Shear strain imposition

A key element in the experimental determination of the stiffness and strength characteristics of a lamina is the imposition of a uniform stress state in the specimen. Such loading is relatively easy for isotropic materials. However, for composite materials, the orthotropy introduces coupling between normal stresses and shear strains and between shear stresses and normal and shear strains when loaded in non-principal material coordinates for which the stress-strain relations are given in Equation (2.88). Thus, special care must be taken to ensure obtaining... 

Nevertheless, if one assumes a static, rather than a thermodynamic, equilibrium, one can attempt to estimate the dependence of the yield stress Oy and the modulus G on the shape and depth of the interparticle potential. Imagine that a gel is subjected to a shear strain Y that homogeneously displaces particles from their positions of static equilibrium. Pairs of particles are pulled apart by this strain, and separations between particle centers of mass should increase roughly by an amount yrQ, where ro = 2a + Dq is the separation between centers of mass in the absence of strain. Hence, the imposition of a strain y increases the gap between particle surfaces from Dq to... 

Dynamic testing is the most commonly used one in the study of polymer properties. Because of its widespread usage, dynamic data have been analyzed in terms of six different functions, as opposed to a single one in stress relaxation and creep. The experiment involves (1) imposition (on a specimen of the material) of either a shear stress or a shear strain which varies sinusoidally with time, and (2) study of the corresponding response. 

FIGURE 6.17 (Bottom) Birefringence for uncrosslinkedPIB after imposition of a shear strain = 2.5. Linear fitting yields 3.07 GPa - for the stress optical coefficient. (Top) Ratio of refractive index components (1 is the flow direction and 2 the direction of the gradient), which equals the value of the shear strain, in accord with the Lodge-Meissner relation (Eq. (6.66)) (Balasubramanian et al., 2005). 

FIGURE 6.18 Normalized difference in thermal diffusivity versus normalized birefringence for polyisobutylene after imposition of a shear strain = 8. The line is the linear fit to the data (Venenis etal., 1999). 

Yamamoto and Onuki found that an externally applied shear strain rate caused strong shear thinning when the shear rate exceeded the inverse relaxation time associated with the slow (a-process) relaxation. " They investigated the disruption of the microstructure (measured by close neighbour separations or bonds ) of the supercooled liquid by the imposition of a shear rate. The bond breakage time, Tb, in ambient and sheared conditions can be fitted to... 

In the field of rubber elasticity both experimentalists and theoreticians have mainly concentrated on the equilibrium stress-strain relation of these materials, i e on the stress as a function of strain at infinite time after the imposition of the strain > This approach is obviously impossible for polymer melts Another complication which has thwarted the comparison of stress-strain relations for networks and melts is that cross-linked networks can be stretched uniaxially more easily, because of their high elasticity, than polymer melts On the other hand, polymer melts can be subjected to large shear strains and networks cannot because of slippage at the shearing surface at relatively low strains These seem to be the main reasons why up to some time ago no experimental results were available to compare the nonlinear viscoelastic behaviour of these two types of material Yet, in the last decade, apparatuses have been built to measure the simple extension properties of polymer melts >. It has thus become possible to compare the stress-strain relation at large uniaxial extension of cross-linked rubbers and polymer melts ... 

Figure4.4.1 shows the shear stress modulus G y, 0 = fn/y as a function of time after imposition of a step shear strain for a commercial low density polyethylene. This particular batch of...

As seen earlier in Problem 12.3 of Chapter 12 and more recently in Figure 14.2, the stress in a polymeric fluid does not decay to zero once deformation is halted. Instead, stress relaxation occurs. Thus, upon imposition of a shear strain y, we expect the shear stress r to be... 

Figure 10.15 Damping of shear stress and reversal of damping as a function of time after startup of shearing in a cone-and-plate rheometer at y = 8 seer for a tumbling nematic, 8CB. In (a) the shearing direction is reversed after imposition of 170 strain units the damping of the stress nscillatinns is rp.vp.rsed. In (h), shear reversal occurs after imposition of 480 strain iiniK fhp damping is not reversed. (From Gu et al. 1993, with permission from the Journal of Rheology.)...

After imposition of a step strain, the ratio of the first normal stress difference, Ni, to the shear stress is equal to the strain, or... 

Laminar mixing is achieved by subjecting the polymer to permanent deformation involving shear, squeeze or elongational flow. In the melt-state, imposition of large strains is accompanied by an increase in the interfacial area between material and system. Laminar mixing is influenced strongly by the initial orientation and location of interfacial elements or additives [3]. 

Factorization of the function concentrated polystyrene solution, time-strain factorability is not valid at short times after the imposition of the step shear. An accurate K-BKZ constitutive equation for shearing flows of this material will be much more complex than that for melt I. Furthermore, in strain histories in which a strain reversal takes place, such as constrained recoil (Wagner and Laun, 1978) or double-step strains with the second strain of sign opposite the first (Doi, 1980 Larson and Valesano, 1986), good agreement... 

Chapter 14 sketches nonlinear properties of polymer solutions, some classical and some quite modem. Strange behaviors can arise in polymer solutions because the normal stress differences are nonzero, i.e., the diagonal components of the pressure tensor can be unequal. Memory effect properties, such as stress and strain relaxations, and responses to imposing multiple strains, are noted. Finally we consider very recent developments in the study of nonlinear effects, such as shear banding and nonquiescent relaxation following imposition of a sudden strain. 

Memory effects are revealed by experiments in which a complex fluid is subject to a time-dependent shear rate. Included under this rubric are measurements of the startup stress when a constant shear rate is suddenly imposed on an initially stationary system, and the stress when a system subject to some nonzero constant rate of strain suddenly has the rate of strain increased, decreased, or reversed. A prominent feature in measurements of stress on sudden imposition of a large rate of strain is stress overshoot, in which the stress first increases to a value much larger than its steady-state value, and then relaxes back to its steady-state value. Contrariwise, if the shear rate applied to a polymer fluid is held constant for a long time and then suddenly reduced, the stress may show undershoot the stress declines to a value well below its steady-state value and then increases back to its steady-state value. Related features have been seen for N. Bird, et al. also note measurements on responses to superposed flows, in particular the combination of a constant rate of shear flow with an oscillatory shear parallel or perpendicular to the constant shear(7). Bird, et al. further assert that multiple oscillations around the steady-state stress are sometimes observed before the steady state is attained. Recent studies involving step strains or oscillatory shear superposed on steady shear are reported by Li and Wang(8). 

Studies of stress overshoot on sudden imposition of constant rate of strain include Osaki, etal. 0) and Inoue, etal. ). Osaki, etal. also report the time dependence of N. Inoue, et al. note a potential artifact perturbing stress measurements, namely shear-induced phase separation. Representative experiments on double strain rates are presented by Oberhauser, et al. 2) and by Wang and Wang(13). The observed stress has a complex time dependence including overshoot and undershoot ... 

As would be expected, the imposition of compressive, shear, or torsional stresses also evokes elastic behavior. The stress-strain characteristics at low stress levels are virtually the same for both tensile and compressive situations, to include the magnitude of the modulus of elasticity. Shear stress and strain are proportional to each other through... 

The response to any deformation that is either very small in its totality, or occurs at very low strain rates, is given by Eq. 4.4. For example, the shear stress, o t) following the sudden imposition at time 0 of shearing at a steady rate, /, is given by ... 

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