Shear modulus yield point

The use of a rotating vane has become very popular as a simple to use technique that allows slip to be overcome (33,34). Alderman et al (35) used the vane method to determine the yield stress, yield strain and shear modulus of bentonite gels. In the latter work it is interesting to note that a typical toique/time plot exhibits a maximum torque (related to yield stress of the sample) after which the torque is observed to decrease with time. The fall in torque beyond the maximum point was described loosely as being a transition from a gel-like to a fluid-like behavior. However, it may also be caused by the development of a slip surface within the bulk material. Indeed, by the use of the marker line technique, Plucinski et al (15) found that in parallel plate fixtures and in slow steady shear motion, the onset of slip in mayonnaises coincided with the onset of decrease in torque (Fig. 8). These authors found slip to be present for... 

The width of the lap shear specimen is generally 1 in. The recommended length of overlap, for metal substrates of 0.064-in thickness, is 0.5 + 0.05 in however, it is recommended that the overlap length be chosen so that the yield point of the substrate is not exceeded. In lap shear specimens, an optimum adhesive thickness exists. For maximum bond strengths, the optimum thickness varies with adhesives of different moduli (from about 2 mils for high-modulus adhesives to about 6 mils for low-modulus adhesives).5... 

Figure 29. Storage shear modulus vs. frequency for System 1. The points are experimental, uncorrected for the apparent yield stress, the lines computed from the relaxation spectrum.

Table 5.4 Comparison of shear modulus C44 from molecular expression and yield-point location (see text).

Compression Load Perpendicular to Rise PSI At Yield Point At 10 S Deflection Compression Modulus PSI Flexural Strength PSI Flexural Modulus PSI Shear Strength PSI Shear Modulus PSI... 

The Doi-Edwards theory of linear viscoelasticity predicts 1.2 for JeG, where is the plateau shear modulus. This value is significantly lower than typical experimental values found in the range 2—4 [3, 71]. This defect of the Doi-Edwards theory, along with its failure of predicting the 3.4 power law for viscosity, has been pointed out by Osaki and Doi [72]. It is associated with the fact that the Doi-Edwards theory yields a relaxation time distribution which is too narrow compared with observed ones [69]. Modifications of the Doi-Edwards theory have been made so as to bring JeG closer to measured values, but no remarkable success has as yet been achieved. 

On the other hand materials deform plastically only when subjected to shear stress. According to Frenkel analysis, strength (yield stress) of an ideal crystalline solid is proportional to its elastic shear modulus [28,29]. The strength of a real crystal is controlled by lattice defects, such as dislocations or point defects, and is significantly smaller then that of an ideal crystal. Nevertheless, the shear stress needed for dislocation motion (Peierls stress) or multiplication (Frank-Read source) and thus for plastic deformation is also proportional to the elastic shear modulus of a deformed material. Recently Teter argued that in many hardness tests one measures plastic deformation which is closely linked to deformation of a shear character [17]. He compared Vickers hardness data to the bulk and shear... 

For concentrated emulsions and foams, Princen [182, 183] proposed a stress-strain theory based on a two-dimensional cell model. Consider a steady state shearing of such a system. Initially, at small values of strain, the stress increases linearly as in elastic body. As the strain increases, the stress reaches a yield point, and then at higher deformation it catastrophically drops to negative values. The reason for the latter behavior is the creation of unstable cell structure that relaxes by recoil. For real emulsions the shear modulus and yield stress are expected to follow the expressions ... 

We have already mentioned that a widely used plot of the experimental results in uniaxial extension is the Mooney one. The straight line obtained by fitting the experimental points with a irasl-squares analysis can be extrapolated to infinite ddbrmation (k = 0) and the value of the reduced force is then 2Cj. In a similar nmnno, the extrapolation to zero deformation = 1) leads to (2C, + 2Q) which is not far from the shear modulus G recorded by measurements at small deformations. The constant 2C2 is the slope of the line. An extensive review of 2Ci and 2Cj by Mark on a great number of elastomeric networks didn t yield an unamlngous molecular explanation of these two parameters. Both Ferry and Graessley however,... 

Other estimates of the ultimate shear strength of amorphous polymers have been made by a number of authors and generally all fall within a factor of 2 of each other (38,77,78). Stachurski (79) has expressed doubt as to the validity of the concept of an intrinsic shear strength based on the value of the shear modulus, G, for an amorphous solid. He questions which modulus is the correct value to use— the initial small strain value or the value at higher strain (the yield point or the ultimate extension). Further, the temperature and strain-rate dependence of both the yield strength and modulus (however defined) suggests that perhaps the ratio of yield strength to modulus is not a true intrinsic material property. We remark however that the temperature and strain-rate dependence of both the yield stress and the shear modulus are often similar. 

In Section 3.1, we examined the mechanical properties of disperse systems that were capable of undergoing viscoplastic flow. In these cases, we considered the stressed state of shear with its characteristic parameters G, ti, and t. The strength of such systems could be characterized by the yield point. When we shift to describing the mechanical behavior of compact and primarily elastic-brittle solids, it is worth using the stressed state of a uniaxial extension in which we replace the shear stress, T, with the extension stress, / the shear modulus G with Young s modulus, E and the resistance to tear, P, with the yield stress, t, as the strength characteristic. 

Figure 12.29 Ratio of shear yield stress to shear modulus as a function of temperature at different strain rates, for amorphous polyethylene terephthalate. Points from unpublished data of Foot and Ward, curves from Argon theory. Strain rates X, 1.02 x CPs +, 21.4 s - V,...

The two basic deformation mechanisms in a polymer are by shear yielding and crazing. In a composite system, such as the MIM feedstock, an additional mechanism, dewetting, is observed [75]. The yield point is actually due to crazing effect or a dewetting effect in which the particle-matrix interface is destroyed and resulting in a dramatic drop in the modulus of the material [59]. 

The increase in gel strength with increase in bentonite concentration above the gel point is consistent with the increase in yield value and modulus. On the other hand, the limited creep measurements carried out on the present suspension showed a high residual viscosity Oq of the order of 9000 Nm s when the bentonite concentration was 45g dm. As recently pointed out by Buscall et al (27) the settling rate in concentrated suspensions depends on 0. With a model system of polystyrene latex (of radius 1.55 vim and density 1.05 g cm ) which was thickened with ethyl hydroxy ethyl cellulose, a zero shear viscosity of lONm was considered to be sufficient to reduce settling of the suspension with = 0.05. The present pesticide system thickened with bentonite gave values that are fairly high and therefore no settling was observed. 

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