Load Sequence Effects Research Articles

Multi-axial fatigue of high-strength concrete: Model-enabled interpretation of punch-through shear test response

This paper aims to fill the gap in multi-axial fatigue characterization of concrete by presenting a comprehensive numerical analysis of data from the punch-through shear test (PTST), which allows control over combined shear and compression loads in the tested ligament. To accurately reproduce the degradation process in this multi-axial configuration, a material model must capture two key effects: (i) dissipative behavior at the inter-aggregate level during subcritical pulsating loading and (ii) fatigue-induced tri-axial stress redistribution in the test ligament. The recently published MS1 model by the authors effectively incorporates these features, thereby enabling a deeper interpretation of the experimental data. The former effect is seamlessly integrated into the model using the Lemaitre-type fatigue hypothesis, facilitating the direct derivation of general evolution equations. The latter effect is efficiently represented through the microplane homogenization framework. The model’s predictions for PTST response under monotonic shear loading with varying levels of radial confinement align well with experimental results. Similarly, the simulated fatigue response accurately reproduces the experimentally observed S-N (Wöhler) curves. Further studies demonstrate the model’s ability to predict the effect of fatigue loading sequence. A thermodynamically-based formulation provides an energetic interpretation of this effect, offering a quantitative breakdown of energy dissipation attributed to individual dissipative mechanisms over the lifetime of the material. The studies show that damage-induced dissipation remains almost constant regardless of different fatigue loading histories.

Statistical Lifetime of Composites Subjected to Random and Ordered Block Loadings

ABSTRACTThis study presents a procedure based on constant amplitude (CA) fatigue data to predict the statistical fatigue lifetime of glass/orthopolyester composites subjected to repeated ordered and random two, three, and six sequences of block loadings. A numerical routine was developed to detect cycle‐by‐cycle the statistical strength degradation progression until failure, assuming that the strength at the end of a block cycle equals the strength at the start of the successive one and that the individual samples' static strength, the amount of degraded strength, and fatigue life share the same rank in their respective cumulative distribution function. Predictions conform to the statistically undetectable loading sequence effects and lightly overestimate the lifetimes of random and ordered high‐to‐low (1/100 cycles) repeated two‐block loadings. The vanishing effect of the loading sequence when the block extents remain fixed, the block extent effects for a given three‐block sequence, and the lifetimes of three‐block loadings were fully predicted. The six‐block sequence's experimental lifetimes with different block loading orders and block extent fell within the predicted lifetimes' cumulative distribution function. A reliable damage rule based on residual strength was proposed and compared to the Miner's rule.

A prediction method for new titanium alloy welded structure fatigue crack growth rate

ABSTRACT For the fatigue life prediction of titanium alloy welded structures used in deep-sea submersibles, a modified model considering the welding characteristics and the load sequence effect is established in this paper. Based on the modified model, the fatigue crack propagation behaviour of the new titanium alloy welded structure under different loading conditions is predicted. The comparison between the prediction results and the test data is analyzed. The prediction ability of the modified model over the conventional model is comparatively analyzed. The results show that the modified model has a strong ability to predict the fatigue crack propagation behaviour of new titanium alloy welded structures under various load spectra.

Finite element modeling of the glass sealing process for solid oxide cell stacks

The sealing process for solid oxide fuel cell (SOFC) and solid oxide electrolysis cell (SOEC) stacks is a vital step in the assembly and manufacturing of these systems. The cell seal and stack seal serve to prevent leakage and the mixing of air with hydrogen and steam during operation. Good seals are critical for reporting accurate cell and stack performance and durability, as leaks can mask degradations and manifest as performance improvement. Predictive modeling of seal materials during sealing processes for SOFC and SOEC stacks has been largely unexplored and could provide design and manufacturing insights for these systems. In this work, finite element modeling was conducted to simulate the assembly and stack sealing of planar cells to capture the densification, viscous flow, and crystallization behavior of the G18 glass ceramic seal material during full scale stack fabrication. The Skorohod-Olevsky viscous sintering material model was implemented in the ANSYS finite element program and modified to account for crystallization effects to simulate the response of the G18 seal material. The effects of initial cell/stack curvature were captured via preliminary stack manufacturing simulations, and its influence on stack sealing quality was studied. Effects of compressive loading sequence and configuration were investigated.

Experimental behaviour and fatigue life prediction of bonded joints subjected to variable amplitude fatigue

The variable amplitude fatigue behaviour of adhesive joints has not been extensively considered in literature and considerable knowledge gaps regarding its underlying mechanisms still exist, hindering accurate life prediction. This study investigates the effect of loading sequence and number of load transitions on single lap joints (SLJs) bonded with a toughened epoxy adhesive. Life prediction is also conducted using established cumulative rules: Palmgren–Miner (PM), Broutman and Sahu (BS) and, Hashin and Rotem (HR). To overcome their limitations, a modified Cortan–Dolan approach is proposed. For this, SLJs were subjected to single transition (low-to-high and high-to-low load transitions at different stages of the fatigue life and with different magnitudes) and multi-block loading spectra with different numbers of transitions.Results showed an extension of the fatigue life for high-to-low transitions. This was attributed to a combination of load interaction effects, as evidenced by an elastoplastic numerical simulation, and non-linear damage accumulation. Conversely, low-to-high transitions exhibited a damaging effect. For single transition spectra, BS and HR models were seen to improve prediction over PM by indirectly considering these effects. The proposed approach further improved this prediction. Multi-block results showed no significant influence of the number of load transitions and were satisfactorily predicted using PM.

Effect of loading sequence on the ultra-low-cycle fatigue performance of all-steel BRBs

Buckling-restrained braces (BRBs) are intended to protect the primary structure of buildings by absorbing most earthquake input energy through the plastic deformation of the steel cores. The ultra-low-cycle fatigue performance of BRBs is crucial for their seismic performance as energy dissipators. Despite the plenty of research on the ultra-low-cycle fatigue behavior of steel members, it remains susceptible if arbitrary loading paths have a major effect on the ultra-low-cycle fatigue life or cumulative plastic deformation (CPD) capacity of BRBs. This paper introduces an experimental campaign of nine supposedly identical BRB specimens subjected to three different loading protocols of similar average strain amplitudes. For each loading protocol, the test was repeated for three times to account for possible uncertainty. The results show that the effect of loading protocol is trivial given the similar average strain amplitudes throughout the loading. The Miner's assumption that the loading sequence has no effect on the fatigue life of BRBs is supported by the test results, however, the proper choice of the Coffin-Masson model's parameters is crucial. The skeleton ratio, which is derived from decomposing the hysteresis curve into a skeleton part and a Bauschinger part and has been used to account for the loading path effects, is shown to be insensitive to varied loading protocols by the test results.

A new fatigue equation for asphalt mixtures considering loading sequence effects

The fatigue life of asphalt mixture has been found to significantly depend on loading sequences. However, the widely used traditional linear fatigue equations are difficult to determine the fatigue life of asphalt mixture subjected to different loading sequences. This study aims to improve these fatigue equations by establishing a fatigue equation considering loading sequence effects. First, the semi-circular bending (SCB) constant amplitude fatigue tests were conducted under the high loading amplitude (σhigh) and low (σlow) loading amplitude, respectively. Then, two of the loading sequences, namely the low-high stress (σlow-σhigh) and high-low stress (σhigh-σlow), were selected to carry out the SCB variable amplitude fatigue tests. Furthermore, the loading sequence effects on the life fractions and fatigue life of asphalt mixtures were analyzed. Finally, the damage equivalent criterion was successfully applied to establish the nonlinear fatigue damage accumulation model and fatigue equation considering loading sequence effects. It was found that the cumulative life fractions of asphalt mixtures under constant amplitude loading are equal to 1, indicating the linear fatigue damage accumulation. The cumulative life fractions corresponding to the σlow-σhigh and σhigh-σlow are greater than 1 and less than 1, respectively, indicating the nonlinear fatigue damage accumulation. The established nonlinear fatigue damage accumulation model can accurately characterize the dependence of fatigue damage accumulation on loading sequences. The established fatigue equations can improve the traditional linear fatigue equations to some extent and accurately predict the fatigue life of asphalt mixtures corresponding to the loading sequences of the σlow-σhigh and σhigh-σlow.

New insights into the load sequence effect: Experimental characterization and incremental modeling of plain high-strength concrete under mode II fatigue loading with variable amplitude

Reinforced concrete (RC) infrastructure typically endures repeated subcritical loading throughout its operational lifespan, potentially compromising structural integrity. A realistic loading condition of these structures consists of constantly changing maximum and minimum load events. Characterizing the fatigue response of concrete proves challenging due to its heterogeneous and quasi-brittle nature, leading to varying fatigue lifetimes depending on the loading sequence. Understanding the impact of this so-called load sequence effect stands as a critical facet in ensuring structural longevity and reliability of current infrastructure. This paper offers insights into this phenomenon, focusing on unraveling the intricate behavior of plain concrete under multistage fatigue loading. Since the experimental investigation of the load sequence effect is highly complex due to the large scatter of test results, a newly developed, mode II test setup was employed. The advantage of this test setup resides in the precise specification of stress state and fracture zone. The systematic investigation of over 50 specimens elucidates the pronounced load sequence effect and provides insight into the underlying mechanisms. Based on these experimental results, a deformation-based incremental modeling approach was developed which considers the effect of loading sequence and provides not only the fatigue life but also the entire evolution of deformation. The experimental recalculation underscores the efficacy of this approach over the conventional Palmgren–Miner (P–M) rule.

Strain-based running-reliability characterisation in time-domain for risk monitoring under various load conditions

This aim of this paper is to characterise the strain-based fatigue life data in time-domain using the newly modelled running-reliability technique that considers the load sequence effect. Current established conventional strain life models do not consider dependence for fatigue life of low or high amplitudes, on which with occur first in the load history. Finite element analysis is carried out to ensure the strain signals are captured at the most critical region during road test at various conditions. Fatigue life of 2.74 × 104 to 6.07 × 105 cycle/block with mean cycle to failure of 4.32 × 106 to 7.00 × 106 cycle/block is predicted based on the cycle sequence effect using cycle-counting method. The newly modelled running-reliability technique is formulated to extract the features of high amplitude excitation obtained from the strain signals for characterising the fatigue reliability features under load sequence effect. Hence, the reliability-hazard relationship for fatigue reliability characterisation of strain-based approach in time-domain using running-reliability technique.

Fatigue damage analysis method of offshore wind turbine foundation

The systems of offshore wind turbines are established in a complex marine environment, and are subjected to all kinds of ocean loadings such as waves, currents and wind for a long time. It is found that offshore wind turbine foundations are seldom damaged due to the problem of strength and stability under normal operation conditions. Most of the damages are caused by the fatigue damage under long-term loads. Aimed to this problem, the monopile foundation of offshore wind turbine is analyzed as an example in this study. The fatigue damage is analyzed systematically using the method of time-domain, combining the rain-flow counting method, S–N curve with linear and nonlinear fatigue damage models. In addition, a modified nonlinear fatigue damage model is proposed based on the Corten-Dolan and Manson-Halford nonlinear fatigue damage models, which can consider the modification of load interactions and the effect of loading sequence. In this way, the short-term fatigue damage value of offshore wind turbine foundation can be obtained. On the basis, the long-term probability distribution function of wind speed is obtained according to the actual monitoring results of wind load, and the fatigue damage value of the offshore wind turbine foundation in the design life can be obtained. Finally, a complete fatigue damage analysis method of offshore wind turbines is proposed, which is applicable to both short-term fatigue damage and long-term fatigue damage.

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.

New investigation of delamination using the VCCT method to predict the damage in bonded composite repair plates subjected to tensile load

PurposeThis study provides an analysis of patch repair for cracked aircraft structures. Delamination is a type of damage that affects the patch's behavior. The purpose of this study is to assess the influence of delamination on repair performance.Design/methodology/approachAn analytical and numerical study using the finite element method was conducted for a cracked plate repaired with a patch containing a pre-existing delamination defect. The method for defining the contact pair surfaces and modeling the delamination interaction within the patch interface is specified using the virtual crack closure technique (VCCT) approach.FindingsThe efficiency of the repair is measured in terms of the J-integral. The effects of delamination initiation, mechanical loading, crack length and patch stacking sequences are presented. It is noted that in mode I, delamination propagation is only significant at node A. The numerical results are in good agreement with those of the analytical solution found in the literature. It is observed that the patch's behavior is strongly dependent on loading, crack size and stacking sequences in terms of reducing the structure's lifespan, especially in the presence of delamination.Originality/valueThe numerical modeling presented by the VCCT approach is highly valuable for studying delamination evolution. The influence of loading, crack size and stacking sequences on repair performance is discussed in this work.

Probabilistic structural integrity assessment of a floating offshore wind turbine under variable amplitude loading

The objective of the present study is to assess the structural integrity of a semisubmersible-type floating offshore wind turbine probabilistically based on fracture mechanics. Although floating offshore wind turbines have been historically much more expensive than their fixed bottom peers, the levelised cost of energy of floating offshore wind turbines has decreased dramatically due to increasing wind turbine size, higher capacity factors, innovative designs, and optimal operational strategies. However, there is still much to be done to bring the cost down, especially from the operational and maintenance standpoint. In this regard, a damage-tolerant approach is a strong alternative to a safe-life design approach that leads to overdesigning. The present study assesses the structural integrity of a semisubmersible-type floating platform with an initial crack assumption using a probabilistic framework, resulting in the quantification of the uncertainty involved in the fatigue crack growth under variable amplitude loading. The present study outcomes can then be used to optimise the structural design, inspection, and maintenance plan. The cycle-by-cycle crack growth is simulated using the modified Paris’ law, which allows accounting for the overload-induced retardation on the crack propagation. Furthermore, the factors influencing crack growth are subjected to a great deal of uncertainty. The present study focuses on the variability caused by the load sequence and interaction effect. To this end, Monte Carlo Simulation is performed to quantify the uncertainty associated with the crack growth by first considering the load sequence effect and then the overload-induced retardation effect.

Residual life assessment of deep rolled railway axles considering the effect of process parameters

Deep rolling is an efficient technique to increase the fatigue life of railway axles. The application introduces compressive residual stresses into the area near the surface, which are the most effective positive influence on fatigue behaviour and remaining service life in presence of a crack. This paper investigates the remaining service life of deep rolled railway axles. Previous research studies are used as basis for this work whereas, firstly, an elaborated crack growth model for common railway axle steels was developed. This model is based on experimental crack propagation results and can consider crack closure as well as load sequence effects and local residual stress conditions. Secondly, a numerical deep rolling simulation model validated with experimental residual stress measurements to determine the introduced residual stress state and to investigate the influence of various process parameters. In this study, the comprehensive outcome of both studies is connected in order to evaluate and compare the residual life of railway axles with the presence of different deep rolling-induced residual stress distributions in-depth. The crack growth study involves combinations of the deep rolling force as one of the most influencing process parameters, load scenarios as well as initial crack sizes and finally discusses the comprehensive results.

Effect of metal loading sequences in CO2 methanation activity on samarium-doped ceria supported bimetallic catalysts

The La/Ni/SDC catalyst from one pot microwave-heating gives higher methanation activity than La–Ni/SDC and Ni–La/SDC from stepwise heating.

Fatigue failure prediction method and constant amplitude equivalence strategy of adhesive interface under variable amplitude loading

The existing commercial software can only predict the fatigue life of homogeneous materials/structures under constant amplitude loading. This work developed a software tool that could predict the fatigue life of the adhesive interface under variable amplitude loading by embedding a modified fatigue cohesive zone model and amplitude variation function. Central to this innovation is the load sequence effect factor (γ), designed to consider nuanced influences like the shock effect of stepped amplitude changes on the fatigue properties. The effects of the block loading sequence on the fatigue life and crack growth rate of the adhesive interface were investigated numerically, and the influence of stepped amplitude on the evolution of a damage zone ahead of the main crack front was observed. It was found that the loading sequence from Low to High (L-H) accelerated the crack growth rate and reduced the fatigue life, and vice versa. Under the same fatigue life, a constant amplitude fatigue equivalence (CAFE) strategy is proposed, which could convert a variable amplitude road spectrum into a constant amplitude load more suitable for the testing bench. The proposed tool and method are also suitable for bi-material interface failure prediction under variable amplitude fatigue loading.

Effect of load details of the successive explosions on the blast behaviors of reinforced concrete beams

SummaryThe objective of this study was to study the effect of load details of successive explosions on the blast behaviors of reinforced concrete (RC) beams. First, the effect of the successive loading of two identical explosions was discussed by considering the influences of standoff distance, charge mass on the failure states, and structural responses (displacement and support reaction force). And keeping the total TNT charge mass of 1 kg unchanged, the effect of loading numbers was investigated by loading two 0.5 kg TNT successively and a single 1 kg TNT on RC beams, respectively. Besides, the successive loading of two different explosions was also considered by investigating the effects of loading sequences and the first explosion induced pre‐damage on the ultimate accumulated damage of RC beams. At last, based on the reaction force and displacement responses, a nonlinear relationship between the dynamic residual load‐carrying capacity and the accumulated residual displacement was obtained to assess the damage states of the tested beams. The results show that the local failure range along the beam span direction (length of peeling‐off and length of spallation) caused by the first blast load did not apparently increase when the damaged beams were subjected to another blast load. With the increase in explosion numbers, depth of compressive crushing increases gradually. At the same stand‐off distance (from 0.25 to 0.45 m), due to the damage accumulation effect, successive loading of two 0.5 kg TNT can trigger more severe local failure but smaller accumulated residual deflection to beams than the single loading of a 1 kg TNT. Besides, when two different blast loads are loaded on tested beams, the loading sequence of the larger one first and then the smaller one (1 kg TNT/0.5 kg TNT at h = 0.45 m) can trigger larger damage to beams than the opposite loading sequence (0.5 kg TNT/1 kg TNT at h = 0.45 m). And for the beams subjected to a smaller blast load first and then a larger one, a stiffer behavior may be triggered by the second blast load on the beam after the first loading of the smaller blast load due to the residual strain in longitudinal reinforcement. Furthermore, based on the nonlinear relationship between residual load‐carrying capacity and residual displacement, the accumulated damage of RC beams was divided into mainly four phases.

A nonlinear fatigue damage accumulation model under variable amplitude loading considering the loading sequence effect

Damage accumulation is nonlinear in the actual fatigue process, and the loading sequence is an important factor under variable amplitude loading. In this paper, a nonlinear fatigue damage accumulation model under variable amplitude loading considering the loading sequence effect is proposed. First, the cumulative rule of fatigue damage under variable amplitude loading is analyzed. It is suggested that the exponential function based on the load cycle ratio can be used to characterize the load sequence effect. Then, a nonlinear fatigue damage evolution equation of materials under constant amplitude load is proposed by taking the static toughness of the material as the damage parameter. Furthermore, the exponent of the load sequence influence parameter is determined as a function of the cycle life and elastic modulus. Then, a fatigue damage accumulation model under variable amplitude loading that considers the effect of the loading sequence is obtained based on the damage equivalence principle. Finally, the model is validated and compared through fatigue test data of five metal materials. It is found that the prediction accuracy of the proposed model is significantly higher than the other two models. In contrast, the difficulty of using the proposed model is lower than that of similar models.

Micro-Scale Numerical Simulation of Fatigue Failure for CFRP Subjected to Multiple-Amplitude Cyclic Loadings Based on Entropy Damage Criterion.

Fatigue failure of carbon fiber-reinforced plastics (CFRPs) under cyclic loadings has attracted the attention of researchers recently. In this study, the entropy-based failure criterion is proposed to investigate the fatigue lifetime of unidirectional CFRPs subjected to multiple-amplitude cyclic loadings. Due to the heterogeneity of CFRPs, a micro-finite element model considering matrix resin and fibers independently is developed, and the entropy-based damage criterion is implemented into a user-subroutine of Abaqus to model the progressive damage of matrix resin. The fatigue lifetime of CFRPs under typical loading sequences consisting of two stages, such as varying from low to high (L-H) or from high to low (H-L) loading sequence, is estimated with the proposed failure criterion. Numerical results show that the initial damage occurs near the area between two fibers, and a transverse crack propagates progressively under the cyclic loading. The difference in predicted lifetime to final failure in L-H and H-L stress levels is 6.3%. Thus, the effect of loading sequence on the fatigue lifetime can be revealed via the proposed entropy-based damage criterion. Comparisons with the conventional linear cumulative damage (LCD) and kinetic crack growth (KCG) theories are also conducted to demonstrate the validity of the proposed method. The entropy-based failure criterion is a promising method to predict the residual strength and fatigue lifetime of CFRP components.