Dilatational plasticity

In Eq. (10) that gives the toughness in dilatational plasticity the factors C and A are dependent on craze microstructure and will not vary significantly. The stress and temperature dependence of the craze velocity while quite determinate in the interface convolution process of craze matter production will also be quite sensitive to micro-structural detail of phase distribution in block copolymers. The appUed stress = Y ... 

We note from the outset that crazing, which is a form of cavitational localization of deformation, can be viewed as a form of transformation plasticity made possible by the long chain molecular nature of the material and the natural molecular entanglements that give rise to well-defined cavitational transformation strains. Therefore, we have called craze plasticity also dilatational plasticity. Thus, if well managed to avoid fracture in the fibrilated craze matter, crazing can be an attractive mechanism of inelastic deformation and a source of toughness. 

Argon, A. S. (1973) Physical basis of distortional and dilatational plastic flow in glassy... 

When determining the radial displacements in the plastic zone, a plastic potential needs to be specified in advance. However, different-form plastic potentials have significant influences on dilatant plastic deformations (Zienkiewicz et al. 1975). In this study the dilatant plastic deformations are assumed to be related to stress levels. A non-linear non-associated flow rule is employed (Clausen Damkilde 2008) ... 

A. S. Argon, Physical Basis of Distortional and Dilatational Plastic Flow in Glassy Polymers , J. Macromol. Sci., Phys. B8, 573-596 (1973). 

Numerous examples of polymer flow models based on generalized Newtonian behaviour are found in non-Newtonian fluid mechanics literature. Using experimental evidence the time-independent generalized Newtonian fluids are divided into three groups. These are Bingham plastics, pseudoplastic fluids and dilatant fluids. 

A wide variety of nonnewtonian fluids are encountered industrially. They may exhibit Bingham-plastic, pseudoplastic, or dilatant behavior and may or may not be thixotropic. For design of equipment to handle or process nonnewtonian fluids, the properties must usually be measured experimentally, since no generahzed relationships exist to pi e-dicl the properties or behavior of the fluids. Details of handling nonnewtonian fluids are described completely by Skelland (Non-Newtonian Flow and Heat Transfer, Wiley, New York, 1967). The generalized shear-stress rate-of-strain relationship for nonnewtonian fluids is given as... 

Power consumption for impellers in pseudoplastic, Bingham plastic, and dilatant nonnewtonian fluids may be calculated by using the correlating lines of Fig. 18-17 if viscosity is obtained from viscosity-shear rate cuiwes as described here. For a pseudoplastic fluid, viscosity decreases as shear rate increases. A Bingham plastic is similar to a pseudoplastic fluid but requires that a minimum shear stress be exceeded for any flow to occur. For a dilatant fluid, viscosity increases as shear rate increases. 

Data for power consumption of Bingham plastic fluids have been reported and correlated by Nagata el alm) and of dilatant fluids by N.AGATA el ul.(2 ) and METZNER et al.i2V). Edwards et ai. M ) have dealt with the mixing of time-dependent thixotropic materials. 

Newtonian flow, and their viscosity is not constant but changes as a function of shear rate and/or time. The rheological properties of such systems cannot be defined simply in terms of one value. These non-Newtonian phenomena are either time-independent or time-dependent. In the first case, the systems can be classified as pseudoplastic, plastic, or dilatant, in the second case as thixotropic or rheopective. 

Polymer rheology can respond nonllnearly to shear rates, as shown in Fig. 3.4. As discussed above, a Newtonian material has a linear relationship between shear stress and shear rate, and the slope of the response Is the shear viscosity. Many polymers at very low shear rates approach a Newtonian response. As the shear rate is increased most commercial polymers have a decrease in the rate of stress increase. That is, the extension of the shear stress function tends to have a lower local slope as the shear rate is increased. This Is an example of a pseudoplastic material, also known as a shear-thinning material. Pseudoplastic materials show a decrease in shear viscosity as the shear rate increases. Dilatant materials Increase in shear viscosity as the shear rate increases. Finally, a Bingham plastic requires an initial shear stress, to, before it will flow, and then it reacts to shear rate in the same manner as a Newtonian polymer. It thus appears as an elastic material until it begins to flow and then responds like a viscous fluid. All of these viscous responses may be observed when dealing with commercial and experimental polymers. 

As discussed earlier, the Plastofrost estimate of the resolidification temperature (semicoke formation) is incorrect for MVB and LVB coals. Thus, that technique does not give the "real plastic range. The best estimate seems to come from using the Plastofrost measurement of the initial fusion temperature and the dilatometer reading of the temperature of maximum dilatation. 

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