Stress Ratio Conditions Research Articles

Effect of Stress Ratio on Stress Intensity Factor of Type I Crack in A7N01 Aluminum Alloy

Taking the mode I crack of finite width plate as the research object, the nodal displacement extrapolation method of type I stress intensity factor is discussed, and the stress intensity factor expressed by nodal displacement is obtained. Taking A7N01 aluminum alloy as the research object, the finite element software ABAQUS was used to numerical simulation and analysis. The effect of stress ratio on stress intensity factor KI was discussed. The results showed that in the same crack size ratio a/W, the stress intensity factor increases with the increase of the stress ratio; at the same stress ratio R, the stress intensity factor increases with increasing crack size ratio. At the same time, change law of the stress intensity factor increase: under the condition of different stress ratio, when a/W≤0.6, the increase of stress intensity factor is almost consistent; when a/W>0.6, the increase of stress intensity factor will increase obviously.

Sand instability under constant shear drained stress path

Experimental findings have revealed that granular soils are vulnerable to pre-failure instability when subjected to constant shear drained (CSD) stress path. Using the concept of loss of uniqueness, it is shown that two dissimilar scenarios and accordingly, two independent criteria for granular soils in loose and dense states may lead to instability under CSD. The instability criteria are then applied in association with a state-dependent elastoplastic constitutive model taking into account possibility of elastic-plastic coupling. Numerical simulations have confirmed that instability in loose sands triggers prior to complete mobilization of the critical state stress ratio. However, instability of sands in dense state instigates at peak mobilized friction angle. A nearly unique linkage between stress ratio and state parameter at the onset of instability is predicted.

Delamination properity of 2060 aluminium lithium alloy laminate

Delamination is an significant property of aluminium lithium alloy laminate for damage tolerance design. Double Crack Lap Shear specimens of "2/1" structure are used for testing delamination properity. Experiments of 2 stress ratio conditions R=0.06, 0.5 are conducted, and 5 stress levels for each stress ratio. Delamination growth data b-N are obtained from 4 crack tips’ locations. The energy release rate, Gd, of the "2/1" structure laminate are calculated. Alderliesten modelis used for describing delamination growth db/dN and energy release rate Gd. Parameters Cd and nd in Alderliesten model are determined for R=0.06 and R=0.5 by linear fitting. An analysis is made by comparing the results of different stress ratio conditons.

Investigation of fracture propagation characteristics caused by hydraulic fracturing in naturally fractured continental shale

Continental shale from the Ordos Basin, China, is naturally fractured and characterized by silty laminae and interbeds that is different from marine shale. To investigate the hydraulic fracture propagation in this kind of shale, hydraulic fracturing experiments were performed in cylinder continental shale samples under different stress ratio conditions, and propagation characteristics of the visible surface fractures, the main fractures as well as the main fracture surfaces were observed and discussed. The results reveal that the visible induced fractures on the sample surfaces primarily extend along natural fractures, bedding planes and interbeds, and situation of crossing beddings and interbeds can be found, which is different from fractures in marine shale that are mainly vertical to bedding planes with some branches. Besides, the main fractures were observed and measured through electronic microscope. They are wavelike and tortuosity tends to increase as stress ratio decreases. Moreover, three dimensional scanner was employed to study the main fracture surfaces, and Area Ratio and Standard Deviation were used to evaluate the roughness. With the decrease of stress ratio, partial vertical fractures can be found on the main fracture surface, and Area Ratio and Standard Deviation get higher, which indicates that the roughness of the main fracture surfaces becomes higher. Therefore, hydraulic fracture propagation characteristics of continental shale are strongly influenced by the stress and some its own properties, including natural fractures, beddings and interbeds. And the result contributes to understanding the mechanism of hydraulic fracture propagation in continental shale formation.

Investigation of Surface Integrity and Fatigue Performance of TC4 Titanium Alloy in Centrifugal Barrel Finishing

This paper aims to improve the surface integrity and fatigue performance TC4 titanium alloy. Centrifugal barrel finishing was taken to enhance surface performance of TC4 titanium alloy. Centrifugal barrel finishing experiments and tensile fatigue test were conducted for investigating the surface integrity and fatigue performance of TC4 titanium alloy. The surface integrity including surface roughness, residual stress, micro-hardness, and microstructure were investigated under different conditions by different methods. The tensile fatigue performance were tested and the fatigue fracture were analysed by SEM. The results show that the centrifugal barrel finishing can make surface roughness value decrease 0.623 μm, and the surface hardness reaches to 420 HV from initial 338 HV, increasing by 24.3%, and the maximum residual compressive stress reaches to -462MPa. The fatigue limit reaches to 445 MPa from initial 374 MPa, increasing by 18.98%. The fatigue life of TC4 titanium alloy increases from 10762 times to 56220 times under the conditions of stress ratio of 0.1 and stress of 610 MPa. The centrifugal barrel finishing can comprehensively improve the surface integrity and tensile fatigue performance of TC4 titanium alloy. DOI: http://dx.doi.org/10.5755/j01.mech.23.6.19849

Experimental and numerical study on nonlinear mechanical properties of laminated woven fabrics

This article presents a nonlinear analysis to explore mechanical properties of the membrane structures made of laminated woven fabrics by numerical simulation and experiments. Stresses-moduli response surfaces are created with the data of stress-strain curves measured from the biaxial test. To apply this method into finite element method (FEM) analysis, complete cubic polynomials of these surfaces are obtained and created the nonlinear material model under user defined subroutine UMAT of ABAQUS. A cruciform specimen is analyzed adapting the nonlinear model, which is subjected to biaxial tensile under the condition of stress ratio of 1:1, 1:2, 2:1, 3:1, 1:3, 0:1 and 1:0. It is shown that the results of nonlinear material model agree well with experimental results.

Particle breakage energy and stress dilatancy in drained shear of rockfills

Particle breakage can be quite considerable even at low-stress levels, and it has a significant influence on the stress dilatancy of rockfill materials. In order to reasonably quantify the energy consumed by particle breakage, which has yet to be satisfactorily addressed, a function of friction ratio relating to the distortional strain and critical state stress ratio is proposed in this paper. The friction ratio references the widely accepted evolution rule of particle breakage and the new calculated energy consumption by particle breakage is proved to result in a reasonable distribution against increasing strain. Then, the rate of energy consumption per unit volume of aggregates is certified and suggested to be a linear relationship with the proposed friction ratio. Additionally, a stress dilatancy relationship for rockfill materials, based on modified Rowe's dilatancy law, is derived and verified by successfully predicting the stress dilatancy of drained rockfill triaxial specimens. It is believed to be an effective stress dilatancy for the study of elastoplastic constitutive model of rockfill materials.

Geogrid-reinforcement and the critical state of graded aggregates used in heavy-haul railway transition subgrade

Abstract The geogrid reinforced graded- aggregates are occasionally used as top geotechnical layer in heavy-haul railway transit subgrade, but the effects of geogrid reinforcement on critical state are rare. The current study considers effects of geogrid reinforcement on critical state line locations of aggregates. For this purpose, a series of consolidated drained triaxial tests were conducted using a large-scale apparatus. Large specimens with various geogrid-spacing were used and a critical state of each specimen was obtained at a relatively large axial strain. The experimental results reveal that the geogrids inclusion causes upward unparalleled shift of CSLs in p-q space where the critical state stress ratio Mc increases with increase in geogrid reinforcement coefficient, Rf. Mathematical expression for critical state stress ratio and geogrid reinforcement coefficient is proposed during monotonic shearing procedure; the similar upward and unparalleled shift of CSL are also produced due to geogrid presence in v-ln(p) space where slope of NCL, λn, keeps constant but the slope of CSL, λc, increases with increase in dilation angle. An empirical equation is set up to express the relationship between, λc/λn, and dilation angle. These experimental findings are helpful for modeling aggregates when considering geogrid reinforcement and dilative behaviors.

Comparison of Hydrostatic Extrusion between Pressure-Load and Displacement-Load Models

Two finite element analysis (FEA) models simulating hydrostatic extrusion (HE) are designed, one for the case under pressure load and another for the case under displacement load. Comparison is made of the equivalent stress distribution, stress state ratio distribution and extrusion pressure between the two models, which work at the same extrusion ratio (R) and the same die angle (2α). A uniform Von-Mises equivalent stress gradient distribution and stress state ratio gradient distribution are observed in the pressure-load model. A linear relationship is found between the extrusion pressure (P) and the logarithm of the extrusion ratio (lnR), and a parabolic relationship between P and 2α, in both models. The P-value under pressure load is smaller than that under displacement load, though at the same R and α, and the difference between the two pressures becomes larger as R and α grow.

Critical state shear strength of an unsaturated artificially cemented sand

This paper presents the results of a set of 22 triaxial tests on an unsaturated artificially cemented sand. The results are used to explore the applicability of a number of unsaturated soil frameworks for interpreting the shear strength. Constant water content triaxial tests were carried out on unsaturated specimens, using the axis translation technique to measure suctions during shearing. The test results on the unsaturated material were referenced against a series of drained and undrained triaxial tests that were carried out on saturated specimens. The results of the unsaturated tests were analysed to investigate the effect of the suction and degree of saturation on the shear strength at the critical state. The results show that the critical state stress ratio in terms of net stress (Ma) was found to be larger than the saturated critical state stress ratio (Ms). It was also found that the stress ratio in terms of suction (Mb) reduced as suction increased (when the degree of saturation reduced below 30%). Interestingly, during the initial desaturation phase when the degree of saturation reduces considerably, the stress ratio Mb was largely unaffected by desaturation. It was only when the suction increased sufficiently that the micro-voids within the cementing material could start to desaturate that a reduction in Mb was seen. This occurred at suctions in excess of the residual suction when the global degree of saturation was changing very little. This implies that the suction is contributing to the strength of the cementing material itself.

Undrained behaviour of granular material and the role of fabric in isotropic and K0 consolidations: DEM approach

The behaviour of granular material was investigated by simulating an undrained triaxial compression test for three-dimensional assembly of ellipsoid particles over a wide range of void ratio, e, and mean confining stress, p′. The assembly was either isotropically consolidated or K0 consolidated prior to undrained shearing up to 30% axial strain to reach steady-state conditions. A unique steady-state line was obtained, irrespective of the consolidation path. The micro-mechanical quantities, such as coordination number and von Mises fabric in terms of second invariant of deviatoric fabric, FvM, also reached steady-state values. The normalised anisotropic fabric variable, A, and the trace of the joint stress–fabric tensor, KF, evolved during undrained simulation and reached the steady-state value at the end of shearing. This forms a unique relationship in KF–p′–e space and the projection of this relationship in e–log(p′) space is the classical steady-state line. This underpins the concept of fabric evolution and steady-state fabric in anisotropic critical state theory. The relationships of state parameter, ψ, and stress ratio at instability, ηIS = (q/p′)IS, were dependent on consolidation path, and the difference was not related to coordination number, but to FvM. However, a new phenomenon was observed that stress ratio, η, at the end of K0 consolidation and ηIS may reach beyond the steady-state stress ratio, M. Experimental data are needed to verify this; until then such behaviour should be regarded as unproven.

Crack growth and splitting failure of silicon nitride ceramic balls under cyclic pressure loads

In order to examine the splitting failures of silicon nitride balls under cyclic pressure loads, fatigue tests of pre-cracked balls were carried out. The cracks of initial length ranging from 0.260 to 0.290mm were observed under different stress ratio conditions and the effects of stress ratio and residual stress on the fatigue strength were investigated. Furthermore, the initial threshold limit of the equivalent stress intensity factor range (ΔKeqth) was measured.

Flow deformation and cyclic resistance of saturated loose sand considering initial static shear effect

In practical engineering, a driving stress often exists and acts on the soil elements, and this stress may have a significant effect on the deformational characteristics and liquefaction resistance of sand when the sand is subjected to seismic loadings. This paper presents a systematic experimental investigation into the undrained cyclic behavior of saturated loose sand with the static shear under both triaxial compression and extension conditions. Various combinations of the magnitude of static stresses and cyclic stresses were considered in the triaxial tests. The results indicate that different static shear stress conditions lead to two distinct failure modes, namely, flow liquefaction and residual deformation failure. The required number of loading cycles for the onset of flow deformation and failure are both related to two stress parameters, i.e., cyclic stress ratio (CSR) and static stress ratio (SSR). In viewing the failure envelope established against the two stress variables CSR and SSR, a critical SSR that identifies the role of the presence of initial static shear stress is obtained: when SSR is less than that critical value, the resistance may increase, whereas the resistance may decrease as SSR becomes larger. In addition, the triggering conditions of flow deformation under cyclic loading can be interpreted with the instability response of sand under monotonic loading. Combined with the observation on the cyclic deviatoric strains developed during and after the flow deformation, a unified interpretation is made to quantify the effects of both the SSR and CSR on the cyclic resistance of loose sand.

Strength criterion for cross-anisotropic sand under general stress conditions

By incorporating the fabric effect and Lode’s angle dependence into the Mohr–Coulomb failure criterion, a strength criterion for cross-anisotropic sand under general stress conditions was proposed. The obtained criterion has only three material parameters which can be specified by conventional triaxial tests. The formula to calculate the friction angle under any loading direction and intermediate principal stress ratio condition was deduced, and the influence of the degree of the cross-anisotropy was quantified. The friction angles of sand in triaxial, true triaxial, and hollow cylinder torsional shear tests were obtained, and a parametric analysis was used to detect the varying characteristics. The friction angle becomes smaller when the major principal stress changes from perpendicular to parallel to the bedding plane. The loading direction and intermediate principal stress ratio are unrelated in true triaxial tests, and their influences on the friction angle can be well captured by the proposed criterion. In hollow cylinder torsional shear tests with the same internal and external pressures, the loading direction and intermediate principal stress ratio are related. This property results in a lower friction angle in the hollow cylinder torsional shear test than that in the true triaxial test under the same intermediate principal stress ratio condition. By comparing the calculated friction angle with the experimental results under various loading conditions (e.g., triaxial, true triaxial, and hollow cylinder torsional shear test), the proposed criterion was verified to be able to characterize the shear strength of cross-anisotropic sand under general stress conditions.

Free vibration analysis of triangular CNT-reinforced composite plates subjected to in-plane stresses using FSDT element-free method

This study conducts the first-known vibration analysis of carbon nanotube (CNT) reinforced functionally graded composite triangular plates subjected to in-plane stresses. The first-order shear deformation theory is applied to study the effect of the transverse shear deformation of the plates and the element-free IMLS-Ritz method is used for numerical computation. Numerical experiments are carried out to examine the convergence and accuracy of the element-free IMLS-Ritz method in its application to the vibration of CNT-reinforced functionally graded composite plates subjected to in-plane stresses. In this study, sets of vibration frequency parameters and mode shapes for various CNT-reinforced functionally graded composite triangular plates are illustrated. The influences of CNT volume fraction, plate thickness-to-width ratio, CNT distribution type, isosceles triangular angle, in-plane stress ratio and boundary conditions on the plate’s vibration behaviors are investigated in detail. These results may serve as a benchmark for future studies.

Influence of stress ratio and moisture condition of loose deposit on dynamic parameters and ground response spectrum

Influence of stress ratio and moisture condition of loose deposit on dynamic parameters and ground response spectrum

An Elasto-plastic Method for Analysing the Deformation of the Railway Ballast

In this study, a series of monotonically drained triaxial tests were conducted using the large-scale cylindrical triaxial apparatus. The effect of particle breakage and confining pressure on the mechanical behaviour of ballast were investigated. Based on the experimental findings, mathematical expressions for critical state stress ratio and specific volume are proposed to incorporate the evolution of particle breakage during monotonic shearing. An elasto-plastic constitutive model is formulated within the critical state soil mechanics framework in order to capture the stress-strain behaviour and degradation of ballast. The non-linear variation of shear strength envelope at a given range of confining pressures is taken into account. Mathematical expressions for shear hardening and stress-dilatancy relations are proposed. The constitutive model is calibrated against the results of large-scale laboratory tests and further validated using experimental results available from past independent studies. It is proved that the proposed method can promisingly predict the deformation of the ballast layer in a typical railway environment.

Observed and predicted behaviour of rail ballast under monotonic loading capturing particle breakage

A substantial amount of experimental evidence suggests that the critical state envelope for ballast is nonlinear, especially at low confining pressure. To study the implications of this nonlinearity and the associated role of particle breakage, monotonically loaded drained triaxial tests were conducted using a large-scale cylindrical triaxial apparatus. A nonlinear critical state envelope is determined in the q–p′ and υ–lnp′ planes. Mathematical expressions for critical state stress ratio and specific volume are proposed to incorporate the evolution of particle breakage during monotonic shearing. In this paper, an elastoplastic constitutive model based on the critical state soil mechanics framework is presented to capture the salient aspects of stress–strain behaviour and degradation of ballast. Constitutive parameters were conveniently determined from large-scale laboratory tests. The model is able to predict the monotonic shear behaviour of ballast corroborating with the laboratory measurements. The proposed model is further validated using experimental results available from past independent studies.

Evaluation of crushing stress at critical state of granulated coal ash in triaxial test

A series of triaxial compression tests was performed on three types of granulated coal ash (GCA) to investigate their shear and crushing behaviour. The experimental results show that GCA displays different dilatancy characteristics to other natural granular materials due to excessive breakage even at low stresses. A simple constitutive model for crushable soils with the ability to predict the mechanical and deformation behaviour of GCA is introduced. This constitutive model uses a new strength parameter, the so-called reference crushing stress, which affects the evolution of the failure state curve. The mean stress when the peak stress ratio reduces to the critical state stress ratio and the mean stress when the peak friction angle reduces to the critical state friction angle were employed to determine the peak strength of GCA in combination with relative density and confining pressure. These three parameters, defined using the critical state concept within the framework of triaxial testing, are examined and their linear correlations are shown. It is also noted that the reference crushing stress strongly correlates with the single particle strength for a given type of GCA and, as such, has some specific mechanical meaning.

Effect of Stress Ratio and Loading Mode on High Cycle Fatigue Properties of Extruded Magnesium Alloys

The aim of this study is to discuss an effect of stress ratio and loading mode on high cycle fatigue performances of extruded magnesium alloys. Axial loading fatigue tests under three conditions of stress ratio, R, of 0, -1 and-1.5, and also rotating bending fatigue tests have been performed in laboratory air at room temperature using hourglass shaped specimens of AZ31, AZ61, AZ80 and T5-treated AZ80 alloy. From the experimental results, some materials showed a specific stepwise S-N curve on which two knees appear. The shape of S-N diagram depended on a kind of tested materials, applied stress ratio and loading mode. It was suggested from the detail observation of fracture surface that fatigue crack initiation mechanism changed from a twin-induced failure mode at high stress amplitude level to a slip-induced one at low stress amplitude level. This transition was determined with the relation between the minimum stress during a fatigue cycle and the compressive yield stress at which deformation twin occurs.