Elastic aftereffect

It is seen from Fig. 2 that the increase of pressure to 3.0-3.5 GPa led to consecutive consolidation of samples. A growth of porosity in samples obtained at pressures higher than 3.0 GPa occurs due to elastic aftereffect. 

The key point in the rheological classification of substances is the question as to whether the substance has a preferred shape or a natural state or not [19]. If the answer is yes, then this substance is said to be solid-shaped otherwise it is referred to as fluid-shaped [508]. The simplest model of a viscoelastic solid-shaped substance is the Kelvin body [396] or the Voigt body [508], which consists of a Hooke and a Newton body connected in parallel. This model describes deformations with time-lag and elastic aftereffects. A classical model of viscoplastic fluid-shaped substance is the Maxwell body [396], which consists of a Hooke and a Newton body connected in series and describes stress relaxation. 

Such process is referred to as the elastic aftereffect and can be found in solid-like systems that reveal an elastic behavior. Elastic aftereffect is mechanically reversible the removal of applied stress results in gradual decrease of strain to zero due to the energy stored in the elastic element. The object thus restores its original shape. At the same time, in contrast to the case of a truly elastic body, the deformation of an object that follows Kelvin s model is thermodynamically irreversible due to the dissipation of energy in the... 

At lowest shear stresses the behavior of bentonite clays may be the same as that of a solid-like system with high viscosity, which is consistent with the Kelvin model and corresponds to region I. The investigation of relaxation properties of coagulation structures forming in these moderately concentrated dispersions of bentonite clays revealed the existence of an elastic aftereffect at low shear stresses. This aftereffect is related to mutual coorientation of anisometric particles that are capable of taking part in rotational Brownian motion without any rupture of contacts. Consequently, the nature of elastic aftereffect is entropic. In such systems high viscosities are related... 

This type of dependence of strain on time is referred to as the elastic aftereffect. It is schematically shown in Figure 3.11. The deformation increases at a declining rate to the limit of = Xq/G, which is determined by the elasticity modulus of Hook s element. 

The elastic aftereffect is encountered in solid-like systems with an elastic behavior. The elastic behavior is reversible when the stress is removed, the strain drops gradually to zero, that is, the initial shape of the body is restored, using the energy stored by the elastic element. However, in contrast to true elastic behavior, the elastic aftereffect is thermodynamically irreversible the dissipation of energy takes place in the viscous element. The damping of mechanical oscillations in rubber, caused by harmonic stresses, is the example of a process conforming to the Kelvin model. 

FIGURE 3.15 Spectrum of the stress relaxation and the elastic aftereffect with two components fast and slow. 

As seen in Figure 3.21, a complete rheological curve contains four characteristic regions. Region I corresponds to low stresses under which the system may demonstrate a solid-like behavior with high viscosity (Kelvin model). This case is characteristic of the already mentioned bentonite clays. The studies of relaxation structures in moderately concentrated suspensions of bentonite clays indicated the appearance of elastic aftereffect at low shear stresses. This effect has an entropic nature, as it is associated with the... 

One such study is the analysis of the nature of elastic deformation, that is, the mechanically reversible behavior of dilute clay suspensions, which find broad use in drilling muds. We will address this subject by presenting a theoretical description of the microrheology of the behavior of a coagulation structure with anisometric particles resulting from the action of small stresses. Under these conditions, the system reveals elastic aftereffect without contact rupture [18]. This phenomenon underlies the ability of clay suspensions to prevent the sedimentation of mineral particles in drilling operation when the bore is stopped. 

Mechanism of Elastic Aftereffect in Structured Dilute Suspensions of Bentonite... 

The rheology of bentonite suspensions has been studied by numerous authors. A peculiar high elasticity (the so-called elastic aftereffect) in the coagulation thixotropic structures that develop in aqueous bentonite suspensions was demonstrated in early studies by Serb-Serbina et al. [30-33]. Under constant shear stress, the strain develops in bentonite suspensions. The strain gradually increases with time and gradually decays, once the shear stress has been removed. Earlier in this chapter. 

FIGURE 3.31 Shear deformation, e, as a function of time during the elastic aftereffect at the stages of fast and slow elastic deformations. 

The processes involved in the elastic aftereffect can be described by a simple rheological model consisting of two Kelvin s elements connected in series, as shown in Figure 3.32a. It is worth emphasizing here that this model is applicable only in the region of low shear stresses, below the onset of Schwedow s creep. From this model, one gets the following values for the slow and fast elastic strain moduli ... 

FIGURE 3.32 The corresponding rheological models describing two stages of the elastic aftereffect. The two Kelvin elements connected in series (a) G, and strains are replaced with a single elasticity modulus, G i (b). 

The deformabilities at these two stages, which corresponding to the different viscous elements, Hf and are different and amonnt to V4 and respectively (Figure 3.32b). Since the time constant of the elastic aftereffect is defined as the ratio of the viscosity to the corresponding elasticity modnlns, the two corresponding viscosities are... 

The analysis of the elastic aftereffect also requires that a particular model be introduced. Let us first examine the first stage of the elastic aftereffect the fast elastic strain related to the appearance of the viscosity, tif (10 -10 )q , where q is the viseosity of water. 

Let us consider the uniform deformation of a unit volume of a disperse system under the condition of a steady-state viscoplastic flow or the slow stage of the elastic aftereffect under the action of a shear stress t. The system consists of flbers of length / and diameter d occupying the volume fraction V. The contact between the crossed flbers can be characterized by the average tangential friction force (which in turn characterizes the mean force of resistance to the shear motion in the contact), Ptg- The number of particles, v, per unit volume of the disperse system is... 

Let us further utilize the literature values of V, /, d and the contact cohesive forces [39-43]. The length / of softwood and hardwood fibers used in the experimental studies was 1-2 mm and 20 un, respectively. The consislaicy of the pulp susp sions was 1% and 2%. The experimental rheological studies conducted in the elastic aftereffect regime were performed with the constant shear stress ranging between 10 and 90 Pa. From the experimental data for 2% softwood pulp 1 = 2 mm), the shear rate... 

Aslanova, M. S. and P. A. Rehbinder. 1954. The influence of adsorption on retarded elastic aftereffect in glass. Doklady AN SSSR. 96 299. 

According to the second postulate of the Boltzmann adopted in his theory of the elastic aftereffect, and the underlying Boltzmann-Volterra model that describes the relaxation phenomena, using a function of heredity [13] action occurred in the past few strains on the stresses caused by deformation of the body at any given time, do not depend on each other and therefore algebraically added. This position has received also the name of a principle of the Boltzmann s superposition. It should be noted that the polymer body superposition principle holds in the upper-bounded the range of deformation, stress and rate of change. 

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