Constant Amplitude Loading Research Articles

A Review of Fatigue Failure and Life Estimation Models: From Classical Methods to Innovative Approaches

This review paper encompasses a comprehensive exploration of fatigue failure and fatigue life estimation techniques which spans from the classical methods to new and innovative approaches. The paper looks into the limitations and advancements of these techniques and highlights their respective strengths and areas for improvement. Some of the models such as artificial neural networks and genetic algorithms exhibit clear advantages in terms of processing speed, accuracy, and adaptability to diverse materials and loading scenarios. For instance, in estimating fatigue life under multiaxial loading, the stress scale factor model emerges as a viable alternative to the critical plane-based approach, as this technique offers superior efficiency under both constant and variable amplitude loadings. Additionally, optimization algorithms such as artificial neural networks and genetic algorithms show promising potential in efficiently estimating fatigue life due to their rapid computational capabilities. Despite the notable successes achieved by these techniques, none of them can be ascribed as a universal model capable of accurately estimating the fatigue life of all materials across diverse operating conditions as each of the techniques possesses its unique strengths and weaknesses, thus, necessitating the study for a better understanding of their applicability. Hence, this paper serves as a valuable compilation of various fatigue analysis techniques, targeted at paving the way towards the development of a universal model capable of handling different materials and loading conditions.

The hysteresis loop on the near-threshold fatigue crack growth curves generated by stepped load reduction and constant-amplitude loading methods in a Ni-based superalloy

Fatigue crack growth (FCG) tests were conducted on compact tension specimens made of a Ni-based superalloy to investigate the near-threshold FCG behaviors using both the stepped load reduction method (LRM) and the constant-amplitude loading method (CALM) at three stress ratios (R = 0.05, 0.5 and 0.7) under ambient condition. It is found that after the FCG threshold being approached by the LRM, a remarkable hysteresis plateau occurs on the subsequent FCG curve generated by the CALM for R ≤ 0.5, resulting a hysteresis loop on the near-threshold region, but the situation becomes complicated at R = 0.7. In the appearance of hysteresis plateau, the FCG life to fracture can be over 107 cycles longer than that without hysteresis plateau. For FCG rate faster than 10−8 m/cycle, the fractography is dominated by transgranular feature which is insensitive to the microstructure of the alloy. In the hysteresis plateau region where FCG rate is lower than 10−9 m/cycle, fractography shows a wide optical dark zone where microstructure-sensitive crystallographic facet feature dominates, while when no hysteresis at R = 0.7, the optical dark zone is too narrow for the fracture feature transition so that crystallographic facet, transgranular as well as mosaic features can be observed simultaneously. As FCG in the hysteresis plateau under the CALM can be significantly slower than that under the stepped LRM, it is recommend that the stepped LRM should be used to generate the material basic FCG curves for fatigue life prediction of high durability structures.

Crack propagation retardation behavior of shattered rim in the railway wheel

Shattered rim, known as “wheel cancer”, is a century-old problem that restricts the reliability of railway wheels. Crack propagation retardation of shattered rim in the railway wheel was investigated in this paper. First, a full-scale wheel-rail bench test rig was used to conduct wheel-rail tests on a wheelset with an interior rim crack taken from service. The interior rim crack did not propagate over the entire 50000 km distance. Cracks initiated from the two through-rim defects and propagated at a slow speed. Then, equivalent tests were conducted to investigate crack propagation behavior of the shattered rim. The crack growth rate increased with the increase of crack length for the specimen under tension–torsion loading, while that decreased with the increase of crack length for the specimens under pure-torsion and compression-tension loading. The crack propagation retardation is attributed to the compression and friction of the crack surfaces. Finally, a model was developed to describe crack propagation retardation in shattered rims. The effective stress intensity factor predicted by the model initially increases and then gradually decreases. The shattered rim has a critical size at different depths from the tread under constant amplitude load. The predicted critical size decreases with the increase of the depth.

Impact of block-loading on the high cycle fatigue strength of superalloy 617M at 973 K

The study demonstrates the positive influence of coaxing on the fatigue strength of alloy 617M under high cycle fatigue (HCF) loading at stress ratio (R) − 1, frequency ≈ 85 Hz, and temperature of 973 K. Tests were performed employing resonance excitation in two patterns viz., constant amplitude loading and block loading using a ‘low-to-high’ pattern. The fatigue limit for the constant amplitude loading pattern was determined to be 320 MPa for a runout criterion of 108 cycles. Upon under-stressing the alloy by application of a block loading pattern, the limit increased to 335 MPa. The increase of stiffness and associated resonance frequency during cycling indicated an initial hardening regime brought about by work hardening followed by a period of secondary hardening owing to precipitations occurring in the matrix. In the later stage, the frequency response also indicated the influence of dynamic strain ageing (DSA) on the alloy behaviour. Comparative microstructural characterisation of specimens is conducted to extend the understanding of coaxing and the resulting changes occurring in the work-hardening behaviour of the alloy.

Fatigue Life Assessment of Corroded AlSi10MgMn Specimens

This study investigates the influence of pre-corrosion damage on the fatigue behavior of AlSi10MgMn high-pressure die-cast specimens, using the statistical distribution of corrosion depths. The analysis is conducted on two different surface conditions: an unmachined rough surface (Ra=5.05μm) and a machined, polished surface (Ra=0.25μm). For the unmachined specimens, the corrosive damage manifests as homogeneously spread localized corrosion, whereas the polished specimens exhibit less uniform but deeper corrosion. The average corrosion depth of the polished specimens is found to be slightly higher (313 μm compared to 267 μm) with a broader depth distribution. Specimens are tested under a constant bending load amplitude in laboratory conditions at a stress ratio of R=0 until fracture. A fracture mechanics-based methodology is developed to assess the remaining fatigue life of corroded specimens, utilizing short and long crack fracture mechanical parameters derived from SENB specimens. This model incorporates a thickness reduction of the critical specimen cross-section based on the corrosion depth distribution and combines it with a small initial crack of the intrinsic defect size (aeff=14μm). Regardless of the surface condition, using the most frequent corrosion depth for thickness reduction provides a good estimate of the long-life fatigue strength, while using the 90th percentile depth allows for a conservative assessment.

Evaluation of Concrete Fatigue Damage with Elastic Wave-based Measurement Techniques

Fatigue damage is a progressive and permanent change in the internal material structure due to cyclic loading. The cyclic loads can be due to wind, waves, temperature variation, and traffic loads. Each cyclic load application introduces micro-damages that accumulate to induce failure. Detecting these micro-damages requires sensitive measuring techniques. Hence this research compares the sensitivity of different measuring techniques applied to fatigue experiments of concrete. The applied NDT are the passive acoustic emission technique (AET) and active ultrasonic measurements. In addition, linear variable differential transformers (LVDTs) are applied as a reference measurement. Accordingly in this research, cylindrical concrete samples are subjected to monotonic and cyclic Brazilian splitting tests. The cylinders are 100 mm in diameter and 150 mm in length. The cyclic load is applied to these samples with a loading frequency of 5 Hz. During the tests, the damage evolution is monitored with AET, ultrasonic measurements and LVDTs. There are eight AE sensors attached to the sample. The two LVDTs are positioned at the center of the sample's front and back side. Besides passively monitoring the acoustic emissions, the AET sensors are also used to do active ultrasonic measurements. The research reports the comparison conducted on the deformations and cracks measured with the LVDTs, the damage growth identified with the AET, and the change in the ultrasonic pulse velocity measurements. In addition, the study also presents the damage analysis capacity of the methods across different types of loading: monotonic, constant amplitude, and stepped fatigue loading. The comparison shows that combination of AET and ultrasonic velocity measurement is a sensitive indicator for damage growth.

In-plane biaxial fatigue life prediction model for high-cycle fatigue under synchronous sinusoidal loading

The unique advantage of in-plane biaxial loading is no rotation of the maximum principal stress during cyclic loading, which has a distinct effect on fatigue life. This study aims to propose a life prediction model for in-plane biaxial fatigue encompassing both in-phase and out-of-phase conditions. For synchronous sinusoidal loadings, an equivalent stress expression is derived using the integral method, accounting for the influences of shear and normal stresses across all planes. The equivalent stress is then compared to a reversed uniaxial constant amplitude loading to predict fatigue life. To validate and compare the model, in-phase and out-of-phase in-plane biaxial fatigue experiments were conducted using 24 nickel-based superalloy cruciform specimens at temperatures of 420℃, 550℃, and 600℃. The results show that the proposed model is superior to conventional stress-invariant based models, with most results staying within the ± 2 error bands. Using the proposed model, the effects of mean tensile stress, biaxiality and phase shift are discussed. Additionally, a novel non-proportional factor is introduced to enhance multiaxial fatigue life prediction by distinctly separating the effects of principal stress and its directional variations.

Effect of local laser heating on fatigue crack propagation rate of AA2524 thin plate

To extend the operational lifespan of the AA2524 aircraft panel, the surface of the AA2524 specimen was locally heated by laser. The specimen’s microhardness distribution and surface residual stress (RS) were tested, as was its fatigue crack growth rate (FCGR). The fatigue fractography of specimen was also observed. The FCGR of specimen after laser heating was predicted by the weight function method (WFM). The consequences indicate that when the laser power is lower than 900 W, the hardness of the heating zone on the surface of the specimen decreases by no more than 10 HV0.5. Compared to the base material (BM) specimen, transverse heating specimen creates a maximum compressive residual stress (CRS) of 32 MPa along the crack extension line. This can effectively stop the crack propagation. When laser power with the transverse heating is 900 W, the crack propagation suppression effect is optimal. The fatigue life of heated specimen is increased by 108.5 % compared to the BM specimen under a constant amplitude load with the maximum load of 2600 N and R of 0.1, and the fatigue life of heated specimen is increased by 46.4 % under a constant amplitude load with the maximum load of 3300 N and R of 0.1. The spacing among 6 adjacent striations of specimen after transverse heating is shortened from 2.79 μm to 0.88 μm compared with the BM specimen. The Walker model, which is based on the WFM, has high accuracy in predicting FCGR of specimen after laser heating under various load conditions. It is evident that local laser heating technology can extend the service life of aviation aluminum alloy panels.

Short Fatigue-Crack Growth from Crack-like Defects under Completely Reversed Loading Predicted Based on Cyclic R-Curve.

Understanding short fatigue-crack propagation behavior is inevitable in the defect-tolerant design of structures. Short cracks propagate differently from long cracks, and the amount of crack closure plays a key role in the propagation behavior of short cracks. In the present paper, the buildup of fatigue-crack closure due to plasticity with crack extension from crack-like defects is simulated with a modified strip yield model, which leaves plastic stretch in the wake of the advancing crack. Crack-like defects are assumed to be closure-free and do not close even under compression. The effect of the size of crack-like defects on the growth and arrest of short cracks was systematically investigated and the cyclic R-curve derived. The cyclic R-curve determined under constant amplitude loading of multiple specimens is confirmed to be independent of the initial defect length. Load-shedding and ΔK-constant loading tests are employed to extend the cyclic R-curve beyond the fatigue limit determined under constant amplitude loading. The initiation stage of cracks is taken into account in R-curves when applied to smooth specimens.

Strain amplitude dependency of cyclic hardening/softening behavior of 490 N/mm2 class steel

Existing studies on the strain amplitude dependency of cyclic softening behavior in structural steels often involve limited cycles or strain amplitudes below 2.5%, failing to provide a comprehensive understanding of stabilized cyclic behavior. This study performed uniaxial tension–compression cyclic loading tests using SN490B structural steel under three loading patterns: constant, variable, and offset constant strain amplitudes. The cyclic hardening and softening behaviors and stress–strain hysteresis loops were compared. Under variable strain amplitude loading, the specimens were subjected to increasing and decreasing strain amplitudes to investigate the strain amplitude dependency of the cyclic hardening and softening behaviors. Under offset constant strain amplitude loading, mean strains were initially introduced in either the tension or compression strain range, followed by cyclic loading with a constant strain amplitude centered around the mean strains. The test results revealed the following: (1) Under constant strain amplitude cyclic loading, the material exhibited cyclic softening and hardening behaviors at strain amplitudes smaller than and larger than 0.5%, respectively; (2) Under variable strain amplitude cyclic loading, increased and reduced strain amplitudes resulted in cyclic hardening and softening behaviors, respectively. The cyclic hardening/softening behavior strongly depended on the strain amplitude. Applying a significant number of cycles after strain amplitude reduction resulted in the stress–strain curves closely resembling those under constant strain amplitude conditions; (3) Even under offset constant strain amplitude cyclic loading conditions with nonzero mean strain, the peak stresses and shapes of the hysteresis loops approached those under constant strain amplitude conditions without mean strain.

Stochastic Modeling of Crack Growth and Maintenance Optimization for Metallic Components Subjected to Fatigue-Induced Failure

Abstract The degradation of metallic systems under cyclic loading is subject to significant uncertainty, which affects the reliability of residual lifetime predictions and subsequent decisions on optimum maintenance schedules. This paper focuses two main challenges in developing a reliable framework for the lifecycle management of fatigue-critical components: constructing a stochastic model that captures uncertainties in crack growth histories, and presenting a computationally efficient strategy for solving the stochastic optimization associated with maintenance scheduling. Polynomial chaos (PC) representation is proposed to propagate uncertainty in the fatigue-induced crack growth process, using a database from constant amplitude loading experiments. Additionally, an optimization strategy is implemented based on Gaussian process surrogate modeling to solve the stochastic optimization problem under maximum probability of failure constraints. The sensitivity of the optimum solution to different probability of failure thresholds is examined. The proposed framework offers a decision support tool for informed decision-making under uncertainty, aiming to mitigate fatigue failure.

Low-cycle fatigue behaviour of concrete-filled double skin steel tubular (CFDST) members for wind turbine towers

Wind energy has the advantages of being clean and renewable. Wind turbine towers endure horizontal cyclic loads that could influence the performance of entire structure. To clarify the low-cycle fatigue behaviour of concrete-filled double skin steel tubular (CFDST) members, a total of 16 specimens were experimented. The hollow, slenderness, and axial compression ratios are specifically designed to clarify the effects on performance under constant amplitude loading and hysteretic loading conditions. The typical failure modes under both loading conditions and the relationship between loop strain, loop bearing capacity, loop energy dissipation, cycle number, and various degradation indices were analysed. Studies indicate that the failure mode under low-cycle fatigue loading is mainly local deformation, which includes transverse fracture occurring at the region between the steel tube and ribbed stiffener, the crushing concrete. Fatigue specimens with different amplitudes exhibit varying shapes of hysteresis responses. Higher amplitudes could enhance damage and significantly reduce fatigue life. Increasing the hollow and axial compression ratios boosts the energy dissipation capacity, and decreasing the slenderness ratio enhances the lateral resistance. A 2 % constant amplitude preload intensifies the degradation of bearing capacity and energy dissipation under subsequent constant amplitude loading.

Required fatigue strength (RFS) – a simple concept for determining an equivalent stress range indicating the necessary minimum joint quality in contrast to the actual modified equivalent strength (MES) method

Abstract This paper treats different fatigue (FAT)-scenarios for determining damage-equivalent stress ranges according to two methods for transforming a stress or load spectrum into a damage-equivalent constant amplitude loading, i.e., the Modified Equivalent Stress (MES) and the Required Fatigue Strength (RFS) concepts. The MES method is suggested by the IIW-recommendations for fatigue design and the RFS method is applied especially in the design of vehicle safety components. The resulting MES- and RFS-ranges are similar, but not equal. The MES-method delivers a damage-equivalent stress range that depends on the selected FAT-value, i.e., the position of the Woehler-curve is decisive. In contrast, the RFS-method results in a damage-equivalent fictitious Woehler-line that indicates the lowest necessary strength quality for a given stress spectrum. The allocation of the modified equivalent stress range to the appertaining bi-linear Woehler-curve does not result in the fatigue life caused by the spectrum. Only in the case of a linear Woehler-curve, the fatigue life is directly obtained. In the case of the RFS-application, the fatigue life is by definition equal to the spectrum length. For durability tests, the modified equivalent stress range (at $${L}_{S}$$ L S cycles) and the associated FAT-Woehler-curve should not be used. However, the Woehler-curve derived by the RFS-method allows experimental durability proofs for any amplitude-cycle combination along it. Furthermore, the required lowest necessary strength also enables the selection of the most cost-effective manufacturing technique and quality. The RFS-Woehler-curve also results in a FAT-value with a defined probability of failure depending on the required safety factor.

Fatigue damage accumulation in a bolted joint subjected to the random loading

Fatigue damage in structures, which escalates with cyclic loading, is traditionally analyzed using blocks of constant amplitude. This study aims to derive the fatigue loading spectrum for the Cirrus SR20 multipurpose airplane and predict the fatigue life of its main spar connection. Using available reference loading data from acrobatic and training aircraft, the loading spectrum was established, and constant amplitude loading blocks were determined through the Rainflow cycle counting and statistical methods. Fatigue damage in the bolted joint was assessed using both linear and nonlinear Miner rules, revealing that results from nonlinear criteria tend to converge towards those from linear predictions as loading blocks increase. This approach provides a robust predictive framework for assessing the fatigue life of airplane components under variable amplitude loadings, potentially enhancing maintenance protocols and structural design durability.

Probabilistic hydrogen-assisted fatigue crack growth under random pressure fluctuations in pipeline steels

The increasing demand for energy and the global threat of climate change have driven the search for alternative energy sources, with hydrogen emerging as a prominent substitute for fossil fuels. The fatigue behavior of pipeline steels under gaseous hydrogen is a critical problem that is impeding the industry's adoption of hydrogen into the current natural gas infrastructure. A brief review of existing hydrogen-assisted fatigue crack growth (HA-FCG) studies, which reveal several key gaps, is given first. Existing HA-FCG models predominantly address constant amplitude loading, while the realistic driving force is random loading in gas pipelines. Also, the current uncertainty quantification studies for HA-FCG focus on material randomness and overlook the large uncertainties associated with random pressure fluctuations. To address these issues, this study proposes a HA-FCG model that utilizes a time-based subcycle approach, allowing for direct application to random spectrum loads without the need for cycle counting. A model parameter as a function of hydrogen operating conditions is introduced to capture the different regimes in HA-FCG, and the model predictions are compared with ASME B31.12 code. Following this, statistical analysis of random pressure fluctuation data collected from natural gas pipelines at multiple locations is performed. The realistic industry pressure data shows distinct statistical features, and it is observed that the high-fidelity data (high sampling frequency) is beneficial for accurate fatigue life predictions. Uncertainty quantification and load reconstruction are performed by the Karhunen–Loève expansion with a post-clipping procedure, leading to a probabilistic HA-FCG analysis. The paper concludes with key findings and suggests directions for future research.

Evaluation of the accuracy and efficiency of the modified maximum variance method for multiaxial fatigue analysis under constant amplitude loading

An optimized version of the Maximum Variance Method (MVM) is employed to determine maximum shear stress amplitudes in high-cycle multiaxial fatigue analysis using the critical plane approach, increasing accuracy and reducing computational burden. This refined approach posits that the MVM assumes that the critical plane is the one subjected to the maximum variance of the shear stress history. Comprehensive statistical analyses, including Analysis of Variance (ANOVA) and multiple comparison techniques such as Tukey’s HSD and Bonferroni correction, were conducted to systematically investigate the impact of critical factors on fatigue resistance, such as mean stress, phase, synchrony, failure criteria, and the strategy for calculating maximum shear stress amplitude. These analyses highlighted significant effects of mean stress and phase on the accuracy of fatigue strength predictions, underscoring the effectiveness of the enhanced MVM in managing complex loading scenarios. The results demonstrate that the proposed methodology performs equal to or better than conventional methods, with significantly lower computational costs.

Fatigue Crack Monitoring Method Based on the Lamb Wave Damage Index.

For practical engineering structures, fatigue is one of the main factors affecting their safety and durability. Under long-term service conditions, the minor damage will be affected by fatigue loading and expand to macroscopic cracks, affecting the structure's service performance. Based on the sensitivity of Lamb waves to minor and initial damage, a damage monitoring method for fatigue crack propagation is proposed. By carrying out fatigue crack propagation tests under constant amplitude loading, the Paris equation of 316L steel and damage signals at different crack growth stages were obtained. Combined with damage monitoring tests and finite element analysis, the relationship between the phase damage index (PDI), amplitude damage index (ADI), signal correlation coefficient, and fatigue crack propagation length was studied. Compared with PDI and ADI, the signal correlation coefficient is more sensitive to crack initiation, which can be selected as the damage monitoring index in the initial stage of crack growth. With the increase of fatigue crack propagation length, the peak time of the direct wave signal gradually moves backward, which shows an obvious phase change. In the whole fatigue crack growth stage, PDI and crack length show a monotonically changing trend. By using the stress intensity factor as the conversion parameter, a prediction model of the fatigue crack propagation rate based on PDI was established. Compared to the fatigue crack propagation rate measured by experiments, the relative error of the predicted results is 10%, which verifies the accuracy of the proposed damage monitoring method.

An enhanced multiaxial low-cycle fatigue life model

To improve the accuracy of predicting multiaxial fatigue life, an enhanced multiaxial low-cycle fatigue life model is proposed based on the FS model. This model introduces a correction parameter for the stress-related term to consider the influence of normal stress and shear stress on the critical plane. The feasibility of the model is investigated, and it is validated using fatigue test data from eight different materials. The results indicate that the proposed model is applicable for both symmetric and asymmetric loading conditions under constant amplitude loading, with highly accurate fatigue life prediction results.

Seismic Response and Collapse Analysis of a Transmission Tower Structure: Assessing the Impact of the Damage Accumulation Effect

This paper delves into the impact of the damage accumulation effect, which leads to the degradation of material strength and stiffness, on the seismic resistance of transmission towers. Building upon the elastic–plastic finite element theory, a mixed hardening constitutive model is derived for circular steel tubes, standard elements in transmission towers, incorporating the damage accumulation effect. A user material subroutine, UMAT, is created within the LS–DYNA framework. The program’s validity and reliability are established through axial constant–amplitude loading tests on single steel tubes. The subroutine is employed to conduct the incremental dynamic analysis (IDA) of an individual transmission tower and to contrast it with the structure utilizing the Plastic Kinematic material model, assessing the discrepancies in tower top displacements and segment damage indices (SDIs) at both macroscopic and microscopic scales. The results shows that the Plastic Kinematic model inflates the seismic performance of the transmission tower. When considering the damage accumulation effect in structural failure, the damage index of the members increases, leading to a reduction in both the structural strength and stiffness. The dynamic response in the plastic phase becomes more pronounced, and the onset of structural failure is accelerated. Consequently, structural analysis under seismic conditions should account for the damage accumulation process. Through the delineation of member and segment damage, the extent of damage to transmission tower segments can be quantitatively assessed. Subsequently, the ultimate load–bearing capacity and the most vulnerable location of the transmission tower can be ascertained. Finally, this paper provides a detailed analysis of the transmission tower collapse process under seismic action and summarizes the mechanism of collapse for the structure.

Effects of single overloads on fatigue crack propagation behaviour of AZ31B magnesium alloy under different temperatures

An experimental study examined the influence of single overload ratio (OLR) on fatigue crack growth (FCG) behaviour in AZ31B magnesium alloy at different temperatures (300 K, 373 K, and 473 K). The results showed that FCG rates and stress intensity factor ranges (ΔK) vary with temperature and overload ratios. After applying a single overload (OL), the FCG rate initially decreased, then increased rapidly, and stabilized at a value consistent with constant amplitude loading (CAL). The fatigue life increased by 86 % to 143 % at 300 K, 75 % to 132 % at 373 K, and 75 % to 134 % at 473 K for OLRs ranging from 1.75 to 2.25 when compared to the fatigue life at CAL. A single overload accumulates energy at the crack tip, forming an overload region with tearing ridges, secondary cracks, dimples, and fatigue striations under varying temperatures.