Effects Of Couple Stresses Research Articles

Modified Reynolds Equation for Different Types of Finite Plates with the Combined Effect of MHD and Couple Stresses

We make an effort to analyze the behavior of squeeze film characteristics of different finite plates with couple stress fluid in the presence of a transverse magnetic field. On the basis of the Stokes couple stress fluid model and hydromagnetic flow model, a modified Reynold's equation is derived, which is solved by using appropriate boundary conditions to obtain squeeze film pressure, load-carrying capacity, and squeeze film time. The graphical representation of the results suggests that the different bearing systems register an enhanced performance with couple stresses compared to that of a bearing system working with a conventional lubricant in the presence of a transverse magnetic field. It is observed that the effect of applied magnetic field on the squeeze film lubrication between different finite plates with conducting couple stress fluids is to increase the load-carrying capacity significantly and to delay the time of approach compared to the corresponding nonconducting Newtonian case. It is seen that for all of the finite plates of different shapes, the circular shape gives the maximum load and time.

A general third-order theory of functionally graded plates with modified couple stress effect and the von Kármán nonlinearity: theory and finite element analysis

Finite element analysis of functionally graded plates based on a general third-order shear deformation plate theory with a modified couple stress effect and the von Karman nonlinearity is carried out to bring out the effects of couple stress, geometric nonlinearity and power-law variation of the material composition through the plate thickness on the bending deflections of plates. The theory requires no shear correction factors. The principle of virtual displacements is utilized to develop a nonlinear finite element model. The finite element model requires C1 continuity of all dependent variables. The microstructural effects are captured using a length scale parameter via the modified couple stress theory. The variation of two-constituent material is assumed through the thickness direction according to a power-law distribution. Numerical results are presented for static bending problems of rectangular plates with various boundary conditions to bring out the parametric effects of the power-law index and length scale parameter on the load–deflection characteristics of plates with various boundary conditions.

Influence of boundary elasticity on a couple stress elastic solid with a mode-III crack

In this article, we develop a linear theory of elastic boundary reinforcement of a couple stress elastic solid subjected to anti-plane deformations. The reinforcement is represented by a thin couple stress elastic coating perfectly bonded to the boundary of the solid. The elastic properties of the coating are taken to be separate from those of the surrounding bulk material. In this context, the model developed here can also be viewed as a more comprehensive representation of the deformation of a couple stress material in which the separate role of surface mechanics is incorporated into the model of deformation. As an example of our theory, we consider the classical problem of a semi-infinite crack in a couple stress material and examine the contribution of the reinforcement to the stress distributions in the vicinity of the crack tip. Our results indicate that the presence of the reinforcing layer on the crack faces eliminates the well-known stress singularity at the crack tip demonstrating the influence of surface and couple stress effects in the model of deformation.

Physical and Mathematical Representations of Couple Stress Effects on Micro/Nanosolids

In the present paper, for linear elastic materials, effects of couple stresses on micro/nanosolids are physically discussed and mathematically represented in the context of the classical, the modified and the consistent couple–stress theories. Then, an evaluation is provided showing the validity and the limit of applicability of each one of these theories. At first, the possible couple stress effects on mechanics of particles and on continuum mechanics are represented. Then, a reasoning comparison with examples is performed to discuss and evaluate the way that each one of these theories represents the couple stress effects. In the context of the classical couple–stress theory, two higher-order material constants are introduced in addition to the conventional ones to capture the microstructure rigid rotation effects. Recently, two alternative theories, the modified couple–stress and the consistent couple–stress theories, with only one additional material constant are introduced with contradictory points of view. Authors of these two alternative theories gave apparently strong motivations for their opposed points of view. Therefore, through the present paper, it will be convenient to analyze the essential points of view based on which these alternative theories are proposed since they lead to exactly opposed conclusions. Thus their essential points of view are discussed and evaluated showing their consistency with the fundamental concepts of the couple stress effects. It has been shown that the scientific bases of these two alternative theories are not consistent with the representation of the couple–stress effects on micro/nanocontinua. Based on discussions and results through the paper, both the modified theory and the consistent theory represent, only, simplifications for the classical couple–stress theory but they did not able to well represent the possible effects of couple stresses and they are limited for only two categories of linear elastic materials problems. This demolishes the scientific points of view based on which the two theories are proposed.

Reaction–Diffusion–Stress Coupling Effect in Inelastic Oxide Scale During Oxidation

Stress is induced in a thermally grown oxide scale during high-temperature oxidation. Under certain conditions, the oxidation causes plastic deformation. An inhomogeneous growth strain formulation is proposed based on evolution equations. Using the inhomogeneous growth strain, a reaction–diffusion–stress coupling elastic–plastic model, which accounts for factors, such as the chemical reaction, kinetics of the oxide scale and diffusion of reactant species, is developed for the analysis of stress and effects of stress on these factors in the oxide scale during high-temperature oxidation. Numerical results reveal large compressive stresses and a significant stress gradient in the oxide scale with the largest compressive stress at the oxide/substrate interface and the lowest compressive stress at the oxygen/oxide interface, which is consistent with experimental observations. The stress developed in the oxide scale has an influence on the oxidation reaction rate and distribution of the reactant species concentration, which in return affects the stress distribution.

Inertial MHD Couple Stress Effects on Infinitely Wide Slider Bearings

This article presents a numerical study of magnetohydrodynamic (MHD) infinitely wide plane inclined slider bearings including both fluid inertia and non-Newtonian couple stress effects. Fluid inertia forces are considered in the film fluid using a simplified form of the Navier-Stokes equations. The non-Newtonian couple stress behavior of the lubricant is described based on the microcontinuum Stokes theory. The governing equations are discretized by finite differences using a boundary layer–type equations resolution. The resulting algebraic equations are solved using the Gauss-Seidel method. It is found that the couple effects of fluid inertia forces, MHD, and non-Newtonian couple stresses provide a significant improvement in the slider bearing load capacity compared to the case of the noninertia Newtonian nonconducting lubricant. The use of conducting lubricant diminishes the negative effect of inertia forces on the friction coefficient.

The Effect of Couple Stress on Hydrodynamic Rotating Flow

An investigation carried to understand the motion of an incompressible couple stress fluid between two rigid non-conducting plates when both the fluid system and the plates are in solid body rotation with a constant angular velocity about an axis normal to the plates. The flow is generated in the system by the impulsive accelerated motion of the upper plate in its own plane, while the lower plate is held stationary. Exact analytical solution for the velocity of the fluid is obtained by the Laplace transformation operational method. Numerical computations are carried to understand the simultaneous effects of rotation and couple stress parameter on the flow with respect to time. The observations reveal that, with the enhancement of rotation and couple stress parameters, the velocity of the fluid will be diminished, but with the extension of time the velocity of the fluid will be enriched.

Response of harmonic sources in couple stress thermoelastic medium with state space approach

Purpose – The purpose of this paper is to investigate the two-dimensional problem in couple stress thermoelastic medium for a half space is established and state space approach has been applied to solve the problem. Design/methodology/approach – Normal mode analysis is used to obtain the exact expressions for normal stress, tangential stress and couple stress. Numerical calculation is prepared for these quantities and depicted graphically for a special model. Findings – The expressions for normal stress, tangential stress and couple stress are obtained numerically and depicted graphically to see the couple stress effect. Originality/value – It is found that couple stress effect decrease the value of normal stress components for circular frequency equal to 0.5 for small values of the wave number and then increases whereas the values of normal stress components decrease first and then increase monotonically for circular frequency equal to 0.1 when the force is applied in normal direction and the values of tangential stress components and couple stress components decrease for all values of wave number. But the values for normal stress components, tangential stress components and couple stress components increase when the force is applied in tangential direction.

Corrosion Behavior of X80 Pipeline Steel under Coupling Effect of Stress and Stray Current

Corrosion Behavior of X80 Pipeline Steel under Coupling Effect of Stress and Stray Current

A couple stress fluid modeling on free convection oscillatory hydromagnetic flow in an inclined rotating channel

This study focuses analytically on the oscillatory hydromagnetic flow of a viscous, incompressible, electrically-conducting, non-Newtonian fluid in an inclined, rotating channel with non-conducting walls, incorporating couple stress effects. The model is then non-dimensionalized with appropriate variables and shown to be controlled by the inverse Ekman number (K2=1/Ek), the hydromagnetic body force parameter (M), channel inclination (α), Grashof number (Gr), Prandtl number (Pr), oscillation frequency (ω) and time variable (ωT). Analytical solutions are derived using complex variables. Excellent agreement is obtained between both previous and present work. The influence of the governing parameters on the primary velocity, secondary velocity, temperature (θ), primary and secondary flow discharges per unit depth in the channel, and frictional shear stresses due to primary and secondary flow, is studied graphically and using tables. Applications of the study arise in the simulation of the manufacture of electrically-conducting polymeric liquids and hydromagnetic energy systems exploiting rheological working fluids.

Static characteristics of a fluid film bearing with TiO2 based nanolubricant using the modified Krieger–Dougherty viscosity model and couple stress model

Static characteristics of a journal bearing operating on TiO2 based nanolubricant is obtained by a variable viscosity approach. The predicted shear viscosities of TiO2 based nanolubricant at different volume fractions and aggregate particle sizes are obtained using modified Krieger–Dougherty model and are found to be in good agreement with experimental shear viscosities. The modified Reynolds equation considers the Krieger–Dougherty viscosities and couple stress effects of TiO2 nanoparticle additives at different volume fractions and particle sizes. Results reveal a significant improvement in load carrying capacity of journal bearing operating on TiO2 based nanolubricant as compared to plain oil without TiO2 nanoparticles.

Exact solutions for two-dimensional laminar flow over a continuously stretching or shrinking sheet in an electrically conducting quiescent couple stress fluid

A mathematical study of heat and flow of couple stress MHD fluids over permeable stretching/shrinking surfaces is undertaken in the present paper. Exact solutions for both flow and temperature fields under a boundary layer approach are targeted. In the absence of couple stress field the results completely collapse onto the special cases available in the literature. Obtained closed form solutions provide valuable knowledge for the velocity and temperature profiles as well as skin friction coefficient and Nusselt number. Dissimilar to the already known for a noncouple Newtonian fluid, double solutions exist over a stretching sheet, and triple solutions are present over a shrinking sheet, if couple stress effects are taken into consideration.

Investigations on the effects of surface texture on the performance of a porous journal bearing operating with couple stress fluids

In the present work, the hydrodynamic lubrication of a porous journal bearing is investigated with considering the effects of surface texturing at three different locations on the bearing surface operated with couple stress fluids. Darcy’s equation is used to account for the effects of porous region of the bearing. The Stokes constitutive equations used for taking couple stress effects into account and the sinusoidal wave texture equation for texture at different locations on the bearing surface are used for deriving modified Reynolds equation. Centre differencing approach of finite difference scheme is adopted for discretisation of governing equations. It has been found that couple stress fluids improved the bearing performance. Moreover, the texture imposed on the bearing surface gives significant effects. Three configurations (configurations 1, 2 and 3) have been considered in the present work at three different locations and bearing performance characteristics have been calculated. The results revealed that the texturing improved the bearing performance in case of configuration 2 in comparison to two other locations (configurations 1 and 3).

Effects of Slip Factors and Couple Stresses for Stagnation Point Flow over a Moving Plate

An investigation is presented for the two-dimensional and axisymmetric stagnation flows of a couple stress fluids intrude on a moving plate under partial slip conditions. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The important physical parameters of skin friction coefficients of the fluid are also obtained. The homotopy analysis method (HAM) is employed to obtain the analytical solution of the problem. Also, the convergence of the solutions is established by plotting graphs of convergence control parameter. The impacts of couple stresses and slip conditions on the flow and temperature of the fluid have been observed. The numerical comparison for the considered fluid is compared with previous solutions as special case.

General approach on chemistry and stress coupling effects during oxidation

In this paper, the mechanism of growth strain is discussed based on the irreversible evolving equations by considering the coupling effects of stress and chemical reaction during isothermal oxidation, and a simple model relating the growth strain and the oxide thickness is developed. If the effect of the stress on the chemical reaction is not taken into account, the model reduces to the Clarke assumption. The expression of Dox is exhibited, and its value can be determined by experiments. The stress evolving equations are derived, where the viscoplastic strain of the oxide and metal and the growth strain of the oxide are considered. Numerical results are given and compared with results from experiments and the existing model. There is good agreement between the proposed model and the experimental data.

Hydro-mechanical coupling mechanism on joint of clay core-wall and concrete cut-off wall

The joint of clay core-wall and concrete cut-off wall is one of the weakest parts in high earth and rockfill dams. A kind of highly plastic clay is always fixed on the joint to fit the large shear deformation between clay core-wall and concrete cut-off wall, so the hydro-mechanical coupling mechanisms on the joint under high stress, high hydraulic gradient, and large shear deformation are of great importance for the evaluation of dam safety. The hydro-mechanical coupling characteristics of the joint of the highly plastic clay and the concrete cut-off wall in a high earth and rockfill dam in China were studied by using a newly designed soil-structure contact erosion apparatus. The experimental results indicate that: 1) Shear failure on the joint is due to the hydro-mechanical coupling effect of stress and seepage failure. The seepage failure will induce the final shear failure when the ratio of deviatoric stress to confining pressure is within 1.0–1.2; 2) A negative exponential permeability empirical model for the joint denoted by a newly defined principal stress function, which considers the coupling effect of confining pressure and axial pressure on the permeability, is established based on hydro-mechanical coupling experiments. 3) The variation of the settlement before and after seepage failure is very different. The settlement before seepage failure changes very slowly, while it increases significantly after the seepage failure. 4) The stress-strain relationship is of a strain softening type. 5) Flow along the joint still follows Darcian flow rule. The results will provide an important theoretical basis for the further evaluation on the safety of the high earth and rockfill dam.

Analysis of couple stress fluid lubricated partially textured slip slider and journal bearing using narrow groove theory

A theoretical model of partially textured slip slider and journal bearing lubricated with couple stress fluids is developed using narrow groove theory (NGT). The partially textured slip bearing configuration is analyzed using couple stress effects. The nondimensional pressure and shear stress expressions are derived based on one-dimensional analysis using modified Reynolds equation. The partially textured slip parameters used in the analysis are: nondimensional texture length; nondimensional depth of recess; land with slip to recess region ratio; and nondimensional slip coefficient. Partially textured slip is effective in the case of parallel slider and concentric journal bearing lubricated with couple stress fluids to yield an improvement in load capacity and reduction in coefficient of friction.

Effect of Surface Roughness and Couple Stresses on Squeeze Films between Curved Annular Plates

The combined effects of couple stresses and surface roughness patterns on the squeeze film characteristics of curved annular plates are studied. The Stokes (1966) couple stress fluid model is included to account for the couple stresses arising due to the presence of microstructure additives in the lubricant. In the context of Christensen's (1969) stochastic theory for the lubrication of rough surfaces, two types of one-dimensional roughness patterns (circumferential and radial) are considered. The governing modified stochastic Reynolds type equations are derived for these roughness patterns. Expressions for the mean squeeze film characteristics are obtained. Numerical computations of the results show that the circumferential roughness pattern on the curved annular plate results in more pressure buildup whereas performance of the squeeze film suffers due to the radial roughness pattern for both concave and convex pads. Further the squeeze film time is longer (shorter) for the circumferential (radial) roughness patterns. Improved squeeze film characteristics are predicted for the couple stress lubricant.

Anti-plane electro-mechanical behavior of piezoelectric composites with a nano-fiber considering couple stress at the interfaces

Many nanostructures are assumed to be characterized by couple stress effects. Based on the couple stress theory and surface/interface theory, the anti-plane electro-mechanical behavior of piezoelectric composites with a nano-fiber is studied, and the effect of stress and electric displacement at the interface on the size-dependent behavior is examined. By introducing a decoupling function, the governing equations in piezoelectric materials are simplified into two classical governing equations. The displacement and electric potential are expressed by Bessel functions. By satisfying the boundary conditions around the nano-fiber with surface/interface effect, the expanded coefficients are obtained. Excellent agreement with the previous results validates this model. It can be concluded that the interface around the nano-fiber shows greater effect on the stress than that on the electrical fields, and the interface effect increases greatly due to the existence of couple stress. The effect of material properties of nano-fiber on the stress and electric field under different coupling stresses is also examined.

Effect of couple-stresses on the stress intensity factors for a crack in an infinite elastic strip under tension

Stresses around a crack in an infinite elastic strip are evaluated based on linearized couple-stress theory under uniform tension. The crack is perpendicular to the stress-free edges of the strip. Solutions are constructed both for a half-plane and for a strip. First, the boundary conditions at the stress-free surfaces are satisfied using a Fourier transform. Next, the mixed boundary value conditions with respect to the crack are reduced to dual integral equations. To solve these equations, differences in the displacement and the rotation at the crack are expanded through a series of functions that are zero -valued outside the crack. The unknown coefficients in each series are solved in order to satisfy the boundary conditions inside the crack using the Schmidt method. The stresses are expressed in terms of infinite integrals, and the stress intensity factors are determined using the integrand characteristics for an infinite value of the variable of integration. Numerical calculations are conducted for selected crack configurations, and the effect of the couple-stresses on the stress intensity factors is revealed.