Proposed Fatigue Model Research Articles

Fatigue evaluation on the effect of impact pits with various impact conditions by a CDM‐based approach

AbstractThis work aims to quantitatively evaluate the influence of the impact velocity, location, and angle of a spherical foreign object on fatigue lives. A continuum damage mechanics (CDM)–based fatigue approach is proposed to evaluate the fatigue behavior. The experiments on a cast AlSi7Mg1 aluminum alloy with a low‐velocity impact pit are used to validate the proposed fatigue model. The comparison between the predicted lives with the experimental data indicates an excellent agreement. Based on the proposed model, the effects of various impact velocities, locations, and angles are investigated. It is found that the velocities have negligible influence on the fatigue life in low‐velocity impact cases once the pit depth is the same. The most dangerous impact location for 90° normal impact cases is inferred to be a distance away from the boundary surface. The 45° transverse impact close to the boundary is different from other studied oblique impacts and has a longer life than the corresponding normal impact. This study uses a feasible method to predict the effects of different impact conditions and provides useful guidance for engineering applications.

Jk-integral applied to mixed-mode fatigue crack propagation and life prediction in metal welding interface

In this paper, an innovative fatigue crack propagation model of metal welding interface is investigated based on the concept of Jk-integral (k = 1, 2) in elastic–plastic material, including the prediction of crack propagation path and life. In order to validate the effectiveness of the present fatigue model, the experiments of mixed-mode interface fatigue cracks are carried out on compact tensile shear specimens of N36 zirconium alloy using DIC methods. The results demonstrate that the fatigue crack only propagates along the interface under mode I loading where the relationship between the crack growth rate da/dN and ΔJ1 (the J1-integral range per loading cycle) is logarithmic linear. As for mode I/II mixed-mode loading, interface cracks start to propagate along the interface when J1 reaches Jint-C (the interface fracture toughness). When Jtotal (the vector sum of J1 and J2) reaches Jsub-C (the substrate fracture toughness), the crack deflects to the substrate in the Jtotal direction. In this case, da/dN shows a two-stage logarithmic linear relation with ΔJtotal (the Jtotal-integral range per loading cycle) under mixed-mode loading, and the critical Jtotal at the beginning of crack deflection is approximately matching the specific value. The theoretical deflection angle (i.e. the Jtotal direction) calculated from the corresponding J1 and J2 at the beginning of crack deflection is wellconsistentwiththe actual deflection angle observed in experiments. Moreover, the model can clearly describe the two-stage process from the crack propagation along the interface to the crack deflection to the substrate under mixed-mode loading. It is concluded that the proposed fatigue model based on Jk-integral can accurately predict the fatigue crack propagation path and lifetime of metal welding interface.

Analysis and Modeling of Aged SAC-Bi Solder Joints Subjected to Varying Stress Cycling Conditions.

Solder joints are subjected to varied stress cycle circumstances in the electronic packaging service life but are also influenced by aging. There has been limited investigation into the influence of aging and varying cycles on SnAgCu-Bi (SAC-Bi) solder joint fatigue. Cyclic fatigue tests were performed on solder joints of several alloys, including SnAgCu (SAC305), SnAgCu-Bi (SAC-Q), and SnCu-Bi (SAC-R). Individual solder joints were cycled under varying stress levels, alternating between mild and harsh stress levels. At least seven samples were prepared for each alloy by alternating between 25 mild stress (MS) cycles and three harsh stress (HS) cycles until the solder joint broke off. The impact of aging on Bi-doped solder joints fatigue under varied amplitude stress was examined and predicted for 10 and 1000 h under 125 °C. Because of the "Step-up" phenomenon of inelastic work, a new fatigue model was developed based on the common damage accumulation (CDA) model. The experimental results revealed that aging reduced the fatigue life of the tested solder alloys, particularly that of SAC305. According to the CDA model, all solder alloys failed earlier than expected after aging. The proposed model uses the amplification factor to assess inelastic work amplification after switching between the MS and HS cycles under varying stress amplitude conditions. The amplification factor for the SAC-Bi solder alloys increased linearly with fracture initiation and substantially followed crack propagation until the final failure. Compared with existing damage accumulation models, the proposed fatigue model provides a more accurate estimation of damage accumulation. For each case, the cut-off positions were examined. The SAC-Q amplification factor increased linearly to 83% of its overall life, which was much higher than that of SAC305 and SAC-R. This study identified three distinct failure modes: ductile, brittle, and near intermetallic compound (IMC) failure. It was also observed that SAC-Q with an organic solderability preservatives (OSP) surface finish was more susceptible to brittle failure owing to the excessive brittleness of the alloy material.

Modeling of Multiple Fatigue Cracks for the Aircraft Wing Corner Box Based on Non-ordinary State-based Peridynamics

In the current research, we propose a novel non-ordinary state-based peridynamics (PD) fatigue model for multiple cracks’ initiation and growth under tension–tension fatigue load. In each loading cycle, the fatigue loading is redistributed throughout the peridynamic solid body, leading to progressive fatigue damage formation and expansion in an autonomous fashion. The proposed fatigue model parameters are first verified by a 3D numerical solution, and then, the novel model is used to depict the widespread fatigue damage evolution of the aircraft wing corner box. The modified constitutive damage model has been implemented into the peridynamic framework. Furthermore, the criteria and processes from multiple initiations to propagation are discussed in detail. It was found that the computational results obtained from the PD fatigue model were consistent with those from the test data. The angular errors of multiple cracks are within 2.66% and the number of cycles errors are within 15%. A comparison of test data and computational results indicates that the fatigue model can successfully capture multiple crack formations and propagation, and other behaviors of aluminum alloy material.

Multiaxial high-cycle fatigue failure and life prediction based on critical plane method

Multiaxial high-cycle fatigue failure criterion and life prediction is important for structural components under complex low stress. A new multiaxial high-cycle fatigue damage parameter based on the plane of maximum shear stress is proposed, which includes the maximum shear stress amplitude, normal stress amplitude and maximum equivalent normal stress. The maximum equivalent normal stress is defined in the form of SWT stress function considering the influence of mean stress. The feasibility of the proposed failure criterion and life prediction model is verified by test data of different materials. The predicted results show that the life prediction error of the proposed fatigue model is basically within three times by comparing with McDiarmid, Matake, Crossland and Papadopoulos fatigue models.

Numerical Study on Vibration Response and Fatigue Damage of Axial Compressor Blade Considering Aerodynamic Excitation

Axial compressor blades with a deformed initial torsion angle caused by aerodynamic excitation resonated at the working speed and changed the rule of fatigue damage accumulation. The fatigue life of a blade has a prediction error, even causing serious flight accidents if the effect of torque causing damage deterioration of the blade fatigue life is neglected. Therefore, in this paper, a uniaxial non-linear fatigue damage model was modified using the equivalent stress with torsional shear stress, and the proposed fatigue model including the torsional moment was used to study the compressor blade fatigue life. Then, the blade numerical simulation model was established to calculate the vibration characteristics under complex loads of airflow excitation and a rotating centrifugal force. Finally, the blade fatigue life under actual working conditions was predicted using the modified fatigue model. The results show that the interaction between centrifugal and aerodynamic loads affects the natural frequency, as the frequencies in modes dominated by bending deformation decreased whereas those dominated by torsional deformation increased. Furthermore, the blade root of the suction surface showed stress concentration, but there is an obvious difference of stress distribution and amplitude between the normal stress and the equivalent stress including torsional shear stress. The additional consideration of the torsional shear stress decreased the predicted fatigue life by 4.5%. The damage accumulation rate changes with the loading cycle, and it accelerates fast for the last 25% of the cycle, when the blade fracture may occur at any time. Thus, the aerodynamic excitation increased the safety factor of blade fatigue life prediction.

A fatigue model based on M-integral in notched elastic–plastic material

In this paper, an innovative fatigue model is investigated based on the concept of M-integral in notched elastic–plastic material. The contribution of notch and plastic zone damage to the lifetime of material are taken into account in the present fatigue model. The new form of fatigue damage evolution rate (dAD/dN) and fatigue driving force (ΔM) are introduced, where AD deontes the equivalent damage area of notch, plastic zone and cracks, N is the number of cycles, and ΔM corresponds to the M-integral range per load cycle. The fatigue experimental evaluations of a typically elastic–plastic material (e.g., No. 45 steel) with a circular notch have been carried out to validate the effectiveness of the present fatigue model. For experimental study, the change of the total potential energy (CTPE) is introduced to measure the value of M-integral. The results demonstrate that dAD/dN shows an apparent power law relation with ΔM in notched elastic–plastic material. The slope n and intercept λ of lg(dAD/dN)-lg(ΔM) curve has linear correlation with the initial notch radius R, but not with applied stress σ. Moreover, the model can clearly describe the two-stage process from the initiation of microcracks to the growth of macrocracks in notched body. It is concluded that the proposed fatigue model based on M-integral can accurately predict the fatigue lifetime of the notched elastic–plastic material.

Tensile Fatigue Behavior of Polyester and Vinyl Ester Based GFRP Laminates-A Comparative Evaluation.

Fatigue loading is critical to fibre reinforced polymer composites due to their anisotropic and heterogenous nature. This study investigated the tensile fatigue behaviour of polyester and vinyl ester based GFRP laminates to understand the critical aspects of failure mode and fatigue life under cyclic loading. GFRP laminates with two different resin systems (polyester and vinyl ester), two different stress ratios (0.1 and 0.5) and two different environmental conditions (air and water) were investigated at an applied stress of 80%, 60%, and 40% of the ultimate capacity. Based on the investigated parameters (i.e., resin types, stress ratio, environmental conditioning, and maximum applied stress), a fatigue model was proposed. Results show that the resin system plays a great role in fatigue failure mode while the stress ratio and environmental condition significantly affect the tensile fatigue life of GFRP laminates. The types of resin used in GFRP laminates and environmental conditions as input parameters in the proposed fatigue model are a unique contribution.

Modeling detrimental effects of high surface roughness on the fatigue behavior of additively manufactured Ti-6Al-4V alloys

This article presents a fatigue model that can robustly capture the effect of high surface roughness on the fatigue crack initiation of additively manufactured Ti6Al4V (AM Ti64) alloys in the moderate cycle fatigue regime based on nonlinear finite element (FE) analyses and the theory of critical distances. We propose two methods to use surface measurements of AM components to create FE models, viz., surface topography of the component is explicitly represented in the FE models or a simplified geometrical model, which has only a single sinusoidal-shaped notch, is proposed to replace the surface topography in the FE models. The geometrical parameters of the simplified model are derived based on the MOTIF method (ISO 12085) and its parameters are determined by using the leave-one-out cross-validation method. In the moderate cycle fatigue regime, the stress applied to components is below the yield stress, but the high surface roughness acts as a stress raiser and causes local plasticity at surface valleys. Thus, a nonlinear hardening elasto-plasticity model is employed in the FE models to capture the cyclic mechanical behavior of AM Ti64 alloys. Afterward, the fatigue analyses are performed by employing our in-house C++ software within which fatigue indicator parameters (FIPs) are computed by post-processing the finite element results. In the present work, the Smith-Watson-Topper (SWT) parameter is used as an FIP and is computed at every element in the FE mesh, i.e., the local FIP. Subsequently, to account for the stress gradient effect in the proposed fatigue model, the SWT parameter is averaged over a so-called critical area to compute a nonlocal FIP. The physical fidelity of the proposed fatigue model is shown by a good agreement between the predicted fatigue life cycles based on the nonlocal FIP and the corresponding experimental data. Moreover, the predicted fatigue cycles obtained from the simplified geometrical model also yield good accordance to the experimental data, thus we can model the effect of the surface roughness on the fatigue properties of AM Ti64 in an efficient way.

A fatigue model for track-bed materials with consideration of the effect of coarse grain content

Abstract Previous studies showed that the permanent strain of interlayer soil in the French conventional railway substructure is highly dependent on the volumetric coarse grain content fv (volumetric ratio of coarse grain to total sample). This study developed a fatigue model allowing the effects of coarse grain content fv, stress state and number of loading cycles N on permanent strain to be accounted for. Data from the multi-stage loading cyclic tests of interlayer soil conducted at six different fv values (0%, 5%, 10%, 20%, 35% and 45%) and five different maximum deviator stress Δqmax values (10 kPa, 15 kPa, 20 kPa, 25 kPa and 30 kPa) were reviewed and used for this purpose. The model parameters were determined by fitting the results from the tests at fv = 0%, 5% and 35%. In order to validate the proposed fatigue model, the determined model parameters were then used to simulate the tests at fv = 10%, 20% and 45%. The results obtained showed that the proposed model can well describe the permanent strain after a certain number of loading cycles, in the case of plastic shakedown.

Material Configurational Forces applied to mixed-mode fatigue crack propagation and life prediction in elastic-plastic material

Within the framework of material configurational mechanics, an innovative fatigue model based on configurational force is proposed to predict the mixed-mode fatigue crack propagation in elastic-plastic material. This fatigue mode can provide the estimation of crack initiation, crack deflection, and residual fatigue lifetime simultaneously. The configurational-force fatigue model has the following basic stipulations: (a) the onset of crack growth occurs when the resultant of configurational forces reaches a critical value; (b) the crack growth takes place along the direction of resultant configurational force vector; and (c) the growth rate of mixed-mode fatigue crack is correlated to the equivalent range of material configurational forces. In order to validate the accuracy of the newly proposed fatigue model, a series of experiments are constructed by the compact tension shear specimen. The mixed-mode fatigue crack growth path and rate are obtained under different mixed-mode loading conditions. In addition, numerical implementation of configurational-force fatigue model is performed in elastic-plastic material. The results show that the mixed-model fatigue crack deflections predicted by the configurational-force fatigue model are in good agreement with experimental observations. Meanwhile the fatigue crack growth rate in elastic-plastic material has the power law relation with the equivalent range of material configurational forces, which is regardless of mixed-mode loading. It is demonstrated that the configurational-force fatigue model is able to provide a more convenient and accurate procedure to predict the mixed mode elastic-plastic fatigue crack propagation and lifetime.

Fatigue life prediction of composite laminates by fatigue master curves

In this paper, fatigue master curves are adopted to predict fatigue life of composite laminates made by unidirectional and braided fiber reinforced composite. Fatigue failure is then determined by Puck’s criterion. Uniaxial and multiaxial S-N curve could be obtained from the fatigue master curves. Fatigue lives of composite laminates made by unidirectional carbon and glass fiber reinforced composite are predicted by the proposed method. To extend the fatigue master curve to predict the braided composite laminate, tensile-tensile, compressive-compressive and tensile-compressive fatigue experiments are carried out in this paper. The predictions from the proposed fatigue model are compared with various experimental results and reasonably good agreement is observed.

Modeling NSM FRP strengthened RC beams under fatigue due to IC-debonding

This paper presents an analytical model proposed to predict the flexural fatigue behavior and fatigue life of reinforced concrete (RC) beams strengthened with near-surface mounted (NSM) fiber reinforced polymer (FRP) reinforcements subject to intermediate crack-induced debonding failure. In deriving this model, a trilinear behavior is assumed for the bond-slip relationship of FRP-concrete interface. Based on a model previously developed for strengthened beams under monotonic loading, the proposed fatigue model considers the fatigue bond heterogeneity by imposing a degradation law for the peak interfacial shear stress. Theoretical solutions to the flexural behavior throughout the fatigue life are obtained by imposing appropriate boundary conditions. The predicted fatigue life under debonding failure mode and flexural behavior (e.g., tensile strain of the NSM reinforcement) are further verified by comparisons with existing experimental data, where good agreement is reached. The subsequent parametric study shows that higher concrete compressive strength and bond strength of NSM improves the flexural behavior under fatigue and elongates the fatigue life. The diameter and Young’s modulus of the NSM reinforcement have insignificant effect on the fatigue flexural behavior.

Residual stress and fatigue behavior of riveted lap joints with various riveting sequences, rivet patterns, and pitches

The residual stress of multi-rivet structures is related with the riveting sequence, the rivet pattern, and the pitch due to the deformation interaction of different rivets. The stress amplitude of riveted structures subjected to the cyclic loads is affected by the residual stress, which increases the difficulty in the prediction of fatigue life. In this article, the riveting processes for single-row and triple-row riveted lap joints with various riveting sequences, rivet patterns, and pitches are studied numerically and experimentally. The residual stresses for both types of riveted structures are verified by the testing data. Significant difference appears in the residual stress field for riveted lap joints with various riveting sequences and rivet patterns. The decrease in the rivet pitch increases the compressive residual stress at the edge of the rivet hole. Furthermore, the fatigue life prediction model is developed for multi-rivet structures, in which the coupling effect of residual stress and cyclic load is considered. The fatigue experiments are conducted for riveted lap joints with various riveting sequences, rivet patterns, and pitches. The accuracies of the numerical results obtained from the Homan model and the developed model are compared with the experimental data. The proposed fatigue model shows better performance to predict fatigue life for multiple rivet structures.

Pervious concrete under flexural fatigue loading: Performance evaluation and model development

Pervious concrete (PC) is used for parking lots and streets that are subjected to repeated wheel loading, therefore it is necessary to characterize the fatigue life (N) of PC for pavement design. This research investigates the behavior of PC beams made with two aggregates (angular and round) and three porosity levels (20%, 25% and 30%) under flexural fatigue loading in three stress ratios (SR:) 0.75, 0.8, and 0.85. The results showed that N is controlled by SR, while porosity showed no statistically significant effect on flexural fatigue. Two-parameter Weibull distribution was fitted to the test data to generate fatigue models at different reliability levels. Using the existing model for portland cement concrete (PCC) for PC results in an overestimation of N for SR > 0.75 due to the highly porous and brittle macrostructure of PC. Existing PCC model agrees with the proposed PC model in predicting N at 0.5 < SR < 0.75, while overestimates N at SR < 0.5. The proposed fatigue model can be used in the thickness design of PC pavements.

Stress–cycle curves for concrete beams with fibre-reinforced polymer using runout data

The use of externally bonded fibre-reinforced polymer (FRP) increases the fatigue life of reinforced-concrete beams due to a reduction in the steel stress level when compared with unstrengthened beams. For steel stresses up to 80% of the yield stress, fatigue failure is normally marked by the gradual deterioration of the steel reinforcement, which leads to a stress transfer to the FRP, until failure. Higher steel stresses are associated with FRP debonding, while steel stresses below the fatigue limit will never lead to fatigue failure. In this work, the maximum likelihood estimation method was used to determine stress–cycle curves and confidence intervals. Experimental data with runouts of fatigue tests found in the literature and generated through an experimental programme were used to adjust the fatigue model. The aim was to characterise the large scatter between the results of fatigue tests from different sources. The proposed fatigue model was found to represent accurately the slope of the fatigue curve for FRP-strengthened beams.

High-Temperature Low Cycle Fatigue Life Prediction and Experimental Research of Pre-Tightened Bolts

Bolted connections are widely used in various mechanical structures due to their superior fastening properties. However, vibration and fatigue loads in the structure are likely to cause fatigue failure of the bolted joints, especially those under high temperature, such as in aero-engines. This paper mainly studies the low-cycle fatigue life of the pre-tightened bolts working at a high temperature. A novel test fixture is designed for fatigue tests, and low cycle fatigue tests of pre-tightened bolts are conducted at the temperatures of 550 °C and 650 °C, respectively. Furthermore, a new low cycle fatigue model that is based on the Von Mises equivalent stress/strain criterion is proposed. Meanwhile, the proposed model is used to predict the high-temperature low cycle fatigue life of pre-tightened bolts according to the stress/strain results obtained by finite element analysis. There is good agreement between the experimental results and those obtained by theoretical prediction, which validates the accuracy of the proposed fatigue model. Research results will provide a theoretical basis for the low cycle fatigue life prediction of pre-tightened bolts.

Fatigue assessment of a notched member under combined LCF and HCF loading

Steam turbine last stage blades can experience a wide range of load spectra during their lifetime, which involves both Low Cycle Fatigue (LCF) and High Cycle Fatigue (HCF) phenomena.In the paper a numerical model is proposed for considering this specific load spectrum in the fatigue life assessment of turbine blade components made of high strength precipitation-hardening steels.The method is based on cyclic isothermal stress and strain controlled fatigue test results of notched and un-notch specimen up to the HCF-regime. Moreover, stress controlled tests on notched specimens with different stress ratios were performed in order to evaluate the influence of mean stress and to derive a local Haigh diagram. The Highly Stressed Volume (HSV) has been used to transfer characteristic fatigue properties from specimens to a critical area (notched part) of a turbine blade. Furthermore, the real operating conditions of the component were used to allow the application of Palmgren-Miner damage rule.An ad-hoc MATLAB® software has been developed for the post-process of Finite Element Analysis (FEA) results, in particular for the automatic calculation of the HSV on the critical areas of the component. The proposed fatigue model has been finally applied on a real case study (blade dovetail) using appropriate safety margins for reliable design assessment.

Computational mixed mode failure analysis under fatigue loadings with constant amplitude and overload

The integrity of engineering structures can be often compromised under cyclic loading due to the propagation of the pre-existing cracks. Therefore, computationally feasible fatigue crack growth models are essential for the residual strength analysis. In the present paper, a new fatigue design model is developed for the failure assessment of mixed-mode I/II crack situations subjected to cyclic loading with either a constant amplitude or overload. A fracture mechanics-based methodology takes into account Kujawski’s crack growth law, Wheeler’s retardation model and the maximum principal stress criterion in order to estimate the residual life and crack path. Furthermore, the experimental investigation of two cracks emanating from a hole subjected to mixed mode loading is performed. Then, such a crack problem is numerically simulated applying the finite element method. The predictive capacity and accuracy of the proposed fatigue model are assessed by means of the literature-based experimental and calculated crack growth data.

A fatigue damage meso-model for fiber-reinforced composites with stress ratio effect

This work presents a fatigue damage meso-model for fiber-reinforced plastic composites, in which the effect of stress ratios on the off-axis fatigue behavior is taken into account. The non-dimensional effective stress concept is introduced in the continuum damage mechanics method. Damage growths and fatigue failure are studied along axial, transverse and shear directions at meso-scale level. The proposed model is validated through numerical simulations that describe the meso fatigue damage accumulation and the fatigue life for off-axis unidirectional fiber-reinforced plastic composite laminates of arbitrary fiber orientation under different stress ratios. It is shown that the fatigue damage behavior and fatigue life for off-axis unidirectional glass/epoxy and carbon/epoxy composite laminates are adequately described by the proposed fatigue model over the range of different stress ratios.