacts effectively. An algorithm for modelling fatigue crack evolution and growth was developed based on this model, employing a time-incremental strategy in conjunction with a linear cumulative damage method. This algorithm was implemented in ABAQUS using a user element subroutine (UEL). The effectiveness of the proposed model and algorithm is validated through examples of fatigue crack growth in a plate under cyclic loading with varying frequencies. The results demonstrate agreement with experimental and computational findings reported in the literature. Additionally, the model was applied to scenarios involving frequency-variable cyclic loadings, yielding reasonable outcomes. Analysis of these examples confirms the model's utility in predicting fatigue crack growth under diverse alternating load conditions.

Fatigue load spectrum generation of Indonesian high-speed trains

The high-speed trains designed and constructed in Indonesia will use Aluminum alloy Al 6061-T6 as a structural material. Aluminum alloys are prone to fatigue failure due to the absence of endurance limit of the material, hence fatigue life prediction has to be carried out. Fatigue cracks could initiate at the defects of welded joints. Analyzing the fatigue load spectrum of critical locations in the train structures is crucial to predicting fatigue life. These critical locations are selected from areas with high static stress and stress concentration. The loads are analyzed using the multibody dynamic with rigid body assumptions and track roughness following UIC Standard Code 518. The finite element method is used to calculate the stresses from the loads generated by the multibody dynamic. The load sequence is further analyzed with rainflow counting method, and the load exceedance curve can be constructed. Finally, the Miner Linear Cumulative Damage Model is used to predict fatigue life.

Simulation Study on Methods for Reducing Dynamic Cable Curvature in Floating Wind Power Platforms

As a key component connecting a floating wind turbine with static sea cables, dynamic cables undergo significant tensile and bending loads caused by hydrostatic pressure, self-weight, waves, and ocean currents during service, which can lead to fatigue failure. Thus, dynamic and fatigue analyses are necessary for the design and operation of dynamic cables. In this study, a fatigue analysis of the three-core four-layer armored dynamic cable used in a semisubmersible floating wind turbine was carried out at a water depth of 25 m. The Miner linear cumulative damage method, based on material S-N curves, was used to predict fatigue life. The results indicate that, at 10 times the safety factor, the dynamic cables meet the design requirement of a 30-year service life in the studied marine environment. The maximal curvature of the dynamic cable always appears at the exit of the bend stiffener, even beyond the allowed point. Adding weights to the section where the cable exits the bend stiffener and adjusting the bend stiffener’s hanging angle can both reduce the curvature at the bend stiffener exit. The scheme of adjusting the bend stiffener’s hanging angle is preferred, for it is easier for simultaneous adjusting and inducing much smaller extra stress in the cable. As the hanging angle increases, the curvature at the bend stiffener exit decreases, while the maximal effective tension and maximal von Mises stress gradually increase. For certain operating conditions, especially with higher waves, it is better to adjust the hanging angle to avoid excessive curvature and, meanwhile, ensure the increase in the stress within a reasonable range.

Evaluation of damage and failure analysis of CPVC pipes

In this paper, the work we have carried out has focused on the failure analysis of CPVC (chlorinated polyvinyl chloride) pipes. We stimulated the damage by notch effect and evaluated its properties using models available in the literature, specifically, the linear damage of Miner, the normalized damage and the unified theory. Burst tests allowed us to obtain ultimate pressure and time parameters for the virgin specimens and the residual parameters for the damaged ones. Then, we analyzed the effect of defect on the mechanical behavior of the studied structures; we found that the mechanical properties of the material were lost as defects increased. An observation and analysis of the pressure drop and thereafter the residual ultimate resistance brings out acceleration from it around the critical depth. Then, an evaluation of the static damage of the studied CPVC pipes was made according to model based on the experimental results of the burst tests and on the modification of the unified theory concepts and the static damage. Indeed, we evaluated the static damage of blank and notched tubes using mainly burst pressure parameters.

A fully coupled thermo-hydro-mechanical elastoplastic damage model for fractured rock

A detailed and fully coupled thermo-hydro-mechanical (THM) model for fractured rock is presented. This model distinguishes itself by harmoniously integrating elastoplastic material behaviour with a continuum damage mechanics framework. Solid matrix displacement, pore and fissure water pressures and temperature of the solid are introduced as the primary nodal variables. The ingenuity of this research is embedded in the intricate coupling of THM processes with plastic deformation and damage mechanics in a double porous medium, a venture that significantly broadens the remit of existing methodologies. The model is implemented using finite element method (FEM) and validation is achieved by comparing the FEM results against existing literature numerical outcomes describing linear and elastoplastic continuum damage behaviour of fractured rock. The model also exhibits an extraordinary proficiency in reproducing experimental triaxial test results, using THM components conjoined with elastoplastic bounding surface aspects and inherent hardening effects. It is imperative, nonetheless, to underscore the model's sensitivity to certain material properties, inclusive of strength parameters, leakage coefficients, and permeability attributes. This fully coupled THM model provides a comprehensive and sophisticated tool for investigating the behaviour of fractured rock under various loading conditions. It can help us better understand the physics of fractured rock behaviour and contribute to the development of more accurate and reliable models for engineering applications, such as CO2 injection.

A modified nonlinear cumulative damage model for combined high and low cycle fatigue life prediction

AbstractAero‐engine turbine blades are subject to combined high and low cycle fatigue (CCF) loadings during operations. In this paper, a modified nonlinear cumulative damage model is developed based on linear damage accumulation theory and static toughness exhaustion to predict the CCF life of turbine blades and common blade materials. An interaction factor is created to reflect the integrated effect of high cycle fatigue and low cycle fatigue (HCF‐LCF). Available test data from TC4 alloy and other two alloy materials, together with two turbine blades are utilized to validate the robustness and accuracy of the proposed approach. Comparative results demonstrate that the proposed model holds better performance in life predictions under CCF loadings.

Data-Driven Structural Health Monitoring: Leveraging Amplitude-Aware Permutation Entropy of Time Series Model Residuals for Nonlinear Damage Diagnosis.

In structural health monitoring (SHM), most current methods and techniques are based on the assumption of linear models and linear damage. However, the damage in real engineering structures is more characterized by nonlinear behavior, including the appearance of cracks and the loosening of bolts. To solve the structural nonlinear damage diagnosis problem more effectively, this study combines the autoregressive (AR) model and amplitude-aware permutation entropy (AAPE) to propose a data-driven damage detection method. First, an AR model is built for the acceleration data from each structure sensor in the baseline state, including determining the model order using a modified iterative method based on the Bayesian information criterion (BIC) and calculating the model coefficients. Subsequently, in the testing phase, the residuals of the AR model are extracted as damage-sensitive features (DSFs), and the AAPE is calculated as a damage classifier to diagnose the nonlinear damage. Numerical simulation of a six-story building model and experimental data from a three-story frame structure at the Los Alamos Laboratory are utilized to illustrate the effectiveness of the proposed methodology. In addition, to demonstrate the advantages of the present method, we analyzed AAPE in comparison with other advanced univariate damage classifiers. The numerical and experimental results demonstrate the proposed method's advantages in detecting and localizing minor damage. Moreover, this method is applicable to distributed sensor monitoring systems.

Study on biaxial bending fatigue performance of Engineered Cementitious Composites (ECC)

Structural components such as bridge deck, highway pavement and thin-walled roof dome often are subjected to the biaxial and even multi-axis stress state due to the external load. Also, the fatigue effect cannot be ignored due to the moving vehicle load in the design of these structures. If engineering cementitious composites (ECC) is used in the above traditional concrete structures, their performance, such as easy cracking and short service life can be greatly improved. However, the biaxial bending fatigue performance of ECC should be analyzed in detail. At present, the biaxial bending test methods of cement-based materials include biaxial bending test (BFT) and centrally loaded round panel test (RPT). This study used both RPT and BFT test methods to analyze the biaxial fatigue performance of ECC and used four-point bending test (4PBT) uniaxial fatigue test as a reference. The stress levels S were set as 0.5, 0.6 and 0.7. The uniaxial and biaxial bending fatigue failure procedures of ECC were analyzed by plotting the three-stage deflection development curve, the fatigue damage and strain relationship curve based on the linear cumulative fatigue damage theory, and the S–N curve. The fatigue life of ECC biaxial bending specimens was greater than that of uniaxial bending specimens. At S = 0.5, the fatigue life: BFT > RPT. At S = 0.6, the fatigue life of BFT and RPT specimens was close. At S = 0.7, the fatigue life: BFT < RPT. With increasing stress level, the fatigue life of BFT specimen decreases more than that of RPT specimen. The lognormal distribution model and Weibull distribution model were used to fit the uniaxial and biaxial bending fatigue life of ECC, respsectively. Using the double logarithmic fatigue equation, fatigue life under the failure probability PF of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 was derived. The survival rate represents the level of safety reservation, which could provide reference and basis for the design of ECC bridge deck and highway pavement with different safety reservation requirements.

Research on point-supported rotational semi-rigid energy-dissipation connection for precast-cladding-panel at connection level

A novel point-supported rotational semi-rigid energy-dissipation connection for precast cladding panels (PRSEC) is proposed in this paper. The PRSEC, utilizing combined mechanical mechanisms involving friction and bending parts, could transform from a rigid connection into a flexible energy-dissipative connection as the seismic action increased. Theoretical predictions of PRSEC are presented, followed by a coordinated design method with the precast cladding panels. Subsequently, monotonic and cyclic loading tests are conducted to investigate the semi-rigid characteristic of PRSEC. Two distinctive working stages, the static friction stage and the sliding friction stage, are clearly captured in the monotonic test results. Additionally, the cyclic tests reveal that the PRSEC specimens exhibit favorable hysteretic performance, characterized by a stable load capacity, favorable deformation ability, and efficient energy dissipation capacity. The NAO friction pads exhibit a fragmented damage pattern, while the brass friction pads demonstrate a linear scratch damage pattern. No cracks or tears are observed on the surface of the bending part, which demonstrated a track-like deformation mode. Both PRSEC specimens with NAO and brass friction pads show satisfactory low-cycle fatigue performance. Furthermore, finite element analyses are conducted using Abaqus to reveal the working mechanism of the friction and bending parts. The influence of the relative parameters is also summarized based on both experimental and numerical analyses. Subsequent research would be conducted to analyze the interaction between PRSEC and precast cladding panels at the structural level to provide a reference for the design of structures employing PRSEC.

Study on fatigue life estimation method of welded structure of lifting machinery

The fatigue strength of lifting machinery structure has always been an important issue in ensuring safety. In order to effectively and accurately evaluate the fatigue life of lifting machinery structure, this paper based on Miner linear cumulative damage theory and S-N curve in British BS 7608 standard, the fatigue life calculation of metal welded structure is carried out. Taking the large-scale bridge crane of hydropower station as an example, the nominal stress of the corresponding key parts is obtained by applying the actual load in the finite element model, and the stress time history is calculated, and then the safe service life of the structure is estimated, which provides an effective and feasible method for evaluating the fatigue residual life of the crane. The example analysis shows that the calculation method is convenient and reliable, which provides a scientific basis for accurately estimating the fatigue life of welded structure of lifting machinery.

Numerical modeling and fatigue analysis of the dynamic response of main pump cable in nuclear power plant

Abstract The structural temperature rise and thermal stress caused by operation current and ambient temperature are some of the main factors affecting cable fatigue life. Combined with the operating and environmental conditions of the main cooling pump of the nuclear power plant, the thermal-structural coupling field numerical modeling and fatigue analysis of the 6kV single-core and three-core cable of the main pump is carried out. Based on obtaining the steady-state operating current, the motor start-up transient current, and the circulating ambient temperature, the thermal-structural coupling field numerical model of the main pump cable is established using the load transfer method to obtain the thermal and stress field distribution of the internal structural layer. The load history of one cycle is extracted for the fatigue numerical simulation of the main pump cable. The stress time history of the cable structure layer was constructed by the stress calculation results and the load time history of a single period, and the fatigue life of the main pump cable was obtained based on the S-N curve of the main insulation material and the Miner’s linear cumulative damage theory. The simulation results show that the force acting on the main pump cable by the operating current and ambient temperature is an approximately symmetric cyclic load of constant amplitude. The life cycle of the cable can reach 2.235*e4 times, and the overall life of the cable is about 63.97 years. This study can provide theoretical guidance for the safety and reliability design and state operation and maintenance of the main pump cable of the nuclear power plant.

Fatigue strength assessment of aluminium welded joints under variable amplitude loading using the Peak Stress Method

One of the simplest and most efficient ways to design lightweight structural components is the combination of welding and aluminum alloys. However, welded joints are extremely sensitive to fatigue failure and making accurate lifetime predictions is still challenging when Variable Amplitude (VA) loading conditions are involved. Among all design criteria available in the literature, the present investigation focuses on the Peak Stress Method (PSM), an engineering finite element (FE)-based approach to rapidly assess the fatigue strength of welded joints. In more detail, the PSM suggests modelling both weld toe and weld root as sharp V-notches having null tip radius and correlates their fatigue strength using the intensity of the local linear elastic asymptotic stress distributions described by the Notch Stress Intensity Factors (NSIFs). The theoretical formulation of the PSM for the fatigue strength assessment of welded joints subjected to VA loadings has been recently proposed by combining its Constant Amplitude (CA) formulation with the Palmgren-Miner's cumulative linear damage rule. Such VA formulation has been successfully validated against a large bulk of experimental fatigue results generated by testing welded joints made of structural steels under uniaxial as well as multiaxial loadings. In the present investigation, the VA formulation of the PSM has been further validated against experimental data relevant to welded joints made of aluminium alloy under VA loadings.