Shear sandwich geometry

FIGURE 10.13 Diagrammatic representation of the shear sandwich geometry. (Adapted from Dynamic Mechanical Analyser 2980 Operator s Manual, TA Instruments, New Castle, DE, 1996.)... 

The instrument for determination of shear moduli was a Rheometric Scientific dynamic mechanical thermal analyzer, model DMTA V. Round shear sandwich geometry was used. The instrument was inverted so that the sandwich fixtures and sample were in water. A water-jacketed 1000 mL Pyrex cylinder supplied by Rheometric Scientific allowed control of temperature with a circulating temperature bath. A sinusoidal linear shear was applied by moving a flat plate between two identical disk-shaped samples over a specified range of frequencies. The two identical disk-shaped samples were sandwiched between the moving plate and two 12 mm diameter plates (called studs) fastened to a frame. The dynamic frequency sweeps to obtain the loss shear modulus, G", from 0.16 Hz to 318 Hz were reported in log scale. For our purposes the applied initial static force was 0.05 N. Sample size was 12 mm diameter and 0.7 mm thickness. The sample was equilibrated at 40°C for 12 hours prior to starting the series of measurements. Shear moduli were measured from high to low temperature with an equilibration time of 2 hours at each temperature. The sequence of measurements was 40°C, 30°C, 25°C, and 15°C. 

The electrical impedance method, in which complex voltage/current ratios are measured without the need to determine absolute values of force, displacement, or velocity, can also be applied to soft solids the Fitzgerald transducer apparatus, - which uses shear sandwich geometry, is an example which provides considerable versatility and precision. 

A simple illustration is shown in Fig. 6-5 an electromagnetic drive causes periodic shearing of two discs with shear sandwich geometry. The complex ratio of driving force to velocity is the same as that given in equations 21 to 23 of Chapter 5 ... 

The geometries commonly used for measurements in instruments generating a linear or axial motion are listed in Table 2-1. With the exception of the shear sandwich, all require a solid sample. The drawings and associated formula... 

Shear Sandwich. In this geometry a rectangular sample is sheared between fixed and movable plates in a horizontal (or vertical) position. There are usually two sample sections with the movable plate situated between them. This mode of deformation is used only for very soft samples. The shear sandwich fixture is not shown in Fig. 5.49. 

FIG. 6-1. Geometries, coordinates, and dimensions for investigation of soft viscoelastic solids (in addition to those shown in Fig. 5-1). (a) simple shear sandwich (b) simple elongation (c) torsion of bar with rectangular cross-section. 

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

Suppose we want to analyze the stresses in the two stiffeners. The geometry of the sandwich-blade stiffener is actually more complicated and less amenable to analysis than is the hat-shaped stiffener. Issues that arise in the analysis to determine the influence of the various portions of the stiffeners include the in-plane shear stiffness. In the plane of the vertical blade is a certain amount of shear stiffness. That is, the shear stiffness is necfessary to transfer load from the 0° fibers at the top of the stiffener down to the panel. In hat-shaped stiffeners, that shear stiffness is the only way that load is transferred from the 0° fibers at the top of the stiffener down to the panel. Thus, shear stiffness is the dominant issue in the design. And that is why we typically put 45° fibers in the web of the hat-shaped stiffener. 

Apart from the short beam shear test, which measures the interlaminar shear properties, many different specimen geometry and loading configurations are available in the literature for the translaminar or in-plane strength measurements. These include the losipescu shear test, the 45°]5 tensile test, the [10°] off-axis tensile test, the rail-shear tests, the cross-beam sandwich test and the thin-walled tube torsion test. Since the state of shear stress in the test areas of the specimens is seldom pure or uniform in most of these techniques, the results obtained are likely to be inconsistent. In addition to the above shear tests, the transverse tension test is another simple popular method to assess the bond quality of bulk composites. Some of these methods are more widely used than others due to their simplicity in specimen preparation and data reduction methodology. 

Example 7.3 Effect of Viscosity Ratio on Shear Strain in Parallel-Plate Geometry Consider a two-parallel plate flow in which a minor component of viscosity /t2is sandwiched between two layers of major component of viscosities /q and m (Fig. E7.3). We assume that the liquids are incompressible, Newtonian, and immiscible. The equation of motion for steady state, using the common simplifying assumption of negligible interfacial tension, indicates a constant shear stress throughout the system. Thus, we have... 

As mentioned in Section 3.8, use can be made of composite beams. In a sandwich beam, such as that shown in Fig. 3.26, the core usually has lower values of Young s and shear modulus than the thin faces. The Young s modulus of the faces and core will be denoted by and E, respectively. One approach to stress analysis in these sandwich beams, is to transform the cross-section into a geometry with an equivalent flexural rigidity but consisting of a single material. This transformation is shown in Fig. 4.10 in which the core is replaced by the same material as the faceplates but with a width bE IE ). In sandwich beams, the faces are usually much thinner than the cores and the equivalent flexural rigidity can be written approximately as... 

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