Variable Amplitude Loading Research Articles

Prediction of Fatigue Crack Initiation under Variable Amplitude Loading: Literature Review

Metallic materials are widely employed in engineering constructions, and one of the most common failure mechanisms in metals is fatigue failure. Even though metal fatigue has been studied for almost 160 years, many problems remain unsolved. Fatigue in metal occurs when the metallic material is subjected to varying loads, resulting in failure due to damage accumulation. The fatigue process consists of a buildup of damage that leads to crack initiation, followed by a period of crack growth until the critical flaw size is reached. The sum of a start phase and a propagation phase represents the total life. To better understand the fatigue phenomenon at its different stages and predict the fatigue life, various types of prediction models have been developed and reported in the literature. This paper reviewed the different models that include microstructure scale parameters that can be used to predict how fatigue cracks start under variable amplitude loading, including the Modified Tanaka-Mura Model, Acoustic Second Harmonic Generation, and the Probability of Crack Initiation on Defects. For perfect life prediction under variable amplitude loading, a stress-based approach, a strain-based approach, and a continuum damage mechanics approach are reviewed. The purpose of this paper is to get overview of the current state of approaches to the life prediction of fatigue crack initiation with variable amplitude. Finally, gaps in knowledge about the prediction of fatigue crack initiation under variable loading at high temperatures are pointed out.

Fretting fatigue under variable amplitude shear loading blocks considering partial slip regime: Experimental/numerical analysis

Generally, the fretting fatigue problem is treated with constant amplitude loading. However, this condition is not the reality for industrial applications. The objective of this work is to propose a numerical methodology for the life assessment of components subjected to fretting fatigue under variable amplitude loading and to study the effects of these loads. For this, experimental tests were carried out by applying H-L (High-Low) and L-H (Low-High) loading blocks to the tangential load, that is, the contact normal load and the amplitude of the bulk fatigue load were kept constant while the tangential load has its alternating amplitude. The numerical methodology proposed for fretting fatigue life assessment includes the wear effect and crack propagation. The multiaxial fatigue parameter SWT, the theory of critical distance TCD, and Miners’ linear rule were used to compute the damage in the crack nucleation phase. The node-displacement algorithm based on Archard’s law was applied to account wear. In the crack propagation phase, the CDM (critical direction method) was used to estimate the crack initiation angle considering the worn contact surface, and then the crack is modeled and propagated. The still limited range of experimental data done in this work for fretting fatigue under varying loading blocks seems to indicate that the loading sequence has an effect on the accumulated fatigue damage, mainly to the H-L loading sequences. Based on this observation, a new non-linear damage model was proposed. Using this new damage model, the life estimation results were within a scatter band of 1.2.

Dynamic response of single-bucket foundation in clay under vertical variable amplitude cyclic loadings

The application of multi-bucket foundation has an increasing trend in deeper water. The horizontal dynamic response of multi-bucket foundation mainly depends on the vertical cyclic behavior of single bucket in this multi-bucket foundation. In order to investigate the vertical dynamic response of single bucket foundation, a series of 1g model tests were carried out under vertical cyclic loadings in over-consolidated clay. Test results show that the vertical displacement of model bucket increases and the stiffness of bucket-soil decreases with the increase of cyclic loading level parameter ζb, which is defined as the ratio of maximum force in loading cycle and static ultimate capacity. The vertical capacity increased by about 23% and 19.5% after constant amplitude unidirectional loading and variable amplitude loading, respectively. And the vertical capacity remains unchanged after constant amplitude bi-directional loading. The vertical displacement and stiffness of bucket-soil increase with the increase of cyclic times N. Superposition theory was applied to express the vertical displacement and stiffness of bucket-soil under vertical variable amplitude cyclic tests. The stiffness law was also analyzed using the spring model. The study on the vertical behavior of single-bucket foundation can provide some reference for the design of multi-bucket foundation.

Predicting fatigue crack growth through the small and long crack regimes for a military transport aircraft loading spectrum using FASTRAN

Predicting fatigue crack growth across the small and long crack regimes in airframe components is a challenging task. Current fracture mechanics methods require, amongst other things, high fidelity small crack growth rate data and a thorough understanding of the different behaviours of small and long cracks. This paper presents a case study where a fatigue crack growth prediction of Aluminium Alloy 7075-T7351 coupons tested to a military transport aircraft loading spectrum, from nucleation to failure, is attempted using the most recent version of the linear-elastic fracture mechanics-based analysis tool FASTRAN v5.76. The military transport aircraft loading spectrum was applied to different coupon configurations to show the effectiveness of FASTRAN for a range of crack growth scenarios. Crack growth rate data for the prediction in the near-threshold region was experimentally obtained from small cracks using quantitative fractography and this data is shown to be a determining factor in the accuracy of the prediction. This paper highlights the challenges faced by engineers in predicting fatigue crack growth under variable amplitude loading from nucleation to failure and demonstrates the ability of FASTRAN to accurately predict load history effects. Areas for continued improvement are identified with the aim of accurate and reliable fatigue crack growth prediction in a range of structures, conditions, and scenarios.

Experimental investigation of crack opening loads in an aircraft load spectrum

The concept of plasticity-induced fatigue crack closure is indispensable in explaining many fatigue crack growth phenomena; and it is now widely applied in advanced fatigue life evaluation procedures. This concept has been extensively investigated experimentally over the past sixty years using different methods. However, most of these investigations are related to constant amplitude loading or simple load cases such as single or multiple overloads or block loading. In contrast, there are currently no experimental studies investigating crack closure under variable amplitude loading or load spectra, which are more realistic scenarios. This can be attributed to the many difficulties associated with the evaluation of crack opening loads for large numbers of fatigue cycles, including sensor sensitivity, signal noise, data limits, etc. Recently, the authors proposed an advanced piezoelectric sensor for cycle-by-cycle crack opening load measurements, which addresses the above limitations. In this work, the piezoelectric sensor is utilised to investigate crack closure under a typical transport aircraft load spectrum. In particular, it is demonstrated that crack opening load levels can change significantly from cycle-to-cycle, and these levels are typically larger than for constant amplitude loading at the same R-ratio. The relative density plot of crack opening load levels reveals three distinct regions, which can be associated with certain load sequences. The outcomes of this research are important for the development and validation of spectrum compression algorithms as well as advanced fatigue life evaluation procedures.

Residual stress stability of HFMI-treated transverse attachments under variable amplitude loading with the P(1/3) and the linear spectrum

The potential of HFMI treatment to increase fatigue life under service loading remains in debate. However, some recent studies show that even under variable amplitude loading (VAL), fatigue strength is increased compared to untreated welds. Discussions generally focus on the stability of initial compressive residual stresses, which may be reduced during VAL due to high peak stresses. In this context, the potential of HFMI treatment is often only attributed to residual stress stability. This study presents further results on the effect of VAL with a P(1/3) and a linear load spectrum on the residual stress stability of HFMI-treated transverse stiffeners (TS) made of mild steel (S355) and high-strength steel (S700M). The impact of random, High-Low and Low-High loading sequences on the fatigue strength as well as on the residual stress behaviour of HFMI-treated joints will be discussed.

Multiaxial fatigue life estimation based on weight-averaged maximum damage plane under variable amplitude loading

An innovative critical plane determination approach with weight-averaged largest fatigue damage is proposed, in which the material failure modes can be considered. If material exhibits shear cracking behavior, a strain-based critical plane model with shear failure mode is selected to evaluate the weight function. Otherwise, other one with tensile failure mode is adopted. According to the proposed critical plane, a multiaxial fatigue lifetime estimation methodology is established for evaluating fatigue life. And, six kinds of materials are employed to validate the validity of presented methodology. The validation results reveal the presented methodology can estimate the orientation angles of failure plane accurately and supply satisfactory fatigue lifetime estimations for both shear and tensile failure mode materials. Furthermore, the proposed critical plane framework can be extended to be utilized with stress-based fatigue criteria, and prediction results show a good agreement with experimental data by another two materials.

Research on Damage Mechanism and Performance-Based Design Process of Reinforced Concrete Column Members

In order to understand the seismic damage assessment of reinforced concrete column members, the coupling relationship between the capacity degradation and the accumulated hysteretic energy and the displacement history was considered. The energy-based damage index under the random variable amplitude loading history was proposed. On the basis of preliminary research, the corresponding relationship between the damage index and the construction member parameters and seismic parameters was established, the damage mechanism was analyzed according to the damage index, and then the performance-based design process was proposed. It was found that increase in the stirrup ratio can slow down the damage, and the slowing effect was initially fast and then slows. When the reinforcement ratio is doubled, the damage index decreased by 0.063. The longer the earthquake duration was, the more serious the damage was, and this phenomenon was more obvious when the ductility coefficient was larger. With the increase in the ductility coefficient, the damage continuously increased. Therefore, it is an effective way to decrease the damage by controlling the ductility coefficient. Among all the influencing factors, the fundamental period and seismic intensity contributed more significantly to the damage indicators. When the damage index (performance objective) was determined, the target stirrup ratio can be obtained according to the proposed performance design process, that is, this design process can be used in the performance-based design. The design method based on damage index can make up for the deficiency that the design method based on the ductility coefficient does not consider the earthquake duration.

Fatigue crack propagation model and life prediction for pantographs on High-Speed trains under different service environments

The fatigue crack growth of a weld toe on the upper arm of a pantograph was investigated to predict the fatigue crack propagation life of the pantograph under normal and corrosive conditions. First, samples were subjected to four-point bending tests and simulations under the two conditions, and Paris law parameters were obtained. Second, constant-amplitude loads were determined through the equivalent treatment of variable-amplitude loads. Based on the Paris model, crack propagation was simulated using the finite element method for the two environments, and results showed a relationship between the crack length a and the stress intensity factor KI. The service life of the pantograph was predicted using the Paris law. Results indicated that the pantograph could run about 958,000 km and 7,660 km in normal and corrosive environments, respectively, after the development of its fatigue crack from a surface crack into a through-thickness crack.

Fatigue Crack Propagation under Christmas Tree Load Pattern

Most mechanical components are subject to dynamic loads, which can cause failure in service. This study aims to evaluate the effect of variable amplitude loadings on fatigue crack growth (FCG) in CT specimens produced with the AA2024-T351 aluminum alloy. Specifically, it is intended to predict the FCG rate when the specimen is subjected to a complex loading pattern, named the “Christmas Tree Spectrum”. Crack growth is simulated by node release, which occurs when the cumulative plastic strain at the crack tip reaches a critical value (110%) that is supposed to be a material property. It is therefore assumed that cyclic plastic deformation is the main damage mechanism. The specimen was subjected to four different load patterns: the 6–60 N low-frequency constant amplitude load (CAL); the 6–21 N high-frequency CAL; the Christmas Tree (15–9) and the Christmas Tree (9–3) patterns. The Christmas Tree 15–9 load pattern is defined by nine increments of +15 N and −9 N followed by eight increments of +9 N and −15 N. The results indicate that the Christmas Tree (15–9) pattern increases crack tip damage relative to the constant amplitude loading. This is attributed to small variations in material hardening, particularly during the unloading phase of the load block. On the other hand, the Christmas Tree (9–3) pattern did not show a significant effect, indicating the importance of the range of small-amplitude cycles. The crack closure phenomenon is usually used explain the effect of loading parameters, but this is an exception.

Very High Cycle Fatigue Damage of TC21 Titanium Alloy under High/Low Two-Step Stress Loading

Very high cycle fatigue (VHCF) tests were carried out under variable amplitude loading for TC21 titanium alloy. The first level of high amplitude loading was set as 950 MPa close to yield strength, and the second level of low amplitude loading was determined between 435 MPa and 500 MPa where fatigue cracks initiated at the specimen subsurface under constant amplitude. The results indicate that the high/low stress block significantly reduced the cumulative fatigue life of low stress amplitude, and the fatigue crack initiation site changed from the specimen subsurface under constant loading to the specimen surface under stress block. Based on continuum damage mechanics, the fatigue damage model of two-step stress block was established to estimate the fatigue damage process. The prediction of cumulative fatigue life generally agreed with the experimental data. The cumulative fatigue damage of the stress block was related to the stress amplitude and the cycle ratio, which determined the stress fatigue damage and its interaction damage. The surface crack initiation in the stress block accelerated fatigue damage of low stress amplitude, reducing the cumulative life.

Fatigue crack growth behavior of marine steel under variable amplitude loading-combining DIC technique and SEM observation

This paper experimentally studies the fatigue crack growth (FCG) behavior of AH36 grade marine steel under variable amplitude loading. FCG testing is conducted using compact tension specimens. Digital image correlation technique (DIC) is employed to study the evolution of strain distribution and cyclic fatigue characteristics. Fractographic analysis is performed to explore the overload retardation mechanism. Results indicate that the FCG rate varies significantly under overload application, leading to the extension of fatigue life by 1.03, 1.18 and 2.42 times under the overload ratios (OLRs) of 1.5, 2.0 and 2.5. Reasonable evaluation of the fatigue performance depends on the loading history. Extension of the fatigue life for periodic overload (POL) cases is not a simple superposition of that under two single ones, the interaction effect between the adjacent tensile overloads cannot be neglected. Greater plastic dissipated energy corresponds to more severe plastic deformation at larger OLRs and crack lengths. The larger strain accumulation at the crack tip should account for the greater FCG resistance and more evident overload retardation effect. The fresh fracture surface is destroyed at a certain region after overload due to the premature contact of the crack flanks, confirming that overload induced crack closure exists.

Intralaminar crack growth rates of a glass fibre multiaxial laminate subjected to variable amplitude loading

The literature shows that variable amplitude loading can be much more severe than constant amplitude loading in a fatigue damage context. However, the underlying physical explanations for this are still unknown. Therefore, this paper investigates if the local energy release rate at each intralaminar crack tip in a tension/tension fatigue loaded multidirectional laminate can be used to determine the crack growth rate of these cracks subjected to variable amplitude loading. The local energy release rate is investigated through a developed finite element model in which any number of cracks can be included to account for their interaction. The position of the cracks is determined based on previous experimental work. The experimental results from the previous work are compared to the numerical results in this work. At similar crack density levels the energy release rates increase in the variable amplitude tests compared to constant amplitude tests, but not enough to significantly impact the crack growth rate. It is concluded that less than 5% of the increased crack density rate and crack growth rate caused by variable amplitude block loading is due to increases in local energy release rate. The primary reason is more likely found on a microstructural level.

Compressive fatigue response of Al-Si10-Mg bionic thin tubes under constant and variable amplitude loading

In this study, two different lattice structures are mimicked from the Euplectella aspergillum. These lattice structures are used to design novel bionic tubes. Bionic tubes are fabricated with Al-Si10-Mg material using selective laser melting (SLM) process. The work investigates the thin tubes' dynamic response under cyclic fatigue loading; with constant and variable amplitude. Fatigue stiffness, fatigue life, and fracture mechanism of the bionic thin tubes are compared with honeycomb based thin tubes. The deformation and fracture behavior of the thin tubes under constant and variable amplitude is compared. Results showed that the portion of fatigue life spent in damage initiation and propagation depends on the stress amplitude and design. Also, the fracture mechanism is independent of stress amplitude and depends on fatigue loading and design type. Finite element modelling (FEM) is used to compare the stress distribution in different lattices. Numerical results showed the dependence of stress distribution on the loading and tube type. Overall, when novel bionic tubes are compared with honeycomb based thin tubes, the bionic tubes showed better fatigue performance. The newly designed bionic tubes can be used as grid-stiffened structures and structural applications.

Effect of heat treatment on the variable amplitude fatigue life and microstructure of the novel bioinspired Ti‐6Al‐4V thin tubes fabricated using Selective Laser Melting process

AbstractIn this study, thin tubes are mimicked based on the architecture of Euplectella aspergillum and studied for fatigue performance under variable amplitude loading. The thin tubes are fabricated with Ti‐6Al‐4V material using the selective laser melting (SLM) process. SLM printed components are always subjected to residual stresses, which can reduce fatigue performance of the components. Heat treatment effect on the fatigue performance, microstructure, and residual stress is studied. Complex geometry and sharp corners in the bioinspired tubes result in stress concentration, which further reduces the fatigue performance. The value of residual stresses at the sharp corners is dependent on the height of the tube, thickness of struts, and intersection of different struts. Heat treatment significantly reduces the residual stresses and increases the fatigue life of the thin tubes; however, strength decreases after heat treatment. Heat‐treated thin tubes showed a higher concentration of (α + β) phase, which results in decreased residual stress and improved ductility of the thin tubes. Advanced bionic thin tubes can be used for lightweight crash boxes, sandwich panels, bio‐implants, grid stiffened structures, etc.

Virtual special issue: Variable amplitude loading—Fracture mechanics and cumulative damage modeling

Virtual special issue: Variable amplitude loading—Fracture mechanics and cumulative damage modeling

Determination of the critical defect and fatigue life of high-speed railway axles under variable amplitude loads

High-speed railway axles are suffered from extremely complex variable amplitude (VA) loads during operation. However, in the design codes and operation maintenance of railway axles, most of them are based on the equivalent constant amplitude (CA) load spectrum to perform the fatigue resistance design by using the traditional nominal stress method, and carry out the routine inspection based on running experiments and data. In this paper, an innovative time-domain stepwise fatigue assessment (TSFA) approach has been introduced to include the influence of VA loads on the accumulated damage and fatigue crack propagation. Based on this procedure, the fatigue load spectrum from the multi-body system (MBS) dynamics simulation was integrated into the fatigue damage and remaining lifetime assessment of the axles. The calculation indicates that the safe lifetime of the powered and non-powered axles under the time-domain loading is considerably larger than the design value, which shows that the axle could safely operate until they are retired. However, for an original crack with the morphology ratio of 0.6 propagating to 45.0 mm, the lifetime of the powered and non-powered axle is sharply reduced to 1.32, and 2.07 years, respectively. Compared with the classical nominal stress method, the newly-developed TSFA procedure could produce a more conservative but practical result.

Fatigue life prediction considering temperature effect for carbon fibre reinforced composites under variable amplitude loading

Fatigue life prediction method based on stress normalization was proposed to reduce the influence of material property dispersion on life for CFRC (carbon fibre reinforced composites). In order to consider the effect of temperature on fatigue damage, a temperature influence factor was introduced into the fatigue limit equation and the life prediction method under variable amplitude loading at high temperature. Combined with the rainflow cycle counting and Miner linear damage accumulation rule, the proposed fatigue life prediction method was verified by the experimental results of composite multidirectional laminates under constant amplitude and variable amplitude loadings at various temperatures, and the prediction errors are within a factor of 5.

Research on fatigue reliability prediction model and structural improvement of welded drive axle housing based on master S‐N Curve method

AbstractFatigue reliability prediction of welded structures is mainly based on nominal stress or hot spot stress method, but there are some problems such as grid sensitivity and joint geometry dependence. The Master S‐N curve method can solve these problems well, but the corresponding reliability model needs to be studied. In this paper, the fatigue reliability model of welded structures based on the Master S‐N curve method is studied. Considering the randomness of life and the correlation of failure, a reliability model is proposed, which reduces the computational burden by establishing a median damage‐random threshold rule. Taking the welded drive axle housing as an object, the system reliability is analyzed under the bench test condition, and verified by the experimental data. After the verification, this method is used to predict the reliability of the axle housing under variable amplitude loading collected in the test field, and the results are verified by Monte Carlo (MC) method. When the P‐S‐N curves are parallel, the model is accurate, which is the characteristic of the Master S‐N curve method. This method only needs to input the median damage value of the weak part, which is easy to be applied. This method can speed up the reliability prediction cycle of welded structures, which is beneficial to product innovation and optimal design. Finally, an improved design scheme is proposed for the weak parts of welding, and the effects of welding leg width, welding depth, and closed weld on fatigue life are revealed.

Correction to: An Improved Prediction Model on Fatigue Crack Growth Rate under Variable Amplitude Loads for Metallic Materials

Correction to: An Improved Prediction Model on Fatigue Crack Growth Rate under Variable Amplitude Loads for Metallic Materials