Cyclic Stress Range Research Articles

Time-dependent fatigue reliability analysis of heavy-haul railway steel bridges

Fatigue of heavy-haul railway bridges has been an ongoing concern due to the excessive stresses and frequent cyclic effects of freight trains. Current fracture-based fatigue research, which promotes fatigue reliability analysis caused by crack propagation, is challenged by the dilemma between the detailed modeling of cyclic stress and the reflection of temporal characteristics of loading conditions. In addition, due to the strong non-Gaussian nature of the fatigue limit state function and the computational inefficiency of integrating finite element analysis, current time-dependent reliability methods need to be further developed. To evaluate the fatigue reliability of heavy-haul railway steel bridges considering the temporal dependence of cyclic train loading, a time-dependent fatigue reliability methodology is developed in this study with two innovations. Firstly, a cyclic stress range model is proposed based on the load analysis at the bridge level, which can capture the time-dependent characteristics of the incurred stress range throughout service life. Then, an improved outcrossing rate method for strong non-Gaussian fatigue limit state functions is developed to reduce the computational costs associated with reliability analysis integrated with the finite element model. The developed time-dependent fatigue reliability methodology is then applied to a heavy-haul railway steel truss bridge located in Shandong, China, which proves its efficiency and accuracy in evaluating the time-dependent fatigue reliability of heavy-haul railway steel bridges. Furthermore, the developed methodology is able to provide insight into the balance between bridge fatigue damage and freight volume, and it is found that the combination of small train axle weight and high operation frequency is the optimal solution to achieve the fatigue reliability of the steel bridge while fulfilling the freight demand.

Molecular dynamics simulation of thermomechanical fatigue properties of Ni-based single crystal superalloys

In this paper, the thermomechanical fatigue (TMF) properties of Ni-based single crystal superalloys are studied by molecular dynamics simulations. Two different cyclic deformation mechanisms of superalloys are found under TMF loadings. The sample has a higher cyclic stress range, plastic strain energy density and a shorter fatigue life under Out-of-phase TMF loading than those under In-phase TMF loading. Moreover, the low-temperature tension half-cycle is more favorable for dislocations and stacking faults to cut into the γʹ precipitate phase, causing an earlier failure of superalloys under Out-of-phase TMF loading, which attracts more attention in actual operation.

Welding residual stresses and their relaxation under cyclic loading in welded S550 steel plates

This paper presents experimental and numerical investigations to determine the surface and through-thickness welding residual stresses and their relaxation in butt-welded plates under fatigue actions. The X-ray diffraction measurement validates the accuracy of thermal–mechanical analyses in estimating the as-welded residual stresses and their relaxation under cyclic loading. The experimental findings reveal that the relaxation of residual stresses occurs mostly within the first loading cycle. The amount of relaxation depends on the plastic deformation incurred, and hence the maximum load of the cyclic loads. The residual stress and its relaxation affect the stress ratio without changing the cyclic stress range.

Probabilistic relationships between strain range, stress range and loading cycles. Application on ASTM A969 steel

Fatigue life estimations can be made by considering the Δσ-N or Δ∊-N curves. Reliable estimations allow engineers designing save stress levels in structures or machines. In this paper, the Weibull distribution is combined with the Stüssi function to model the quantiles of the Δσ-N and Δ∊-N curves and the Ramberg-Osgood relationship. The nonlinear Stüssi function offers a good geometric approach to model the relationship Δσ-N or Δ∊-N and the Weibull distribution is the most adequate to handle lifetime magnitudes as load cycles N. To show the application of the proposed model, simulated and experimental data of ASTM A969 steel are evaluated.

Nonlinear damping properties of recycled aggregate concrete short columns under cyclic uniaxial compression

Although recycled aggregate concrete (RAC) has been studied intensively over past two decades, its damping property is still not analyzed sufficiently. In this paper, a nonlinear damping model for RAC prisms subjected to cyclic uniaxial compression are presented. Then with the combination of the compressive strength and damping property of RAC, an optimum recycled concrete aggregates (RCA) content including particle size and replacement percentage are recommended. The cyclic uniaxial compression test was conducted to investigate the dynamic modulus and nonlinear damping property of RAC, meanwhile tests for the RAC’s static compressive strength and modulus of elasticity were also carried out. Then based on the nonlinear damping model and compressive strength, relationships among the compressive strength, damping property, load indicators and RCA content are analyzed to obtain the optimum RCA content. Test results indicate that RAC obtains a higher loss factor than NAC. The loss factor of RAC is an increasing power function of RCA particle size and a decreasing power function of RCA replacement percentage. However, the compressive strength and dynamic modulus of RAC decreases compare with that of natural aggregate concrete. The different choice of cyclic uniaxial compression load indicators (cyclic stress range, stress level or strain range) has significance impact on RAC damping property and optimum RCA content.

An assessment of effects of non-stationary operational conditions on wind turbine under different wind scenario

PurposeThe non-stationary operational wind loads vary in time and site and has remarkable effect on wind turbine drive train. The purpose of this paper is to determine the effects of wind class 3 and 7 on the life of wind turbine drive train. The two-wind class 3 and 7 are described by average wind speed and weight factor and effects of two variables on wind energy generation and wind turbine drive train studied.Design/methodology/approachThe load distribution method is used to calculate stress range cycles for wind class 3 and 7. To determine the rise of force on wind turbine drive train, the load cycle method is proposed. The fatigue damage model is studied with respect to influence of different wind speeds and wind shear factor and then results analysed accordingly. Also sensitivity analysis has been carried out to assess the percentage of drop of energy generation and rise of tangential force for wind class 3 and 7. Linear fit method is used to determine the inclination of wind variation and wind shear of wind class 3 and 7. In this regard, two practical wind sites fall under the wind class 3 and 7 and 1.5 MW wind turbine have been taken in to account.FindingsThe results showed that the average rise of force on wind turbine drive train is 37.5% which can influence the drop in energy 34.7% for wind class 3. Similarly, the results of wind class 7 are showing that the average rise in force and drop in energy found to be 49.05% and 51.16%, respectively. The wind class 7 have higher tendency of wind fluctuations and weight factor that can cause a damage to wind turbine drive train components. The results showed that when wind speed increases to rated power 11.5 m/s the damages occurred and remain steady. Similarly, when weight factor increased from 0.18 to onwards the damage occurred. The increased wind loads increased the tangential loads on the wind turbine decreased life of the gearbox.Originality/valueThe results of study suggest that wind turbine should be design according to site specific wind environment for maximum energy generation and lowers the wind loads on the drive train component.

Fatigue behavior of prefatigued reinforced concrete beams rehabilitated with near surface mounted carbon fiber reinforced polymer reinforcement

AbstractThis paper investigates the influence of cyclic preloading on the fatigue behavior of reinforced concrete (RC) beams rehabilitated with near surface mounted (NSM) carbon fiber reinforced polymer (CFRP) reinforcement. The study includes eight RC beams with dimensions of 152.4 × 152.4 × 1,521 mm. Strengthened and nonstrengthened specimens were tested under monotonic loading to obtain the flexural static capacity. Two strengthened specimens were tested as a reference under constant amplitude cyclic stress without prefatiguing. Four nonrehabilitated RC beams were prefatigued to simulate service loading conditions. Later, these RC beams were rehabilitated with NSM CFRP reinforcement and tested under the same cyclic stress range of the reference specimens. Mid‐span deflection, strain of tension steel rebars and CFRP rods, stiffness degradation, and energy dissipation were analyzed and evaluated. Experimental results show that the rehabilitated prefatigued RC beams had similar stiffness degradation and failure modes to the reference strengthened RC beams. The rehabilitated RC beams had an improvement in the fatigue responses when compared to the reference strengthened RC beams. Moreover, the postfatigue monotonic behavior of the rehabilitated RC beams showed an increase in the elastic modulus and a decrease in ductility.

Undrained cyclic shear behaviour of weathered tephra

Weathered tephra is prevalent across volcanic islands like the North Island of New Zealand and is composed of volcanic airfall materials that have been subjected to various soil processes. Understanding their undrained response to cyclic loading is essential for geotechnical engineering applications in these regions because of frequently occurring local earthquakes. The authors describe for the first time the cyclic undrained behaviour of a weathered, clay-rich and highly sensitive tephra through triaxial tests. The weathered tephra experiences brittle failure and exhibits higher friction than sedimentary clays. Cyclic contour diagrams, covering the whole compressional and extensional range of stress conditions, are used to compare the cyclic shear strength of Pahoia tephra with those derived for sedimentary clays. It is found that weathered tephra: (a) is more resistant to small cyclic loading; (b) fails within a smaller range of cyclic shear stresses; and (c) exhibits a cyclic shear strength that peaks at zero average shear stress, in contrast to sedimentary clays where cyclic shear strength peaks at small compressive average stress.

Evaluation and Modeling of the Fatigue Damage Behavior of Polymer Composites at Reversed Cyclic Loading.

Understanding the composite damage formation process and its impact on mechanical properties is a key step towards further improvement of material and higher use. For its accelerated application, furthermore, practice-related modeling strategies are to be established. In this collaborative study, the damage behavior of carbon fiber-reinforced composites under cyclic loading with load reversals is analyzed experimentally and numerically. The differences of crack density evolution during constant amplitude and tension-compression block-loading is characterized with the help of fatigue tests on cross-ply laminates. For clarifying the evolving stress-strain behavior of the matrix during static and fatigue long-term loading, creep, and fatigue experiments with subsequent fracture tests on neat resin samples are applied. The local stress redistribution in the composite material is later evaluated numerically using composite representative volume element (RVE) and matrix models under consideration of viscoelasticity. The experimental and numerical work reveals the strong influence of residual stresses and the range of cyclic tension stresses to the damage behavior. On the microscopic level, stress redistribution dependent on the mean stress takes place and a tendency of the matrix towards embrittlement was found. Therefore, it is mandatory to consider stress amplitude and means stress as inseparable load characteristic for fatigue assessment, which additionally is influenced by production-related and time-dependent residual stresses. The phenomenological findings are incorporated to a numerical simulation framework on the layer level to provide an improved engineering tool for designing composite structures.

A hybrid analysis procedure enabling elastic design rule assessment of monoblock-type divertor components

This paper presents a simplified rule-based elastic analysis procedure (and its rationale) for the structural integrity assessment of the structural pipe component within monoblock divertor plasma facing components (components constructed from a tungsten block with through cooling pipe and copper interlayer). It is first demonstrated that the conventional fully elastic finite element analysis method used in an elastic code rule assessment must be modified when applied to monoblocks to overcome the problems caused by the assembly of multiple materials (with different yield strengths and different coefficients of thermal expansion causing residual stress). This is done by comparing the result of a fully elastic model with a more representative elasto-plastic model incorporating residual stress simulation. The results show that due to the expected high levels of residual stress, the desired elastic modelling of the structural pipe component can only be used to determine cyclic stress range (but not absolute stress), and even then, only if accompanied by elasto-plastic simulation of the non-structural interlayer (to apply the correct levels of differential expansion loads from the tungsten). This mixed elastic-elasto-plastic method is used in the proposed procedure, and applies the elastic code rules employing cyclic stress range, i.e. rules for ratchetting and fatigue. Additional rules for critical heat flux and allowable material temperatures are added. Example results of an assessment using the procedure are also presented for an ITER-like monoblock divertor target component.

Tensile stresses in fine blanking tools and their relevance to tool fracture behavior

Abstract In order to enhance the productivity of the fine blanking process there is a tendency to apply high strength tool materials with superior resistance to wear and plastic deformation such as WC-Co hard metals. Due to the mean stress sensitivity of these high strength materials under fatigue loading conditions, there is a need to describe the tool load situation including previously unconsidered tensile tool load components and mean stress. To this end a finite element-based tool load analysis was performed that describes the cutting process and the tool's retraction from the remaining sheet material. The tool load was revealed to contain significant tensile components that occur during tool retraction. Their location on the lateral punch surface coincides with origins of tool fracture in two thirds of investigated fine blanking punches that failed close to the cutting edge in an industrial production scale fine blanking environment. The influence of friction between punch and sheet on the magnitude of the cyclic stress range and mean stress that act locally at the tool surface was investigated. As one of the main results, a first approximation for a surface quality requirement for fine blanking tools made of WC-Co hard metal was quantitatively estimated as a function of the friction coefficient based on linear elastic fracture mechanics.

Quantitative evaluation of bonding strength for hard coatings by interfacial fatigue strength under cyclic indentation

The adhesion of coating to substrate is an important factor governing the performance and durability of coated engineering components. Existing evaluation methods cannot produce quantitative measurement of bonding strength for strong adherent coating. This paper proposes a novel evaluation method based on the cyclic spherical indentation (CSI) test, which uses successive indentations of a spherical ball onto a coated specimen to induce the detachment of the coatings along the interface. Compared with earlier methods, this method creates only adhesive failures, which only occur during elastic deformation of the substrate, yet it is applicable to coating with strong bonding. The evaluation method creates a curve of shear stress range versus failure cycles for each coating/substrate system. These curves can be used directly to compare the bonding strength of hard coatings.

Using DOProC method in reliability assessment of steel elements exposed to fatigue

Fatigue crack damage depends on a number of stress range cycles. This is a time factor in the course of reliability for the entire designed service life. Three sizes are important for the characteristics of the propagation of fatigue cracks - initial size, detectable size and acceptable size. The theoretical model of fatigue crack progression can be based on a linear fracture mechanic. Depending on location of an initial crack, the crack may propagate in structural element e.g. from the edge or from the surface. When determining the required degree of reliability, it is possible to specify the time of the first inspection of the construction which will focus on the fatigue damage. Using a conditional probability and Bayesian approach, times for subsequent inspections can be determined. For probabilistic modelling of fatigue crack progression was used the original and new probabilistic method - the Direct Optimized Probabilistic Calculation (“DOProC”), which uses a purely numerical approach without any simulation techniques or approximation approach based on optimized numerical integration.

Fatigue damage prediction of short edge crack under various load: Direct Optimized Probabilistic Calculation

Fatigue crack propagation depends on a number and value of stress range cycles. This is a time factor in the course of reliability for the entire designed service life. Three sizes are important for the characteristics of the propagation of fatigue cracks - initial size, detectable size and acceptable size. The theoretical model of a fatigue crack progression can be based on a linear elastic fracture mechanics (uses Paris-Erdogan law). Depending on location of an initial crack, the crack may propagate in structural element (e.g. from the edge or from the surface under various load) that could be described by calibration functions. When determining the required degree of reliability, it is possible to specify the time of the first inspection of the construction which will focus on the fatigue damage. Using a conditional probability and Bayesian approach, times for subsequent inspections can be determined based on the results of the previous inspection. For probabilistic modelling of a fatigue crack progression was used the original and a new probabilistic method - the Direct Optimized Probabilistic Calculation ("DOProC"), which uses a purely numerical approach without any simulation techniques or approximation approach based on optimized numerical integration. Compared to conventional simulation techniques is characterized by greater accuracy and efficiency of the computation.

Probabilistic prediction of fatigue damage based on linear fracture mechanics

Paper describes in detail and gives example of the probabilistic assessment of a steel structural element subject to fatigue load, particular attention being paid to cracks from the edge and those from surface. Fatigue crack damage depends on a number of stress range cycles. Three sizes are important for the characteristics of the propagation of fatigue cracks - the initial size, detectable size and acceptable size. The theoretical model of fatigue crack progression in paper is based on a linear fracture mechanics. When determining the required degree of reliability, it is possible to specify the time of the first inspection of the construction which will focus on the fatigue damage. Using a conditional probability, times for subsequent inspections can be determined. For probabilistic calculation of fatigue crack progression was used the original and new probabilistic methods - the Direct Optimized Probabilistic Calculation (“DOProC”), which is based on optimized numerical integration. The algorithm of the probabilistic calculation was applied in the FCProbCalc code (“Fatigue Crack Probabilistic Calculation”), using which is possible to carry out the probabilistic modelling of propagation of fatigue cracks in a user friendly environment very effectively.

Inspection Based Probabilistic Modeling of Fatigue Crack Progression

Attention to the fatigue cracks in steel structures and bridges has been paid for a long time. Fatigue crack damage depends on a number of stress range cycles. Three sizes are important for the characteristics of the propagation of fatigue cracks - the initial size, detectable size and acceptable size. The theoretical model of fatigue crack progression in paper is based on a linear fracture mechanics. When determining the required degree of reliability, it is possible to specify the time of the first inspection of the construction which will focus on the fatigue damage. Using a conditional probability, times for subsequent inspections can be determined. For probabilistic calculation of fatigue crack progression was used the original and new probabilistic methods - the Direct Optimized Probabilistic Calculation (“DOProC”), which uses a purely numerical approach without any simulation or approximation techniques. The algorithm of the probabilistic calculation was applied in the FCProbCalc code (“Fatigue Crack Probabilistic Calculation”), using which is possible to carry out the probabilistic modelling of propagation of fatigue cracks in a user friendly environment very effectively.

DOProC-based reliability assessment of steel structures exposed to fatigue

Summary Attention to the fatigue cracks in steel structures and bridges has been paid for a long time. In spite of efforts to eliminate the creation and propagation of fatigue cracks throughout the designed service life, cracks are still revealed during inspections. Fatigue crack damage depends on a number of stress range cycles. This is a time factor in the course of reliability for the entire designed service life. The failure rate increases in the course of time and the reliability decreased. If possible propagation of the fatigue crack is included into the failure rate, it is necessary to investigate into the fatigue crack and define the maximum acceptable degradation. Three sizes are important for the characteristics of the propagation of fatigue cracks. These are the initial size, detectable size and acceptable size. The theoretical model of fatigue crack progression is based on a linear fracture mechanics. A tension flange has been chosen for applications of the theoretical solution suggested in the studies. Depending on location of an initial crack, the crack may propagate from the edge or from the surface. Regarding the frequency, weight and stress concentration, those locations rank among those with the major hazard of fatigue cracks appearing in the steel structures and bridges. When determining the required degree of reliability, it is possible to specify the time of the first inspection of the construction which will focus on the fatigue damage. Using a conditional probability, times for subsequent inspections can be determined. For probabilistic calculation of fatigue crack progression was used the original and new probabilistic methods – the D irect O ptimized Pro babilistic C alculation (“DOProC”), which uses a purely numerical approach without any simulation techniques. This provides more accurate solutions to probabilistic tasks, and, in some cases, to considerably faster completion of computations. FCProbCalc code has been developed using the aforementioned techniques. By means of FCProbCalc (which stands for F atigue C rack Prob ability Calc ulation), it is possible to carry out the probabilistic modelling of propagation of fatigue cracks in a user friendly environment and to propose a system of regular inspections which should reveal damage to the structure, using the described computational procedures.

Analysis and Optimization of the Start-up Process based on Badaling Solar Power Tower Plant

Abstract As the mutual movement of the sun and the earth cause alternating night and day, solar power tower plants face frequently start and stop operations for solar radiation being its energy source. Besides, in the start and stop process of solar tower power plants, key components such as receivers, drum and turbine face rapid changes in temperature and pressure. Therefore, how to select and set reasonable start-up parameters, reducing start-up time was crucial to improve operating efficiency and ensure the operational life of the solar tower power plants. In this paper, how to determine the temperature rising curve of water in the drum during the start-up process was studied. The range of thermal stress and cyclic stress of the drum during start-up were calculated. Genetic algorithms were used to optimize the start-up operation. According to the design parameters of Badaling solar power tower plant, after optimization, the start-up time of the drum was 55 min while the origin time was 120 min. Moreover, it is obvious that the higher rated parameters are, such as rated temperature of the drum, the better is the effect of the optimization methods.

Prediction of short fatigue crack growth of Ti‐6Al‐4V

ABSTRACTIt is observed that the short fatigue cracks grow faster than long fatigue cracks at the same nominal driving force and even grow at stress intensity factor range below the threshold value for long cracks in titanium alloy materials. The anomalous behaviours of short cracks have a great influence on the accurate fatigue life prediction of submersible pressure hulls. Based on the unified fatigue life prediction method developed in the authors' group, a modified model for short crack propagation is proposed in this paper. The elastic–plastic behaviour of short cracks in the vicinity of crack tips is considered in the modified model. The model shows that the rate of crack propagation for very short cracks is determined by the range of cyclic stress rather than the range of the stress intensity factor controlling the long crack propagation and the threshold stress intensity factor range of short fatigue cracks is a function of crack length. The proposed model is used to calculate short crack propagation rate of different titanium alloys. The short crack propagation rates of Ti‐6Al‐4V and its corresponding fatigue lives are predicted under different stress ratios and different stress levels. The model is validated by comparing model prediction results with the experimental data.

Fatigue Reliability-based Inspection and Maintenance Planning of Gearbox Components in Wind Turbine Drivetrains

This paper introduces a reliability-based maintenance plan for wind turbine gearbox components. The gears and bearings are graded based on their fatigue damage and a maintenance map is developed to focus on those components with higher probability of fatigue failure and lower level of reliability. The main aim of this paper is to propose a method for developing the “vulnerability map” which can be used by maintenance teams to identify the components with lower reliabilities. The fatigue damage for gears and bearings are calculated at rated wind speed by the SN curve approach. The load duration distribution (LDD) method is used to obtain the stress range cycles for gears and load range cycles for bearings from the load and load effect time series obtained from a global response analysis. During routine inspection and maintenance, the vulnerability map can be used to find the faulty component by inspecting those with highest probability of failure rather than examining all gears and bearings. Such maps can be used for fault detection during routine maintenance and can reduce the down time and efforts of maintenance team to identify the source of problem. The proposed procedure is exemplified by a 750kW gearbox and a vulnerability map is developed for this case study gearbox.