Arbitrary Cyclic Loading Research Articles

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.

Generalized cyclic bond-slip model of rebar embedded in concrete under lateral pressure: Parameter calibration and numerical implementation

For some reinforced concrete members, the bond-slip between rebar and concrete is sometimes affected by the lateral pressure, e.g., the beam-column joint with the axial load induced by the column. For such cases, a cyclic bond-slip behavior taking into account the effect of lateral pressure is of great significance for seismic numerical analysis of these members/structures. So far, however, there is no available numerical approaches which can consider the cyclic bond-slip behavior of RC member under lateral pressure. Therefore, this study presents a generalized bond-slip model, which can consider the effect of cyclic loads and lateral pressure simultaneously. Based on the existing test data, the key parameters of the model are calibrated, so that the model can be used for arbitrary cyclic loading history and is easy to be implemented into existing displacement-based numerical code. Furthermore, a four-node zero-thickness bond element is developed in commercial software ABAQUS. The proposed model is implemented into the bond element and verified by the experimental results. The bond element is preliminarily applied to the force–displacement analysis of reinforcing bars in the beam-column joint, and the feasibility of the model in member-level analysis is discussed based on the numerical results.

A stress-weighted ductile fracture model for steel subjected to Ultra Low Cycle Fatigue

A new criterion is proposed to simulate the initiation of ductile fracture due to Ultra-Low Cycle Fatigue (ULCF). Building on previous research, the new fracture criterion broadens the scope of ULCF models to account for a broader range of multi-axial stress and strain states that may be encountered in steel structures. The model formulation, supported by observations from finite element plasticity simulations of void growth and fractographic analyses of fracture surfaces, describes damage accumulation as a function of plastic strain, stress triaxiality, and the Lode stress parameter. The damage rate model is integrated over arbitrary cyclic loading histories of local strains and stresses to predict ULCF fracture. The proposed criterion (termed the Stress Weighted Ductile Fracture Model – SWDFM) is supported by a series of 66 coupon scale experiments on two grades of low-carbon structural steel (A572 and A36). These tests interrogate a range of positive and negative stress triaxiality with absolute values between 0.1 and 1.6, Lode stress parameters between 0 and 1, and monotonic and cyclic loading histories. The SWDFM criterion, which requires the calibration of only two material parameters for the materials investigated in this study, is evaluated against the experimental test data using an average-error assessment as well as a cross-validation analysis. Three other ULCF rupture criteria are similarly assessed and compared. The SWDFM is shown to accurately predict ULCF initiation over a wide range of stress states and loading histories, suggesting that the model represents well the micro-mechanical mechanisms of ULCF.

A unified direct method for ratchet and fatigue analysis of structures subjected to arbitrary cyclic thermal-mechanical load histories

In this paper, the distinction between material ratchetting and structural ratchetting is clarified, and the concept of constant life diagram is extended to depict low cycle fatigue life boundary in structural design. To provide a novel one-stop solution for structural fatigue and ratchetting problems, a Unified Procedure for Fatigue and Ratchet Analysis (UPFRA) has been proposed. The UPFRA has been successfully applied to two different engineering structures considering complex geometry and temperature-dependent material properties. By comparing the results with ABAQUS step-by-step inelastic analysis, the UPFRA has been verified to be a robust engineering tool with great accuracy, usability, and efficiency.

Experiment and Modeling on Macro Fiber Composite Stress-Induced Actuation Function Degradation

The effect of stress depolarization will cause actuation function degradation of a piezoelectric actuator, which can eventually trigger function failure of the piezoelectric smart structure system. In the present study, we experimentally demonstrate the degradation process of the actuation function of the Macro Fiber Composite (MFC) piezoelectric actuator. Actuation function degradation data of MFC actuators undergoing cyclic loads with four different stress amplitudes have been measured. Based upon the experimental results, the radial basis function (RBF) neural network learning algorithm was adopted to establish a neural network model, in order to predict the actuation function degenerative degree of the MFC actuator, undergoing arbitrary cyclic load within the concerned stress amplitude range. The maximum relative error between the predicted result and our experimental result is 4%.

Shakedown of porous material with Drucker-Prager dilatant matrix under general cyclic loadings

This paper is concerned with the shakedown limit states of porous ductile materials with Drucker-Prager matrix under cyclically repeated loads. Using the hollow sphere model and Melan’s shakedown theorem based on time-independent residual stress fields, a macroscopic fatigue criterion is derived for the general conditions of cyclic loads. First, the case of the hollow sphere subjected to pure hydrostatic loading is studied and the limit states of collapse by fatigue or by development of mechanism are derived. Then, the general case involving shear effects with any arbitrary cyclic load fluctuations ranging from the pulsating load to the alternating one is considered. The key idea is in two steps: (i) the choice of appropriate trial stress and trial residual stress fields and (ii) then maximizing the size of the load domain in the spirit of the standard lower shakedown theorem. The new macroscopic shakedown criterion depends on the porosity, the friction angle, Poisson’s ratio, the two stress invariants of the effective stress tensor and the sign of the third one. Together with the limit analysis-based yield criterion corresponding to the sudden collapse by development of a mechanism at the first cycle, it defines the safety domain of porous materials subjected to cyclic load processes. Interestingly, it is found that the safe domain is little sensitive to variations of the friction angle, however, it is considerably reduced compared to the one under monotonic loads obtained by limit analysis. Finally, a comparative study between the analytical results and numerical predictions performed by micromechanics-based finite element simulations is conducted for different porosities and friction angles.

Modelling of Hysteresis Behavior of Ceramic Matrix Composites

Under cyclic loading, the fiber-reinforced ceramic matrix composites exhibits hysteresis behavior due to the friction stress. When the matrix/fiber debonding occurs, the shear stress is transferred by friction stress on the debond surface. The friction stress is derived from the equilibrium equation of debond fiber in the unit cell. The result indicates that friction shear stress of a single debond fiber can be described by bilinear law due to the static friction and sliding friction. The nonlinear characteristic of friction stress at macro scale attributes to the distribution of the fiber pullout length. The hysteresis loops arise due to the friction stress and the shape is dominated by the evolution of friction during loading/unloading process. The model decoupled the shear stress into two independent terms: the first term represents the shear stress on well bond interface and the second term represents friction shear stress on debond interface. The method developed in this paper is employed to study the hysteresis behavior of C/SiC composite subjected to arbitrary cyclic load. The hysteresis behavior of C/SiC composite is predicted and compared with experimental data.

Degradation forecast for PEMFC cathode-catalysts under cyclic loads

Abstract Degradation of Fuel Cell (FC) components under cyclic loads is one of the biggest bottlenecks in FC commercialization. In this paper, a novel experimental based algorithm is presented to predict the Catalyst Layer (CL) performance loss during cyclic load. The algorithm consists of two models namely Models 1 and 2. The Model 1 calculates the Electro-Chemical Surface Area (ECSA) and agglomerate size (e.g. agglomerate radius, rt,agg) for the catalyst layer under cyclic load. The Model 2 is the already-existing model from our earlier studies that computes catalyst performance with fixed structural parameters. Combinations of these two Models predict the CL performance under an arbitrary cyclic load. A set of parametric/sensitivity studies is performed to investigate the effects of operating parameters on the percentage of Voltage Degradation Rate (VDR%) with rank 1 for the most influential one. Amongst the considered parameters (such as: temperature, relative humidity, pressure, minimum and maximum voltage of the cyclic load), the results show that temperature and pressure have the most and the least influences on the VDR%, respectively. So that, increase of temperature from 60 °C to 80 °C leads to over 20% VDR intensification, the VDR will also reduce 1.41% by increasing pressure from 2 atm to 4 atm.

1 g Model Tests on the Displacement Accumulation of Large-Diameter Piles Under Cyclic Lateral Loading

Abstract Large-diameter monopiles are an established foundation type for offshore wind energy converters. A crucial aspect in the design of such piles is the bearing behavior under cyclically acting wind and wave loads, namely the accumulation of deflections and rotations under these loads. Regarding the prediction of the behavior under cyclic one-way load, some empirical approaches and also numerical simulation methods exist. In contrast, the behavior under cyclic two-way loading is widely unclear and must be investigated by pile tests. This paper presents the results of 1 g model tests with large-diameter piles in sand under arbitrary cyclic loading types. It was found that for almost rigid large-diameter piles, the effect of the loading type on the rate of displacement accumulation could be accounted for by a function which is almost independent on the system parameters, e.g., pile stiffness or relative density of the sand, but dependent on load eccentricity. The maximum accumulation rate occurs for asymmetric two-way loading. Using the functions found in the tests, a prediction of displacement accumulation for load spectra consisting of packages of arbitrary loads becomes possible. For flexible piles, a different effect of the loading type on the rate of displacement accumulation was observed. Here, asymmetric two-way loading was obviously not more unfavorable than one-way load.

An equivalent stress parameter for multi-axial fatigue evaluation of welded components including non-proportional loading effects

This paper presents a comprehensive investigation into non-proportional multi-axial fatigue of welded components by introducing an equivalent structural stress parameter that takes into account of load-path non-proportionality in addition to plate thickness and stress state effects. This is accomplished by formulating a “moment of load path” or “MLP” based fatigue damage parameter that provides a consistent treatment of load-path non-proportionality under arbitrary multi-axial loading conditions for which cycle counting can be consistently performed by means of a previously developed path-dependent maximum range (PDMR) cycle counting procedure. To examine its broad applicability and effectiveness, non-proportional multi-axial test data obtained using different components, joint types, and loading conditions from various sources are analyzed using the newly developed equivalent stress parameter. The results show that the new equivalent stress parameter enables not only an effective consolidation of all multi-axial test data (up to about 300 tests) analyzed in this paper into a narrow band, but also the demonstrated transferability between the master S-N curve (dominated by test data under uniaxial cyclic loading conditions) adopted by the 2007 ASME Div 2 and API 579 RP/ASME FFS-1 Codes and the consolidated S-N curve dominated by severe non-proportional multi-axial cyclic loading conditions. As a result of the present development, a unified fatigue evaluation procedure based on the newly proposed effective stress parameter and a single master S-N curve can be implemented for arbitrary cyclic loading conditions regardless of stress multi-axiality or load path proportionality.

Hysteresis loop model of unidirectional carbon fiber-reinforced ceramic matrix composites under an arbitrary cyclic load

The microstructure of unidirectional fiber-reinforced ceramic matrix composites is described by a cylindrical unit cell that is then discretized by a set of friction elements. Equilibrium equations resulting from the displacement increment balance between the fiber and matrix are constructed and solved, and the distributions of stress and displacement are obtained. Interfacial debonding, fiber fracture and matrix cracking are considered to simulate the hysteresis loops. Finally, the method developed in this paper is employed to study the interfacial sliding and hysteresis loops of a SiC/CAS composite subjected to arbitrary cyclic load. The results are discussed and compared with experimental data.

A reliability model for SAC solder covering isothermal mechanical cycling and thermal cycling conditions

This paper presents an alternative to the use of energy-based methodologies for life cycle predictions of solder interconnects. Isothermal mechanical cycling testing has been conducted using joint-scale solder samples on a novel testing apparatus. The test data shows that work as a single parameter is insufficient in predicting failure; nor does the inclusion of cyclic frequency and mean temperature improve work-based methodologies. Here, a novel semi-empirical approach is presented in which stress, strain, strain rate and temperature are individually treated to create a model capable of predicting material behaviour under arbitrary cyclic loading conditions. The model constants are fitted to the results of the isothermal mechanical cycling tests, using load drop as a measure of damage. The calibrated model is then employed to predict the failure of a BGA device under thermal cycling. The modelling results show state-of-the-art agreement with the test data and superiority over Morrow model constants from literature that have been applied to this data set.

Application of h‐adaptive FEM and Zarka's approach to analysis of shakedown problems

AbstractThe Zarka shakedown approach and the h‐adaptive finite element method are applied to evaluate residual stresses resulting from arbitrary cyclic loading. Two error indicators are used to refine the mesh: the explicit residual one which controls accuracy of the momentum balance and the interpolation error indicator which controls approximation of the modified back stresses. Validation tests performed for the Zarka method of simplified shakedown analysis suggest that such an approach may be used to obtain a quick estimate of residual states with the error acceptable for engineering purposes. Thus, it has been applied to compute residual stresses arising from service load in railroad rails. Copyright © 2004 John Wiley & Sons, Ltd.

A numerical stress calculation procedure for a fiber-fiber kinetics model with Coulomb and viscous friction of connective tissue

A material model based on fiber–fiber Coulomb and viscous friction for connective tissue was introduced in references Mijailovic (1991) and Mijailovic et al. (1993). A numerical procedure was developed in reference Mijailovic (1991) by considering sliding of fibers as a contact problem between bodies, and results were verified by experiments. Another numerical approach, much more stable and efficient, for stress calculation in case of Coulomb friction only, was proposed in reference Kojic et al. (1998). This paper represents an extension of the numerical algorithm of reference Kojic et al. (1998) to include viscous friction between fibers. The complex history of sliding is traced by dividing the current sliding length between fibers on a number of segments. The computational procedure is simple, numerically reliable and provides stress calculation for arbitrary cyclic loading of connective tissue material in tension, shear, and tension and shear simultaneously. Typical hysteresis loops can be reproduced by using the proposed numerical algorithm. The model is implemented into a finite element program PAK (Kojic et al., 1996), with a possibility of solving real problems of connective tissue. Solved examples illustrate the main features of the fiber–fiber kinetics model and of the developed numerical procedure.

Micromechanical life prediction for composite laminates

A recently developed micromechanics model, the bridging model, is incorporated to predict S– N relationships of composite laminates subjected to arbitrary cyclic loading. For this prediction, only minimum number of input data concerning constituent properties and laminate geometric information are required. The laminate failure mode can be clearly displayed. The prediction has been made for a number of angle ply glass/epoxy laminates under tensile fatigue. Good correlation has been found between the predicted results and available experimental data. For the glass/epoxy system under consideration, it is shown that laminate delamination cannot occur when the laminate has a ply angle of θ⩽8° or θ⩾44°.

A numerical algorithm for stress integration of a fiber-fiber kinetics model with Coulomb friction for connective tissue

Complex behaviour of connective tissue can be modeled by a fiber-fiber kinetics material model introduced in Mijailovic (1991), Mijailovic et al. (1993). The model is based on the hypothesis of sliding of elastic fibers with Coulomb and viscous friction. The main characteristics of the model were verified experimentally in Mijailovic (1991), and a numerical procedure for one-dimensional tension was developed considering sliding as a contact problem between bodies. In this paper we propose a new and general numerical procedure for calculation of the stress-strain law of the fiber-fiber kinetics model in case of Coulomb friction. Instead of using a contact algorithm (Mijailovic 1991), which is numerically inefficient and never enough reliable, here the history of sliding along the sliding length is traced numerically through a number of segments along the fiber. The algorithm is simple, efficient and reliable and provides solutions for arbitrary cyclic loading, including tension, shear, and tension and shear simultaneously, giving hysteresis loops typical for soft tissue response. The model is built in the finite element technique, providing the possibility of its application to general and real problems. Solved examples illustrate the main characteristics of the model and of the developed numerical method, as well as its applicability to practical problems. Accuracy of some results, for the simple case of uniaxial loading, is verified by comparison with analytical solutions.

On a new method of evaluation of the inelastic state due to moving contacts

The prediction of damage and wear of materials under repeated moving contacts requires first the determination of the limit response in terms of stress and strain. The simulation necessary to calculate the limit response could be performed with classical finite elements and an incremental treatment of the loading history, resulting in lenghtly are repeated calculations. For steady-state moving contacts, the stationary methods allows a quick evaluation of the stabilized state. These procedures cannot be used in the case of an arbitrary cyclic loading resulting, for example, from small oscillatory contacts. In this paper, a new finite element approach is developed for structures subjected to an arbitrary cyclic loading. It is based on an original intergration scheme which allows direct determination of the stabilized state of stresses, strains and internal parameters. This asymptotic state could be either an elastic shakedown, a plastic shakedown or ratchetting for an elastic-plastic material. Elastic and plastic shakedown states are easily obtained with this method. Applications to fretting fatigue and wear in relation to material fatigue properties are presented.

USEFUL SCALAR PARAMETERS FOR MULTIAXIAL FATIGUE DEFORMATION STUDIES

Abstract— Two scalar parameters relating to stored energies are defined along an arbitrary cyclic loading path for an isotropic elastic‐plastic continuum. The definitions of the parameters are introduced in the one‐dimensional case. The tensorial generalization is developed firstly under the mechanical point of view and secondly focusing attention on the thermodynamical rates. The case of the usual cyclic traction test is studied in order to suggest an interest in the proposed parameters in the quasi‐reversible range and in the subsequent transition range between reversibility and quasi‐perfect plasticity.

Scatter characteristics of fatigue life in normalized 0.21% carbon steel plain specimens: Goto, M., Nisitani, H. and Yakushiji, T. J Soc Mater Sci Jpn (Feb. 1993) 42 (473), 163–168 (in Japanese)

This paper presents a comprehensive investigation into non-proportional multi-axial fatigue of welded components by introducing an equivalent structural stress parameter that takes into account of load-path non-proportionality in addition to plate thickness and stress state effects. This is accomplished by formulating a “moment of load path” or “MLP” based fatigue damage parameter that provides a consistent treatment of load-path non-proportionality under arbitrary multi-axial loading conditions for which cycle counting can be consistently performed by means of a previously developed path-dependent maximum range (PDMR) cycle counting procedure. To examine its broad applicability and effectiveness, non-proportional multi-axial test data obtained using different components, joint types, and loading conditions from various sources are analyzed using the newly developed equivalent stress parameter. The results show that the new equivalent stress parameter enables not only an effective consolidation of all multi-axial test data (up to about 300 tests) analyzed in this paper into a narrow band, but also the demonstrated transferability between the master S-N curve (dominated by test data under uniaxial cyclic loading conditions) adopted by the 2007 ASME Div 2 and API 579 RP/ASME FFS-1 Codes and the consolidated S-N curve dominated by severe non-proportional multi-axial cyclic loading conditions. As a result of the present development, a unified fatigue evaluation procedure based on the newly proposed effective stress parameter and a single master S-N curve can be implemented for arbitrary cyclic loading conditions regardless of stress multi-axiality or load path proportionality.

Effect of non-proportional loading on creep-fatigue properties of 304 stainless steel at low strain ranges near the elastic region: Asayaman, T., Aoto, K. and Wada, Y. Nucl Eng Des (Mar. 1993) 139 (3), 299–309

This paper presents a comprehensive investigation into non-proportional multi-axial fatigue of welded components by introducing an equivalent structural stress parameter that takes into account of load-path non-proportionality in addition to plate thickness and stress state effects. This is accomplished by formulating a “moment of load path” or “MLP” based fatigue damage parameter that provides a consistent treatment of load-path non-proportionality under arbitrary multi-axial loading conditions for which cycle counting can be consistently performed by means of a previously developed path-dependent maximum range (PDMR) cycle counting procedure. To examine its broad applicability and effectiveness, non-proportional multi-axial test data obtained using different components, joint types, and loading conditions from various sources are analyzed using the newly developed equivalent stress parameter. The results show that the new equivalent stress parameter enables not only an effective consolidation of all multi-axial test data (up to about 300 tests) analyzed in this paper into a narrow band, but also the demonstrated transferability between the master S-N curve (dominated by test data under uniaxial cyclic loading conditions) adopted by the 2007 ASME Div 2 and API 579 RP/ASME FFS-1 Codes and the consolidated S-N curve dominated by severe non-proportional multi-axial cyclic loading conditions. As a result of the present development, a unified fatigue evaluation procedure based on the newly proposed effective stress parameter and a single master S-N curve can be implemented for arbitrary cyclic loading conditions regardless of stress multi-axiality or load path proportionality.