Normal Stress Components Research Articles

Dynamic modulus characteristics of saturated clays under variable confining pressure

Dynamic loadings, induced by earthquakes and other causes, will lead to the cyclic variation of both shear stress and normal stress components on the soil elements. A series of cyclic triaxial tests with and without variable confining pressure were carried out to investigate the coupling effects of cyclic shear stress and cyclic normal stress on the normalized shear modulus, G/Gmax, characteristics of saturated clays. Results indicated that both the phase differences and ratios between the cyclic deviatoric stress and cyclic confining pressure exerted a constant and pronounced influence on the G/Gmax, indicating that the G/Gmaxproperties under combined loadings will be more representative of actual field conditions than from single-loading conditions. A modified hyperbolic model considering the effects of cyclic confining pressure was further proposed.

Investigation of Stress Status in the Micro-Space of Surface and Subsurface Layer

One of main issues when evaluating or analysing quality and functional properties of work-piece is identification of status of residual stress. Every treatment or machining process generates residual stress in the surface and subsurface layers of the material structure. The residual stress has a large influence on the functional properties of the components. The article is focused on the method of triaxial measurement of residual stress after machining the surface of sample by high feed milling technology. Significance of triaxial measuring is the capability of measuring in different angles so it is possible to acquire stress tensor containing normal and shear stress components acting in the spot of measuring, using a Cartesian coordinate system.

Impact of viscosity variation and micro rotation on oblique transport of Cu-water fluid

This study inspects the influence of temperature dependent viscosity on Oblique flow of micropolar nanofluid. Fluid viscosity is considered as an exponential function of temperature. Governing equations are converted into dimensionless forms with aid of suitable transformations. Outcomes of the study are shown in graphical form and discussed in detail. Results revealed that viscosity parameter has pronounced effects on velocity profiles, temperature distribution, micro-rotation, streamlines, shear stress and heat flux. It is found that viscosity parameter enhances the temperature distribution, tangential velocity profile, normal component of micro-rotation and shear stress at the wall while it has decreasing effect on tangential component of micro-rotation and local heat flux.

Analysis of Residual Stresses in High Speed Milled Aluminum Alloys

The purpose of this study is to evaluate, from high speed machining tests, the behavior of the residual stresses induced in samples of AA 6082-T6 and AA 7075-T6 aluminum alloys. This study includes an exhaustive analysis of residual stress anisotropy from diameters of Mohr's circles. The combination of process parameters was modified in order to evaluate the stress changes introduced in different zones of the surfaces generated. A method of micro-indents, which includes the adaptation of a universal measuring machine, was used to determine, with high accuracy, the normal components of residual stress in several directions. The obtained results reveal that although, in the alloy 7075-T6, the normal components are lower, in the alloy 6082-T6, these normal components tend to be grouped into smaller intervals and also, to show a more homogeneous directional behavior when the cutting conditions are more severe.

Numerical measures of non-proportionality degree in incomplete contact subjected to fretting fatigue loading

Fretting fatigue failure is a fatigue fracture that initiates at a surface area where fretting has occurred. Fretting fatigue life assessment under multiaxial loading is a rather complex task, as the stresses at contact interface are multiaxial. A phase-shift between stress components leads to lower equivalent stress values calculated by most of available multiaxial fatigue criteria and therefore to an increased estimated fretting fatigue life. In this study a correlation based non-proportionality factor is introduced to predict the fretting fatigue lifetime under non-proportional stressing. The proposed factor is based on a statistical correlation of normal and shear stress components and does not depend on the choice of the coordinate system. A two dimensional finite element model is used to extract the stress components at crack initiation site. Moreover, to enhance the fretting fatigue lifetime assessment, stress-based Findley multiaxial fatigue criterion is modified by introducing the non-proportionality factor. A series of experimental data of high strength CrNi steel, taken from literature, are used to investigate the effect of non-proportional stressing on fretting fatigue life prediction.

On the Dynamic Characteristics and the Soil Compaction under the Influence of the Mole Plow

The development of many processes associated with changes in soil properties in the construction of irrigation and civil engineering requires justification of the geometric parameters and modes of operation of the tools, which are used to implement these processes. One of the tools for the implementation of such processes is mole plough. To conduct the research the authors have chosen a model in which the soil is considered as a viscoelastic medium, and can be formalized by Kelvin-Voigt model in solving the task of interaction of mole plough with soil. In the course of research we have built the physical equations that relate the stress components with strain rate taking into consideration modules of elasticity, viscosity and time of loading by using the method of analytical transformations the generalized Hooke's law and the equations for linear connection components of stress with strain rate. The authors obtained the stress components of the soil at the contact surface, depending on its mechanical properties, geometric parameters of the mole plough and its speed of movement. The time of deformation was determined from the equation of speed of passage of the wave stresses in a continuous medium. Application of regression equations that relate the changes in soil density with hydrostatic and maximum tangent stress allowed predicting changes in soil density depending on the geometrical parameters of the mole plough, the speed of its movement and mechanical properties of the soil. Finally, we obtained the components of resistance forces to the movement of mole plough in the soil depending on the mechanical properties of the soil, as well as geometrical parameters and speed of tool movement. To sum up, on the basis of the analysis of the dynamics of contact interaction of mole plough with soil the components of normal and shear stresses of the soil at the contact surface are installed. We have determined the direction and value of soil compaction and components of the resistance forces of the soil the movement of mole plough depending on its geometric parameters, the speed of the translational movement and the mechanical properties of the soil. The change functions of the density of the soil under the influence of the mole plough were obtained.

Numerical analysis on effect of annealing mc-Si ingot grown by DS process for PV application

Silicon solar cells play a crucial role in Photo voltaic (PV) application. We have numerically investigated thermal stress and normal stress components (Sigma 11, Sigma 22, Sigma 33 and sigma 12) by using finite volume method. The maximum thermal stress has low value at the centre region for 900K and 700K annealing temperatures comparing all the cases. The maximum thermal stress at peripheral region is low for 700K annealing compared to 900K annealing. The annealing effect of mc-Si ingot normal stress components is discussed. At 700K annealing temperature the normal stress in 11 and 33 direction has lower maximum and at the 900K annealing temperature the normal stress in 22 and 12 direction has lower maximum.

Nonlinear buckling and postbuckling behavior of cylindrical shear deformable nanoshells subjected to radial compression including surface free energy effects

The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic pressure load in the presence of surface free energy effects. To this end, Gurtin-Murdoch elasticity theory is implemented into the first-order shear deformation shell theory to develop a size-dependent shell model which has an excellent capability to take surface free energy effects into account. A linear variation through the shell thickness is assumed for the normal stress component of the bulk to satisfy the equilibrium conditions on the surfaces of nanoshell. On the basis of variational approach and using von Karman-Donnell-type of kinematic nonlinearity, the non-classical governing differential equations are derived. Then a boundary layer theory of shell buckling is employed incorporating the effects of surface free energy in conjunction with nonlinear prebuckling deformations, large deflections in the postbuckling domain and initial geometric imperfection. Finally, an efficient solution methodology based on a two-stepped singular perturbation technique is put into use in order to obtain the critical buckling loads and postbuckling equilibrium paths corresponding to various geometric parameters. It is demonstrated that the surface free energy effects cause increases in both the critical buckling pressure and critical end-shortening of a nanoshell made of silicon.

Coupled texture and non-Schmid effects on yield surfaces of body-centered cubic polycrystals predicted by a crystal plasticity finite element approach

Understanding and modeling the plastic deformation of body-centered cubic (BCC) metals involves considering non-Schmid (NS) driving forces to move dislocations. Here, the deformation of individual single crystals results not only from the resolved shear stress along the direction of slip (Schmid law) but also from shear stresses resolved along directions orthogonal to the slip direction as well as the three normal stress components (NS effects). In this work, we develop a multiscale model, called non-Schmid crystal plasticity finite element (NS-CPFE), to calculate the elastic-plastic deformation response of BCC polycrystals. The model accounts for coupled Schmid and NS effects through the modification of the driving shear stresses for both the 〈11¯1〉{110} and 〈111¯〉{112} slip families. The model is validated using data from the literature and then applied to calculate polycrystalline yield surfaces through the finite element (FE) cell approach. Using the model, we perform an in-depth study of the relative importance of different terms taken in the NS contribution to the driving force for slip. Results show that for a random texture or relatively weak textures, the NS shear stress components acting normal to the Burgers vector have no effect on the polycrystalline yield surface. However, for a relatively strong transversely isotropic texture, we find an interesting result: NS shear and normal stress components can negate the effects of texture on asymmetry and plastic anisotropy. In particular, the calculations performed for the best-fit NS constants for Ta, Mo, and W show that disparate sets of NS constants for the same material coupled with preferred texture can significantly influence the shape of the polycrystalline yield surface.

Propagation of Acoustic Waves Caused by the Accelerations of Vibrating Hand-Held Tools in Viscoelastic Soft Tissues of Human Hands and a Mechanobiological Picture for the Related Injuries

As is well known, hand-arm vibration syndrome (HAVS), or vibration-induced white finger (VWF), which is a secondary form of Raynaud’s syndrome, is an industrial injury triggered by regular use of vibrating hand-held tools. According to the related biopsy tests, the main vibration-caused lesion is an increase in the thickness of the artery walls of the small arteries and arterioles resulted from enlarged vascular smooth muscle cells (VSMCs) in the wall layer known as tunica media. The present work develops a mechanobiological picture for the cell enlargement. The work deals with acoustic variables in solid materials, i.e., the non-equilibrium components of mechanical variables in the materials in the case where these components are weakly non-equilibrium. The work derives an explicit expression for the infinite-time cell-volume relative enlargement. This enlargement is directly affected by the acoustic pressure in the soft living tissue (SLT). In order to reduce the enlargement, one can reduce either the ratio of the acoustic pressure in the SLT to the cell bulk modulus or the relaxation time induced by the cell osmosis, or both the characteristics. Also, a mechanoprotective role of the above relaxation time in the cell-volume maintenance is noted. The above mechanobiological picture focuses attention on the pressure in an SLT and, thus, modeling of propagation of acoustic waves caused by the acceleration of a vibrating hand-held tool. The present work analyzes the propagation along the thickness of an infinite planar layer of an SLT. The work considers acoustic modeling. As a general viscoelastic acoustic model, the work suggests linear non-stationary partial integro-differential equation (PIDE) for the weakly non-equilibrium component of the average normal stress (ANS) or, briefly, the acoustic ANS. The PIDE is, in the exponential approximation for the normalized stress-relaxation function (NSRF) reduced to the third-order linear non-stationary partial differential equation (PDE), which is of the Zener type. The unique advantage of the PIDE is that it presents a compact model for the acoustic ANS in an SLT, which explicitly includes the NSRF, thereby enabling a consistent description of the lossy-propagation effects inherent in SLTs. The one-spatial-coordinate version of this PDE in the planar SLT layer with the corresponding boundary conditions is considered. The relevance of these settings is motivated by a conclusion of other authors, which is based on the results of the frequency-domain simulation in three spatial coordinates. The boundary-value problem at arbitrary value of the stress-relaxation time (SRT) and arbitrary but sufficiently regular shape of the external acceleration is analytically solved by means of the Fourier method. The obtained solution is the steady-state acoustic ANS and allows calculation of the corresponding steady-state acoustic pressure as well. The derived analytical representations are computationally implemented. Propagation of the pressure waves in the SLT layer at zero and different nonzero values of the SRT, and the single-pulse external acceleration is presented. They complement the zero-SRT and zero-SRT-asymptote results with the results for various values of the SRT. The obtained pressure values are, at all of the space-time points under consideration, meeting the condition for the adequateness of the linear model. In the case where the SRT is zero, the results well agree with the ones obtained by using the simulation software package LS-DYNA. The dependence of the damping of acoustic variables in an SLT on the SRT in the present third-order case significantly generalizes the one in the second-order linear systems. The related resonance effect in the waves of the acoustic pressure propagating in an SLT is also discussed. The effects of the NSRF-originated memory function provided by the present third-order PDE model are necessary for proper simulation of the pressure, which is of special importance in the aforementioned mechanoboiological picture. The results obtained in the work present a viscoelastic acoustic framework for SLTs. These results open a way to quantitatively specific evaluation of technological strategies for reduction of the vibration-caused injuries or, loosely speaking, achieving “zero’’ injury.

Triaxial Measurement of Residual Stress After High Feed Milling Using X-ray Diffraction

Surface integrity has been an important research topic in the last decades. Machining generates residual stresses in the surface and subsurface layers of the structural elements. The residual stress has a large influence on the functional properties of the components. X-ray diffractometry is a non-destructive method applicable for the measurement of residual stresses in surface and subsurface layers of components. The article deals with the method of triaxial measurement of residual stress after machining the surface of sample by high feed milling technology. Significance of triaxial measuring is the capability of measuring in different angles so it is possible to acquire stress tensor containing normal and shear stress components acting in the spot of measuring, using a Cartesian coordinate system. For comparison, a simple measurement of residual stresses in the point indicates the stress direction only in normal direction of the measured surface.

Effect of magnetic field on the hydrodynamic permeability of a membrane built up by porous spherical particles

In this paper, an analysis of steady, axi-symmetric Stokes flow of an electrically conducting viscous incompressible fluid through spherical particle covered by porous shell in presence of uniform magnetic field is presented. To model flow through the swarm of spherical particles, cell model technique has been used, i.e. porous spherical shell is assumed to be confined within a hypothetical cell of the same geometry. At the fluid-porous interface, the stress jump boundary condition for tangential stresses along with continuity of normal stress and velocity components are used. Four known boundary conditions on the hypothetical surface were considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta−Morse’s) condition. The effect of stress jump coefficient, Hartmann number, and dimensionless permeability of the porous region as well as particle volume fraction on the hydrodynamic permeability and streamlines were discussed. The patterns of streamlines were also obtained.

Numerical solution of the beam pure bending problem in the framework of the theory of elastic materials with voids

The beam pure bending problem is solved numerically in the framework of the theory of elastic materials with voids, also called the elastic micro-dilatation theory. This theory describes a particular case of Mindlin’s type media with microstructure and contains only non-zero micro-dilatations. The physical meaning of the model involves a more comprehensive description of the stress-strain state of porous media, in which the volume pore fraction changes in response to applied external loads. In this paper we consider a generalized variant of the theory with surface effects. The finite element method is used to find a solution to the beam pure bending problem. The semi-inverse analytical micro-dilatation solution is compared with the FEM solution. It is shown that, unlike the analytical solution, in the FEM solution all the components of the stress-strain tensors are not equal to zero. There are also self-equilibrated normal stress components in the width direction and shear stress components in the cross section perpendicular to the neutral plane. In the numerical solution, all the stress boundary conditions are accurately satisfied on the free surfaces of the beam. Comparison of analytical and numerical simulation results shows that the analytical solution allows one to obtain sufficiently precise estimates to predict the influence of non-classical scale effects and surface effects on the effective stiffness and stress state of porous beams.

Triaxial Measurement Method for Analysis of Residual Stress after High Feed Milling by X-Ray Diffraction

Abstract Surface integrity is a broad term which includes various quality factors affecting the functional properties of parts. Residual stress is one of these factors. Machining generates residual stresses in the surface and subsurface layers of the structural elements. X-ray diffractometry is a non-destructive method applicable for the measurement of residual stresses in surface and subsurface layers of components. The article is focused on the non-destructive progressive method of triaxial measurement of residual stress after machining the surface of sample by high feed milling technology. Significance of triaxial measuring is the capability of measuring in different angles so it is possible to acquire stress tensor containing normal and shear stress components acting in the spot of measuring, using a Cartesian coordinate system.

On the behavior of a three-dimensional fractional viscoelastic constitutive model

In this paper a three-dimensional isotropic fractional viscoelastic model is examined. It is shown that if different time scales for the volumetric and deviatoric components are assumed, the Poisson ratio is time varying function; in particular viscoelastic Poisson ratio may be obtained both increasing and decreasing with time. Moreover, it is shown that, from a theoretical point of view, one-dimensional fractional constitutive laws for normal stress and strain components are not correct to fit uniaxial experimental test, unless the time scale of deviatoric and volumetric are equal. Finally, the model is proved to satisfy correspondence principles also for the viscoelastic Poisson’s ratio and some issues about thermodynamic consistency of the model are addressed.

A problem of thick circular plate in modified couple stress thermoelastic diffusion with phase-lags

Purpose The purpose of this paper is to investigate the two-dimensional axisymmetric problem in a homogeneous, isotropic modified couple stress thermoelastic diffusion (TD) medium in the context of dual-phase-lag model. Design/methodology/approach The Laplace and Hankel transforms have been applied to find the general solution to the field equations. The components of displacement, stresses, temperature change and chemical potential are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. Findings The components of normal stress, tangential stress, tangential couple stress, temperature change and chemical potential are obtained numerically and depicted graphically to see the effect of dual-phase-lag diffusion (DLD), dual-phase-lag heat transfer (DLT) and TD models in the absence and presence of couple stress parameter. Originality/value Comparisons are made in the absence and presence of couple stress DLD, DLT and TD models.

Unilateral contact problems with a friction

The boundary contact problem for a micropolar homogeneous elastic hemitropic medium with a friction is investigated. Here, on a part of the elastic medium surface with a friction, instead of a normal component of force stress there is prescribed the normal component of the displacement vector. We give their mathematical formulation of the Problem in the form of spatial variational inequalities. We consider two cases, the so-called coercive case (when elastic medium is fixed along some part of the boundary) and semi-coercive case (the boundary is not fixed). Based on our variational inequality approach, we prove the existence and uniqueness theorems and show that solutions continuously depend on the data of the original problem. In the semi-coercive case, the necessary condition of solvability of the corresponding contact problem is written out explicitly. This condition under certain restrictions is sufficient, as well.

Shear banding in large amplitude oscillatory shear (LAOStrain and LAOStress) of polymers and wormlike micelles

We investigate theoretically shear banding in large amplitude oscillatory shear (LAOS) of polymers and wormlike micelles. In LAOStrain we find banding at low frequencies and sufficiently high strain rate amplitudes in fluids for which the underlying constitutive curve of shear stress as a function of shear rate is non-monotonic. This is the direct analogue of quasi steady state banding seen in slow strain rate sweeps along the flow curve. At higher frequencies and sufficiently high strain amplitudes we report a different but related phenomenon, which we call `elastic' shear banding. This is associated with an overshoot in the elastic (Lissajous-Bowditch) curve of stress as a function of strain. We suggest that this may arise widely even in fluids that have a monotonic underlying constitutive curve, and so do not show steady state banding under a steadily applied shear flow. In LAOStress we report banding in fluids that shear thin strongly enough to have either a negatively, or weakly positively, sloping region in the underlying constitutive curve, noting again that fluids in the latter category do not display steady state banding in a steadily applied flow. This banding is triggered in each half cycle as the stress magnitude transits the region of weak slope in an upward direction, such that the fluid effectively yields. Our numerics are performed in the Rolie-poly model of polymeric fluids, but we also provide arguments suggesting that our results should apply more widely. Besides banding in the shear rate profile, which can be measured by velocimetry, we also predict banding in the shear and normal stress components, measurable by birefringence. As a backdrop to understanding the new results on shear banding in LAOS, we also briefly review earlier work on banding in other time-dependent protocols, focusing in particular on shear startup and step stress.

A cross-anisotropic formulation for elasto-plastic models

A cross-anisotropic formulation for elasto-plastic constitutive models based on a non-uniform scaling of the stress tensor is described. Taking advantage of the material symmetries characterising cross-anisotropy, only two scaling factors, one for the normal stress components and one for the shear stress components, are required. It is shown that the formulation can be easily introduced in already implemented models with minor modifications. The performance of this formulation is investigated by reproducing the strength variation of anisotropic rocks in triaxial tests. The numerical simulation of an unsupported excavation is also presented to show the effect of different scaling factors and bedding plane orientations.

Reynolds Stress Structures in the Hybrid RANS/LES of a Planar Channel

The near-wall cycle of hybrid RANS/LES is studied by calculating the flow through a planar channel. Statistical results are commented on and related to instantaneous structures which are extracted from the flow field. The problematic structures in the artificial near-wall cycle, well known to be super-streaks, are identified and quantified. The calibration of such closures provides a correct mixing length argument in the logarithmic layer. However because of these overly intense streamwise streaks, it is impossible to simultaneously predict the Reynolds streamwise normal and shear stress components correctly. Further, because the location of the RANS-LES interface changes spatially and temporally, we see these structures are more free to move vertically and this further worsens statistical results.