Stress Jump Research Articles

Influence of Stress Jump Condition at the Interface Region of a Two-Layer Nanofluid Flow in a Microchannel with EDL Effects

The influence of stress jump conditions on a steady, fully developed two-layer magnetohydrodynamic electro-osmotic nanofluid in the microchannel, is investigated numerically. A nanofluid is partially filled into the microchannel, while a porous medium, saturated with nanofluid, is immersed into the other half of the microchannel. The Brinkmann-extended Darcy equation is used to effectively explain the nanofluid flow in the porous region. In both regions, electric double layers are examined, whereas at the interface, Ochoa-Tapia and Whitaker's stress jump condition is considered. The non-dimensional velocity, temperature, and volume fraction of the nanoparticle profiles are examined, by varying physical parameters. Additionally, the Darcy number, as well as the coefficient in the stress jump condition, are investigated for their profound effect on skin friction and Nusselt number. It is concluded that, taking into account the change in shear stress at the interface has a significant impact on fluid flow problems.

Enhanced finite element formulation incorporating stress jumps and interface behavior in structures with embedded linear inclusions

AbstractWhen linear inclusions are embedded into a matrix, a perturbation is introduced in the boundary value problem written at the macroscale. Such inhomogeneity can provoke sharp gradients in the solution and a correct evaluation of the interface stress state reveals necessary when localized material degradations can lead to global failure mechanisms. In order to account for such refined description in large‐scale structural problems, a novel enhanced implicit finite element formulation is presented. The standard displacement approximation is improved by means of a kinematic enrichment aimed at reproducing the local interaction between the matrix and the inclusion. The microscale interface behavior can then be directly evaluated from the stress jump arising in the bulk. From a computational point of view, this translates in solving an additional local equilibrium equation. The static boundary conditions at the inclusion ends are thus exactly verified and a good precision is achieved with minimal meshing effort and code modifications. The proposed model is applied to elementary and structural examples involving singularities and it is compared to other modeling strategies with focus both on global and local quantities as well on the convergence properties and corresponding CPU times of the approximated solution.

Comparison of Rheological Characteristics and Mechanical Properties of Fossil-Based and Bio-Based Polycarbonate

Fossil-based PC, bisphenol-A polycarbonate (BPA-PC), is polymerized using bisphenol-A, which is derived from fossil-fuel based chemicals. Bio-based polycarbonate (bio-based PC) is polymerized using isosorbide, which is taken from plants. Accordingly, bio-based PC does not contain toxic polymerization chemicals. The rheological characteristics of fossil-based PC and bio-based PC samples, including viscosity, storage and loss moduli, and melt tension, were studied and compared. The mechanical properties of tensile behavior and impact strength were also measured and discussed. The shear viscosity curves and storage and loss moduli patterns of the bio-based PC were found to be somewhat different from those of fossil-based PC. The bio-based PC had higher tensile strength and elastic modulus than the fossil-based PC. The fossil-based PC exhibited a stress jump in the high strain region of the stress-strain curve, while the bio-based PC exhibited no stress jumps. The bio-based PC had a lower impact strength than the fossil-based PC. The cross-section of the fractured impact specimen of the bio-based PC showed only mirror regions, while that of the fossil-based PC showed both mirror regions and misted regions.

Effect of fluid-porous interface conditions on steady flow around and through a porous circular cylinder

Purpose – The purpose of this paper is to implement the numerical analysis based on finite volume method to compare the effects of stress-jump (SJ) and stress-continuity (SC) conditions on flow structure around and through a porous circular cylinder. Design/methodology/approach – In this study, a steady flow of a viscous, incompressible fluid around and through a porous circular cylinder of diameter “D,” using Darcy-Brinkman-Forchheimer’s equation in the porous region, is discussed. The SJ condition proposed by Ochoa-Tapia and Whitaker is applied at the porous-fluid interface and compared with the traditional interfacial condition based on the SC condition in fluid and porous media. Equations with the relevant boundary conditions are numerically solved using a finite volume approach. In this study, Reynolds and Darcy numbers are varied within the ranges of 1 < Re < 40 and 10-7 < Da < 10-2, respectively, and the porosities are e=0.45, 0.7 and 0.95. Findings – Results show that the SJ condition leads to a much smaller boundary layer within porous medium near the interface as compared to the SC condition. Two interfacial conditions yield similar results with decrease in porosity. Originality/value – There is no published research in the literature about the effects of important parameters, such as Porosity and Darcy numbers on different fluid-porous interface conditions for a porous cylinder and comparison the effects of SJ and SC conditions on flow structure around and through a porous circular cylinder.

Slow Motion of a Porous Sphere Translating Along the Axis of a Circular Cylindrical Pore Subject to a Stress Jump Condition

The coupled flow problem of an incompressible axisymmetrical quasisteady motion of a porous sphere translating in a viscous fluid along the axis of a circular cylindrical pore is discussed using a combined analytical–numerical technique. At the fluid–porous interface, the stress jump boundary condition for the tangential stress along with continuity of normal stress and velocity components are employed. The flow through the porous particle is governed by the Brinkman model and the flow in the outside porous region is governed by Stokes equations. A general solution for the field equations in the clear region is constructed from the superposition of the fundamental solutions in both cylindrical and spherical coordinate systems. The boundary conditions are satisfied first at the cylindrical pore wall by the Fourier transforms and then on the surface of the porous particle by a collocation method. The collocation solutions for the normalized hydrodynamic drag force exerted by the clear fluid on the porous particle is calculated with good convergence for various values of the ratio of radii of the porous sphere and pore, the stress jump coefficient, and a coefficient that is proportional to the permeability. The shape effect of the cylindrical pore on the axial translation of the porous sphere is compared with that of the particle in a spherical cavity; it found that the porous particle in a circular cylindrical pore in general attains a lower hydrodynamic drag than in a spherical envelope.

Strain hardening and jump-like deformation of ultrafine polycrystalline Al-Li solid solutions at 0.5 K

This is a study of the effect of microstructure created by severe plastic deformation (SPD) and annealing on strain hardening and jump-like deformation in Al-Li alloys. It is shown that under tension at 0.5 K, SPD processed polycrystals retain a significant strain hardening rate and have high strength and ductility. SPD also simulates unstable (jump-like) flow of the polycrystals owing to dislocation dynamics that shows up as stress jumps in the tension curve. The average amplitude of the jumps increases with strain, while the dislocation amplitude distribution corresponds to collective motion of dislocation avalanches with a distinctive scale. Jump-like deformation is partially suppressed by high-temperature annealing, while the distribution of the jump amplitudes is described by a power law. The relationship established between the coefficient of strain hardening and the average stress jump amplitude suggests a common dislocation dynamic for strain hardening and jump-like deformation at low temperatures. The observed features of low-temperature plastic deformation are treated as a consequence of changes in the grain sizes and density of dislocations owing to SPD and annealing.

On stability of elastic domain during isothermal solid-solid phase transformation in a tube configuration

Under isothermal quasi-static stretching the phase transition of a superelastic NiTi tube involves the formation (during loading) and vanishing (in unloading) of a high strain (martensite) domain. The two events are accompanied by a rapid stress drop/rise due to the formation/vanishing of domain fronts. From a thermodynamic point of view, both are instability phenomena that occur once the system reaches its critical state. This paper investigates the stability of a shrinking cylindrical domain in a tube configuration during unloading. The energetics and thermodynamic driving force of the cylindrical domain are quantified by using an elastic inclusion model. It is demonstrated that the two domain fronts exhibit strong interaction when they come close to each other, which brings a peak in the total energy and a sign change in the thermodynamic driving force. It is proved that such domain front interaction plays an important role in controlling the stability of the domain and in the occurrence of stress jumps during domain vanishing. It is also shown that the process is governed by two nondimensional length scales (the normalized tube length and normalized wall-thickness) and that the length scale dependence of the critical domain length and stress jump for the domain vanishing can be quantified by the elastic inclusion model.

Strain rate effects on sand and its quantitative analysis

Strain rate effects on the stress—strain behavior of sand were investigated by performing special plane strain and triaxial compression tests on saturated and air-dried sand specimens. In these tests, the loading strain rate was changed many times by a factor of up to 1 000 during otherwise monotonous loading at a constant axial strain rate. Test results show that the stress jump upon a stepwise change in the strain rate decays with an increase in the irreversible strain when monotonous loading continues at the changed strain rate and the amount of stress jump is essentially proportional to the instantaneous stress. Based on the amount of these stress jumps, a parameter β called the rate-sensitivity coefficient is introduced to represent the quantity of the observed viscous properties of sand, which equals 0.021 3 and 0.024 2 respectively for Hostun and Toyoura sands. Further analyses on the results indicate that the effect of the presence of pore water is deemed to be negligible with sand and the β value is rather independent of loading method, wet condition and confining pressure.

Effect of Porous Fraction and Interfacial Stress Jump on Skin Friction and Heat Transfer in Flow Through a Channel Partially Filled with Porous Material

Effect of Porous Fraction and Interfacial Stress Jump on Skin Friction and Heat Transfer in Flow Through a Channel Partially Filled with Porous Material

Implementation of the Stress Jump Condition in a Control-Volume Finite-Element Method for the Simulation of Laminar Coupled Flows in Adjacent Open and Porous Domains

Laminar coupled flow of a Newtonian fluid in adjacent open and fluid-saturated porous domains is modeled using the continuity and the Navier-Stokes equations in the open domain, and a continuity equation and the Brinkman-Forchheimer equations in the porous domain. At the interface, a jump condition is used with two adjustable coefficients: one related to an excess viscous stress and the other to an excess inertial stress. This mathematical model is solved using a control-volume finite-element method and a novel procedure for incorporating the interfacial stress jump condition. The solutions of two illustrative example problems are also presented and discussed.

Viscous Flow Past a Spherical Void in Porous Media: Effect of Stress Jump Boundary Condition

Viscous Flow Past a Spherical Void in Porous Media: Effect of Stress Jump Boundary Condition

Viscous Flow Past a Porous Spherical Shell—Effect of Stress Jump Boundary Condition

Using the stress jump boundary condition for the tangential stresses at the porous liquid interface along with the continuity of the velocity components and normal stress, the uniform viscous flow past a porous spherical shell with external radius r1 , internal radius r2 is studied. The flow inside the porous region is governed by Brinkman equation. The flow in the liquid region is governed by the Stokes equation. The flow field is computed by matching the boundary conditions at the porous-fluid interface. The effect of stress jump coefficient β on the flow field is very much felt. An increase in the drag with permeability is found for different R , different ratio of r1 ∕ r2 , and also a change in magnitude of the drag for different values of stress jump coefficient β is observed. Also, the variation of torque and shear stress with permeability and the stress jump coefficient is discussed.

The stress jump of a semirigid macromolecule after shear: Comparison of the elastic stress to the birefringence

In this work it is shown that the amount of stress retained at the instant of shear cessation, denoted as the elastic stress by Doi, and not the total shear stress is proportional to the shear equivalent of the optic birefringence even in the nonlinear shear stress–shear rate region. The system studied was xanthan gum in a viscous solvent, fructose dissolved in water, and may be considered as a system with rigid constraints. Coaxiality of the elastic stress and refractive index ellipsoids has been predicted theoretically for these systems; however, previous studies have only compared the total stress to the birefringence which generally leads to invalidation of the stress‐optic relation. The results of this work have three consequences; it reinforces the fact that stress jumps are present, the stress‐optic relation is only true when the elastic and not the total stress is used, and two unique types of stress constitute the total stress as predicted by theory for systems with rigid constraints.

Atomistic modelling of cavitation of glassy polymers

Abstract A detailed atomistic approach has been used to investigate the molecular segment kinematics as a glassy, atactic polypropylene system was dilated by 30%. The microstructural stress-dilatation response consisted of smooth, reversible portions bounded by sudden, irreversible stress jumps, but when compared to the microstructural stress-strain curve of the shear simulation, the overall trend more closely resembled macroscopic stress-strain curves. The peak negative pressure was in the neighbourhood of 12% dilatation, with a corresponding secondary maximum in the von Mises shear stress. The peak negative pressure was relieved by a stress jump that signalled cavitation, which was most pronounced in the large system. The cavities were found to be flat and irregular; for the large system that had been dilated by 20%, the cavities extended 0.5 to 0.8 nm with a characteristic thickness of 0.080 nm, and the total cavity volume fraction was 0.02. The surface energy of the cavities was estimated to be 53.4mJ...

Influence of non-classical elastic-plastic constitutive features on shock wave existence and spectral solutions

T he influence of non-classical elastic-plastic constitutive features on dynamically moving discontinuities in stress, strain and material velocity is investigated. Non-classical behavior here includes non-normality of the plastic strain increment to the yield surface, plastic compressibility, pressure sensitivity of yield and dependence of the elastic moduli on plastic strain. D rugan and S hen's (1987) analysis of dynamically moving discontinuities with strain as well as stress jumps in classical materials is shown to be valid for a broad class of non-associative material models until deviation from normality exceeds a critical (non-infinitesimal) level. For these non-classical materials, an inequality that bounds the magnitude of the stress jump is derived, which is information not obtainable from a standard spectral analysis of a shock. For the special case of stress discontinuities with continuous strain or for quasi-static deformations, this inequality is shown to rule out jumps in specific projections of the stress tensor unless the non-normality is sufficiently large. These results invalidate a recent claim in the literature that an infinitesimal amount of non-normality permits moving surfaces of discontinuity in stress (with no strain jump) near the tip of a dynamically advancing crack tip. Using a very general plastic constitutive law that subsumes most non-classical (and classical) descriptions currently in use, a complete closed form solution is obtained for the plastic wave speeds and eigenvectors. A novel feature of the analysis is the clarity and completeness of the solutions. If the elastic part of the response is isotropic, one plastic wave speed equals the elastic shear wave speed, while the other two possible wave speeds depend in general on the stress and plastic strain within the shock transition layer. Concise necessary and sufficient conditions for real eigenvalues and for vanishing eigenvalues are derived. The real eigenvalues are classified by numerical sign and ordering relative to the elastic eigenvalues. The geometric multiplicity of plastic eigenvectors associated with elastic eigenvalues is shown to depend on the stress state within the shock transition layer. These solutions, several of which hold for arbitrary elastic anisotropy, are also applicable to acceleration waves and localization problems and to materials with dependence of the elastic moduli on plastic strain. Such elastic-plastic coupling is shown to imply a non-self-adjoint fourth order tangent stiffness tensor even if the plastic constitutive law is associative.

Instrument effects on stress jump measurements

Stress jumps occur in fluids that possess a viscous contribution to their total stress. On cessation of shear, such a fluid will show an instantaneous loss of stress, while some of the stress will remain and subsequently decay in some manner, either exponential or otherwise. The results in this paper show that filtering, present in most rheometers, will eliminate the stress jump and not allow its measurement. The torque head inertia for a spring-type torque measuring system is found to greatly influence the measurements and a stress jump is not seen. In fact, the material's true stress relaxation behaviour is far from that measured. The force rebalance torque measuring system is found to accurately measure stress jumps.

Errata: Stress Jump at the Inception of Shear and Elongational Flows of Dilute Polymer Solutions, Due to Internal Viscosity [J. Rheol., 31, 495–510 (1987)

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Stress Jump at the Inception of Shear and Elongational Flows of Dilute Polymer Solutions due to Internal Viscosity

All versions of the internal viscosity (IV) model for polymer chain dynamics lead to the prediction that the inception of flow from a rest state is accompanied by a stress jump at t=0. For the general case of long chains (large number of submolecules, N), the jump is predicted here for the onsets of simple shear flow and elongational flow at constant deformational rate. The exact model formulation (i.e., following Booij and van Wiechen) is used, without the need to approximate deformational velocities in the Cerf/Peterlin sense, and rigorous closed‐form solutions are presented. This is apparently the only rheological prediction now available for the large N IV model using the rigorous formulation. Intermediate steps in the analysis demonstrate the extent to which the motions of beads are correlated with those of neighbors at various distances in the linear sequence; the effect is small and depends slightly on φ/f. Final results show that viscosity jumps are independent of deformational rate and depend on both φ and φ/f, where φ is the IV coefficient and f the bead/solvent friction coefficient. Experiments on stress jumps and subsequent transients are thus potentially able to evaluate φ alone, unlike steady‐state experiments which respond only to φ/f. Predictions for shear flow are also compared with those made using the Cerf/Peterlin linearization approximation, showing that the two diverge severely at high values of φ/f.

On the kinetics of stress jumps during plastic deformation of crystals

This is a study of jump parameters for the case of twinning in Cu + 7 at.% Al single crystals at 295 K over a wide range of effective mass M and stiffness K of the crystal-machine system. The stress jump amplitude is shown to be independent of K, the jump time Δt and the deformation kinetics to depend essentially on the parameters K and M and the stress measured near the crystal to be practically constant throughout Δt. This relaxation process is analyzed with allowing for the inertia of the loading system effective mass. The approach used is well suitable both for the experimental results of this work and for the generally known jump parameters at cryogenic temperatures and during the Portevin-Le Chatelier effect. The condition of the jumplike character of the deformation is formulated: the strain rate sensitivity of the flow stress must be below critical, which depends on the parameters M and K. The experimentally observed features of deformation process during the jump may not be explained without allowance for the interrelation of microscopic processes responsible for the jump and the inertia of the loading system effective mass.