Shear deformation, resistance

The shear deformation potential for the (111) and (100) valley minima determined by fits to the data of Fig. 4.10 are shown in Table 4.5 and compared to prior theoretical calculations and experimental observations. The deformation potential of the (111) valley has been extensively investigated and the present value compares favorably to prior work. The error assigned recognizes the uncertainty in final resistivity due to observed time dependence. The distinguishing characteristic of the present value is that it is measured at a considerably larger strain than has heretofore been possible. Unfortunately, the present data are too limited to address the question of nonlinearities in the deformation potentials [77T02]. 

However, this expression assumes that the total resistance to flow is due to the shear deformation of the fluid, as in a uniform pipe. In reality the resistance is a result of both shear and stretching (extensional) deformation as the fluid moves through the nonuniform converging-diverging flow cross section within the pores. The stretching resistance is the product of the extension (stretch) rate and the extensional viscosity. The extension rate in porous media is of the same order as the shear rate, and the extensional viscosity for a Newtonian fluid is three times the shear viscosity. Thus, in practice a value of 150-180 instead of 72 is in closer agreement with observations at low Reynolds numbers, i.e.,... 

Neglecting the elastic forces, lumping the geometric factors into a constant, b, and assuming the plastic shear deformation is x/r, yields the plastic resistive force ... 

Hardness measures the resistance of a material to a permanent change of shape. That is, the resistance to shear deformation (not the resistance to a volume change). The precursor to a permanent shape change is a temporary elastic shape change, and a shear modulus determines this. Therefore, the first necessity for high hardness is a high shear modulus. 

From these results and those in Figures 7a and 7b the following can be concluded about the effects of silicone block introduction at intermediate temperatures the resistance to craze initiation is reduced by 60-70%, the resistance to shear deformation by 40-50%, and the resistance to craze fracture by about 40%. Thus both modes of plastic deformation are made easy relative to brittle failure. The origins of... 

As entanglement density increases, the craze stress rises, shear deformation becomes more favorable, the extension ratio of craze fibrils and of shear deformation zones reduce, and average fatigue life and resistance to fatigue crack propagation are enhanced. 

FCP resistance for the SINs increases with PU content up to 50% and is better in the prepolymer material than in the one-shot material, since the former always has larger values of percent energy absorption. With respect to micromechanisms of failure, the generation of discontinuous growth bands associated with shear yielding is involved in the SINs from the one-shot procedure. On the other hand, the fracture surfaces of the SINs from the prepolymer procedure show extensive stresswhitening phenomenon which is associated with the cavitation around PU domains and localized shear deformation. 

As a quantitative measure of the extent to which a confined phase is capable of resisting a shear deformation, we introduce in Section 5.6.2 the shear stress Txz. For a fluid bridge a typical shear-stress curve r (aSxo) is plotted in Fig. 5.18. Regardless of the thermodynamic state and the thickness (i.e., s ) of a bridge phase, a typical stress curve exhibits the following features ... 

Steady-state shear rheology typically involves characterizing the polymer s response to steady shearing flows in terms of the steady shear viscosity (tj), which is defined by the ratio of shear stress (a) to shearing rate y ). The steady shear viscosity is thus a measure of resistance to steady shearing deformation. Other characteristics such as normal stresses (Ai and N2) and yield stresses (ffy) are discussed in further detail in Chapter 3. 

Dynamic shear rheology involves measuring the resistance to dynamic oscillatory flows. Dynamic moduli such as the storage (or solid-like) modulus (G ), the loss (or fluid-like) modulus (G"), the loss tangent (tan 8 = G"IG ) and the complex viscosity ( / ) can all be used to characterize deformation resistance to dynamic oscillation of a sinusoidally imposed deformation with a characteristic frequency of oscillation (o). 

The modulus is the most important small-strain mechanical property. It is the key indicator of the "stiffness" or "rigidity" of specimens made from a material. It quantifies the resistance of specimens to mechanical deformation, in the limit of infinitesimally small deformation. There are three major types of moduli. The bulk modulus B is the resistance of a specimen to isotropic compression (pressure). The Young s modulus E is its resistance to uniaxial tension (being stretched). The shear modulus G is its resistance to simple shear deformation (being twisted). 

In flexure or shear, as in the previous case of compression, plastics reinforced with short fibers are probably better than those with continuous fibers, because in the former with random orientation of fibers at least some of the fibers will be correctly aligned to resist the shear deformation. However, with continuous-fiber reinforcement if the shear stresses are on planes perpendicular to the continuous fibers, then the fibers will offer resistance to shear deformation. Since high volume fraction (f>() can be achieved with continuous fibers, this resistance can be substantial. 

Membrane shear modulus A measure of the elastic resistance of the membrane to surface shear deformation that is, changes in the shape of the surface at constant surface area (Equation 60.8). (Units 1 mN/m = 1 dyn/cm)... 

Viscosity is a measure of the resistance of a liquid to shear deformation, i.e., a measure of the ratio between the applied shearing force and the rate of flow of the liquid. If a tangential force difference, F, is applied to two parallel planes of area. A, which are separated by a distance, d, the viscosity, r, is given by the expression ... 

For solid films Le., films with a shear modulus), there is an additional resistance to bending arising from the resistance to shear deformations. This results in a nonzero curvature modulus even for a system which is elastically isotropic in the bulk. As shown below, this is not the case for systems with zero shear modulus isotropic fluids show no resistance to bending deformations. 

A low value of Poisson s ratio implies a high resistance to shear deformation. True or False ... 

---