Variable Amplitude Loading Research Articles

Multiaxial Fatigue Life Assessment of Integral Concrete Bridge with a Real-Scale and Complicated Geometry Due to the Simultaneous Effects of Temperature Variations and Sea Waves Clash

In the present study, the authors attempted to predict the fatigue lifetime of a real-scale integral concrete bridge with H-shaped steel piles resulting from working and environmental conditions. In this regard, various types of nonproportional variable amplitude loads were applied on the bridge, such as temperature variations and sea waves clash. To this end, CATIA software was used to model the real-scale bridge with its accessories, such as a concrete deck, concrete anchors (walls), I-shaped concrete beams (Ribs), and steel piles. Subsequently, stress analysis was performed to determine the critical area apt to fail. The results showed that steel piles are the most critical bridge components. As a result, in future analysis, the purpose will be to study this critical area, and the effect of relative humidity on the fatigue properties of concrete was ignored. Subsequently, the time history of stress tensor components in the critical area was obtained by performing transient dynamic analysis. Various well-known equivalent stress fatigue theories (von Mises, Findley, Dang Van, McDiarmid, Carpinteri–Spagnoli, Modified Findley, Modified McDiarmid, and Liu–Zenner) were utilized to calculate the equivalent stress caused by the simultaneous effect of temperature variations and sea waves clash. Eventually, the fatigue life of the structure was predicted by employing the rainflow counting algorithm and the Palmgren–Miner damage accumulation rule. The results indicated a reduction in the multiaxial fatigue life of the structure under the simultaneous effects of two phenomena, the daily temperature variations and the sea waves clash, of approximately 87% and 66%, respectively, compared with the fatigue life of the structure under either the effect of temperature changes or the effect of sea waves clash, separately. Therefore, it was necessary to consider all the cyclic loads in the structural design step to estimate the fatigue life of the structure. Moreover, the findings of this case study revealed that the lowest value of multiaxial fatigue lifetime is related to the application of the Liu-Zenner criterion. In other words, this criterion is more conservative than the other used criteria.

Numerical analysis of fatigue crack growth under SuperBlock2020 load sequence

The components are usually submitted to variable amplitude loading, and it is important to understand the mechanisms explaining fatigue crack growth (FCG) rate variations. The relative importance of residual stresses and crack closure, in particular, is a controversial issue. This work studies a specific load pattern, called Super Block 2020, composed of four pairs of load blocks of different amplitude (A, B, C and D) and the same maximum load, separated by overloads. The transition from the overloads to the constant amplitude load blocks occurred alternatively from the maximum or minimum loads of the overload cycles. These patterns, called i1 and i2 for load blocks i (i = A, B, C or D), produce different residual stresses ahead of crack tip. A numerical procedure was followed to predict FCG rate in the 2024-T351 aluminium alloy, based on cumulative plastic strain. This approach includes the effects of material hardening, crack tip blunting, crack closure and partial crack closure. A significant difference was found between FCG rate and crack increments produced by i1 and i2 load blocks. The numerical predictions are according the experimental trends and crack closure was found to be the main mechanism behind FCG trends.

Subcycle fatigue crack growth and equivalent initial flaw size model for fatigue life assessment under arbitrary loadings for Al-7075

A novel fatigue-life prediction methodology combining a subcycle fatigue crack growth (FCG) analysis and equivalent initial flaw size (EIFS) concept is proposed in this paper. This research focuses on extending a previously developed time-based subcycle fatigue crack growth model to a near-threshold regime and under multiaxial loadings. First, the threshold FCG behavior using subcycle FCG is discussed, and a new temporal kernel function to include intensity factor corresponding to the near-threshold region is proposed. Following this formulation, the multiaxial load case scenario is considered for mixed-mode FCG using a critical plane approach. Next, the general multiaxial loading is converted to an equivalent uniaxial loading for life prediction. Next, model predictions under arbitrary loadings (e.g., uniaxial and multiaxial, constant and variable amplitude loading, and random spectrums) are compared with experimental data from open literature and internal testing. Multiple conclusions and potential future work have been suggested using the proposed model.

Study on fatigue damage laws and life prediction of CRTS-II ballastless track slab

To analyze the fatigue damage laws and fatigue life prediction, six full-size CRTS-II ballastless track slabs were tested under fatigue cyclic loading conditions. The main parameter considered was the fatigue load level that ranged from 0.5 to 0.675 Pu (the ultimate static capacity). The results indicate the following: (1) the slab under the load level of 0.5 Pu showed a slight reduction in capacity and deflection after 3,000,000 cycles, and its residual strength was only reduced by 3%. (2) the fatigue limit of the slab cannot exceed 0.6Pu (survived 2,000,000 cycles), because the stiffness and the residual deflection of the slab increased significantly at the increased the load level. (3) Based on the Palmgren-Miner cumulative damage criterion and the test results, the fitted formulas obtained from experimental results can predict the fatigue life of the slabs under both constant amplitude fatigue load and variable amplitude load.

Prediction of variable amplitude fatigue crack growth life based on modified grey model

Grey model has been several applications on fatigue crack, with prediction on fatigue crack growth life curve often serving as milestones. A typical difficulty in predicting the fatigue crack growth life curve is the retardation of crack growth caused by the overload effect. Overload retardation, resulting in the lack of experiment data points in the retardation interval and the deflection of crack growth curve, is a long-term challenge for predicting fatigue crack growth. We improve the ability of grey model to predict fatigue crack growth life by second order B-spline interpolation, an interpolation for local data points. It combines the trend of local data point to deal with the retardation interval, and interpolates multiple data points in the retardation interval when there is a lack of local data, and uses a metabolic grey model to construct the prediction formula of crack growth. In the study involving variable amplitude load and multiple overload fatigue crack growth experiments, the proposed method is proved to improve, with statistical significance, the predictive ability on the whole range of experiment data. The method is simple and accurate. Consequently, it is conducive to solve the problem of fatigue crack growth life of engineering structure.

Cyclic behaviors of SHS columns subjected to small amplitude loading

Structural components can be subjected to a limited number of cyclic large drifts during strong earthquakes (e.g., Northridge earthquake, 1994; Kobe earthquake, 1995), as well as many cyclic small amplitude loading during long-duration earthquake excitations (e.g., Tohoku earthquake, 2011). Traditional studies on cyclic behaviors of structural components mainly focused on large drifts and neglected small amplitude loading, rendering them inadequate to represent different seismic loading cases. Square hollow section (SHS) columns are widely used in low- and middle-rise steel building structures in Japan. The bottoms of the first story columns yield under severe earthquakes, even though the strong-column-weak-beam concept is adopted during building design. To better understand the deformation capacities and hysteretic behaviors of steel columns under cyclic small amplitude loading, tests on 26 SHS columns were carried out in this study. The width-to-thickness, axial force, shear span ratios, and loading history of the columns were the main test parameters. The loading histories consisted of monotonic loading, variable amplitude loading, and several constant small amplitude loadings. All specimens exhibited local buckling at the bottom of the columns. Under small amplitude loading, it was observed that the strength of the specimens deteriorated slightly within a certain number of cycles, while the restoring force decreased rapidly afterwards. The stability limit concept was proposed to represent the point when the column’s strength starts to deteriorate rapidly; it is based on the axial deformation in the flange in the local buckling region. Accurate prediction methods for the stability limit values and the numbers of cycles until the stability limits were reached were also proposed.

Material-independent stress ratio effect on the fatigue crack growth behavior

It is well known that the fatigue life prediction for engineering structures with crack-like defects is a challenging issue, especially under variable amplitude loading. Although numerous models have been proposed, the intrinsic relationship between the stress ratio and fatigue crack growth (FCG) rate of materials is still unclear. In this study, we proposed a new FCG model containing a material-independent equivalent factor N through energy principle during crack growth, which could theoretically illustrate the effect of stress ratio on the FCG rate of metallic materials. The experimental verification indicates that the new model provides a more accurate relation between the stress ratio and FCG rate in various sorts of metallic materials. This model would be an effective strategy to the fatigue life prediction of cracked components under variable amplitude loading.

Characteristic Tearing Energy and Fatigue Crack Propagation of Filled Natural Rubber.

Below the incipient characteristic tearing energy (T0), cracks will not grow in rubber under fatigue loading. Hence, determination of the characteristic tearing energy T0 is very important in the rubber industry. A rubber cutting experiment was conducted to determine the T0, using the cutting method proposed originally by Lake and Yeoh. Then, a fatigue crack propagation experiment on a edge-notched pure shear specimen under variable amplitude loading was studied. A method to obtain the crack propagation rate da/dN from the relationship of the crack propagation length (Δa) with the number of cycles (N) is proposed. Finally, the T0 obtained from the cutting method is compared with the value decided by the fatigue crack propagation experiment. The values of T0 obtained from the two different methods are a little different.

A Nonlinear Fatigue Damage Model Based on Equivalent Transformation of Stress

It is rather difficult for engineers to apply many of the fatigue damage models for requiring a knee point, material-dependent coefficient, or extensive testing, and some of them are only validated by a fatigue test of two-stage loading rather than higher-stage loading. In this paper, we propose a new model of fatigue cumulative damage in variable amplitude loading, which just requires the information of the S-N curve determined from the fatigue experiment. Specifically, the proposed model defines a stress equivalent transformation way to translate the damage of one stress to another stress through simple calculation. Experimental data of fatigue including two-, three-, and four-block loading verify the superiority of the proposed model by comparing it with the Miner model and Manson model. The results show that the proposed model can be generalized to any type of loading and presents a better prediction. Therefore, the advantage of the proposed model can be easily used by an engineer.

Fatigue and creep-fatigue crack growth in aviation turbine disk simulation models under variable amplitude loading

This study analyzes the simulation model configuration and its loading conditions in fatigue and subsequent crack growth tests. Following the simulation principles, a full-size 3D finite element analysis of a representative GTE turbine disc was performed. With the aim of reproducing the simulation model, the in-service critical zone of both the stress–strain state and damage accumulation is studied. Based on the parametric computations, the block type loading conditions of the simulation models are determined and verified. Experimental study of the surface crack growth rate in the simulation model under harmonic and block loading at elevated temperature is performed for the fatigue and creep-fatigue interaction conditions. To interpret the experimental data, we calculate the nonlinear stress intensity factor distributions along the semielliptical crack front for flaws growing on the inner surface of the hole in the simulation model using numerical procedures. It is found that in terms of the nonlinear fracture resistance parameters, the sections of the fatigue fracture diagrams form one common curve representing the previous and subsequent increasing stages of block loading in pure fatigue and creep-fatigue interaction loading conditions. The possibility of using the proposed simulation model, tested under variable amplitude loading, to assess the structural integrity of GTE turbine disks is discussed.

Transient delamination growth in GFRP laminates with fibre bridging under variable amplitude loading in G-control

To predict fatigue-driven delamination growth in real structures, it is inevitable to understand delamination growth under real load spectra, also known as in-service loads, which most commonly are variable amplitude load patterns. In this work, delamination growth in glass fibre-reinforced polymer laminates subjected to two-level block amplitude loading is investigated using a pure moment loaded DCB test configuration for G-controlled cyclic testing. The variable amplitude load patterns consist of single- and periodic repeated load amplitude changes. The method utilises a digital image-based technique that allows for precise tracking of delamination fronts in translucent materials. The work characterises transient crack growth phenomena following load amplitude changes with emphasis on the actual fatigue crack growth rate. The load amplitude changes may increase the crack growth rate by factors of 5–6 in comparison to the crack growth rate in constant amplitude base-line tests. Periodic repeated load amplitude changes particularly increase the fatigue crack growth. For example, after just 10 periodic repeated low- and high-load blocks, the delamination has extended more than a factor of 2 times the delamination extension predicted from a non-interaction model based on constant amplitude data. The effect of the frequency of load amplitude changes on the fatigue crack growth is also investigated. Frequent load amplitude changes are proven to increase the fatigue crack growth significantly because of the transient crack growth responses following the load amplitude changes.

Development of higher-order displacement discontinuity method to simulate fatigue crack growth in brittle materials

The 2D displacement discontinuity method (2D. DDM) is an indirect boundary element technique in which the stresses and displacements are expressed through normal and shear displacement discontinuities. The governing equations of fatigue crack growth are mostly power equations that depend on the stress intensity factor range. Accurate calculation of displacement discontinuity has importance in fatigue analysis of DDM. Therefore, in this study, DDM is extended using cubic variations of displacement discontinuity for ordinary and crack tip elements. This method also uses an appropriate algorithm based on the linear elastic fracture mechanics (LEFM) principle to analyze crack growth under cyclic fatigue loading. This process is accomplished by assuming the homogeneity of brittle material and the small plastic zone of the crack tip compared to the crack dimension. The condition of applying constant and stationary variable amplitude loading was provided. The algorithm is designed based on an iterative process, and the new incremental elements gradually are added to the crack tip until the failure criteria are reached; The size of these elements at each step of growth depends on the crack growth rate in the previous step. Therefore, the fatigue modeling of the structures with multiple cracks and different growth rates is enabled. Virtual crack criteria were employed to improve the accuracy and speed of analysis, which involves crack tips with a slower growth rate. Moreover, the direction of crack propagation is evaluated using the maximum circumferential stress criterion. Examples of simple and multi-fractured structures under constant and variable amplitude load are considered. Comparison of results with literature data shows excellent agreement with high accuracy.

A methodology for detection of crack initiation in adhesively bonded joints under constant and variable amplitude fatigue loading

ABSTRACT The use of adhesively bonded joints is increasing in the lightweight design; however, their fatigue performance in safe-life design is challenging. Therefore, a combination of damage-tolerant design and Structural Health Monitoring (SHM) is often considered. The present work deals with a new approach for detection of crack initiation in adhesively bonded single lap joints (SLJ) subjected to constant and variable amplitude fatigue loading. For this purpose, the so-called backface strain method is used, in which a strain gauge for damage monitoring is placed at a highly sensitive point in the overlap area of SLJs. A striking converging-diverging trend in strain amplitude curves was attained in the tests subjected to constant amplitude loading, which was in a good agreement with the onset of crack initiation observed with video-microscopy. Additionally, this methodology was demonstrated on the SLJs subjected to variable amplitude loading using an additional farfield (outside of the overlap area) strain gauge, which showed a high potential for detection of crack initiation.

Low-cycle fatigue life evaluation of buckling-restrained braces based on cumulative plastic deformation curves

To quantitatively evaluate the low-cycle fatigue life of buckling-restrained braces (BRBs), an evaluation method for BRBs based on the combination of the CPD curves and CPD measurement meter (CMM) is established herein. The difference between two CPD curves (i.e., the CPD curves under constant strain amplitude loading history (C-CPD) and under random strain amplitude loading history (R-CPD)), and their selection criteria to evaluate the low-cycle fatigue life of BRBs are discussed. An example under the variable strain amplitude (VSA) loading history and an example under the multiple earthquakes are carried out. Finally, the CPD limit values of BRBs in the ANSI/AISC 341-10 and FEMA-450 are discussed by statistical analysis of the test results of BRBs. The analysis results show that the C-CPD curve can be used to evaluate the low-cycle fatigue life of BRBs under the VSA loading, and the R-CPD curve can be used to evaluate the low-cycle fatigue life of BRBs under the multiple earthquakes. The degree of reliability of the current CPD limit value is not enough. A CPD limit curve is recommended in this study to quantify the low-cycle fatigue performance of BRBs.

On fatigue life scatter under variable-amplitude load history

Fatigue life scatter under a variable amplitude load history is determined by many factors such as the amplitudes of the individual load cycles, the number of the load cycles with different load levels, and the differences between the load levels as well. Besides an brief overview on the studies and experiments on the scatter of fatigue life under variable amplitude load histories, the present paper conducted a series of fatigue tests, demonstrates the life scatters under different load histories, and discusses the dominant factors of fatigue life scatter. It shows that all the load cycles play their roles for the life scatter.

Fatigue reliability analysis of dented pipelines

The present study carries out fatigue reliability analyses of oil and gas pipelines containing unconstrained plain-smooth dents under the variable amplitude loading caused by cyclic internal pressure. The API 1156 S-N curve and Miner’s rule are employed to establish the limit state function for fatigue, and the stress concentration at the dent is accounted for based on findings reported in the literature. The reliability analysis is carried out on two pipeline examples containing dents with depths ranging from 2% to 5% of the pipe diameter. The examples are subjected to cyclic internal pressures at the discharge and suction ends of a compressor station on an actual in-service oil transmission pipeline. In the context of the cyclic pressure records considered in the present study, the analysis results suggest that fatigue failure of dents under suction-end pressure cycles is highly unlikely, whereas the probability of fatigue failure of dents under discharge-end pressure cycles can be significant if the diameter-over-wall thickness ratio of the pipeline is large. This study provides a methodological framework to carry out reliability-based fitness-for-service assessments of dented pipelines with respect to fatigue.

Correlations between crack initiation and crack propagation lives of notched specimens under constant and variable amplitude loading

AbstractThis paper starts with an overview of the application of the three guidelines (GL) of the German Research Association of Mechanical Engineers (FKM). Each of these provides algorithms for calculating fatigue lives of components under constant or variable amplitude loading, however, with underlying different failure criteria, that is, technical crack initiation life (GL‐nonlinear), fatigue crack growth life (GL‐fracture mechanics), and total fracture life (GL‐linear). Since the GL‐linear only considers linear‐elastic material behavior in the fracture fatigue life calculation, the guideline is not capable for the LCF and is not able to take sequence effects into account. For a better approximation of fracture fatigue lives, the elastic–plastic material behavior has to be taken into account. This paper introduces the U‐Concept which has been evaluated from a large structural durability database from the literature with more than 1,500 experiments for constant and more than 700 experiments for variable amplitude loading. The U‐Concept is a small add‐on to the local strain approach (LSA) which is the backbone of the GL‐nonlinear. It enables (1) to directly calculate the fatigue life to total fracture based on elastic–plastic material behavior according to the LSA or (2) to estimate the remaining fatigue life from crack initiation to fracture without a crack growth simulation. Furthermore, the U‐Concept needs no experimental determined crack growth parameters, the only necessary material parameter is the ultimate tensile strength Rm. The U‐Concept is therefore easy applicable for industrial users and increases the accuracy of the approximated fatigue lives by considering the elastic–plastic material behavior.

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.

Strain sequence effect on fatigue life and fracture surface topography of 7075-T651 aluminium alloy

The paper studies the effect of strain-loading sequence on fatigue lifetime and fracture surface topographies in 7075-T651 aluminum alloy specimens. Fatigue tests were performed in two ways: (i) constant-amplitude loading and (ii) two series of variable amplitude loading with non-zero mean strain values. The topography of the fatigue fractures was measured over their entire surfaces with the help of an optical confocal measurement system. The results of fatigue tests in the form of equivalent strains, εaeq, such as the weighted mean of strain components, εa1, εa2, and fatigue life, Nf, were used as the sum of the partial number of cycles N1, and N2. This study indicates, inter alia, that the values of the fracture surface parameter core height Sk, found in the two-step loading program, are linearly dependent on the equivalent strain, and logarithmically dependent on the fatigue life.

Consideration of the transient material behavior under variable amplitude loading in the fatigue assessment of nodular cast iron using the strain‐life approach

AbstractThe consideration of realistic load assumptions is important for the fatigue design of highly stressed nodular cast iron components for wind energy application. Especially in case of overloads causing elastic–plastic deformation, residual stresses may have a strong impact on fatigue life. In strain‐controlled fatigue tests with constant and variable amplitudes, the influence of overloads on lifetime was investigated. During fatigue testing, the transient material behavior, cyclic hardening, cyclic relaxation of the residual stresses, and quasi‐static creep effects of the EN‐GJS‐400‐18‐LT was recorded and evaluated. To quantify the influence of the transient material behavior on the calculated lifetime, fatigue analyses are carried out with the strain‐life approach, both with and without consideration of the transient material behavior. The results show that conservative damage sums are derived if the transient material behavior, especially the relaxation of tensile residual stresses, is neglected.