Simple shear geometry

Fig. 18. The simple shear geometry used to characterise the interfacial friction the fluid thickness is e. The top plate limiting the sample is translated at the velocity and transmits this velocity to the fluid. The bottom plate is immobile, and the local velocity of the fluid at the bottom interface is Vs. The fluid is submitted to a simple shear, with a shear rate y = (Vt-VsYe. The velocity profile extrapolates to zero at a distance b below the interface, with...

The only observation of a stick-slip transition in a simple shear geometry is the unique experimental study of Laun [39]. This controlled stress experiment not only observed a stick-slip transition but also explicitly recorded the time scale (a few milliseconds) on which the boundary condition (BC) evolved from... 

The above description refers to a Lagrangian frame of reference in which the movement of the particle is followed along its trajectory. Instead of having a steady flow, it is possible to modulate the flow, for example sinusoidally as a function of time. At sufficiently high frequency, the molecular coil deformation will be dephased from the strain rate and the flow becomes transient even with a stagnant flow geometry. Oscillatory flow birefringence has been measured in simple shear and corresponds to some kind of frequency analysis of the flow... 

Data can be obtained from tests in uniaxial tension, uniaxial compression, equibiaxial tension, pure shear and simple shear. Relevant test methods are described in subsequent sections. In principle, the coefficients for a model can be obtained from a single test, for example uniaxial tension. However, the coefficients are not fully independent and more than one set of values can be found to describe the tension stress strain curve. A difficulty will arise if these coefficients are applied to another mode of deformation, for example shear or compression, because the different sets of values may not be equivalent in these cases. To obtain more robust coefficients it is necessary to carry out tests using more than one geometry and to combine the data to optimize the coefficients. 

Measurements of Viscosity and Elasticity in Shear (Simple Shear) Shear viscosity J] and shear elasticity G are determined by evaluating the coefficients of the variables x and x, respectively, which result when the geometry of the system has been taken into account. The resulting equation of state balances stress against shear rate y (reciprocal seconds) and shear y (dimensionless) as the kinematic variables. For a purely elastic, or Hookean, response ... 

Fig. 1 At the level of the approximation we use in this chapter, all experimental shear geometries are equivalent to a simple steady shear. We choose our system of coordinates such that the normal to the plates points along the z-axis and the plates are located at z = j. Between two parallel plates we assume a defect-free well aligned lamellar phase. The upper plate moves with the velocity in positive x direction, the lower plate moves with the same velocity in negative A direction. The y-direction points into the xz-plane. We call the plane of the plates Cry-plane) the shear plane, the x-direction the flow direction, and the y-direction the vortidty direction...

For a simple geometry (/ = 0) undergoing simple shear flow, the above equation simplifies to... 

The aim of the present work has been to establish correlations between bulk macroscopic response of polymer melts under flow and the behaviour at a molecular level as seen by SANS, and to discuss the results in the frame of molecular theories. Two simple and well defined geometries of deformation have been investigated uniaxial elongation and simple shear. The... 

In cone-plate geometry, the velocity field of a simple shearing flow has the following components in a spherical coordinate system (2,23,29) ... 

The stress in viscoelastic liquids at steady-state conditions is defined, in simple shear flow, by the shear rate and two normal stress differences. Chapter 13 reviews the evolution of both the normal stress differences and the viscosity with increasing shear rate for different geometries. Semiquantitative approaches are used in which the critical shear rate at which the viscosity starts to drop in non-Newtonian fluids is estimated. The effects of shear rate, concentration, and temperature on die swell are qualitatively analyzed, and some basic aspects of the elongational flow are discussed. This process is useful to understand, at least qualitatively, the rheological fundamentals of polymer processing. 

A first step in the validation of this approach is to test simple specimens under controlled conditions and to compare predictions with measured failure load values. First lap shear geometries were examined, then an L-geometry was studied in more detail. The bond-line in these small specimens was very similar to that in the quasi-unidirectional fracture specimens as the small dimensions allow panels to be pressed uniformly after assembly (which is not the case for industrial top-hat stiffeners). 

Figure 2-9. A number of simple flow geometries, such as concentric cylinder (Couette), cone-and-plate, and parallel disk, are commonly employed as rheometers to subject a liquid to shear flows for measurement of the fluid viscosity (see, e.g., Fig. 3-5). In the present discussion, we approximately represent the flow in these devices as the flow between two plane boundaries as described in the text and sketched in this figure.

The mechanical properties discussed above all have the major common feature of being measured by deforming a specimen continuously at a given rate until it fails. The deformation mode (uniaxial tension, uniaxial compression, plane strain compression, or simple shear) may vary, but these differences can be roughly taken into account by imposing criteria (such as yield criteria) to describe the stress states imposed on specimens by different deformation geometries. 

Figure 4 Standard lap shear geometries (a) simple lap joint test, ASTM D-1002 (b) laminated lap shear joint test, ASTM D-3165 (c) double lap joint test, ASTM D-3528.

The corresponding relation is shown in Figure 1.8. It illustrates a general feature of the elastic behavior of mbbery solids although the constituent chains obey a linear force-extension relationship (Fq. (1.1)), the network does not. This feature arises from the geometry of deformation of randomly oriented chains. Indeed, the degree of nonlinearity depends on the type of deformation imposed. In simple shear, the relationship is predicted to be a linear one with a... 

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