Variable Amplitude Loading Conditions Research Articles

Study of fatigue crack propagation on modified CT specimens under variable amplitude loadings using machine learning

This study focuses on predicting fatigue crack paths and fatigue life in modified compact tension specimens, under mixed mode and variable amplitude loading conditions, using Machine Learning techniques. Mixed-mode conditions were induced by using specimens that incorporated holes with different radii and center coordinates. Initially, multiple Finite Element Method (FEM) simulations were conducted to determine the fatigue crack path for different configurations. Subsequently, several configurations were selected for experimental fatigue testing, in which the fatigue crack path was monitored and recorded. The final phase of the study involved Machine Learning (ML) techniques, specifically Artificial Neural Networks (ANN) and k-Nearest Neighbors (kNN), to predict fatigue crack propagation. The models were trained using different numerical and experimental data. Predicted results were then compared with experimentally tested data, and the behavior and accuracy of the models were evaluated. Overall, the implemented models demonstrated the ability to predict fatigue crack path with average deviations (ANN – 1.19 mm; kNN – 1.10 mm) closely resembling results obtained through Finite Element simulations (1.65 mm). The models were also able to predict fatigue life with average errors of 10.1 % (ANN) and 16.7 % (kNN), all achieved with a reduction of computational costs greater than 90 %.

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.

Life prediction of 6201-T81 aluminum alloy wires under fretting fatigue and variable amplitude loading

Fretting fatigue tests under variable amplitude loading were performed on 6201-T81 aluminum alloy wires of an AAAC 900 MCM conductor. The loading program consisted of a three-block loading history, defined using vibration data of a transmission line located in the center-west region of Brazil. Two previously developed methodologies for life prediction of wires under fretting fatigue, based on the Theory of Critical Distances and on a master fatigue curve, were extended to variable amplitude loading conditions. The good agreement between measured and predicted lives indicated that both methodologies can be useful for fatigue analysis of wires of overhead conductors.

A fatigue crack growth prediction model for cracked specimen under variable amplitude loading

The objective of this study was to propose a crack growth prediction model for cracked specimens under large and variable amplitude loading conditions. In this study, the concept of change in net-section strain energy was applied to simulate elastic–plastic fracture behavior, and three-dimensional fitting of the results with respect to changes in the net-section strain energy, load ratio, and crack growth rate was performed to create the crack growth prediction model. The validity of the generated model was examined using comparisons with experimental data as well as simulation results from existing crack growth models under several variable loading conditions.

Fatigue Life Analysis of Automotive Cast Iron Knuckle under Constant and Variable Amplitude Loading Conditions

The main aim of the present paper is to assess the fatigue lifetime of ductile cast iron knuckles as one of the critical components of an automotive steering system. To this end, a real driving path, including various maneuvers, such as acceleration, braking, cornering, and moving on various types of road roughness, was considered. Different load histories, which are applied on various joints of the component (i.e., lower control arm, steering linkage, and Macpherson strut), were extracted through Multi-Body Dynamics (MBD) analysis of a full vehicle model. The achievements of previous studies have proved that the steering knuckle fails from the steering linkage and due to the rotational motion. Therefore, only this destructive load history was considered in future analyses of the present study. The CAD model was created using Coordinate Measuring Machine (CMM) data and some corrections in CATIA software. Furthermore, transient dynamic analysis was performed, and the time history of von Misses equivalent stress was obtained at the root of the steering linkage (which is exactly the location of failure based on the laboratory data as well as finite element simulations validated by the author in the previous studies). To predict the fatigue life of a component, two different methodologies were considered. Firstly, some well-known criteria were employed for equalization of load spectrum to a Constant Amplitude Loading (CAL). Then, fatigue analysis under sinusoidal loading was performed. Secondly, the fatigue life of the component considering Variable Amplitude Loading (VAL) was predicted using the Critical Plane Method (CPM), employing the Rain-flow cycle counting technique, and utilizing the Miner–Palmgren damage accumulation rule. Eventually, to evaluate the prediction accuracy of different methodologies, the obtained results were compared with the full-scale axial variable amplitude fatigue test which was performed by the corresponding author. The results indicated that the prediction of variable amplitude fatigue lifetime by Finite Element (FE) analysis in the time domain has about 21% error compared to reality. Additionally, the relative error between the results obtained from two different methodologies is about 20%, which is acceptable due to the scattering of the fatigue phenomenon results, the complex geometry of the part, and the complicated loading.

A modified fatigue damage model considering loading sequence effect

A modified fatigue damage model is proposed considering the loading sequence effect under variable amplitude loading conditions. The transition sequence is obtained from the counting sequence by an equivalent rainflow counting method and is used to provide the loading sequence information for fatigue damage accumulation prediction. Rainflow counting matrix and sequence transition matrix are formulated based on the rainflow counting sequence and the transition sequence. The relation between the two matrices and the original loading sequence is evaluated in detail. In the deterministic fatigue estimation, the rainflow counting matrix and the sequence transition matrix are integrated into the proposed modified damage model based on the linear damage rule. Mean stress transition is applied to the rainflow counting matrix for loading level effect. Existing experimental data are used to validate the fatigue damage estimation from the deterministic framework. In order to evaluate the fatigue under random loading conditions, the rainflow counting matrix and sequence transition matrix are mapped to one-dimensional exponential and Laplace distributions based on the stationary random process. Numerical simulation is conducted to validate the proposed mapping distributions. Meanwhile, the impact of the correlation length on the proposed distributions under stationary random loading sequence is investigated as well. Finally, with the given distributions of the rainflow counting matrix and sequence transition matrix, a reconstruction procedure is simulated and discussed for probabilistic fatigue estimation. The proposed model provides a sophisticated approximation to the original loading sequence with a sequence transition effect. The proposed modified fatigue damage model corrects the deficiencies of the linear damage rule with sufficient sequence information from the originally applied loading. Furthermore, the probabilistic fatigue estimation can evaluate the accumulated fatigue damages under a random loading process with the sequence transition effect.

Experimental investigation of high frequency pulse loading on fatigue crack growth in 5052-H32 series aluminum

In the marine industry, designers utilize 5052-H32 marine grade series aluminum for its strength to weight ratio, and the ability of this series to resist marine corrosive environments. During the operating lifetime of a marine vessel, it experiences constant and variable amplitude loading conditions from the sea environment, plus overloads/underloads in the form of high frequency pulses. These high frequency pulses can influence the fatigue crack growth behavior of the aluminum structure. Foundational models like Wheeler and Willenborg have previously been used to predict effects of underloads/overloads on fatigue crack growth, but have proven to be inadequate for all high frequency pulse loading conditions. In this paper, we coupled observations of the crack growth path obtained using an optical microscope with detailed measurements of surface strain fields using Digital Image Correlation (DIC) to elucidate the effects resulting from these high frequency pulses. An experimental test matrix was developed for applying pulses of varying amplitude and frequency to gain fundamental understanding of the characteristics of the high frequency pulses on crack growth behavior. Experimental results indicated there is a novel crack kinking behavior which results in retardation of the fatigue crack growth. Using DIC, we identified changes in the plastic zone ahead of the crack tip that mimic a hard inclusion, affecting not only the crack path, but also the crack opening displacements and subsequent crack growth rates. This work provides a foundation for understanding effects of high frequency pulses on crack growth to enable future development of a model incorporating the effects of the plastic zone on the growth mechanisms.

Effects of load interactions on the onset of stage two of high pH stress corrosion cracking

The aim of this study was to investigate load interactions that influence crack geometry evolution during the early stages of the High pH Stress Corrosion Cracking (HpHSCC). Variable amplitude loading waveforms were designed to simulate the underload-minor-cycle pressure fluctuations found during the operation of gas pipelines. The role of underload cycles and minor cycles in intergranular crack growth was investigated. It is found that underload cycles form the cyclic plastic zone at the crack tip, and that assists secondary crack initiation. The crack growth rate under the variable amplitude loading condition approximates the crack growth rates caused by low R-ratio cycles, i.e., acts as if all the cycles contained major stress changes. It is argued that small load fluctuations are non-propagating cycles unless they are followed by a major underload cycle. The possible load interactions between minor cycles and underload cycles are studied. It is discussed how an increase in the number of minor cycles between two underload events produces acceleration factors of up to 2.6. These findings imply that avoiding large internal pressure fluctuation delays the onset of stage 2 of HpHSCC and extends the line pipes operating lifetime.

Fatigue Characteristic of Designed T-Type Specimen under Two-Step Repeating Variable Amplitude Load with Low-Amplitude Load below the Fatigue Limit

In order to investigate the non-linear fatigue cumulative damage of joints in ocean structural parts, one type of low carbon steel Q345D was employed to prepare designed T-type specimens, and a series of fatigue experiments were carried out on the specimens under two-step repeating variable amplitude loading condition. The chosen high cyclic loads were larger than the constant amplitude fatigue limit (CAFL) and the chosen low cyclic loads were below the CAFL. Firstly, the S-N curve of designed T-type specimen was obtained via different constant amplitude fatigue tests. Then, a series of two-step repeating variable load were carried out on designed T-type specimens with the aim of calculating the cumulative damage of specimen under the variable fatigue load. The discussions about non-linear fatigue cumulative damage of designed T-type specimens and the interaction effect between the high and low amplitude loadings on the fatigue life were carried out, and some meaningful conclusions were obtained according to the series of fatigue tests. The results show that fatigue cumulative damage of designed T-type specimens calculated based on Miner’s rule ranges from 0.513 to 1.756. Under the same cycle ratio, the cumulative damage increases with the increase of high cyclic stress, and at the same stress ratio, the cumulative damage increases linearly with the increase of cycle ratio. Based on the non-linear damage evaluation method, it is found that the load interaction effect between high and low stress loads exhibits different damage or strengthening effects with the change of stress ratio and cycle ratio.

Variable amplitude fatigue behavior and modeling of cast aluminum

AbstractMost of the research reported in the literature on cast aluminum alloys is related to constant amplitude loading, while in most applications such components are subjected to variable amplitude loading conditions. In this work, fatigue performance of high pressure die cast (HPDC) A356‐T6 aluminum alloy is evaluated using a real industrial load spectrum. Mean stress effect was also studied by conducting variable amplitude fatigue tests under two different mean stress conditions. Fatigue life estimations were performed following S‐N approach as well as fracture mechanics approach using direct summation method as well as FASTRAN program assuming the defects as initial cracks. The size of fatal defects measured from fracture surfaces as well as the maximum defect size estimated by extreme value statistics were used in fatigue life estimations. The results of life estimations are compared and discussed with reference to the experimental results.

Influence of load interaction and hydrogen on fatigue crack growth behavior in steel pipelines under mean load pressure fluctuations

AbstractCrack propagation in near neutral pH (NNpH) environment causes significant threat to pipeline integrity. Internal pressure fluctuations during pipeline operation create variable amplitude loading condition that can propagate corrosion fatigue cracks in NNpH environments. This study is aimed at understanding the effect of load interaction due to mean load pressure fluctuations on crack propagation in pipeline steel under NNpH conditions. The loading condition involved underload followed by an overload at set intervals among minor cycles. The effect of minor cycles, magnitude of overload, and NNpH environment were considered and compared to control test in air. Results showed optimum reduction in crack growth rate at low magnitude of overload in mean load pressure fluctuation. Mini striations observed on fracture surface suggest the contributions of minor cycles to crack propagation due to load interaction. Significant increase in crack growth at high magnitude of overload in NNpH environment indicates the influence of hydrogen.

Dynamic mechanical behaviors of interbedded marble subjected to multi-level uniaxial compressive cyclic loading conditions: An insight into fracture evolution analysis

Rocks in civil and mining engineering usually experience rather complex stress disturbance. Rock dynamic mechanical behaviors under constant stress amplitude condition have been widely studied. However, the rock fracture evolution characteristics subjected to multi-level cyclic loading conditions are not well understood. In this work, multi-level cyclic compressive loading experiments were performed on marble with interbed orientation of 0°, 30°, 60° and 90°. Anisotropic fracture evolution characteristics were revealed using dynamic stress strain descriptions and post-test CT scanning technique. Results show that rock fatigue deformation, strength, lifetime, dynamic elastic modulus and damping ratio are all impacted by rock structure. The interbed structure plays a dominant role in fracture evolution compared with natural fracture and pyrite band. Rock stiffness degrades and damping ratio increases with the increase of interbed orientation. In addition, a two-phase damage accumulation pattern was found for marble under multi-level cyclic loading condition. A damage evolution model was first established to model damage accumulation, the proposed model fits well to the experimental data. Moreover, post-test CT scanning reveals the internal crack coalescence pattern and failure mode is impacted by the interactions of interbeds, natural fracture and pyrite bands. The rock bridge structure in marble with 60° and 90° interbed orientation alters the crack propagation path. Although the crack pattern is relatively simple at rock bridge segment, much more energy is needed to drive crack propagation. The testing results are expected to improve the understanding of the influence of rock structure on fracture evolution when subjected to variable stress amplitude loading conditions.

Effects of Axial and Multiaxial Variable Amplitude Loading Conditions on the Fatigue Life Assessment of Automotive Steering Knuckle

In this paper, the author has attempted to investigate the effects of different loading conditions including axial and multiaxial variable amplitude loading (VAL) on the fatigue life assessment of automotive components under various maneuvers. To this end, a case study was conducted on the cast iron steering knuckle of a passenger car. In fact, the various VAL histories are entered on the three joints of knuckle, namely steering linkage, lower control arm, and MacPherson strut. However, previous studies have shown that this high super-critical component fails through the steering linkage. Moreover, the rotation of the steering linkage is the most destructive load. Hence, in this research, different loading cases such as axial (destructive load as means 1 channel), multiaxial (only relates to loading on the joint of knuckle and steering linkage means 3 channels), and full multiaxial (including all loading time histories means 9 channels) were considered. Afterward, finite element analysis was performed for each case, and fatigue life of the component was predicted under different conditions. Next, fatigue life of the component was evaluated using the time histories of stress tensor in the root of steering linkage which is extracted by transient dynamic analysis and applying probabilistic approach based on the Liu–Zenner equivalent stress criterion. Eventually, the responses from both techniques were compared in different cases. The results reveal that life predicted using two methods are slightly different. But, the results of probabilistic approach are more accurate than the results of FEM in comparison with experimental data for the axial state. Also, one of the major achievements of this study is that for the components with complex geometry and under multi-input loading like the steering knuckle, it is essential to perform fatigue analysis by considering all real conditions and cannot be only focused to the destructive loading.

Fatigue life prediction under variable amplitude loading using a microplasticity-based constitutive model

We predict the fatigue life of a P355NL1 steel alloy under variable amplitude loading conditions using a newly-developed small-strain-based implicit plasticity model. The core idea behind the fatigue model is its capability to capture the inelastic work dissipation due to microplasticity whose critical value determines the fatigue life. Fatigue tests under different variable amplitude load spectra are simulated numerically and the results are compared with experimental data as well as other models for fatigue. It is shown that the model is able to describe the experimental data better than current empirical approaches, using only a few measured, physically motivated parameters.

Fatigue damage of designed T-type specimen under different proportion repeating Two-Step variable amplitude loads

In order to investigate the fatigue damage evolution of typical joints of River-Sea-Going Ship (RSGS) under a repeating two-step variable amplitude (VA) loading condition, and to estimate the influence of the damage of low amplitude load below the fatigue limit and the interaction effect between the high and low amplitude loads on the fatigue life of the structure, a series of fatigue experiments of designed T-type specimen (DTS) under different repeating two-step VA loading conditions were carried out in this work, which are designed according to hull structure characteristics and actual service conditions of RSGS. The experimental results show that the interaction damage value (Dnl) firstly increases and then decreases with increasing the cycle ratio of low to high amplitude load from 1 to 5. The value of Dnl is negative when the cycle ratio is relatively large, not less than 4.5 in the current study, which indicates that the effect of loading interaction not only doesn’t cause damage but has a beneficial effect on the fatigue life of the DTS. The X-ray Diffraction (XRD) analysis was carried out subsequently at the fatigue crack initiation region with the aim of confirming the material characteristic at the microcrack tip changing from work-hardening state to work-softening state with the cycle ratio increasing.

Interpretation of the effect of hydrostatic test in components working under pressure

After construction and installation, the natural gas and oil transport structures must undergo hydrostatic tests before their installation and periodically during commissioning. These hydrostatic tests can be classified into two categories: resistance test and leak proof test. The application of an overload is a spectacular phenomenon and can be used as an example while testing components working under pressure. This is a destructive control method. If a critical fault, with respect to the proof test, exists in the pipeline, the latter is destroyed. If not, (i.e., not broken), the lower than critical defects will see their subsequent propagation by fatigue slowed down or even eliminated due to the effect of overload. Tow-dimensional finite element method is utilized to analyze the plasticity-induced crack closure phenomenon in a cracked pipe under variable amplitude loading conditions. To accurately capture this process the choice of material model employed is of significant importance, therefore this paper considers the Lemaitre-Chaboche model, with isotropic hardening and nonlinear kinematic hardening. The study shows significant results obtained while employing this model.

A new algorithm for fatigue life assessment of automotive safety components based on the probabilistic approach: The case of the steering knuckle

In the present paper, the author has attempted to examine fatigue life of automotive safety components under axial variable amplitude loading conditions. To this end, the time components of stress tensor in the critical area of the knuckle and Liu-Zenner criterion were used to calculate the time history of equivalent stress. Then, the probability distribution function (PDF) of stress was extracted by applying the stress level counting technique. The Fourier curve fitting method was employed in order to formulate the PDF. Subsequently, the fatigue life of the component was estimated using the probabilistic approach. Finally, the results of the higher order of Fourier curve fitting and different counting ranges were compared with the experimental results. Thus, the best algorithm for precisely determining fatigue life of automotive components was obtained.

Effect of overload on fatigue crack growth behavior of thin copper foil

Smart stress-memory patch (SSMP) which consists of electrodeposited copper foil has been proposed as a sensor to measure fatigue loading for structural health monitoring in previous researches. In this study, the fatigue crack growth behavior of the copper foil was examined under constant amplitude loading with single overload and variable amplitude loading in order to evaluate the applicability of SSMP to the actual loading conditions. Under the overload condition, the fatigue crack growth rate gradually decreased after the overload and reached a minimum value, and then recovered to the baseline. Since the retardation behavior was different from one of thick specimen, a new model to quantify the crack growth in the thin specimen was proposed based on a modified Wheeler model. The proposed model successfully reproduced the fatigue crack growth curve under the single overload condition. Additionally, the proposed model was extended to the variable amplitude loading conditions by including cycle-by-cycle calculation procedure. The results showed that the fatigue crack growth behavior can be represented by the proposed model under the variable amplitude loading condition. Therefore, the feasibility of applying SSMP to actual loading conditions was demonstrated.

A novel approach to model fretting-fatigue in multiaxial and non-proportional loading conditions

This article proposes a new method for determining the behavior and service life of contact areas of parts subjected to fretting-fatigue. The first objective was to be able to predict the service life of contact parts with various curvature radii from fretting-fatigue tests on laboratory test geometries such as cylinder-plane. The second objective was to be able to predict the service life for variable amplitude and multiaxial loading conditions from laboratory tests in constant amplitude loading conditions.

Fatigue analysis of ductile and brittle behaving steels under variable amplitude multiaxial loading

AbstractThe analysis of fatigue behavior under multiaxial variable amplitude stress states, despite its wide applicability, has not been fully studied. Issues such as varying degrees of nonproportionality of the load history, cycle counting, damage accumulation, failure behavior of the material, and mean stress fluctuations which can significantly affect the results of these analyses have not been well understood. In this study, a methodology for the analysis of fatigue behavior under multiaxial variable amplitude loading conditions is employed which accounts for the aforementioned issues. At its core, the applied methodology uses critical plane analysis based on the failure behavior of each material to assess the fatigue damage. In order to evaluate the performance of the analysis method, axial, torsional, and combined axial‐torsional variable amplitude tests were performed on one ductile and one brittle behaving steel. The applied methodology resulted in close estimation of the experimental fatigue life for both ductile and brittle behaving steels.