Testing shear modulus determination

Deformation behaviour Biaxial, parallel thread tests Shear behaviour Determination of shear modulus Relaxation behaviour... 

The continuing search to determine the shear modulus and shear strength consists of a collection of tests. Several tests are discussed because each has faults, as will be seen, and because, to some extent, there is no universal agreement on the best way to measure the shear properties. 

Another test used to determine the shear modulus and shear strength of a composite material is the sandwich cross-beam test due to Shockey and described by Waddoups [2-17]. The composite lamina... 

The shear modulus of a material can be determined by a static torsion test or by a dynamic test employing a torsional pendulum or an oscillatory rheometer. The maximum short-term shear stress (strength) of a material can also be determined from a punch shear test. 

Unlike the methods for tensile, flexural, or compressive testing, the typical procedure used for determining shear properties is intended only to determine the shear strength. It is not the shear modulus of a material that will be subjected to the usual type of... 

A test method to evaluate the shear stress capability of a seal material is reported [36], An electrolyte-anode-electrolyte trilayer was glass sealed to two metal interconnect plates as shown in Figure 5.11. Shear testing was done in two different modes, constant loading rate and constant displacement rate, to determine the shear modulus and viscosity. 

Here (pc is the volume fraction of the core and ac its radius. This equation has not been widely tested owing to a paucity of data. Thorough characterisation allows all the terms to be determined except (pm and/L. The packing fraction can be found by extrapolation to zero concentration of a plot of the high frequency shear modulus as a function of volume fraction since this corresponds to the volume fraction before the chains come into contact. The functionality of the link can be used as an adjustable parameter. For the system here a good fit is found with /l = 8/3, as shown in Figure 6.27. 

ISO 14129 1997 Fibre-reinforced plastic composites - Determination of the in-plane shear stress/shear strain response, including the in-plane shear modulus and strength, by the plus or minus 45 degree tension test method... 

The stress strain curve is recorded and the modulus determined at a shear strain of 25 %. For the quadruple test piece, the shear strain is half the measured deformation divided by the thickness of one rubber block. The shear stress is the applied force divided by twice the area of a bonded face of one block. 

The fiber modulus and matrix shear modulus are also required for the analysis. The fiber s coordinates are recorded directly from the stage controllers to the computer. The operator begins the test from the keyboard. The x and y stages move the fiber end to a position directly under the debonder tip the z stage then moves the sample surface to within 4 yum of the tip. The z-stage approach is slowed down to 0.04 jan/step at a rate of 6 steps/s. The balance readout is monitored, at a load of 2 g the loading is stopped, and the fiber end returned to the field of view of the camera. The location of the indent is noted and corrections are made, if necessary, to center the point of contact. Loading is then continued from 4 g in approximately 1 g increments. Debond is determined to have occurred when an interfacial crack is visible for 90-120° on the fiber perimeter. The load at which this occurs is used to calculate the interfacial shear stress at debond. 

The strength of adhesion between the fiber and matrix could also be expected to play a role in this change in failure mode. The interfacial testing system (ITS) provides comparative data on the interfacial shear strengths of the bare and sized E-glass fibers in real composites. A handbook value of 76 GPa [19] was used for the tensile modulus of E-glass fibers and the matrix shear modulus was previously determined as 1.10 GPa. Table 4 lists the mean interfacial shear strength, standard deviation (SD), and number of fiber ends tested for the two fiber types. 

For anisotropic materials torsion is discussed in the books by Love, Lekhnitskii175 and Hearmon185. The torque M now depends not upon one elastic constant only, as in the isotropic case, but upon two. This makes the determination of shear modulus by a torsion test a difficult task and requires careful experimentation. Early work on this for polymers was done by Raumann195, by Ladizesky and Ward205 and by Arridge and Folkes165. 

The problem of definition of modulus applies to all tests. However there is a second problem which applies to those tests where the state of stress (or strain) is not uniform across the material cross-section during the test (i.e. to all beam tests and all torsion tests - except those for thin walled cylinders). In the derivation of the equations to determine moduli it is assumed that the relation between stress and strain is the same everywhere, this is no longer true for a non-linear material. In the beam test one half of the beam is in tension and one half in compression with maximum strains on the surfaces, so that there will be different relations between stress and strain depending on the distance from the neutral plane. For the torsion experiments the strain is zero at the centre of the specimen and increases toward the outside, thus there will be different torque-shear modulus relations for each thin cylindrical shell. Unless the precise variation of all the elastic constants with strain is known it will not be possible to obtain reliable values from beam tests or torsion tests (except for thin walled cylinders). 

The test pieces are similar to that used to determine shear modulus. The results are taken by dividing the maximum force required by the total bonded area of one pair of samples. 

A variety of rheological tests can be used to evaluate the nature and properties of different network structures in foods. The strength of bonds in a fat crystal network can be evaluated by stress relaxation and by the decrease in elastic recovery in creep tests as a function of loading time (deMan et al. 1985). Van Kleef et al. (1978) have reported on the determination of the number of crosslinks in a protein gel from its mechanical and swelling properties. Oakenfull (1984) used shear modulus measurements to estimate the size and thermodynamic stability of junction zones in noncovalently cross-linked gels. 

Oakenflill et al. (1989) presented a method for determining the absolute shear modulus (E) of gels from compression tests in which the force, F, the strain or relative deformation (S/L) are measured with a cylindrical plunger with radius r, on samples in cylindrical containers of radius R, as illustrated in Figure 3-47. Assuming that the gel is an incompressible elastic solid, the following relationships were derived ... 

Oakenfull, D. G., Parker, N. S., and Tanner, R. I. 1989, Method for determining absolute shear modulus of gels from compression tests. J. Texture Stud. 19 407-417. 

The Soxhlet extraction method discussed in Section 6.6 can be used to separate the sol and gel fractions of a gel in the gelation regime, allowing direct determination of the gel fraction gel- Percolation theory expects the molar mass of a network strand M to be the same as the characteristic molar mass in the sol fraction. Hence, M can be determined by the size exclusion chromatography methods of Section 6.6, applied to the sol fraction. Equation (7.93) is tested in Fig. 7.19, where the shear modulus is shown to be proportional to Pgei/M. ... 

Elastic modulus and Poisson s ratio were determined by uniaxial compression test. Young s modulus was 31.9 GPa, Poisson s ratio was 0.27, and shear modulus was 12.6 GPa. 

Some engineers arc surprised that a standard test for determining Young s modulus is not available, despite acceptance of its limitation to low strains. An ASTM method conducted in flexure was withdrawn in 1995. For load-bearing applications more appropriate properties are shear modulus and compression modulus, from both of which. some c.sti-mate of Young s modulus can be made. 

A test method for shear modulus is described in ISO 1827 (BS90.3, Part A14). A bonded quadruple shear test piece, which may or may not have prcvk u.sly been mechanically conditioned, is deformed to a maximum shear strain of. 30%, and the result is reported as shear modulus at 25% strain. A second method in the same standard involves loading the test piece so that adhesion strength between rubber and substrate can be determined. No corresponding ASTM method is available. 

Shear modulus can be determined by a static torsion test or by a dynamic test using primarily a torsional pendulum (ASTM D 2236). Also used is an oscillatory rheometer test. The torsional pendulum is applicable to virtually all plastics and uses a simple specimen readily fabricated by all commercial fabricating processes or easily cut from fabricated part. The moduli of elasticity, G for shear and E for tension, are ratios of stress to strain as measured within the proportional limits of the material. Thus the modulus is really a measure of the rigidity for shear of a material or its stifihess in tension and compression. For shear or torsion, the modulus analogous to that for tension is called the shear modulus or the modulus of rigidity, or sometimes the transverse modulus. 

Dynamic loading problems in the offshore environment depend on either estimated or measured values of shear modulus. In practice, in situ determination of shear wave velocity on land has been used as the best approximation to the actual values for laboratory tests on samples (Richart, 1975). The techniques for using these seismic methods and data acquisition techniques to determine shear wave velocity for land-based applications have been well developed. The problem in the marine environment has been to develop methods to determine in situ shear wave velocity measurements both at the seabed surface and at known depths in the sediment column, which can be determined in a cost-effective manner. 

To solve the problem of measuring shear wave velocity in the soil column, a seismic cone penetrometer has been developed. The seismic cone contains a triaxial set of geophones (i.e., detectors) incorporated in a conventional in situ piezocone. It is typically pushed into the soil from the seabed or from the bottom of an advancing borehole. The source is typically a hydraulically driven spring hammer located on the seabed. It is ideally coupled to the sediment surface and preferentially generates horizontally polarized shear waves. It is important to decouple the drill rods and tools from the seismic cone prior to testing because compression wave energy may be transmitted. This allows the full characteristics of the soil in terms of shear modulus to be determined. 

Maximum shear modulus of soil (G ) is the fundamental property of the soil in geotechnical earthquake engineering application. The most reliable methods to determine the maximum shear modulus of soil are those conducted in the field. This is because the laboratory soil testing of undisturbed soil samples is often subjected to errors due to sample disturbance. Evenifthe disturbance is minor in advanced technique of sampling, time and expense may be substantial. Hence in the present study shear wave velocity obtained from the cross hole test is utilized to compute the maximinn shear modulus of the soil using the formula discussed earlier. 

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