Equivalent Stress Amplitude Research Articles

Fatigue performance of innovative open-rib orthotropic steel deck for super-long suspension bridge

This paper presents experimental and numerical studies on the fatigue performance of an innovative orthotropic steel deck (OSD) with open-ribs, apple-shaped cut-outs, and additional transverse ribs, which is employed by the Zhangjinggao Yangtze River Bridge. This bridge is set to become the world's longest suspension bridge upon completion. A full-scale section of the OSD was fabricated and subjected to fatigue loading with a total cycle of 12.3 million times. The interested cracking-prone fatigue details include rib-to-deck and rib-to-crossbeam welded joints, along with the apple-shaped cut-outs of the crossbeam. Experimental results indicated that fatigue cracks initiated separately beneath the deck plate, on the flange of the rib, and at the rib-to-crossbeam welded joint, with equivalent stress amplitudes of 159 MPa, 148 MPa, and 99 MPa at 2 million cycles, respectively. In addition, detailed finite element model of the OSD was developed using ABAQUS and validated against the experimental results. The effects of the geometry dimensions and structural details of the bridge deck, longitudinal ribs, crossbeams and transverse ribs that influence the fatigue performance of this OSD were analyzed and discussed. Parametric analyses revealed that increasing the thickness of the deck plate, the thickness or the height of the longitudinal rib, and the number of transverse ribs can effectively reduce the stress amplitudes at corresponding fatigue details, which therefore improves their fatigue performance. This study provides useful references for the fatigue evaluation and design of OSDs with open-ribs and apple-shaped cut-outs.

Study on fatigue properties with composite waveform and variable amplitude of TC21 titanium alloy pulsed laser-arc hybrid welded joints

TC21 titanium alloy is widely used in the manufacturing of key components such as aerospace industry, its welded structure in actual service is often subjected to the cyclic loading with composite waveform and variable amplitude and leads to fatigue failure. Therefore, in this work, the composite waveform and variable amplitude fatigue properties of TC21 titanium alloy pulsed laser-arc hybrid welded joints were investigated in this paper, and the micro-deformation mechanism and crack initiation mechanism of welded joints under different initial maximum cyclic stresses were revealed. The results indicated that the micro-deformation mechanism was the competition between twinning and dislocation slip in the α′ phase at low stress. When the initial maximum cyclic stress increased, the generation and slip of dislocation dominated, and the main distribution of dislocations gradually transitioned from the α′ phase to the β phase. This caused the phase transition in the β phase to the α phase, which increased the energy at the α/β phase interface and reduced the resistance of fatigue microcrack initiation accordingly, thus promoting fatigue failure. In addition, pores were the main factor of fatigue failure for welded joints. Therefore, in this work, the influence of defect size, location and shape on the fatigue life of welded joints was considered to develop a fatigue life prediction model based on the control parameter Z-parameter and equivalent stress amplitude. The predicted composite waveform and variable amplitude fatigue life of TC21 titanium alloy welded joints was within the triple error band.

Effects of mean stress on the fatigue properties of core‐in‐sheath‐type carbon/glass hybrid thermoplastic composite rods: Experimental investigation and practical predictive method

AbstractA systematic acquisition of fatigue test data was conducted under different stress ratio conditions to investigate the effect of mean stress on the fatigue properties of carbon/glass hybrid thermoplastic composite rods. Our findings revealed that as the stress ratio increased with a higher mean stress, the stress dependency of the fatigue life also increased, and the slope of the S‐N curve became gentler. Under identical stress ratio conditions, hybrid rods with a greater volume fraction of carbon fiber exhibited the highest strength and a more gradual slope of the S‐N curve. To account for mean stress effects, an equivalent stress amplitude was introduced, resulting in data collapse at around 107 cycles, rendering this approach an industrially useful method to predict fatigue behavior when working with limited experimental datasets. This study presents a practical technique for estimating fatigue strength under mean stress through a weighted average efficiency and equivalent stress amplitude.

A simple fatigue methodology for filled natural rubbers under positive and negative R ratios

This paper suggests a simple methodology to optimize the uniaxial fatigue predictions for filled natural rubbers. In this study, the stress ratio R effect on rubber fatigue life is investigated numerically. For this purpose, a Finite Element model is developed to determine both amplitude and mean stress values in the critical zone of the considered specimen. The suggested model incorporates the R ratio effect using an equivalent stress amplitude. It is proven that the new model can efficiently describe the fatigue life for a large R -value interval with higher accuracy.

Developing statistical tools to analyze historical stress-controlled fatigue data in additively manufactured austenitic stainless steel

The development of robust fatigue property data sets for additively manufactured 316L austenitic stainless steels is hindered by the small sample sizes, inconsistent reporting of material properties and processing conditions, and differences in testing procedures for current sources of testing data. By applying standardization and categorization protocols to account for these shortcomings, historical data sets were aggregated into a single large data set and analyzed in greater detail, providing new levels of insight into the stress-controlled fatigue behavior of additively manufactured materials. Using this single aggregated data set, scatter was quantified using an eigenvalue analysis, and a multi-variable statistical model for predicting the mean fatigue life was developed. Interactions between variables and the sensitivity to different loading conditions were then identified, with the scatter in the data being attributed to differences in testing and post-processing condition such as surface condition and heat treatment, and the model was used to identify the role that each variable plays in determining fatigue life. An analysis of the fatigue responses across the aggregated data set using clustering algorithms allowed two distinct trends to be identified and attributed to the differing roles of microstructure and porosity on the resulting fatigue lives across different equivalent stress amplitude ranges.

Fatigue behavior of copper thin films

In this study, to investigate the mean stress effect on fatigue life of a 12 μm thick copper thin film, fatigue tests were performed at four maximum stress levels for a wide range of stress ratios. Tensile and creep tests were also performed to obtain the reference mechanical properties of the copper thin film tested. The fatigue behavior of copper thin films depended on the regions of the stress ratio and the modified Goodman and Gerber equations could not describe the mean stress effect on fatigue life well. The Haigh diagram was constructed using stress vs. life curve data obtained in this study, and the constant life curve was approximated by three straight lines. The Haigh diagram for copper thin films can be classified into three regimes: fatigue, fatigue-creep, and creep, depending on the fracture mode. The fatigue life can be well described with the equivalent stress amplitude calculated from the constant life curve, regardless of stress ratio.

Fatigue strength evaluation of scale railway axle with surface defect considering mean stress effect

In order to evaluate the notch fatigue strength of transition groove in railway axle, a series of fatigue tests were conducted on small specimens and press-fitted axles containing surface defects. Based on the experimental and finite element (FE) analyses, a novel method considering mean stress effect was proposed to evaluate the fatigue strength of scale railway axle with surface defect. It is found that press-fitted axles exhibit significantly lower notch fatigue strength than small specimens. Furthermore, the theory of critical distance (TCD) provides a good correlation between the notch fatigue strength of small specimens and experimental results. FE analyses revealed that the press-fitting reduces the fatigue strength of the transition groove through increasing stress concentration and introducing a mean tensile stress that decreases with an increase in the applied loading. To account for the mean stress effect, the axial stress at the groove is corrected as an equivalent stress amplitude at R = -1 based on Goodman relation. Through the combination of TCD and Goodman relation, an estimated fatigue strength with an error of less than 11 % can be achieved for the scale railway axle with surface defect.

Multiaxial Fatigue Analysis of Connecting Bolt at High-Speed Train Axle Box under Structural Subharmonic Resonance.

Based on the dynamic characteristics of the axle box front cover of high-speed trains in the subharmonic resonance state, the nonlinear single-degree-of-freedom (SDOF) model was proved to be reasonable, and reasons for the ineffectiveness of the common prevention methods for preventing bolt failure were analyzed firstly. Then, dynamic stress of the bolt was simulated by innovatively adopting the linear method based on frequency response analysis. The stress simulation method was verified to be practical under the subharmonic resonance state by analyzing and comparing the experimental and numerical results of the bolted front cover. It was proved that the linear method was accurate enough to simulate the dynamic stress of bolts, which is of great engineering significance. In addition to the transverse resonance stress of bolts caused by drastic vertical vibration of the front cover, the tensile resonance stress at the root of the first engaged thread was too large to be neglected on account of the first-order bending modes of bolts. Next, equivalent stress amplitude of the multiaxial stresses was obtained by means of the octahedral shear stress criterion. Finally, fatigue life of bolts was predicted in terms of S-N curve suitable for bolt fatigue life analysis. It argued that the bolts were prone to multiaxial fatigue failure when the front cover was in subharmonic resonance for more than 26.8 h, and the fatigue life of bolts could be greatly improved when the wheel polygonization was eliminated by shortening the wheel reprofiling interval.

The damage mechanism of tension-tension fatigue interaction with creep damage of the compacted graphite cast iron alloy at high temperatures

The tension-tension fatigue test of the compacted graphite cast iron (CGI) alloy was carried out by RDL100 universal testing at 500 °C and 550 °C, respectively. A tension-tension trapezoidal load is applied to the CGI specimen. Because of the time-dependent deformation at elevated temperatures, the stress–strain curve presents hysteresis loops, and the area of the hysteresis loop increases gradually with continuous cyclic loading and sustained loading times. Intergranular and transgranular cracks in the microstructure accelerate the CGI alloy fracture failure. The fatigue life is sensitive to the short loading time and decreases with the sustained loading time exponentially under the tension-tension fatigue condition. The short holding time has a great influence on the fatigue life of CGI. The fatigue behavior of CGI alloys and the influence of holding time on the fatigue life can be characterized by y = aexp(bx) (a and b are constants, can be fitted through the test data). In addition, the fatigue life of CGI alloy can be predicted by the ductility depletion method. But the equivalent stress amplitude needs to be modified to eliminate the effects of oxidation damage.

An equivalent strain energy density model for fatigue life prediction under large compressive mean stress

In this work, a modified Smith-Watson-Topper (SWT) model is proposed for the consideration of large compressive and tensile mean stresses. Firstly, the maximum normal stress in the original SWT model is replaced with equivalent stress amplitude, and the SWT parameter is thereafter interpreted as equivalent strain energy density (ESED). The newly proposed ESED model gives improved prediction results in fatigue life, especially under conditions with large compressive mean stress. Secondly, the applications of different mean stress correction (MSC) models are investigated with their limitations carefully examined. In order to improve the ESED model with higher accuracy, a new exponential MSC model is proposed. Moreover, an additional parameter concerning the dependency of material on mean stress is proposed. With the exponential MSC model incorporated, the ESED model is validated with experimental data from several different materials, and shows obviously improved prediction results compared with SWT model and some recent life prediction models.

Variable-amplitude fatigue behavior of M30 high-strength bolts in end-plate connection joints

High-strength bolts are widely used in connection joints for steel structures. In this paper, the variable-amplitude fatigue behavior of M30 high-strength bolts in end-plate joints is studied. Variable-amplitude fatigue tests were carried out on 19 M30 high-strength bolts using an Amsler pulse fatigue tester. Four cyclic stress amplitude loading modes, including Low to High (L-H), High to Low (H-L), Low to High to Low (L-H-L), and High to Low to High (H-L-H), were applied to the test specimens. In addition, the variable-amplitude fatigue life of M30 high-strength bolts was studied using two forms of cumulative damage models. The stress - fatigue life (S-N) curve was plotted using the equivalent stress amplitude. The obtained S-N curve was compared with the existing bolt fatigue S-N curve and the current specifications. Finally, fatigue fracture was analyzed from macro and micro perspectives. It was found that for most specimens, fatigue fracture occurs at the first joint thread between the bolt and nut, while for a few bolts, fatigue fracture occurs at the joint between the bolt head and bolt. With a fatigue life of 2 million cycles as the threshold, the fatigue limit is 107.5 MPa, which is 2.67 times higher than that specified by ANSI/AISC 360 – 16. Additionally, the fatigue properties of high-strength bolts in end-plate connections are better than those in bolted sphere joints at higher stress levels. At low stress levels, the contact pressure formed by the extrusion of the end-plate reduces the fatigue life of the bolts. Furthermore, unlike the constant-amplitude fatigue fracture, the variable-amplitude fatigue fracture has an obvious load change boundary line.

Loading history effect on ratcheting behavior: Modelling and simulation

In this paper, an elastoplastic constitutive model is developed to describe the effect of loading history on the ratcheting. The loading history variable is introduced to record stress history variation during cyclic loading, such as equivalent peak stress and equivalent stress amplitude. Based on Ohno-Wang model, an improved kinematic hardening rule is proposed to simulate the ratcheting effect by establishing the nonlinear evolution equation of ratcheting parameter. A new memory evanescence term is introduced to the plastic strain range memory surface. The evanescence term is activated to describe the difference of yield stress evolution during ratcheting and strain-controlled cyclic loading as the plastic strain range radius exceeds a certain threshold. Compared with the experiments and existing models, the results show that the proposed model can better capture the ratcheting effect with loading history.

A new stress-based model to predict the fatigue life of 880-grade pearlitic rail steel under uniaxial ratcheting conditions

This work explores a comparative analysis to verify the applicability of the existing stress-based model to predict life under ratcheting for pearlitic rail steel. The walker model is the most accurate of the available models, but its application is limited owing to the intricacy involved and the experimental reliance on its constant (γ) assessment. As a consequence, a novel stress-based life prediction model is proposed in this study. The applicability of the different models, and the proposed one, is described using equivalent stress amplitude vs life plot, stress deviation plot, error distribution box plots, and probability density function plots.

Biaxial tension-torsion fatigue properties of A588 steel weld joint for high-speed train bogie

The biaxial tension-torsion in-phase fatigue properties of the specimens taken from the welded joint and the base material of an A588 steel train bogie were investigated comparatively. The relation between the equivalent stress amplitude and the cyclic fatigue life of the specimens was obtained. The experimental results indicate that the fatigue life of the welded joint specimen is higher than that of the base material specimen at the higher applied stress amplitude, while the fatigue life becomes closer with decreasing the applied stress amplitude. There is a critical stress between 368 MPa and 396 MPa dominating the fatigue damage behaviors of welded joint specimens. The fatigue crack initiation is prone to occur at the boundary between the base material zone and the heat-affected zone when the stress amplitude is higher than the critical stress, while the cracks originated from the weld metal zone when the stress amplitude is lower than the critical stress. The transition of fatigue damage behaviors was analyzed comprehensively based on the microstructure and the residual stress distribution of welded joint specimens. The present research may provide an important clue for the fatigue performance optimization of the welded metallic components.

Non-local volumetric approach to analysis defect's shape influence on specimens durability subjected to bending and torsion

The influence of defect features on fatigue behaviour is a complex trivial issue. Although the important advances over the last decades, the dialectical relationship between the defect orientation and durability is not clearly understood. The paper aims at studying the influence of the orientation of elliptical defects on the durability of samples made of C45 steel. Three types of samples with elliptical defects were subjected to cyclic bending and torsion (R = -1) in the form of a one-sided notch oriented at various angles, namely 45, 60 and 90°. The stress analysis was performed using local and non-local methods in order to determine an equivalent stress amplitude. The stress fields surrounding the defects were evaluated via three-dimensional numerical models. Then, the results were compared with the results obtained for smooth samples. The results show that the defect orientation has a higher effect under bending loading than under torsion and that the defects oriented perpendicularly to the longitudinal axis of the specimen are more detrimental.

Tensile low-cycle fatigue performance and life prediction of high-strength bolts

Monotonic tensile tests and tensile low-cycle fatigue tests have been conducted to explore the low-cycle fatigue life of high-strength bolts, which is an important property to guarantee the connections do not occur low-cycle fatigue failure before their connected members under earthquakes. Large-deformation performance and failure modes of bolts were numerically simulated based on the damage constitutive relation which was investigated by the tensile tests of smooth and notched specimens. The results show that complete uniaxial constitutive relation of the bolt material, namely 20MnTiB steel, and the displacement from tensile load response of smooth specimens in the numerical simulation can be better described by the Swift flow stress model. The GTN damage model of the steel was calibrated by tensile tests and finite element models of notched specimens. With the decrease of the notch radius, the tensile capacity of the notched specimen increases while the ductility gets worse. The calibration parameters of GTN damage model can be applied to simulate the load-displacement response and fracture behavior of notched specimens accurately. In order to obtain a more targeted GTN model under different stress states, the quantitative relation between equivalent plastic strain during nucleation and stress triaxiality was proposed, which provided an important reference for establishing fatigue damage models of various bolted joints in the numerical simulation. Both the fatigue failure modes of the bolts under cyclic displacement with constant amplitude and the fatigue life based on the tensile capacity degradation were obtained from the fatigue tests. The fatigue brittle fracture and plastic elongation of the shank are the two fatigue failure modes of the bolt. Typical regional characteristics are presented in the bolt fatigue fracture, with beach-like fatigue bands in the expansion area. Under different failure modes, the capacity degradation can better determine the fatigue life of bolts. The methods for predicting fatigue life were proposed based on cyclic displacement amplitude, equivalent stress amplitude and local plastic strain. A good prediction result was proved by the phenomena that the predicted fatigue life based on the cyclic displacement amplitude and local plastic strain was basically within the scatter band of 1.5. Moreover, the fatigue design parameters of bolts given by the equivalent stress amplitude method provide a reference for establishing a unified fatigue design theory.

ASSESSMENT OF THE RESIDUAL LIFE-TIME OF THE ELEMENTS OF THE CENTRIFUGAL PUMP OF THE ENERGY INSTALLATION ON THE BASIS OF STATISTICAL ASSESSMENT OF FATIGUE WITH PREDICTED WEAR DUE TO CORROSION

In this article, the residual resource of a centrifugal pump was anticipated, which operates an overestimated resource in the pumping line of a nuclear power plant. The results of theoretical and numerical modeling of its stress-strain state with a change in the geometry of the hull parts are presented. Three-dimensional FE models have been developed that take into account the actual geometry of pump parts, as well as a forecast of their possible changes during further operation. The change in the geometry of the structure is taken into account on the basis of extrapolation of data on the thickness of the hull walls obtained over a long service life. Calculations to determine the static strength are made for the main operating mode of the pump (under normal operating conditions). In places of welds, the cyclic strength was checked separately, while taking into account the decrease in their strength due to an increase in equivalent stress amplitudes by dividing them by the coefficient of reduction in the strength of the weld. The process of thinning of the wall of the pump housing under the action of erosive-corrosive wear is modeled. This process is random, so it was modeled taking into account the equations of wear growth kinetics. As a result of the research, the damage parameter and the probability of failure-free operation of the structure were obtained. These parameters are determined taking into account the predicted values of the percentage thinning of the pump housing wall and the obtained characteristics of the statistical deformation state of the structure.

Validation of crack initiation model by means of cyclic full-scale blade test

Wind turbine rotor blades are subject to highly dynamic loads and designed for life cycles of at least 20 years, which means that materials are subjected to high-cycle fatigue. Fatigue is a design-driving loading for current and future blades. Bond lines of blades are exposed to a multi-axial stress-state due to the anisotropic thin-walled blade structure and curved, tapered, twisted, and airfoil-shaped blade geometry. To eliminate undesirable failure modes and thus increase the reliability of wind turbine rotor blades, standards and guidelines recommend that the multi-axial stress-states be taken into consideration for the limit state analysis. In addition, thermal residual stresses that develop during manufacture can have a significant impact on the fatigue life of the bond line. By means of a cyclic full-scale blade test of a commercial 81.6m long offshore blade, we validate a crack initiation model, which takes into account multi-axial thermal and mechanical stress-states, as well as the probabilistic stress-life, to predict the edge of crack initiation in the adhesive as well as the span-wise position. Both observations agreed well with the simulations. All residual normal stress components and cross-sectional plane shear stress made up the major part of the mean equivalent stress, while the mechanical stress amplitude components - longitudinal, peel, and cross-sectional plane shear stress - made up the major part of the equivalent stress amplitude.

Fatigue Optimization of Structural Parameters for Orthotropic Steel Bridge Decks Using RSM and NSGA-II

This study presents an optimization flow for structural parameters of orthotropic steel bridge decks (OSDs) based on the fatigue performance and the structural weight. The effects of structural parameters, namely, the thicknesses of the deck plate, the U-rib, the diaphragm, and the longitudinal diaphragm, on equivalent fatigue stress ranges were investigated using surrogate modelling based on the response surface methodology (RSM). Finally, the Pareto optimum front was obtained via the nondominated sorting genetic algorithm II (NSGA-II). The results show that the established surrogate response surface model can predict the local equivalent stress amplitudes well. The deck thickness is the most significant factor for the fatigue performance of the deck to U-rib weld and the U-rib to diaphragm weld. The objectives of minimizing the equivalent stress range and the total structural weight are truly conflicting, and the optimum solutions for structural parameters can be obtained from the Pareto optimum front.

Multiaxial fatigue behavior and life prediction of 2198-T8 Al-Li alloy notched tubular specimen based on DIC technique

2198-T8 aluminum-lithium alloy is an advanced aeronautical engineering material. The multiaxial fatigue tests of notched specimens are conducted with the variables of notch diameter, notch number, and equivalent stress amplitude, respectively. The strain field and fatigue life are characterized and calculated by digital image correlation (DIC) technique. The results show that: the fatigue life decreases with the increase of notch diameter, number of notches, and the equivalent stress amplitude. The strain curves calculated by VIC-3D are similar to those obtained by the testing. The normal and shear strain concentration becomes obvious at 80% to 90% fatigue life, and the surface cracks appear at 95% fatigue life, typical multiaxial fatigue morphologies including tire patterns and wear fatigue striations are observed on the fracture surface. The feasibility of the DIC technique to characterize multiaxial fatigue behavior is verified. The modified SWT model provides fine life prediction results with all predicted data within a factor of two.