Range Of Mean Stresses Research Articles

Continuum damage mechanics-based fatigue life prediction of L-PBF Ti-6Al-4V

The fatigue behavior and life of additively manufactured Ti-6Al-4V are very dependent on its heterogeneous microstructure, which in turn results from its fabrication process. In this paper, a fatigue damage model based on continuum damage mechanics was proposed to predict the high-cycle and very-high-cycle fatigue life at various stress ratios of Ti-6Al-4V fabricated by laser powder bed fusion (L-PBF). Model predictions were found to be in good agreement with experimental results for the different stress ratios considered. The model was found to be sufficiently robust to predict the fatigue life of other titanium alloys over a range of mean stress. The primary novelty is the incorporation of a tensorial formulation for anisotropic fatigue properties and the nonlinear effect of mean stress, which extended the model applicability to a wide range of stress ratio from -1 to 0.5. The results provide new insight into mean stress effects on fatigue of L-PBF Ti-6Al-4V up to the very-high-cycle fatigue regime.

Mechanical properties of unbound limestone aggregates replaced by recycled glass aggregate for pavement in Canada/Quebec

This study investigated the use of recycled glass aggregate (RG) as unbound base/subbase material. The experimental tests included compaction, Los Angeles, Micro-Deval, and California bearing ratio (CBR) tests. In this regard, a fine proportion of course limestone aggregate (MG20) was replaced by RG with size ranging from 0 to 5 mm based on the volumetric method. Adding RG to the coarse aggregate improved durability in wet conditions, which is more representative of the field condition of Canada/Quebec, but decreased in dry conditions. CBR values decreased with increasing RG inclusion, but all blends with 0%–100% RG in the fine fraction of MG20 met minimum requirements for unbound granular layers in Quebec. A simple model predicting the resilient modulus values of these materials based on CBR values at different stress levels was suggested. This equation estimates Mr values of various aggregate-RG blends under a wide range of mean stresses based on their CBR values.

Microstructure features induced by fatigue crack initiation up to very-high-cycle regime for an additively manufactured aluminium alloy

Fatigue failure can still occur beyond 107 cycles, i.e. very-high-cycle fatigue (VHCF), in many metallic materials, such as aluminium alloys and high-strength steels. For VHCF of high-strength steels, a fine granular area (FGA) surrounding an inclusion is commonly identified as the characteristic region of crack initiation on the fracture surface. However, no such FGA feature and related crack initiation behaviour were observed in VHCF of conventionally cast or wrought aluminium alloys. Here, we first reported the distinct mechanisms of crack initiation and early growth, namely the microstructure feature and the role of FGA in VHCF performance for an additively manufactured (AM) AlSi10Mg alloy. The AM pores play a key role in fatigue crack initiation similar to that of the inclusions in high-strength steels, resulting in almost identical FGA behaviour for different materials under a range of mean stress with a stress ratio at R < 0 or R > 0. The profile microstructure of FGA is identified as a nanograin layer with Si rearrangement and grain boundary transition. This process consumes a large amount of cyclic plastic energy making FGA undertake a vast majority of VHCF life. These results will deepen the understanding of VHCF nature and shed light on crack initiation mechanism of other aluminium and AM alloys.

Probabilistic fatigue life assessment of steel rail-bridge in dual response surface framework

A new probabilistic fatigue life assessment (PFLA) procedure is proposed considering dynamic effects of train loading, possible enhancement of axle load, and uncertainty there-in. In conventional PFLA, Monte Carlo simulation (MCS) is used to simulate stochastic load. Thereafter, rainflow counting method is used to obtain mean stress ranges. However, it is well-established now that only mean stress range may not depict the detailed stochastic nature of train axle load time-histories. Moreover, such MCS-based PFLA is computationally demanding for real-life complex structures, and routine implementation of it is quite troublesome due to dearth of skilled engineers in advanced fatigue analysis and interface software. To circumvent this, the proposed PFLA procedure resorts to dual response surface method (DRSM), which yields explicit equations for mean as well as standard deviation of stress range. Using these equations, the proposed approach directly relates fatigue life with the input factors (train speed, axle load, etc.) through an excel spreadsheet without requiring MCS. The effectiveness of the proposed procedure is elucidated through an existing steel railway bridge in India. The accuracy of the approach is also validated with four other steel bridges practically failed in fatigue. The results show that the proposed PFLA is in excellent agreement with the most accurate direct MCS-based PFLA, and the practical data obtained from failed steel bridges; whereas, the conventional moving load analysis-based deterministic fatigue life assessment approach yields significantly deviated results. Also, the proposed DRSM-based PFLA approach is observed to be computationally more efficient than the conventional direct MCS-based PFLA.

Mean stress sensitivity of sintered iron and steel

Abstract There is a well-based correlation between the pulsating amplitude σ A(R = 0) and the alternating amplitude σ A(R = – 1) in fatigue testing of sintered iron and steel which permits to predict the mean stress sensitivity and the pulsating amplitude if the alternating endurance limit σ A(R = – 1) has been measured. Without loss of precision the relationship can be extended from smooth unnotched specimen geometries to notched geometries if only the stress concentration factor is known. The coefficients of the predictive equation depend on the brittleness of the material, a systematic approach to take the brittleness into account is still missing. In Haigh diagrams, the slope of the σ A–σ m diagram with tensile mean stresses can be linearly extrapolated also into the compressive mean stress range σ m &lt; 0.

A new approach to the Haigh diagram of sintered steels from unalloyed iron to heat treated conditions

ABSTRACT Systematic investigations on the fatigue strength of heat treated sintered steels with notched specimens are barely found in the literature, especially at stress ratios other than R = −1. For that reason a larger study was initiated with the aim to provide a base for safe estimates of fatigue strengths also for heat treated components. This work deals with one possibility to design a Haigh diagram for the positive mean stress range beyond R = −1. Starting point is a new approach to determine the mean stress sensitivity M. As all equations derived are based on averages, in extreme cases individual test results can deviate by more than 20% from the calculated value. Regularly, however, deviations around ±10% are observed.

Strength Testing of Sandstone Under Multi-Axial Stress States

A true triaxial apparatus was designed and fabricated to achieve multi-axial stress states with prismatic specimens. The device, which is a modification of the University of Minnesota plane-strain apparatus, is equipped with piston assemblies that generate the intermediate principal stress. A closed-loop, servo-hydraulic load frame is used to control the major principal stress, while the minor principal stress is developed by fluid pressure. A stress path was developed to perform experiments under various states of stress at constant mean stress. Results from strength testing on Dunnville sandstone under conventional compression and extension are compared with the results performed under multi-axial stress states. Failure data were plotted in principal stress space to investigate the effect of intermediate stress on strength. A plane fitting method was used to obtain the material parameters of two, six-sided Paul–Mohr–Coulomb failure surfaces, which capture the strength characteristics of the sandstone over a range of mean stress.

An integrated methodology for fatigue life prediction of carbon fiber-reinforced polymer matrix composites under constant and variable R-ratio loadings

The progress in the anisomorphic constant fatigue life (CFL) diagram approach for efficiently identifying the fatigue of carbon fiber-reinforced composites under constant waveform loading over the whole range of mean stress is reviewed. The asset of this approach is the concept of critical stress ratio. The anisomorphic formulation of CFL diagram is flexible enough not only to increase the number of segments to accommodate the transient change in sensitivity to mean stress, but also to take a generalized form that considers the effect of temperature as well as the effect of variability in fatigue life. The anisomorphic approach is shown to succeed in describing the asymmetric and nonlinear CFL diagrams for carbon fiber composites of different kinds. It is suggested that the classic procedure for prediction of spectrum loading fatigue life of composites using the Miner rule with the rain flow cycle counting method is powered by integrating with the anisomorphic CFL diagram approach.

Temperature-dependent constant fatigue life diagram for press-formed short carbon fiber reinforced polyamide composite

Fatigue strength of a short carbon fiber reinforced polyamide (SCF/PA) composite fabricated using a press forming technique is examined. Unlike an injection-molded SCF/PA composite, this one exhibits in-plane isotropy as well as through-thickness uniformity. Fatigue tests on the SCF/PA composite are carried out at different stress ratios and temperatures, respectively. The fatigue test results show that the S–N relationship for the SCF/PA composite significantly depends on stress ratio, and fatigue degradation occurs most rapidly at the critical stress ratio, regardless of test temperature. The fatigue stress for a given life decreases with temperature. The reduction in fatigue strength with temperature correlates well with the reduction in static strength with temperature. Accordingly, the effect of temperature on fatigue life for each of different constant values of stress ratio can approximately be removed by normalizing fatigue stress with respect to static strength. The full shape of constant fatigue life diagram for the press-formed SCF/PA composite is identified for each of different test temperatures. It is shown to incline toward the direction of positive mean stress, regardless of test temperature. A difference in shape of CFL diagram between the press-formed and injection-molded composites is addressed. This study demonstrates that the anisomorphic constant life diagram approach with temperature as the parameter allows adequately predicting the constant fatigue life diagram and thus the S–N curve for the SCF/PA composite over the whole range of mean stress at any temperature in the tested range.

Strain localization and elastic-plastic coupling during deformation of porous sandstone

Results of axisymmetric compression tests on weak, porous Castlegate Sandstone (Cretaceous, Utah, USA), covering a range of dilational and compactional behaviors, are examined for localization behavior. Assuming isotropy, bulk and shear moduli evolve as increasing functions of mean stress and Mises equivalent shear stress respectively, and as decreasing functions of work-conjugate plastic strains. Acoustic emissions events located during testing show onset of localization and permit calculation of observed shear and low-angle compaction localization zones, or bands, as localization commences. Total strain measured experimentally partitions into: A) elastic strain with constant moduli, B) elastic strain due to stress dependence of moduli, C) elastic strain due to moduli degradation with increasing plastic strain, and D) plastic strain. The third term is the elastic-plastic coupling strain, and though often ignored, contributes significantly to pre-failure total strain for brittle and transitional tests. Constitutive parameters and localization predictions derived from experiments are compared to theoretical predictions. In the brittle regime, predictions of band angles (angle between band normal and maximum compression) demonstrate good agreement with observed shear band angles. Compaction localization was observed in the transitional regime in between shear localization and spatially pervasive compaction, over a small range of mean stresses. In contrast with predictions, detailed acoustic emissions analyses in this regime show low angle, compaction-dominated but shear-enhanced, localization.

Effects of temperature and stress ratio on fatigue life of injection molded short carbon fiber-reinforced polyamide composite

The effects of temperature and stress ratio on fatigue life of short carbon fiber-reinforced polyamide-6 composite have been examined. Static tension and compression tests are carried out at room temperature (RT), 50°C and 70°C, respectively. For each of these temperatures, constant amplitude fatigue tests are performed at different stress ratios. Experimental results show that the temperature dependence of static strength can be described by a single equation of the Arrhenius type in the range higher than room temperature for each of tension and compression. The tensile strength turns to be smaller than the compressive strength at high temperature. The effect of temperature on fatigue life can approximately be removed by normalization of fatigue stress with respect to static strength, regardless of stress ratio. The asymmetry and nonlinearity in constant fatigue life diagram turns to be more significant with increasing temperature, and they can adequately be modeled by means of the anisomorphic constant fatigue life diagram. The temperature-dependent anisomorphic constant fatigue life diagram approach is also tested. It is demonstrated that this method allows adequately predicting the S-N curves for any stress ratios as well as the constant fatigue life curves for the whole range of mean stress at any temperature in a range that includes the test temperatures.

Constitutive Model for the Undrained Compression of Unsaturated Clay

AbstractThis paper proposes a constitutive model to describe the isotropic compression response of unsaturated, compacted clay under undrained conditions over a wide range of mean stresses. The tot...

Hardening in porous chalk from precompaction

Knowledge of compactant behavior and the associated subsidence for high porosity carbonate formations is crucial in applications such as enhanced oil recovery. To gain insights into inelastic compaction and failure modes of a porous chalk under different loading histories, triaxial compression experiments were conducted on a high porosity (45 %) chalk, tested using three stress paths: no precompaction (virgin rock), precompacted to 30 MPa, and precompacted to 60 MPa. For the virgin chalk with no precompaction under triaxial compression, the transition from axial splitting to shear fracturing to compaction banding was observed. By precompacting the specimens to mean stresses of 30 and 60 MPa, the brittle failure regime expanded. In 60 MPa precompacted specimens, shear fracture was observed over a larger range of mean stress. Furthermore, precompaction increased the internal friction angle due to permanent volume change, but the cohesion decreased due to damage.

On the nature of pressure dependence in foams

Present study explores the physical background of pressure dependence observed in the yield behavior of solid foams by analyzing the partition of strain energy and stress distribution in the struts that make up the foam. To this end, transversely isotropic Kelvin foam models of three different relative densities are utilized in FE analysis to probe the yield surface along various biaxial and triaxial stress paths for a wide range of mean stress. From a macroscopic viewpoint, it is observed that in addition to well-documented quadratic dependence of yielding on mean stress there also exists a linear pressure dependence, which has not been properly addressed in the literature. Partition of strain energy at the time of macroscopic yielding into bending and stretch modes of deformation within struts provides a unique tool with which the dominant deformation mode that drives yielding can be identified as a function of the stress path followed. Analysis of FE results indicates that positive mean stress, as compared to negative mean stress, provides a strong configurational stability in deformation kinematics that limits bending mode and promotes the stretch mode of deformation in struts. Increasing the fraction of strain energy stored in stretch mode effectively increases the critical strain energy of yielding and, thereby, delays the onset of microscopic yielding. Negative mean stress, on the other hand, results in a weak configurational stability where bending mode is more prominent. Furthermore, it seems that the degree of this already weak stability quickly decays with the magnitude of negative mean stress and completely disappears when (and if) the stabilizing effect of joint stiffness is exceeded. We conclude that this contrasting behavior is the main source of (i) linear pressure dependence observed in the yield behavior as well as (ii) the stronger effect of linear pressure in low-density foams.

Response of Castlegate sandstone to true triaxial states of stress

A suite of true triaxial tests were performed on Castlegate sandstone to assess the influence of the intermediate principal stress on mechanical response and failure. Five independent deviatoric stress states were employed, for which the intermediate principal stress ranged from equal to minimum compression (axisymmetric compression) to maximum compression (axisymmetric extension). For each deviatoric stress state, five constant mean stress tests were conducted, covering mean stresses ranging from brittle to ductile failure. At low mean stresses, shear bands formed, and the peak stress required to induce failure decreased with increasing intermediate principal stress. Thus, failure at low mean stresses depends on the third invariant of deviatoric stress. Shear bands formed under all deviatoric stress states and over a wide range of mean stresses. The band angle (defined as the angle between the band normal and the direction of maximum compression) decreased with increasing mean stress. There was no clear trend in band angle with respect to intermediate principal stress; however, a small trend would be obscured by data scatter due to specimen variability. At higher mean stresses, no localization was observed. The upper bound mean stress at which shear localization occurred increased with increasing intermediate principal stress. Therefore, the mean stress that demarcates the brittle‐ductile transition depends on the third invariant of deviatoric stress.

Advanced dynamic finite element analysis of a skew steel railway bridge

The aim of this paper is to present advanced modelling techniques for dynamic analysis of steel railway bridges. Finite element analyses of a case study skew bridge are carried out and the results are compared with available field measurements. Initially, eigenvalue analyses of different models are carried out in order to obtain the fundamental mode shapes and bridge frequencies and to assess the capability of each model to capture the dynamic behaviour of the bridge. Single-span, three-span and full bridge models are investigated with different elements such as shell, beam and combinations of these. A very good agreement between the fundamental dynamic properties of the bridge and empirical results is found. Following the eigenvalue analyses, time history dynamic analyses are carried out using the full bridge model. The analyses are carried out for different train speeds and the strain histories are compared with available field measurements. In terms of fatigue assessment, the mean stress range values obtained from the strain histories at selected locations on the bridge members are also compared to each other. The results show that a full bridge model using a combination of beam and shell elements is a reasonably accurate and computationally efficient way of capturing the dynamic behaviour of a bridge and estimating the mean stress range for fatigue damage calculations.

Hydrostatic compression model for sandy soils

Based on elastic considerations, a new four parameter model of the hydrostatic compression curves of sandy soils is presented. Using a unique set of parameters, this model is capable of accurately representing the infinite family of compression curves that result when soil is subjected to stresses below particle breakage. The parameters are readily estimated from two hydrostatic tests conducted at different initial densities during loading and unloading stages. The resulting equations are able to predict the effect of progressive stiffness increase and compressibility reduction that occur as void ratio decreases during both loading and unloading conditions. The same normalized stress scale employed for the hydrostatic compression curves can also be used to describe the steady state line, which leads to a unique framework for representing the stress–void ratio curves of sandy soils. A comprehensive series of simulations on 13 different types of sandy soils in both loose and dense states was performed under a wide range of mean stresses during loading and unloading conditions. The simulations gave very satisfactory agreement with published experimental results.

Probabilistic Fatigue Evaluation of Riveted Railway Bridges

A probabilistic fatigue assessment methodology for riveted railway bridges is presented. The methodology is applied to a typical, short-span, riveted U.K. railway bridge under historical and present day train loading. On the loading side, the problem is randomized through dynamic amplification and traffic volume; on the resistance side, the S-N curves and the cumulative damage model are treated probabilistically. Model uncertainty is represented by the ratio between actual and calculated stresses, the latter obtained through finite element analysis. Annual response spectra for a fatigue-critical connection are developed through Monte Carlo simulation, which show that there is a continual and accelerating increase in the mean stress range experienced by the connection with time. S-N curves proposed in United States and United Kingdom codes are used in combination with Miner’s rule, to estimate the remaining fatigue life of the connection for different target failure probabilities. Parametric studies reveal...

On the Cyclic Stability and Fatigue Performance of Ultrafine-Grained Interstitial-Free Steel under Mean Stress

This paper reports on the fatigue performance of an ultrafine-grained (UFG) interstitialfree (IF) steel deformed at various mean stress levels. The UFG microstructure was achieved using equal channel angular extrusion processing at room temperature (RT) and along an “efficient” route, giving way to the formation of high angle grain boundaries (HAGBs) with a high volume fraction. The current study not only confirms the previous finding that a high volume fraction of HAGBs promotes cyclic stability, but also inquires into the role of mean stress level on the cyclic stability. It is shown that the UFG IF steel exhibits a stable cyclic deformation response in the lowcycle fatigue regime within the medium applied mean stress range of -75 to 75 MPa. The corresponding fatigue lives can still be predicted with the Smith-Watson-Topper approach within this range. Furthermore, the present study demonstrates that the evolution of mean strains with cyclic deformation can be linked to the evolution of mean stresses in strain-controlled loading.

Effects of increasing traffic loads on the fatigue reliability of a typical welded bridge detail

Fatigue reliability of bridge details needs to account for increased loads caused by the ever-increasing traffic flows and axle weights traversing a bridge. In this paper, a two-stage crack growth model and a failure assessment diagram, the latter accounting for the fracture event, are used to evaluate the reliability of a cover plate detail. A methodology is presented for tackling the case of evolving over time loads. To this end, different assumptions regarding the increase in the mean stress range, number of applied cycles and maximum loads are made. Accordingly, for each of the cases considered, the impact on the fatigue detail's reliability is determined. The results for these evolving load cases are compared with the case where loading remains constant over time. It is found that increase in the mean stress range contributes significantly towards the decrease in the detail's reliability. By comparison, the type of assumed growth pattern as well as increase in the maximum load and number of applied cycles affect the reliability results to a lesser degree.