Local Stress Ratio Research Articles

Notch fatigue behavior of Ti-6Al-4V alloy in transition region between low and high cycle fatigue

The load-controlled and displacement-controlled fatigue tests of Ti-6Al-4V alloy notched specimen under the remote stress ratio of 0.1 were carried out in order to investigate notch fatigue behavior in a wide range of fatigue life from low to high cycle fatigue. The elastic-plastic finite element analysis of notched specimen under cyclic loading was also conducted to investigate the variation of local stress ratio at notch root and its influence on fatigue life. It was found that the local stress ratio at notch root varies from the remote stress ratio of 0.1 in high cycle region to −1 in low cycle region, where the transition region is defined as the region of local stress ratio variation. Taking account of the local stress ratio variation at notch root, fatigue life was predicted based on the SWT parameter combined with the FEA was in good agreement with the experimental results. It is suggested based on these local stress variation and fatigue life prediction that the low cycle fatigue life predicted assuming the stress ratio of −1 would give an unsafe side prediction in the transition region.

Creep to inertia dominated stick-slip behavior in sliding friction modulated by tilted non-uniform loading.

Comprehension of stick-slip motion is very important for understanding tribological principles. The transition from creep-dominated to inertia-dominated stick-slip as the increase of sliding velocity has been described by researchers. However, the associated micro-contact behavior during this transition has not been fully disclosed yet. In this study, we investigated the stick-slip behaviors of two polymethyl methacrylate blocks actively modulated from the creep-dominated to inertia-dominated dynamics through a non-uniform loading along the interface by slightly tilting the angle of the two blocks. Increasing the tilt angle increases the critical transition velocity from creep-dominated to inertia-dominated stick-slip behaviors. Results from finite element simulation disclosed that a positive tilt angle led to a higher normal stress and a higher temperature on blocks at the opposite side of the crack initiating edge, which enhanced the creep of asperities during sliding friction. Acoustic emission (AE) during the stick-slip has also been measured, which is closely related to the different rupture modes regulated by the distribution of the ratio of shear to normal stress along the sliding interface. This study provided a more comprehensive understanding of the effect of tilted non-uniform loading on the local stress ratio, the local temperature, and the stick-slip behaviors.

Kinking Behavior of S-N Curve for Ti6Al4V Alloy Notched Specimen under a Load-Controlled High Cycle Fatigue Test

Notch fatigue behavior of Ti-6Al-4V titanium alloy has been investigated under a load-controlled high cycle fatigue test. The S-N curve was kinked at the critical nominal stress amplitude, where the plastic deformation nucleated at notch root. The plastic zone size at the critical nominal stress amplitude was almost equal to the size of 4 grains of the present Ti-6Al-4V alloy, which were the same findings as in the 2024-T4 alloy used in the previous study. Above the critical nominal stress amplitude, the local stress ratio at notch root decreased with increasing nominal stress amplitude. The critical nominal stress amplitudes normalized by the cyclic yield stress were almost the same for Ti-6Al-4V alloy and the 2024-T4 alloy. The significant decrease of the local stress ratio with increasing nominal stress amplitude was observed in the 2024-T4 alloy with low cyclic yield stress and low cyclic hardening coefficient compared to the Ti-6Al-4V alloy with high cyclic yield stress and high cyclic hardening coefficient.

Variation of local stress ratio and its effect on notch fatigue behavior of 2024-T4 aluminum alloy

Fatigue tests and finite element analysis of notched specimen were carried out to investigate the variation of local stress ratio at notch root and its influence on fatigue strength. The S–N curve of 2024-T4 aluminum alloy was kinked at the critical nominal stress amplitude, above which the local stress ratio became low due to the development of local plastic deformation at notch root. The predicted fatigue lives based on linear fracture mechanics approach were in agreement with the experimental results below the critical nominal stress amplitude. The predicted fatigue lives based on the SWT parameter, where the variation of local stress ratio was taken into account, were in good agreement with the experimental results above the critical nominal stress amplitude.

Fatigue crack nucleation and propagation in aluminum alloy plates with cold expanded holes

Analysis of the literature shows that in some cases existing technological methods of processing, including cold expansion, are the effective means to improve fatigue durability of structural elements with holes. The effect of cold expansion (1−3 %) on the stress state and fatigue durability of aluminum plates with functional holes under uniaxial cyclic loading was studied. The fatigue crack growth in the plates with a thickness t = 6 mm and width of 60 mm with a central hole diameter of 8 mm and 10 mm of aluminum alloy D16chТ (2024-T3) was investigated. Fatigue test was carried out under constant amplitude loading at stress ratio R = σmin/σmax = 0 and room temperature. Here σmin, σmax are the minimum and maximum stresses, respectively. The stress range was 147 MPa, loading frequency was 25 Hz. The mechanical properties of the alloy at room temperature were: yield strength σY = 300 MPa, tensile strength σU = 430 MPa. For all tested specimens with cold expanded holes the cracks initiation from the edges of holes on the entrance faces mandrel and from middle part for plain hole. Using the finite element method, the distribution of local residual stresses in the vicinity of the expanded hole was calculated. For specimens with cold expanded holes the least compressive stresses were near the entrance face and the largest were in the middle of the hole and near the exit face. With the increase of the cold expansion hole, the difference in values of compressive residual stress along the plate thickness is reduced. The width zone of residual compressive stresses increase with the increase of cold expansion. The dependencies of the number of cycles to crack initiation in aluminum specimens on the local maximum stress and local stresses range in the vicinity of surface hole were obtained. Cold expansion degree of 1% increases the lifetime of the plates to the initiation of fatigue crack length of 0.25 mm in 1.5-3 times as compared with plane plates. A similar dependence is observed for cold expansion of 2%. With further increase of cold expansion degree up to 3% the lifetime to fatigue crack initiation is increased in 7−10 times as compared with plane plate. By using the finite element method, the distributions of local stress range, maximum and minimum local stress near the hole depending on the number of loading cycles and cold expansion were built. In the middle section of the specimen the local stress ratio in the second half-cycle of load decrease with increasing of distance from the edge of the hole and with the increase of cold expansion. The lowest value of local stress ratio was obtained at cold expansion degree of 3% and it is constant across thickness of plate.

A new proposal for assessment of the fatigue strength of steel butt‐welded joints improved by peening (HFMI) under constant amplitude tensile loading

AbstractExperimental fatigue data for butt‐welded joints in as‐welded condition and under constant amplitude tensile loading were analysed using the effective notch stress system and a new master curve analysis that takes the local stress ratio, Rlocal, into account. The local stresses needed for computation of Rlocal are calculated with the notch strain approach in conjunction with the reference radius concept.The main focus was to predict with the derived master curve the fatigue strength of peened butt‐welded joints. The lowest surface residual stresses after peening were first estimated based on reported measurements and an analytical lower bound result. The predictions showed quite similar strength dependences and FAT values as reported for high‐frequency mechanical impact treated welds for applied stress ratio R = 0.1. The benefits of peening reduce faster for higher strength steels when R increases. When R = 0.5, the FATs are practically the same for all steel grades.

Assessment of fatigue strength of steel butt-welded joints in as-welded condition – Alternative approaches for curve fitting and mean stress effect analysis

Experimental fatigue data for butt-welded joints in as-welded condition and under constant amplitude tensile loading (secondary bending included) were analyzed using the nominal stress system and the notch stress system. Two approaches were used; a standard fitting procedure and minimization of the sum of squared perpendicular distances from a line with a fixed and free slope. In all cases, the latter method gave better agreement between the experimental and predicted fatigue life and fatigue strength. The analyses showed both with all broken specimen data included and with reduced data that the FAT225 curve, as recommended by IIW, might be too optimistic for the notch stress approach in the case of butt-welded joints in as-welded condition. It was also found that use of the local stress ratio instead of the applied stress ratio might explain many issues concerning current observations and apparent inconsistencies in reported literature.

A study of changes in deep fractured rock permeability due to coupled hydro-mechanical effects

This paper presents a numerical study of the hydro-mechanical behaviour of a fractured rock domain at 1000m depth below the land surface as a function of different levels of fluid pore pressure. A 2D fractured rock domain is adopted based on data obtained from outcrop mapping, displaying multiple fracture sets, fracture intersections, dead-end and curved fractures. A continuum based numerical model is used to evaluate the effects of compressive boundary stresses, cracking by tension failure in the intact rock and fractures and shear displacement along fractures on its equivalent permeability. Two in situ stress boundary conditions are considered: an isotropic case SR1 with the two horizontal boundary compressive stresses having the same magnitude, and an anisotropic case SR2 with the ratio between these compressive stress components set to be 2. In the SR2 case, changes in the local stress and stress ratio distributions due to different fluid pore pressure levels are anisotropic and more significant than in the SR1 case, because of tension failures in the intact rock forming bridges between fractures. These failure regions opened new flow connections between fractures and thereby caused important anisotropic changes in the flow paths, and significant decrease in local gradients of fluid pore pressure. The equivalent permeability increases sharply when the fluid pore pressure is approximately 90% of the magnitude of the minimum stress at the boundaries of the fractured rock domain. Results show that the equivalent permeability of the fractured rock domain is most sensitive to the fractures normal stiffness, the permeability of the tension failure regions and the power-law exponent for permeability change.

Fatigue Strength of HFMI-treated and Stress-relief Annealed High-strength Steel Weld Joints

The fatigue strength of welded joints is generally irrespective from the base material yield strength due to notch effects at the weld toe or root, tensile residual stresses by the thermo-mechanical joining process and significant changes in local material properties within the heat-affected zone. An effective way to increase the potential of light-weight design exhibits the application of post-weld treatments. Mechanical methods as the high-frequency mechanical impact treatment (HFMI) reduces the geometrical notch, introduces compressive residual stresses and increases the local hardness in the surface layer of the post-treated weld toe area.In this paper the fatigue strength of HFMI-treated joints superimposed by stress-relief annealing is studied. High-strength steel grades S690 and S960 are investigated in as-welded and HFMI-treated condition, both before and after stress-relief annealing. Fatigue tests at a tumescent stress ratio of R=0.1 show an essential increase of the fatigue strength due to the HFMI-treatment compared to the as-welded condition. In contrary, the superimposed post-heat treatment lowers the fatigue strength of HFMI-treated high-strength steel joints characteristically, but however, the final condition exhibits a higher fatigue strength compared to the initial as-welded state. Special focus is laid on the influence of welding distortion, whereat numerical simulations and experimental strain gauge measurements support the back tracing of the acting mechanism. The results indicate that the final local mean stress state due to clamping of the distorted specimens significantly affects the local effective stress ratio at the weld toe during testing, which basically needs to be considered for the fatigue strength evaluation.

Effect of local stress on the heat-checking morphology in high temperature tool steels under thermal fatigue: Transition from multi-axiality to uniaxiality

Thermal fatigue experiments are performed on a high temperature tool steel X38CrMoV5 (AISI H11), under various maximum temperatures and heating rates. A microscopic interconnected crack pattern (named “heat-checking”) forms on the oxidised surface of the laboratory tubular specimen. A gradual transition is observed, from a “cell-type” cracking at the centre of the specimen to a “parallel cracking” at its extremities. This variation of the morphology is well demonstrated by geometrical and topological characteristics of the crack network (micro-crack orientations, cell shape and node density), which change along the longitudinal axis of the specimen. The thermo-elasto-plastic loading of the specimen is estimated by Finite Element Calculations using ABAQUS™. Whatever the thermal fatigue conditions, a linear correlation can be established between the longitudinal and hoop stress amplitude ratio Δσzz/Δσθθ and the hoop and longitudinal inter-crack spacing ratio dθθ/dzz. It is shown that a stress amplitude ratio close to 1 results in a multi-axial heat-checking, while a uni-axial cracking is generated when Δσzz/Δσθθ is close to or below 0.6. This means that the morphology of the heat-checking pattern (cell or parallel type) can be used as an indicator for the local stress ratio of the thermal fatigue specimen or industrial real tools.

Local stress analysis in granular materials at a mesoscale

SUMMARYThe purpose of this paper is to contribute to the change of scale techniques developed for granular materials. The proposed approach consists in considering an intermediate scale between the macroscales and microscales, called the mesoscale, using the classical homogenization scheme. In this approach, the mesoscale for 2D granular materials was defined at the level of local volumes, called mesodomains, which are local closed structures composed of particles in contact. In this paper, we focused on defining a local stress field at this scale. Two different methods are proposed, both based on the equivalent continuum mean stress but using different approximations of the mean stress tensor for each mesodomain. The two proposed methods were then compared to each other. Analyses performed on the stress field at the mesoscale show that this local field is heterogeneous and, in particular, that its heterogeneity is significantly structured at this scale. The distribution of the local mean stress (first invariant of the local stress tensor) is uniform in any mesodomain, whereas the distribution of the stress deviator (second invariant of the deviatoric part of the local stress tensor) is significantly dependent on the elongation direction and on the elongation degree of the mesodomains. The local stress ratio (ratio of the stress deviator to the mean stress) is higher within the mesodomains that are elongated in the global compression direction than that within the ones elongated in the global extension direction. Copyright © 2011 John Wiley & Sons, Ltd.

Analysis of residual stress distribution along interface asperity of thermal barrier coating system on macro curved surface

AbstractBased on the study of the radial residual stress distribution on the macro curved interfaces of thermal barrier coating system (TBCs) for the hollow curved substrate structures, the hollow four-concentric-circle model was developed. And the concentric-circle model with a fine scaled sinusoidal interface was proposed to describe the stresses distribution on the rough interface of TBCs with macro curved geometry. The influences of the geometric and thermophysical parameters were discussed by the developed model. The results showed that the radial stress on the rough interface can be separated into two sections: the overall level stress from macro surface curvature and the local stress from local asperity of the interface. The overall level stress was determined by the thicknesses and the thermophysical parameters of each layer. It has been found that the ratio of local stress and overall level stress was influenced by the interface asperity, the ratio of elastic modulus and the ratio of thermal expansion coefficients of the layers beside the rough interface. Furthermore, the convex macro curvature of the substrate can induce tensile stress onto the interface. Especially at the sharp corners of the substrate, the small curvature radius can cause high stress which should be taken more care about the occurrence of spalling cracking at interface

Henry Granjon Prize Competition 2009 Winner Category C: “Design and Structural Integrity” EDGE Layer Condition and Fatigue Strength of welds improved by mechanical post-weld treatment

In this paper, investigations about the beneficial effect of high frequency peening methods on the fatigue strength of welds are reported. Recent investigations prove that these methods are effective means of improving the fatigue strength of welded details. In the reported studies, the mode of functioning of these methods, as well as their beneficial effects on fatigue strength, have been experimentally and numerically analyzed and quantified. The results of the experimental studies show that the benefit of high frequency peening methods relies on compressive residual stresses and surface hardening, caused by plastic deformation of the edge layers at the weld toes. The experimentally-determined fatigue strength of new welds and that of already fatigue-pre-loaded welds before the treatment is improved by 80 to 100 percent, as compared with the as-welded condition. Based on the findings, a design model for post-weld treated welds is developed, which allows for the consideration of the beneficial effect of the post-weld treatment for the design of steel structures. The increased fatigue strength is considered in a local design concept, by introducing improvement factors for the local fatigue strength. The local compressive stresses are considered, as well as the local stress ratio.

The Dynamics of the Onset of Frictional Slip

The way in which a frictional interface fails is critical to our fundamental understanding of failure processes in fields ranging from engineering to the study of earthquakes. Frictional motion is initiated by rupture fronts that propagate within the thin interface that separates two sheared bodies. By measuring the shear and normal stresses along the interface, together with the subsequent rapid real-contact-area dynamics, we find that the ratio of shear stress to normal stress can locally far exceed the static-friction coefficient without precipitating slip. Moreover, different modes of rupture selected by the system correspond to distinct regimes of the local stress ratio. These results indicate the key role of nonuniformity to frictional stability and dynamics with implications for the prediction, selection, and arrest of different modes of earthquakes.

The resilience of the logarithmic law to pressure gradients: evidence from direct numerical simulation

Wall-bounded turbulence in pressure gradients is studied using direct numerical simulation (DNS) of a Couette–Poiseuille flow. The motivation is to include adverse pressure gradients, to complement the favourable ones present in the well-studied Poiseuille flow, and the central question is how the scaling laws react to a gradient in the total shear stress or equivalently to a pressure gradient. In the case considered here, the ratio of local stress to wall stress, namely τ+, ranges from roughly 2/3 to 3/2 in the ‘wall region’. By this we mean the layer believed not to be influenced by the opposite wall and therefore open to simple, universal behaviour. The normalized pressure gradients p+ ≡ dτ+/dy+ at the two walls are −0.00057 and +0.0037. The outcome is in broad agreement with the findings of Galbraith, Sjolander & Head (Aeronaut. Quart. vol. 27, 1977, pp. 229–242) relating to boundary layers (based on measured profiles): the logarithmic velocity profile is much more resilient than two other, equally plausible assumptions, namely universality of the mixing length ℓ = κy and that of the eddy viscosity νt = uτκy. In pressure gradients, with τ+ ≠ 1, these three come into conflict, and our primary purpose is to compare them. We consider that the Kármán constant κ is unique but allow a range from 0.38 to 0.41, consistent with the current debates. It makes a minor difference in the interpretation. This finding of resilience appears new as a DNS result and is free of the experimental uncertainty over skin friction. It is not as distinct in the (rather strong) adverse gradient as it is in the favourable one; for instance the velocity U+ at y+ = 50 is lower by 3% on the adverse gradient side. A plausible cause is that the wall shear stress is small and somewhat overwhelmed by the stress and kinetic energy in the bulk of the flow. The potential of a correction to the ‘law of the wall’ based purely on p+ is examined, with mixed results. We view the preference for the log law as somewhat counter-intuitive in that the scaling law is non-local but also as becoming established and as highly relevant to turbulence modelling.

The Strain Estimation of Statically Determinate Structures Subjected to Forced Displacement by Reference Stress Method

It is well known that the inelastic strain accumulation of statically determinate structure subjected to forced displacement is caused by the elastic follow-up due to surrounding elastic region. The author once showed that the relaxation phenomenon of creeping structures during the elastic follow-up can be well estimated by the reference stress method. By applying this result, the author has proposed a simplified method to estimate the creep strain accumulated by the elastic follow-up. It has been shown that elastic follow-up factor can be calculated from the reference stress ratio, which is the ratio of Local Reference Stress and Global Reference Stress. The proposed method was applied to the elastic follow-up of 2-bar model and 2-beam model. For 2-beam model, a simple method has been proposed to estimate the stress-strain relation during the elastic follow-up, and it showed quite good agreement with FEM results. It was also shown that the proposed method can be applied to the plastic strain accumulation due to the elastic follow-up. By comparing with other strain estimation methods such as Neuber's method and Stress Relaxation Locus method, the proposed method was found to be reasonable and precise.

The effect of strain-path reversal on cavitation during hot torsion of Ti-6Al-4V

The effect of strain-path reversal on cavitation behavior during the hot torsion testing of an alpha/beta titanium alloy, Ti-6Al-4V, with a colony-alpha microstructure was established. Optical microscopy was used to measure cavitation parameters such as cavity size, density, and area fraction. It was observed that when the torsion direction is reversed, the cavitation process is reversed as well: i.e., cavity shrinkage takes place. The experimental observations were interpreted in the context of previous models developed for the densification of porous bodies. For this purpose, the models were modified to treat the effect of colony orientation on the local stress state and the accommodation of the externally imposed strain, both of which affect the rate of densification/cavity shrinkage. A modified version of the AFRL PM-consolidation model was shown to provide reasonable estimates of the shrinkage kinetics. An alternate description of cavity shrinkage during reversed torsion, analogous to prior descriptions of cavity growth, was also developed. It was concluded that the absolute magnitude of the cavity shrinkage rate is smaller than its counterpart during growth because the local stress ratio is lower during reversed straining compared to that during forward straining.

Curvature Law of the Wall for Swirling Axial Flows in Rotating Machinery

A new law of the wall accounting for curvature effects in swirling axial flows is derived. The influence of the curvature on the turbulence mixing lengths in both axial and tangential directions is examined theoretically using the Reynolds stress transport equations. For equilibrium flows with weak curvature, identical mixing lengths are derived for the axial and tangential directions. Additionally, the effect of finite local curvature and shear stress ratio on the near-wall velocities is systematically explored. It is found that the curvature effect in swirling axial flows is suppressed by a factor of 1∕(1+σw2) compared to that in curved channel flows, where σw is the ratio of the axial to swirl shear stress. For a given curvature radius, the maximum velocity deviation occurs when the axial-to-swirl shear stress ratio is zero. Finally, the performance of the new curvature law is evaluated by implementing it as a wall function in a well-established CFD code. The new wall function provides improved agreement for swirl velocity distributions inside labyrinth cavities in comparison with existing experimental laser Doppler anemometry measurements.

On the use of critical distance theories for the prediction of the high cycle fatigue limit stress in notched Ti–6Al–4V

Methods are investigated for predicting the high cycle fatigue (HCF) lives of notched cylindrical Ti–6Al–4V specimens using critical distance concepts that employ the stress distribution in the vicinity of the notch. Cylindrical fatigue specimens had circumferential V-notches with a range of elastic stress concentration factors ( k t=1.97–4.07). Notched and unnotched specimens were cycled to failure using a step-loading technique to generate points on a Haigh (Goodman) diagram for a constant fatigue life of 10 6 cycles. Finite element solutions were generated to provide stress distributions for the notched gage sections. The stress distributions were used in the search for a critical distance over which the quantities of mean stress, stress range, or elastic strain energy may contribute to the fatigue process and can be correlated to similar quantities from smooth, unnotched specimens. If the decrease in the local stress ratio at the notch root for high applied stress ratio is accounted for in the analysis, trends independent of applied stress ratio were found in the calculated critical distances. Predictions based upon the results gave accuracy to within 12% of the experimental fatigue limit stresses and illustrate the method has promise for use in fatigue design of Ti–6Al–4V components.

A shear stress‐based parameter for fretting fatigue crack initiation

The purpose of this study was to investigate the fretting fatigue crack initiation behaviour of titanium alloy, Ti–6Al–4V. Fretting contact conditions were varied by using different geometries of the fretting pad. Applied forces were also varied to obtain fretting fatigue crack initiation lives in both the low‐ and high‐cycle fatigue regimes. Fretting fatigue specimens were examined to determine the crack location and the crack angle orientation along the contact surface. Salient features of fretting fatigue experiments were modelled and analysed with finite element analysis. Computed results of the finite element analyses were used to formulate a shear stress‐based parameter to predict the fretting fatigue crack initiation life, location and orientation. Comparison of the analytical and experimental results showed that fretting fatigue crack initiation was governed by the maximum shear stress, and therefore a parameter involving the maximum shear stress range on the critical plane with the correction factor for the local mean stress or stress ratio effect was found to be effective in characterizing the fretting fatigue crack initiation behaviour in titanium alloy, Ti–6Al–4V.