Effect Of Stress Ratio Research Articles

Stress ratio influence on Paris parameter and fatigue driving force pertinent to material properties

Paris model is widely used since it was proposed in 1963 due to simplicity and universality, but it cannot consider stress ratio (R) effect and curve fitting is always needed to obtain Paris parameters when R is changed. Based on Goodman curve and analysis of 22 groups of fatigue crack growth (FCG) data, an analytical FCG rate model is proposed by linking Paris parameters and fatigue driving force at R ≠ 0 (from 0 to 0.5) to those at R = 0 and material constants (tensile strength and fatigue limit at R = −1). Results show that proposed model can well predict FCG behavior at different R values based on Paris parameters at R = 0.

Effect of loading conditions on short fatigue crack propagation behaviours in cast Al[sbnd]Si alloys

The effect of loading conditions on short crack propagation behaviours in cast AlSi alloys was investigated by a combination of photo-microscopy monitoring and post mortem analysis. The findings suggest that the path of short cracks is minimally influenced by loading conditions, whereas loading conditions significantly affect the fatigue crack growth rate (FCGR) and its statistical characteristics. Crack closure effect is observed under zero and negative stress ratio conditions. Roughness-induced crack closure occurs due to the coarse grain microstructure of cast AlSi alloys and the Stage-I mode growth of cracks within grains in the microstructural short crack regime. The high level of plasticity around the crack tip under negative stress ratio conditions has a significant impact on FCGR, resulting in a negative crack opening stress. When the stress ratio exceeds approximately 0.3, short cracks exhibit no crack closure. The load-level effect is observed only at high load conditions with negative stress ratios. Finally, a probabilistic short crack growth model was established using a Bayesian linear regression model to analyse the effect of stress ratio on the uncertainty of FCGR. After considering the crack closure effect, the difference in distributions of FCGR model parameters decreases significantly among different stress ratio conditions.

Numerical prediction for life of damaged concrete under the action of fatigue loads

High-speed railways have become a critical component of modern transportation, and ensuring the stability and durability of high-speed railway concrete under environmental and train fatigue loads is essential for ensuring project safety. This paper employs a numerical simulation method to predict the performance and lifespan of high-speed railroad concrete under fatigue loading with environmental damage. The study analyzes the effects of stress level (0.5–0.8), stress ratio (0.1–0.9), and load frequency (5 Hz–40 Hz) on the fatigue performance and lifespan of railway concrete during bending fatigue loading. A four-point bending numerical model of concrete is developed in this paper, which considers elastic modulus decay and surface cracking, in order to quantify the degradation of concrete properties in response to environmental and load-induced cracks. The numerical model is well-validated with experimental results, and the study establishes a correlation between concrete degradation and environmental and load-induced cracks, as well as the fatigue resistance of high-speed railroad concrete. The bending fatigue frequency of concrete should not exceed 25 Hz at high stress levels of 0.7. This study also shows that environment-induced initial damage will greatly reduce the fatigue resistance of concrete, and fatigue life degradation and elastic modulus decay have a nearly linear relationship. This research provides a crucial foundation for the fatigue design of concrete materials for high-speed railroads.

Undrained permanent deformation characteristics of Yellow River silt under one-way cyclic loads

As a new type of engineering construction filler, it is particularly important to know the shakedown and permanent deformation characteristics of the Yellow River silt under cyclic load. In this study, a series of undrained cyclic triaxial tests for Yellow River silt are carried out by using GDS triaxial apparatus, the effects of relative density, loading frequency, confining pressure and cyclic stress ratio on the development curve of permanent strain are explored. Based on the shakedown theory and combined with the data of permanent strain development curve of Yellow River silt at different stress levels, a calculation model for its critical dynamic stress and limit cyclic stress ratio under shakedown state is determined. Further analysis is conducted on the development law of the permanent strain curve of Yellow River silt under shakedown state, and a prediction model for permanent strain of Yellow River silt considering different parameters was established. Then the accuracy of the model is verified. Combining with splitting summation method, the settlement of foundation can be calculated.

Fatigue Crack Propagation of 51CrV4 Steels for Leaf Spring Suspensions of Railway Freight Wagons.

Leaf springs are critical components for the railway vehicle safety in which they are installed. Although these components are produced in high-strength alloyed steel and designed to operate under cyclic loading conditions in the high-cyclic fatigue region, their failure is still possible, which can lead to economic and human catastrophes. The aim of this document was to precisely characterise the mechanical crack growth behaviour of the chromium-vanadium alloyed steel representative of leaf springs under cyclic conditions, that is, the crack propagation in mode I. The common fatigue crack growth prediction models (Paris and Walker) considering the effect of stress ratio and parameters such as propagation threshold, critical stress intensity factor and crack closure ratio were also determined using statistical methods, which resulted in good approximations with respect to the experimental results. Lastly, the fracture surfaces under the different test conditions were analysed using SEM, with no significant differences to declare. As a result of this research work, it is expected that the developed properties and fatigue crack growth prediction models can assist design and maintenance engineers in understanding fatigue behaviour in the initiation and propagation phase of cracks in leaf springs for railway freight wagons.

Biaxial compressive failure criteria and constitutive model of high-strength geopolymer concrete after high temperature

This paper studies the effect of high temperatures (20℃, 200℃, 400℃, and 600℃) and stress ratios (σ2/σ3) (0.15, 0.3, 0.45, and 0.60) on biaxial compressive strength and strain development patterns of high-strength geopolymer concrete (HGPC). Experimental observations indicate that HGPC exhibits laminar damage similar to ordinary Portland concrete (OPC) before and after exposure to high temperatures, under biaxial compression. Unlike OPC, damage in HGPC initially passes through coarse aggregates at room temperature but shifts predominantly to the aggregate-mortar interface at 600℃. The biaxial compressive strength envelope of HGPC expands with rising temperatures. The increased multiple of biaxial compressive strength (σ3/fm) for HGPC at room temperature rises and then falls with increasing stress ratios, peaking at a stress ratio of 0.45 and surpassing the values for OPC and high-strength concrete (HSC). Before high temperature, the modulus of elasticity of HGPC is higher than that of OPC and decreases with increasing temperature, decreasing by about 45–60% for every 200°C increase, and the reduction is greater than that of OPC. The existing failure criterion is not suitable for HGPC after high temperature, this paper develops a new biaxial compression failure criterion for HGPC before and after high temperature based on Kupfer's criterion, taking into account the effect of temperature. The proposed failure criterion calculation results are well in agreement with the experimental data. A damage constitutive model for HGPC considering the effect of temperature and lateral pressure is also proposed, combining the Weibull distribution model for the ascending branch and a modified empirical model for the descending branch. This combined model effectively predicts the stress-strain relationship of HGPC under various temperature conditions.

Unified SIF at different stress ratios and the physical insight on the exponent of the Paris law

The Paris law has been broadly employed to describe fatigue crack growth (FCG) at steady state. It establishes the relationship between FCG rate and stress intensity factor (SIF) range. However, its physical insight remains an issue of controversy. The study aims to employ dislocation dynamics to explore two aspects associated with the Paris law: how does the stress-ratio affect the application of the Paris law? What is the microcosmic mechanism behind the Paris exponent in Paris law? We limit our exploration on the scenarios that dislocation nucleation and dislocation glide dominate FCG in an ideally isotropic single crystallite. Our exploration revealed that (1) a unified SIF range without empirical parameters could be adopted to account for the stress ratio effect, and this observation is in line with existing experiments, and (2) SIF affects FCG by influencing the nucleation of dislocation sources and activity of dislocations before crack tips. The stress-dependent dislocation nucleation time is correlated with the exponent of the Paris law.

Numerical study of multiple hydraulic fractures propagation in poroelastic media based on energy decomposition phase field methods

This paper proposes a novel phase-filed model for simulating hydraulic fracturing in poroelastic media under complex stress conditions. The main theoretical contribution lies in the fact that a generalized strain energy density decomposition is incorporated to hydraulic fracturing phase field model, which unifies hydrostatic-deviatoric and spectral decompositions and predicts material failure through classical Mohr-Coulomb failure criterion. Based on Biot’s poroelastic theory, an indicator function is used to distinguish between fluid flow in fractures and in pores. The fully coupled equations are solved by combining staggered schemes with Newton-Raphson methods. The proposed model is validated by comparing laboratory experimental results with numerical results. In order to demonstrate the influence of introducing hydrostatic-deviatoric and spectral energy decompositions, we simulated propagation of multiple hydraulic fractures and coalescence of hydraulic fractures with natural fractures. Finally, the effects of stress ratios (σx/σy) on multiple hydraulic fractures are analysed. It is found that when the stress ratio is 2, a more complex hydraulic fracture network is formed in the porous media.

A novel fatigue life prediction methodology based on energy dissipation in viscoelastic materials, synergistic effects of stress level, stress ratio, and temperature

This work introduces a new methodology to predict the fatigue life of viscoelastic materials by considering the creep effect on fatigue behavior under the concurrent effects of stress level, stress ratio, and temperature. The model established based on the total amount of energy dissipated during fatigue loading. To estimate the amount of dissipated energy under varying stress ratios and temperatures, two shift factors, ψcyclic(R,T) and ψcreep(R,T), were derived, attributed to the cyclic and creep parts of fatigue loading. These shift factors were subsequently incorporated into defined equilibrium equations to create the relationship between estimated dissipated energy and fatigue life. The input data for the model consisted of the dissipated energy and cyclic creep values obtained from experiments conducted at a reference stress ratio of 0.5 and reference temperature of 20 °C, together with the storage and loss moduli measured from one dynamic mechanical analysis (DMA) experiment in the temperature range of 15 °C–60 °C on a fully-cured epoxy adhesive. To validate the accuracy of the results, the predicted fatigue life at three temperatures of 20 °C, 40 °C and 55 °C, each loaded under three stress ratios of 0.1, 0.5, and 0.9 were compared with the experiments conducted under the same conditions. Almost all predicted results were in good agreement with the experiments, nevertheless; at the stress ratio of 0.9 at 20 °C, due to the significant change in the cyclic creep behavior, the accuracy of the prediction was lower. The developed model was used as a new constant life diagram (CLD) formulation, which afterwards was further developed to plot three-dimensional constant life diagrams (3-D CLDs) in which the constant life surfaces were a synergistic function of stress ratio and temperature.

Direction-dependent failure envelopes of sand-structure interfaces with snakeskin-inspired surfaces

Snakeskin-inspired surfaces generate direction-dependent interface strengths, with shearing in the cranial direction (i.e.; against the scales) generating greater strength than in the caudal one (i.e.; along the scales). This directionality is enabled by the transfer of load in friction and passive resistances. It is unclear if failure of these interfaces can be captured by models used for purely frictional interfaces. Interface shear tests complemented with particle image velocimetry (PIV) analyses were performed on snakeskin-inspired surfaces with different asperity geometries and on reference rough and smooth surfaces. The results of experiments performed at different initial effective stresses under constant normal stiffness boundary conditions show significant dilation-induced increases in effective stress. These increases were greater during cranial than caudal shearing, producing greater cranial strengths. These surfaces yielded nonlinear failure envelopes, with greater shear to effective stress ratios at smaller effective stresses, while the rough and smooth surfaces mobilized linear failure envelopes. The PIV analyses indicate that the snakeskin-inspired surfaces induce localized strains in the vicinity of the asperities, leading to wavy failure planes. The average shear strains are correlated with the mobilized shear strengths, with increases in effective stress leading to decreases in both strains and stress ratio.

A new method for prediction of fatigue crack propagation life under variable amplitude spectrum loading

This paper proposes a new method for predicting propagation lives for through-thickness cracks under variable amplitude mode-I spectrum fatigue loads. Only the crack opening, i.e., the increasing parts of the load cycles within spectrum profiles are considered for cycle counting and computing their stress ratios. Moreover, a cycle-by-cycle analysis is also performed throughout the spectrum to compute the so-called Spectrum Overload Index (SOL-Index), which is a multiplier applied on stress intensity factor range used within different crack growth retardation models, in which effects of stress ratio are also included. The SOL-Index is calculated using the average of peak loads for all cycles within the spectrum and their percent deviations from the peaks’ average value. Simulation results using the proposed cycle counting method, the integrated crack growth model and the SOL-Index are compared with those from multiple experiments under two different loading spectrums and another study in the literature. The results show that usage of Wheeler's model embodying the Forman or Walker equation and the SOL-Index together yields the closest results to the experiments.

Temporal effective stress response of soil elements below the base of an excavation in sensitive clay

Investigations into the temporally evolving stress state below the base of excavations and underground structures are very scarce, in contrast to studies of horizontal earth pressures during the construction stage. Therefore in this work, the measured temporal response in terms of vertical and horizontal effective stresses and displacements below a tunnel slab at the base of an excavation located in a deep sensitive clay deposit is reported. In addition to the measured unloading response over time, the completeness of the site description and complementary measurements enables future benchmarking of numerical models at boundary and element level. Instrument clusters of earth pressure cells and piezometers were installed at three locations in one cross-section. The monitoring data allows the interpretation of effective stress paths and stress ratios, <i>K</i>=σ'<sub>h</sub>/σ'<sub>v</sub>, at soil element level covering the construction and the serviceability stages. The in situ stress ratios enable a unique comparison to prior laboratory studies of <i>K</i> during unloading. The data presented herein on the evolution of <i>K</i> corroborate, although approximately, previous studies at laboratory scale. Furthermore, at system level, the monitoring data reveal the intricate interplay between deformations resulting from excavation and pile driving.

Probabilistic fatigue stiffness variation of angle-ply GFRP composites considering stress ratio effect

Fiber-reinforced polymer (FRP) composites are frequently used in bridges, wind power installations, and marine floating structures, and there is a growing interest in understanding their fatigue behavior. However, due to a considerable dispersion of the fatigue properties of FRP composites, reliable tools for probabilistic prediction of the fatigue stiffness are required. Thus, in this work, it is proposed a method that uses Bayesian inference and Markov Chain Monte Carlo (MCMC) simulations to estimate the degradation of the stiffness in FRP composites. This methodology is suggested not only to predict the fatigue residual stiffness, but also to consider the reliability of such predictions. Currently, the existing models for stiffness degradation in FRP composites need to fit the model parameters separately under different stress ratios. To address this, a correction term is proposed to describe the relationship between the stress level, stress ratio, fatigue cycles, and residual stiffness. The results achieved validate and prove the effectiveness of the suggested stiffness model, which incorporates four material parameters to calculate the residual fatigue stiffness of FRP composites.

Effect of stage amplitude ratio on dynamic behaviors of sand under wind turbine loading

Offshore wind turbines are subjected to more significant wave and wind environmental loads at extreme weather conditions, making subsoil experience various loading stages with different amplitudes. To investigate the coupling effect of both cyclic shear stress ratio (CSR) and stage amplitude ratio (Ar) between normal and extreme weather conditions, a series of bi-directional simple shear tests with five different Ar and three CSR values were conducted on marine sand using the variable-direction dynamic cyclic simple shear (VDDCSS) apparatus. In the tests, soil samples were compacted under vertical stress and then sheared in undrained conditions by applying two shear stresses acting in different horizontal directions. Test results indicated that the cyclic strain, pore water pressure ratio, and cyclic strength were significantly determined by the value of stage amplitude ratios and the CSRs: at the same CSR, cyclic strains, and pore water pressure increased while cyclic strength decreased with the Ar. Comparing the test data between various cyclic stress ratios found that the CSRs can accelerate shear strains, pore pressure accumulation, and cyclic strength attenuation.

A Fatigue Life Prediction Approach for Resistance Spot Welded Joints with Consideration of the Stress Ratio Effect

A Fatigue Life Prediction Approach for Resistance Spot Welded Joints with Consideration of the Stress Ratio Effect

Blasting effects of the borehole considering decoupled eccentric charge

The investigation of the blasting effects of the borehole considering decoupled eccentric charge is scarce and lacks thorough exploration. The coupled Smoothed Particle Hydrodynamics and Finite Element Method (SPH-FEM) is adopted to study the decoupled eccentric charge blasting effects. The effective stress distribution of rock around the borehole is analyzed and the damage evolution is studied quantitatively with introducing image recognition algorithm. Further, the effect of the decoupling coefficient on blasting effects is investigated. Results show that effective stress distribution presents obvious eccentric characteristics. At the bottom coupling point, the maximum effective stress is observed, and gradually reduces towards the top uncoupling point. The lower part of rock surrounding the borehole exhibits a higher damaged area ratio compared to the upper part for decoupled eccentric charge blasting. With the decoupling coefficient increases from 1.14 to 2.00, the effective stresses at monitoring points are all decreasing and the effective stress ratio first increases and then keeps relatively stable, with the decoupling coefficient of 1.6 as inflection point. As the decoupling coefficient increases to 1.6, the damage extent ratio reaches the peak. The greatest disparity in explosion energy between the coupled and uncoupled sides occurs at a decoupling coefficient of approximately 1.6.

Stress ratio effect on fatigue crack growth assessment via thermoelastic stress analysis

The fatigue performance of welded joint is strongly dependent on welding residual stresses as well as the local geometry of the weld toes. To ensure the structural integrity over time of such components, fine predictive models must be proposed together with efficient experimental methods for their assessment.This study introduces a model based on linear elastic fracture mechanics to forecast fatigue life in service of high strength steel welded joints. This model considers the effect of the local stress ratio (dependent on stabilized residual stresses) on the crack growth rate through the definition of an effective stress range. The use of Thermoelastic Stress Analysis (TSA) is used to perform in-situ monitoring of fatigue cracks on welded joints to experimentally characterize the crack-closure phenomenon at different load ratios. Indeed, under adiabatic conditions, the temperature's first harmonic at the surface of a structure submitted to cyclic loading is proportional to the stress tensor's first invariant's amplitude. As a result, the presence of a surface crack and the non-linearity induced by the alterative opening and closing within one loading cycle can be observed in the immediate temperature response. This phenomenon is used to evaluate a crack-opening rate that is related to the fatigue life of the welded joints.

Small-strain shear stiffness of sand-gravel mixtures

Small-strain shear stiffness (G0) is a key parameter for seismic ground response analysis and performance evaluation of various earth structures and foundations. To account for its pressure and density dependency, G0 has been conveniently correlated to mean effective stress (σm′) and void ratio (e). Such an approach is suitable for conventional uniform materials. However as found in this study, it is not always applicable to estimate the G0 of sand-gravel mixtures (SGMs), because it essentially fails to account for the combined effects of density and gravel content (GC). In this study, aimed at addressing this issue and developing a theoretical framework and empirical correlations suitable for estimating the G0 of SGMs, a series of bender element laboratory tests were carried out on selected SGMs. Specifically, SGMs were obtained by mixing two clean sands – namely New Brighton Sand (mean diameter, D50 = 0.2 mm) and Dalton River Washed Sand (D50 = 0.75 mm) – and rounded pea gravel (D50 = 5.5 mm). Shear wave velocity of specimens having GC = 0, 10, 25, 40 and 60% and prepared at a relative density (Dr) of 20, 30, 45 and 60% was measured at σm′ = 50, 100, 150 and 200 kPa. The laboratory results indicated that G0 of SGMs increases with increasing both the Dr and σm′, whereas the effect of GC would be marginal to significant depending on the limiting and threshold sand contents. To correlate G0 simultaneously with both GC and Dr, the equivalent void ratio (ef(eq)) was adopted. It is shown that the use of ef(eq) makes it possible to uniquely describe the G0 of SGMs for any combination of GC and Dr over the full range of σm′ level applied in this study.

Re-Distribution of Welding Residual Stress in Fatigue Crack Propagation Considering Elastic–Plastic Behavior

The welding residual stress re-distribution behavior during fatigue crack propagation in butt-welded high-strength steel plates for ship construction is investigated based on experimental test results and numerical analyses. The specimens’ initial welding residual stresses are obtained from X-ray for middle tensile (MT) specimens cut from butt-welded high-strength steel plates. Then, fatigue crack propagation experiments on MT specimens are conducted, and a strain gauge is used to measure the residual stress re-distribution field around cracks. A practical fatigue crack propagation simulation procedure is developed with a dynamic update of in-situ welding residual stress, where the residual stress intensity factor Kres of the MT specimen is deduced. The stress ratio effect on Kres during fatigue crack propagation is analyzed and a good agreement between experimental and numerical results is achieved.

Effects of pre-shearing stress ratio on the mechanical behaviours of gap-graded soils subjected to internal erosion

Internal erosion can induce significant changes in the mechanical properties of soils, posing various hazards to dam and dike structures. Despite its importance, our current understanding of this phenomenon remains incomplete. The influence of pre-shearing stress conditions on the mechanical behaviours of soils during the internal erosion process is particularly challenging, as existing experiments have not been able to maintain the constant pre-shearing stress ratios. To bridge this gap in knowledge, this paper presents a series of discrete element method (DEM) simulations focused on gap-graded cohesionless soil. The primary objective of these simulations is to investigate two specific cases of internal erosion: suffusion and suffosion processes. Soil specimens are subjected to different pre-shearing stress ratios in the standard triaxial tests before being submitted to different levels of erosion to study their constitutive responses. The results show that erosion-induced deformation (i.e. suffosion) only starts after a specific amount of mass loss. This mass loss and the pre-shearing stress ratio form a well-defined criterion for triggering suffosion, which is named “suffosion surface”. The volumetric strain is shown to be a better indicator to describe the suffosion process than the commonly used void ratio. The pre-shearing stress ratio significantly influences the suffosion response of the soil sample, with a higher pre-shearing stress ratio facilitating soil failure. Furthermore, soil specimens undergo both deviatoric and volumetric responses during the suffosion process. To this end, new DEM-based statistical equations were proposed to describe the observed mechanisms, which are helpful for the future development of constitutive models to describe internal soil erosion.