General Stress State Research Articles

Study of the yielding of sand under generalized stress conditions using a versatile hollow cylinder torsional apparatus

The hollow cylinder torsional apparatus (HCTA) is particularly suited to studying the mechanical behavior of cross-anisotropic test specimens since both the magnitudes of the three principal stresses and the orientation of the major–minor principal stress axes can be independently controlled. Novel features of the University College Dublin HCTA, particularly the instrumentation and calibration procedures necessary to achieve accurate generalized stress path testing, are presented. The plastic yield behavior of fully saturated Leighton Buzzard sand was studied under generalized stress conditions. Physically identical test-specimens (35.5 mm inner radius, 50.0 mm outer radius and 200 mm in length) were prepared using a water-pluviation technique that reproduced the inherent cross-anisotropic fabric of many natural sand deposits. A series of stress path tests systematically probed the stress space in order to locate segments of yield loci. The deviator stress at yield was found to vary in a well-defined pattern that depended on the magnitude of the intermediate principal stress parameter. However, the deviator stress at yield was largely independent of reorientations of the major principal stress that had occurred during the initial anisotropic consolidation stage of the tests. The experimental yield data was used to show that the Matsuoka–Nakai and Lade yield criteria provide satisfactory predictions of the onset of plastic yielding in sand deposits under generalized stress conditions for routine geotechnical engineering design.

On the effect of a general residual stress state on indentation and hardness testing

During indentation experiments, residual stresses are superimposed on the applied indentation stress field and influence the measurement of the volume of interest. The residual stress state can vary in magnitude and biaxiality, and the resultant error in the measured hardness is difficult to estimate. A prediction of the effect in the contact pressure with and without residual stresses is carried out by a new model that accounts for nonlinearities caused by the von Mises’ flow rule. The model can also be used for the correction of the effect of a general residual stress state on any further analysis of mechanical properties and stress–strain behaviour from the measured indentation data. The model provides an estimation of the measurement uncertainty when the stress ratio or the strength of the material is unknown – a situation that is a commonly encountered with hardness testing of thin films and welded materials.

First Evidence of Altered Immune Responses and Resistance to Air Exposure in the Clam Chamelea gallina Exposed to Benzo(a)pyrene

Effects of benzo(a)pyrene [B(a)P] (at a nominal concentration of 0.5 mg/L) on immune responses of the clam Chamelea gallina were investigated after 1, 7, and 12 days exposure. Total hemocyte count (THC), hemocyte volume, phagocytic activity, lysozyme-like activity in both hemocyte lysate (HL) and cell-free hemolymph (CFH) were measured. As unexpected alterations in hemocyte adhesion capability were observed in short-term hemocyte cultures for phagocytosis assays after a 1-day exposure, an adhesion test (not included in the original experimental setup) was performed after 7 and 12 days of exposure only. The survival-in-air test was carried out to evaluate general stress conditions in B(a)P-exposed clams. No alterations in THC was observed, whereas exposure for 7 and 12 days to B(a)P significantly decreased phagocytic activity and adhesion capability when compared with controls. Significant decreases in lysozyme activity were observed in CFH and HL, with respect to controls. B(a)P was also shown to alter the resistance to air exposure of clams. The LT(50) values fell from 9 days in control clams to 7 days in 1-day-exposed animals, and from 6 days in control clams to 5 days in 7-day-exposed bivalves. No significant variations in LT(50) values were recorded after 12 days of exposure. Results highlight a relationship between B(a)P exposure and alterations in hemocyte functionality and suggest that the contaminant induced irreversible immunosuppression in C. gallina, by altering phagocytic activity, adhesion capability, and enzymatic activity. Conversely, reduction in resistance to air exposure was reversible, suggesting that impairment of important physiological functions of clams occurred in the first phases of exposure only.

A mixed hardening rule coupled with Hill48’ yielding function to predict the springback of sheet U-bending

A mixed hardening model has been used to model the Bauschinger effect. This hardening model is based on Lemaitre and Chaboche nonlinear kinematic hardening theory to consider cyclic behavior and the Bauschinger effect. Hill’48 yielding criterion is used because of the general stress state and relative ease of formulation. The backward Euler return mapping algorithm is applied to calculate the stress and strain increment. The mixed hardening model is implemented based on UMAT subroutine of FEA code ABAQUS. The NUMISHEET’93 benchmark shows that the mixed hardening model coupled with anisotropic yield criteria can give a favorable springback angle prediction.

Fatigue life predictions by integrating EVICD fatigue damage model and an advanced cyclic plasticity theory

An event independent cumulative damage (EVICD) fatigue prediction model was previously developed for the fatigue damage prediction under general multiaxial stress state and loading conditions. The model takes the plastic strain energy as the major contributor to the fatigue damage. The application of the EVICD model does not require a cycle counting method for general random loading. In the current effort, derivations were made to explicitly and directly relate the material constants in the fatigue model to the parameters in the Manson–Coffin equations and the cyclic stress–strain curve of the material. In addition, an advanced cyclic plasticity theory was implemented for the determination of the detailed stress–strain response that was required as the input for the EVICD fatigue model. Three metallic materials were used to demonstrate the capability of the modified fatigue model for the predictions of fatigue lives under different loading conditions. The results show that the fatigue model can provide fatigue life predictions in close agreement with the experimental observations.

Vibration and Stability of Functionally Graded Plates Based on a Higher-order Deformation Theory

In this article, the governing equations of motion for a functionally graded material plate (FGP) based on a higher-order deformation theory in a general state of non-uniform initial stress are derived. The properties of FGP are assumed varied continuously along the thickness of the plate, according to a simple power law of volume fractions of constituents. With the derived governing equations, the natural frequencies and buckling loads of ceramic—FGM—metal plates subjected to an initial stress are investigated. The initial stress is taken to be a combination of a uniaxial extensional stress and a pure bending stress. A ceramic—FGM—metal plate can become an all-FGM, all-ceramic plate, or all-metal plate by modifying the value of material parameter and volume fraction index. The effects of various parameters and initial stresses on the natural frequencies and buckling loads of FGPs are studied.

Reinforcement of a plate with a circular hole by an eccentric circular patch

We study the reinforcement of an infinite elastic plate with a circular hole by a larger eccentric circular patch completely covering the hole and rigidly adjusted to the plate along the entire boundary of itself. We assume that the plate and the patch are in a generalized plane stress state generated by the action of some given loads applied to the plate at infinity and on the boundary of the hole. We use the power series method combined with the conformal mapping method to find the Muskhelishvili complex potentials and study the stress state on the hole boundary and on the adhesion line. We consider several examples, study how the stresses depend on the geometric and elastic parameters, and compare the problem under study with the case of a plate with a circular hole without a patch.

Assessment of plate theories for initially stressed hybrid laminated plates

Abstract This study presents numerical solutions to hybrid laminate plates in a general state of non-uniform initial stress based on various plate theories. Firstly, the governing equations were formulated using Lo’s high-order plate theory. The higher-order terms in Lo’s displacement field were neglected to obtain various simple governing equations based on first-order theory and other higher-order theories. The various governing equations was used to investigate the natural frequencies and buckling loads of hybrid Al/GRFP/Al plates subjected to initial stresses. The effects of various parameters on the vibration frequency and buckling coefficient were examined. The results show that the transverse shear strain, normal strain, initial stress state and thickness ratio of Al to GRFP strongly affect the stability and vibration of hybrid laminate plates.

Influence of the σBStress Factor andyxaB, the Gene for a Putative Exopolysaccharide Synthase under σBControl, on Biofilm Formation

Bacillus subtilis forms structured communities of biofilms encased in an exopolysaccharide matrix on solid surfaces and at the air-liquid interface. It is postulated that nonoptimal growth conditions induce this multicellular behavior. We showed that under laboratory conditions a strain deleted for sigB was unable to form a floating pellicle on the surface of a liquid medium. However, overexpression of yxaB, encoding a putative exopolysaccharide synthase, from a p(Spac) promoter in a sigB-deleted strain resulted in partial recovery of the wild-type phenotype, indicating the participation of the YxaB protein in this multicellular process. We present data concerning the regulation of transcription of genes yxaB and yxaA, encoding a putative glycerate kinase. Both genes are cotranscribed as a single transcription unit from a sigma(A)-dependent promoter during vegetative growth of a liquid bacterial culture. The promoter driving transcription of the yxaAB operon is regulated by AbrB. In addition, the second gene in the operon, yxaB, possesses its own promoter, which is recognized by RNA polymerase containing the sigma(B) subunit. This transcription start site is used under general stress conditions, resulting in increased expression.

Threshold condition of dislocation loop emission from microvoids

This study examines the micromechanics of dislocation loop emission, aiming at determining the threshold condition associated with microvoid growth. The closed form of threshold stress is obtained for edge dislocation in the vicinity of cylindrical void in a general planar macroscopic stress state. The effects of surface energy and lattice friction are accounted for; the former is found to be significant. A prolate-to-oblate shape transition in uniaxial strain due to a higher driving force on slip plane transverse to the loading direction is observed. In the asymptotic condition of a large void, threshold condition is dictated by planar mean stress for general macroscopic stress state.

A new yield and failure criterion for geomaterials

This paper proposes a new isotropic yield and failure criterion for geomaterials under general stress conditions. The new criterion is a function of the three stress invariants and the paper shows the well known criteria by Matsuoka & Nakai (1974) and Lade & Duncan (1975) are included in the new formulation. In order to include different features characterising soil and rock behaviour, the obtained function is successively modified to account for tensile strength and curvature in meridian planes. The influence of each parameter is discussed and finally the comparison between the new criterion and some experimental data on soils and rocks is shown. Finally, the domain of the new criterion is analysed in order to show if the yield function takes negative values also outside the shown elastic domain.

Failure modes of composite sandwich beams

A thorough investigation of failure behavior of composite sandwich beams under three-and four-point bending was undertaken. The beams were made of unidirectional carbon/epoxy facings and a PVC closed-cell foam core. The constituent materials were fully characterized and in the case of the foam core, failure envelopes were developed for general two-dimensional states of stress. Various failure modes including facing wrinkling, indentation failure and core failure were observed and compared with analytical predictions. The initiation, propagation and interaction of failure modes depend on the type of loading, constituent material properties and geometrical dimensions.

Simulation of phonon-limited mobility for nano-scale Si-based n-type non-planar device under general orientation and stress condition

In this manuscript we study the mobility of nano-scale Si-based n-type non-planar devices (e.g. FinFET, Tri-Gate and nanowire). Such devices feature a 1D transport property while the carriers are confined in a 2D plane. As a result, their longitudinal mobility depends strongly on the 1D characteristics of density of states. With added external stress the behaviors of such properties differ further from those of conventional planar devices. We established a physical model to self-consistently solve the subbands and calculate the mobility under a general stress condition, and demonstrated the methodology by calculating the mobility of a simple (100) non-planar device under the choices of two orientations and one longitudinal stress condition at various gate biases.

Constitutive models for power-law viscous solids containing spherical voids

In the analysis of non-linear porous solids, it is commonplace to employ a spherical unit cell owing to the simplicity it affords. The macroscopic constitutive response of the material is then predicted based upon either uniform traction or linear displacement/velocity boundary conditions applied to the outer surface of the cell. In this investigation, we carry out a careful computational analysis of the effect of these two types of boundary conditions on the macroscopic response of the (idealized) porous solid and in particular, we explore the sensitivity of the predicted response to the macroscopic stress, void volume fraction and material non-linearity. The numerical results are then used as a basis for establishing an approximate constitutive model that is expressed in a compact, explicit form. The study is carried out in the context of an incompressible, isotropic power-law viscous matrix material, and the computational analysis is focused on axisymmetric deformation of the unit cell. While the macroscopic strain-rate potential is found to exhibit a dependence on the third invariant of the macroscopic stress deviator, this dependence is slight (particularly for the linear displacement/velocity boundary condition) and, toward developing an approximate strain-rate potential applicable to general macroscopic stress states, a simple averaging scheme is employed to suppress the role of this quantity. Guided by the numerical results as well as by various previously proposed constitutive relations, an approximate generalized elliptic form for the macroscopic strain-rate potential is then proposed. The constitutive potential which is ultimately developed involves a fairly simple dependence upon the void volume fraction and the properties of the matrix material, yet it gives rise to predictions that agree well with the detailed unit cell calculations over the full range of properties and macroscopic stress states considered.

Evaluation of Tensile Strength of Cement-Treated Sand Based on Several Types of Laboratory Tests

There exist differences in the values of the tensile strength of cement-treated soils among results from direct tension, splitting tension, and bending tests. This paper presents numerical simulations that serve to explain such differences in the tensile strength properties obtained from the three types of tests. Finite element (FE)-analyses were performed to simulate the three tests as boundary value problems. A simple elasto-plastic model that simulates the behavior of cement-treated sands under a general three-dimensional stress state was used for these analyses. The analytical results showed that the direct tension tests yield reliable values of the actual tensile strength that will be mobilized under an ideal condition of uniaxial tension. On the other hand, in the splitting tension and bending tests, the tensile strength values are calculated from an external load by assuming a linear-elastic behavior in estimating the stress distribution. However, these values do not correspond to the actual tensile strength. The splitting tensile tests underestimate the tensile strength because the shear failure occurs below the loading strip and restrains further increase of the applied load. On the other hand, the bending tests overestimate the tensile strength because of the redistribution of stresses induced by the strain-softening behavior on the tensile side.

Prediction of Pressure and Density Dependent Failure in Sand-Like Granular Materials under General Stress Conditions

This paper presents a theoretical study of failure modes in sand-like granular materials under general triaxial stress conditions based on a hypoplastic model and a bifurcation analysis. The well developed constitutive model contains the void ratio as a state variable which allows the pressure and density dependent behaviour of the granular materials to be described with a single set of state-independent constitutive parameters. Based on this model a shear bifurcation condition is derived. Loading along various stress paths that can be achieved with a true triaxial test apparatus are simulated numerically. Either localized failure or uniform diffuse failure in granular samples may occur, which is determined based on whether the shear bifurcation condition is met. Effects of confining pressure and initial density are discussed.

Unified Three-Dimensional Revision of Modified Cam Clay Model

According to unified strength parameters obtained from unified strength theory, the slope of critical state line is modified to reflect critical states of different geomaterials under general stress states. Yield function that can consider the effect of the third deviatoricic invariant is proposed, and an elasto-plastic constitutive model is established by adopting non-associated flow rules; furthermore, methods of overcoming singular points on the yield surface are discussed. The proposed model is verified by true triaxial tests of clay, and results show that the model can well predict stress-strain relationships.

Collapse behaviour of unsaturated compacted soil with different initial densities

Very few experimental data on the mechanical behaviour of unsaturated soils exists, particularly on the collapse behaviour under general stress states, because of the technical difficulties and time-consuming nature of measuring suction and deformation. This paper presents the results of a series of controlled-suction triaxial tests on the collapse behaviour of an unsaturated compacted clay with different initial dry densities and suctions. The collapse behaviour here includes deformation characteristics, such as volume changes, and hydraulic characteristics, such as saturation changes. It is found that the wetting-caused collapse mainly depends on the mean net stress and the initial density, and that the volume decrease reaches a maximum when the specimen is under the initial yielding mean net stress. It is also found that the soil-water characteristic curve in terms of suction and degree of saturation shifts upwards with increasing specimen density. The soil-water characteristic curve of a compacted soil mainly depends upon the current density, not directly upon the stress state. In addition, experimental data show that the collapse occurs mainly in an intermediate range of suction levels, which are neither very high nor very low, and that the wetting-caused volume decrease is accompanied by an increase in the degree of saturation.Key words: unsaturated soil, density, triaxial test, suction, collapse, degree of saturation.

Quadruple LVDT local rotational displacement measurement in torsional shear tests

Experience has shown that to obtain pre-failure deformability of geomaterials in laboratory element tests, it is imperative to make local strain measurements. For torsional shear tests, the local measurement is complicated by coupling of the axial, radial, and rotational movement experienced by the soil specimen during shear. The rotational displacement must be isolated from other modes of movement for the interpretation of test results. Existing techniques designed for torsional shear tests under general stress conditions can be complicated and difficult to use. A simplified scheme using two pairs of linear variable displacement transducers (LVDTs) is proposed for local rotational deformation measurement, specifically for cyclic torsional shear tests under constant normal stress conditions. The subtraction of readings within an LVDT pair nullifies displacements at the measurement point caused by axial and radial movement or bulging of the specimen. The same subtraction accumulates and thus isolates LVDT readings caused by rotational movement. The error associated with the simplified set-up is expected to be <0.125%. A series of hollow cylinder torsional shear tests have been performed to verify the effectiveness of the new measurement scheme. The results are repeatable and consistent with well-documented test data.

Passive mechanical properties and structure of the aorta: segmental analysis

This study assessed segmental changes in the mechanical properties of the aorta at low, physiologic and high stresses, in relation with wall composition and morphometry. The aorta of 10 healthy pigs was divided into six thoracic and three abdominal segments. Aortic specimens were mechanically tested to failure, i.e. rupture, using a uniaxial tension device. Elastic modulus-stress curves were obtained for low (part I), physiologic (part II) and high (part III) stresses, and submitted to regression analysis; failure parameters were calculated. Histological evaluation was performed using an image-processing system, with quantification of morphometric parameters and composition of the entire vessel and its layers, i.e. media and adventitia. Significant differences were found in the regression parameters of parts I, II and III, and in failure parameters, suggesting that the proximal segments were stiffer at low stresses, whereas the distal were less extensible, stronger and stiffer at physiologic and high stresses. Image analysis demonstrated significant differences in morphometry and composition among the different layers and segments of the aorta, with higher elastin content proximally and collagen content distally. Good correlations were found between the regression parameters of parts I and II and elastin content, and between the failure and regression parameters of parts II and III and collagen content. Segmental changes exist in the structure and mechanical properties of the aorta, depending on the level of aortic pressure. This information is necessary for understanding aortic function at general non-physiologic stress states.