Shear, pure

Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity identified and measured are uniaxial or simple, biaxial, and pure shear. Uniaxial viscosity is the only one used to characterize fluids. It has been employed mainly in the study of polymer melts, but also for other fluids. For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity ... 

Extensional Viscosity. AH three types of extensional viscosity can be measured (101,103) uniaxial, biaxial, and pure shear. Only a few commercial instmments are available, however, and most measurements are made with improvised equipment. Extensional viscosity of polymer melts can be estimated from converging flow (entrance pressure) or from a melt strength drawdown test (208). 

For ductile materials subjected to pure shear, the reliability is the probabilistic requirement to avoid shear yielding ... 

Assuming that an adequate transition fit is speeified for both the pin hole and eoupling bore, the pin is in double pure shear with the bore of the eoupling, and so the shear stress, L, is given by ... 

Shear strength is measured via a simple single overlap shear specimen of standard dimensions (Fig. 9). In contrast to its simple appearance, the forces in a thin-adherend shear specimen can be quite complex due to the inherent offset loading of the specimen and subsequent bending in the substrates. The single overlap shear test is anything but a pure shear test, but the configuration is easy to manufacture, simple to test and is firmly entrenched in the industry as a primary examination technique for materials qualifications, inspection and process control. 

Engineering constants (sometimes known as technical constants) are generalized Young s moduli, Poisson s ratios, and shear moduli as well as some other behavioral constants that will be discussed in Section 2.6. These constants are measured in simple tests such as uniaxial tension or pure shear tests. Thus, these constants with their obvious physical interpretation have more direct meaning than the components... 

Accordingly, we have supposedly found the shear modulus G.,2. However, a relationship such as Equation (2.107) does not exist for strengths because strengths do not transform like stiffnesses. Thus, this experiment cannot be relied upon to determine S, the ultimate shear stress (shear strength), because a pure shear deformation mode has not been excited with accompanying failure in shear. Accordingly, other approaches to obtain S must be used. 

Find the Tsai-Hill failure criterion for pure shear loading at various angles B to the principal material directions, i.e., the shear analog of Equation (2.134). 

The stress-intensity factors are quite different from stress concentration factors. For the same circular hole, the stress concentration factor is 3 under uniaxial tension, 2 under biaxiai tension, and 4 under pure shear. Thus, the stress concentration factor, which is a single scalar parameter, cannot characterize the stress state, a second-order tensor. However, the stress-intensity factor exists in all stress components, so is a useful concept in stress-type fracture processes. For example. 

In crystals with the LI2 structure (the fcc-based ordered structure), there exist three independent elastic constants-in the contracted notation, Cn, C12 and 044. A set of three independent ab initio total-energy calculations (i.e. total energy as a function of strain) is required to determine these elastic constants. We have determined the bulk modulus, Cii, and C44 from distortion energies associated with uniform hydrostatic pressure, uniaxial strain and pure shear strain, respectively. The shear moduli for the 001 plane along the [100] direction and for the 110 plane along the [110] direction, are G ooi = G44 and G no = (Cu — G12), respectively. The shear anisotropy factor, A = provides a measure of the degree of anisotropy of the electronic charge... 

Rheology is the science that deals with the deformation and flow of matter under various conditions. The rheology of plastics, particularly of TPs, is complex but understandable and manageable. These materials exhibit properties that combine those of an ideal viscous liquid (with pure shear deformations) with those of an ideal elastic solid (with pure elastic deformation). Thus, plastics are said to be viscoelastic. 

FIGURE 25.6 Examples of variable ampUtude fatigue crack growth test signals applied to pure shear specimens to investigate the effects of (a) load severity, (b) load sequence, (c) R-ratio, and (d) dwell periods on crack growth rates. A, B, and C denote peak strain levels. 

Figure 3. Modulus contributions from chemical cross-links (Cx, filled triangles) and from chain entangling (Gx, unfilled symbols) plotted against the extension ratio during cross-linking, A0, for 1,2-polybutadiene. Key O, GN, equibiaxial extension , G.v, pure shear A, Gx, simple extension Gx°, pseudo-equilibrium rubber plateau modulus for a polybutadiene with a similar microstructure. See Ref. 10.

The two-network method has been carefully examined. All the previous two-network results were obtained in simple extension for which the Gaussian composite network theory was found to be inadequate. Results obtained on composite networks of 1,2-polybutadiene for three different types of strain, namely equibiaxial extension, pure shear, and simple extension, are discussed in the present paper. The Gaussian composite network elastic free energy relation is found to be adequate in equibiaxial extension and possibly pure shear. Extrapolation to zero strain gives the same result for all three types of strain The contribution from chain entangling at elastic equilibrium is found to be approximately equal to the pseudo-equilibrium rubber plateau modulus and about three times larger than the contribution from chemical cross-links. 

Under the best of conditions, single lap joint samples do not fail in pure shear due to the tensile and peel forces present at the ends of the overlap. These non-shear forces are exacerbated when using thin gauge adherends. Because of this, the lap joint dimensions as well as the testing rate were modified from the ASTM D-1002 standard as a result of earlier work on thin gauge steel adherends. 

This test has an inherent problem associated with the stress concentration and the non-linear plastic deformation induced by the loading nose of small diameter. This is schematically illustrated in Fig 3.17, where the effects of stress concentration in a thin specimen are compared with those in a thick specimen. Both specimens have the same span-to-depth ratio (SDR). The stress state is much more complex than the pure shear stress state predicted by the simple beam theory (Berg et al., 1972 ... 

Note 4 For a pure shear deformation or flow the stresses (an, 022, C733) are usually all different from each other. 

Note 5 The stress tensor resulting from a pure shear deformation or flow is called a pure shear stress. 

In situ dynamic ETEM studies in controlled environments of oxide catalysts permit direct observations of redox pathways under catalytic reaction conditions and provide a better fundamental understanding of the nucleation, growth and the nature of defects at the catalyst surface and their role in catalysis (Gai 1981-1982 92). The following paragraphs describe the methods of observation and quantitative analyses of the surface and microstmctural changes of the catalyst, and correlation of microstmctural data with measurements of catalytic reactivity. We examine examples of pure shear and crystallographic (CS) shear defects that occur under catalytic conditions. 

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