Experimental study of simple shear flow of monodisperse fibrous composites

Steady-state simple shear flow of epoxide resin and its composites containing 1, 3, or 5 vol. % fiber material was studied at temperatures ranging from 20 to 70°C. Normal stresses were measured. The decrease in viscosity with increasing shear rate, during the formation of a continuous fiber mesh, is interpreted according to the molecular-kinetic theory of flow of continuous media, on the assumption of viscoelastic flow elements with the relaxation time a function of the shear rate. The conditions are established for a transition from the slip mechanism of flow, which involves fiber linkages, to the cluster mechanism of flow.     

Superposition of large butt-end and coaxial torsional and axial shear deformations of homogeneous and fiber-reinforced thick-wall cylinders

A mathematical model of superposition of large butt-end and coaxial torsional and axial shear deformations of homogeneous and fiber-reinforced thick-wall cylinders is constructed. The macroscopic stresses of the reinforced material are additively determined by matrix stresses and by tensile or constrained compression stresses in the reinforcing fibers. The model is based on the numerical solution of two boundary-value problems, one of which corresponds to the butt-end torsion and the other to the coaxial torsion and axial shear. The boundary-value problem on joint deformations is solved with the use of the displacement field determined from the solution to the boundary-value problem on butt-end torsion. The results obtained by applying this method to homogeneous and axially-radially reinforced thick-wall cylinders subjected to butt-end torsion with subsequent coaxial torsion and axial shear are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 465–492, July–August, 2007.     

The excitation mechanism of a shear stress induced rotary wave

The free surface flow in a vertical, cylindrical, rotating container will be considered when axis-symmetric angular and radial shear stress distributions are applied on the free surface. It is well known that in the inviscid case a rotary wave which can be described by a flow potential exists. We want to determine the stability limit of the axis-symmetric base state with respect to the rotary wave for small Ekman and Froude numbers. Under the above assumption, the critical flow conditions can be determined analytically. The results can be verified experimentally using a vertical, cylindrical container partially filled with water where the top lid rotates with a given angular velocity. Thus, the induced air flow will exert shear stresses in the angular and radial direction onto the water surface. Above a certain threshold, rotary waves can be observed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Static analysis of functionally graded beams using higher order shear deformation theory

Displacement field based on higher order shear deformation theory is implemented to study the static behavior of functionally graded metal–ceramic (FGM) beams under ambient temperature. FGM beams with variation of volume fraction of metal or ceramic based on power law exponent are considered. Using the principle of stationary potential energy, the finite element form of static equilibrium equation for FGM beam is presented. Two stiffness matrices are thus derived so that one among them will reflect the influence of rotation of the normal and the other shear rotation. Numerical results on the transverse deflection, axial and shear stresses in a moderately thick FGM beam under uniform distributed load for clamped–clamped and simply supported boundary conditions are discussed in depth. The effect of power law exponent for various combination of metal–ceramic FGM beam on the deflection and stresses are also commented. The studies reveal that, depending on whether the loading is on the ceramic rich face or metal rich face of the beam, the static deflection and the static stresses in the beam do not remain the same.     

Mechanism of shear failure of reinforced rings in bending

The mechanism of failure of a ring due to the shear stresses in the matrix is investigated. It is shown that in the process of shear failure the axial displacement distribution is modified and that the shear failure mechanism depends on the type of loading. The load corresponding to the onset of failure of the ring due to the shear stresses in the matrix does not exhaust the carrying capacity of a reinforced ring with respect to this mode of failure.Institute of Hydrodynamics, Siberian Division of the Academy of Sciences of the USSR, Novosibirsk. Translated from Mekhanika Polimerov, No. 3, pp. 435–444, May–June, 1976.     

一种非矩形平行平板流动腔的定常流分析

高度远小于横向和纵向几何尺寸的平行平板流动腔是当前用以体外研究细胞力学行为的主要工具之一·人们常用的是上下两平行平板是矩形边界的流动腔·这种流动腔内（除入口端和出口端的邻近区域外）的流场是均匀的［１］，因而每次实验只能观测底部培养细胞受一种切应力值的影响情况·本文提出一种上下两平行平板不是矩形的平行平板流动腔·通过对腔内流体作定常流动的流场进行详细分析，给出了流动腔内流速和腔底切应力值的分布·结果发现，利用这种非矩形平行平板流动腔可以同时研究底部培养细胞在多种切应力值下的力学行为·本文理论结果与超声多普勒技术检测流速的实验结果吻合得相当好·     

Effect of the sign of the shear stresses on the shear strength of reinforced plastics

The effect of the sign of the shear stresses on the shear strength has been investigated for a glass-reinforced plastic of the SVAM type with various ratios of the longitudinal and transverse reinforcement in shear in the plane of reinforcement in axes turned through 45° relative to the direction of reinforcement. More than 80 tubularspecimens were tested. The shear strengths T ₄₅ ⁺ and T ₄₅ ^– corresponding to shear stresses of different signs can be found from uniaxial tests in tension and compression in the direction of the reinforcement.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 262–268, March–April, 1971.     

Analysis of functionally graded plates using higher order shear deformation theory

This work addresses a static analysis of functionally graded material (FGM) plates using higher order shear deformation theory. In the theory the transverse shear stresses are represented as quadratic through the thickness and hence it requires no shear correction factor. The material property gradient is assumed to vary in the thickness direction. Mori and Tanaka theory (1973) [1] is used to represent the material property of FGM plate at any point. The thermal gradient across the plate thickness is represented accurately by utilizing the thermal properties of the constituent materials. Results have been obtained by employing a C° continuous isoparametric Lagrangian finite element with seven degrees of freedom for each node. The convergence and comparison studies are presented and effects of the different material composition and the plate geometry (side-thickness, side–side) on deflection and temperature are investigated. Effect of skew angle on deflection and axial stress of the plate is also studied. Effects of material constant n on deflection and the temperature distribution are also discussed in detail.     

Rheological properties of rubbery polymers at low shear stresses

The rheological behavior of the rubbery amorphous polymers SKB-35 (sodium-butadiene rubber), SKN-26M(butadiene-nitrile rubber), and PIB-85 (polyisobutylene) has been investigated in relation to the creep process. The tests were conducted at low shear stresses, in the constant shear stress regime, on the temperature interval from 0 to 100°C using a parallel-plate viscometer. We have shown, for the first time, by a viscometric method that in the high-elastic state rubbery polymers have a particular equilibrium structure corresponding to each temperature. A reduction in temperature leads to molecular ordering processes associated with an increase in the viscosity of the polymer. A temperature rise leads to molecular disordering and a gradual fall in viscosity. At a given temperature the two processes converge to the same value of the equilibrium viscosity. The rate of the process of equilibrium structure formation is determined not only by the temperature but also by the nature of the polymer. The higher the polarity, the more slowly the equilibrium structure is established.Moscow Lenin State Pedagogical Institute, Problem Laboratory of Polymer Physics. Translated from Mekhanika Polimerov, No. 6, pp. 970–974, November–December, 1969.     

Second-approximation shear theory for shallow layered shells and plates

Analysis of a second-approximation refined shear model for shallow layered composite shells and plates with a substantially inhomogeneous structure over the thickness is presented. The tangential displacements and corresponding normal stresses are expressed in the form of a polynomial of the fith degree in the transverse coordinate and contain squared rigidity characteristics. In this way, the accuracy of results and practical coincidence with the 3D solutions is ensured. Based on the refined model, a theory of shallow layered shells is developed. A system of resolving equations of sixteenth power together with appropriate boundary conditions was obtained and solved analytically. It is shown that the area of application of the formed model is extended as compared with the model of the first approximation. The model proposed allows us to examine the stress-strain state of layered composite structures of substantially different thickness and physical-mechanical characteristics of the layers, including the possibility of simulating relatively large shear deformations of rigid layers separated by a low-modulus thin interlayer pliable to transverse shear.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 363–370, May–June, 1998.     

Flow due to a plate that applies an accelerated shear to a second grade fluid between two parallel walls perpendicular to the plate

The velocity field and the shear stresses corresponding to the motion of a second grade fluid between two side walls, induced by an infinite plate that applies an accelerated shear stress to the fluid, are determined by means of the integral transforms. The obtained solutions, presented under integral form in term of the solutions corresponding to the flow due to a constant shear on the boundary, satisfy all imposed initial and boundary conditions. In the absence of the side walls, they reduce to the similar solutions over an infinite plate. The Newtonian solutions are obtained as limiting cases of the general solutions. The influence of the side walls on the fluid motion as well as a comparison between the two models is shown by graphical illustrations.     

Flow due to a plate that applies an accelerated shear to a second grade fluid between two parallel walls perpendicular to the plate

The velocity field and the shear stresses corresponding to the motion of a second grade fluid between two side walls, induced by an infinite plate that applies an accelerated shear stress to the fluid, are determined by means of the integral transforms. The obtained solutions, presented under integral form in term of the solutions corresponding to the flow due to a constant shear on the boundary, satisfy all imposed initial and boundary conditions. In the absence of the side walls, they reduce to the similar solutions over an infinite plate. The Newtonian solutions are obtained as limiting cases of the general solutions. The influence of the side walls on the fluid motion as well as a comparison between the two models is shown by graphical illustrations.     

The lift on a small sphere in a linear shear flow near the interface of two immiscible fluids

Analytical expressions have been derived which predict, to lowest order, the inertial lift and the lateral migration velocity of a rigid sphere translating and rotating in a linear shear flow field near the flat interface of two immiscible fluids. This asymptotic analysis is primarily based on the assumption that the two Reynolds numbers defined by the gap width between the interface and the sphere, the shear rate and the translational slip velocity with which the spherical particle moves parallel to the interface are small. Furthermore, the radius of the sphere is assumed to be small compared to the gap width. To leading order in this creeping flow regime, the linear Stokes equations are obtained and a symmetry argument can be used to show that the Stokes solution does not predict any lift force. The transverse force experienced by the sphere and its migration velocity are due to the small but finite inertial terms in the Navier-Stokes equations, which can be studied by perturbation techniques. By applying a Green's function approach and matched asymptotic methods, which also incorporate the effects of the outer Oseen-like flow regime, the three components comprising the lift velocity have been calculated in closed form: the one induced by the shear rate only, the purely slip induced one and the one due to the interaction of the slip velocity with the shear flow field. The thus obtained expressions for the case of two immiscible fluids with arbitrary density and viscosity ratios extend the results that already exist in the literature for other flow configurations, such as an unbounded shear flow field [1] or a wall-bounded one, where the wall lies either within the leading order Stokes region [2] or in the outer Oseen region [3]. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Helical flow of an Oldroyd-B fluid due to a circular cylinder subject to time-dependent shear stresses

Exact solutions corresponding to the unsteady helical flow of an Oldroyd-B fluid due to an infinite circular cylinder subject to torsional and longitudinal time-dependent shear stresses are established using Hankel transforms. These solutions, presented under series form in terms of Bessel functions J ₀(·), J ₁(·) and J ₂(·), can be easily specialized to give the similar solutions for Maxwell, Second grade and Newtonian fluids performing the same motion. Some characteristics of the motion, as well as the influence of pertinent parameters on the velocity profiles, are underlined by graphical illustrations.     

stresses and reversible deformations during shear flow of polymer solutions and melts

The influence of the accumulated elastic energy on the relationships between tangential stresses, the first difference between the normal stresses and the reversible deformations during isothermal shearing steady-state flow of polymer solutions and melts, is analyzed. It is shown that the reversible deformation in the non-Newtonian flow region is related to the tangential and normal stresses by Lodge's formula, if the thixotropic disruption of the structural flow units is accompanied by the dissipation of the elastic energy accumulated in them; the conservation of the elastic energy accumulated during the flow causes exceeding of the reversible deformation values as compared with the values calculated by Lodge's formula.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 886–895, September–October, 1972.     

A finite element formulation for the analysis of interlaminar shear stresses in layered composite plates

Fiber reinforced composite plates are often highly stressed structures. For an efficient design of such plates interlaminar stresses have to be evaluated as precisely as possible. In this paper we propose a finite element formulation for the analysis of transverse shear stresses in layered composite plates. For this purpose the equilibrium equations are exploited with appropriate shape functions in weak form which leads to a local discrete boundary value problem. Two different models to compute the derivatives of the strains are considered. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Barotropic instability of shear flows

We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop a new method to find the sharp stability conditions. We study the flow with Sinus profile in details and obtain the sharp stability boundary in the whole parameter space, which corrects previous results in the fluid literature. Our new results are confirmed by more accurate numerical computation. The addition of the Coriolis force is found to bring fundamental changes to the stability of shear flows. Moreover, we study dynamical behaviors near the shear flows, including the bifurcation of nontrivial traveling wave solutions and the linear inviscid damping. The first ingredient of our proof is a careful classification of the neutral modes. The second one is to write the linearized fluid equation in a Hamiltonian form and then use an instability index theory for general Hamiltonian partial differential equations. The last one is to study the singular and nonresonant neutral modes using Sturm-Liouville theory and hypergeometric functions.     

Analysis of laminated composite plates using higher-order shear deformation plate theory and node-based smoothed discrete shear gap method

This paper presents a novel finite element formulation for static, free vibration and buckling analyses of laminated composite plates. The idea relies on a combination of node-based smoothing discrete shear gap method with the higher-order shear deformation plate theory (HSDT) to give a so-called NS-DSG3 element. The higher-order shear deformation plate theory (HSDT) is introduced in the present method to remove the shear correction factors and improve the accuracy of transverse shear stresses. The formulation uses only linear approximations and its implementation into finite element programs is quite simple and efficient. The numerical examples demonstrated that the present element is free of shear locking and shows high reliability and accuracy compared to other published solutions in the literature.     

Modelling breakup process of a liquid drop in shear flow

The aim of this paper is to give a contribution within the mathematical modelling of the deformation and breakup of a droplet in a continuous immiscible liquid phase in impulsively started shear flow. Starting from the results of Cristini et al. [V. Cristini, S. Guido, A. Alfani, J. Blawzdziewicz, M. Loewenberg, Drop breakup and fragment distribution in shear flow, J. Rheol. 47 (5) (2003) 1283–1298] we extrapolate a general scheme for the whole breakage process, on the basis of which we formulate a procedure for the computation of the size distribution function at the end of the process.     

Determination of in-plane shear characteristics of composite materials with [±45°] layup

The shear characteristics of a composite with a [±45°] layer layup are measured experimentally by different methods. Investigations were conducted on flat and tubular specimens. The strength and shear modulus were determined by the rail method, the losipescu method, and by applying torsion to thin-wall tubes; only the shear modulus was determined by applying torsion to square plates. Determination of the shear modulus yields quantitatively comparable results, and, at the same time, the scatter of the shear-strength values of the specimens is significant. Maximum strength is achieved on the tubular specimens. The cause of the lower strength values of the flat specimens can be explained by secondary stresses and strains in their effective sections. The influence exerted by the geometry of the specimens on their strength is investigated for specimens tested by the rail and losipescu methods. It is shown that it is possible to increase the strength appreciably by varying the specimen's geometry.Institute of Polymer Mechanics. Latvian Academy of Sciences, Riga, Latvia. AERPAC Company. Netherlands. Translated from Mekhanika Kompozitmykh Materialov, Vol. 32, No. 2, pp. 256–264, March–April, 1996.