Mechanical models Bingham model

A more common body is the plasto-viscoelastic, or Bingham body. Its mechanical model is shown in Figure 8-16C. When a stress is applied that is below the yield stress, the Bingham body reacts as an elastic body. At stress values beyond the yield stress, there are two components, one of which is constant and is represented by the friction ele-... 

Figure 8-16 Mechanical Models for a Plastic Body. (A) St. Venant body, (B) plasto-elastic body, and (C) plasto-viscoelastic or Bingham body.

Nonlinear models of rheological behavior can be approximated by step functions, whereby the existence of a finite yield stress G plays a dominant role. Three typical nonlinear models include the Saint-Venant model of ideal plastic behavior, the Prandtl-Reuss model of an elastoplastic material, and the Bingham model of viscoelastic behavior. The first model can be mechanically approximated by a sliding block, the second by a Maxwell element and a sliding block in series, and the third by a dash pot damping element and a sliding block in parallel (Figure 2.14). 

Phenomenologically, the behavior of polycarbonate can be represented by a mechanical model containing a friction or stick-slip element to represent yielding. Such a model was first introduced by Bingham (See Bingham, (1922) and Reiner, (1971)) to explain the behavior of certain fluids such as paint and later adapted to explain yielding in various materials including polymers with various modifications as shown in Fig, 11.15. 

The over-stress idea can be incorporated into the viscoelastic mechanical models by means of adding sliding elements to describe yield or termination points. With such an application, equations containing viscosity terms are obtained in a form similar to (24.114). For example, Brinson et al. (1975), Renieri et al. (1976), Sancaktar and Brinson (1979, 1980), Sancaktar (1981), Sancaktar and Padgilwar (1982), Sancaktar et al. (1984), and Sancaktar and Schenck (1985) used the modified Bingham model developed by Brinson (1974) to describe the shear and tensile material behavior of structural adhesives in the bulk and bonded forms ... 

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. 

Bingham, and Aul (4) described a mechanical constant flow controller similar to the Knox device. Flow controllers of this type are now commercially available from several sources, Figure 6.5 shows a cut-away of the Brooks Model 8744 flow controller. A constant high pressure is applied at the inlet (A), pushing the spring loaded diaphragm (B) downward. This closes a variable orifice (not shown). An appropriate opening of the needle valve... 

The analysis of full rheological curve illustrates how the complex mechanical behavior can be subdivided into several regions, and how within each of these regions it can be represented by a simple model that utilizes only one or two constant parameters. For this reason, such phenomena as Schwedov s creep and Bingham s viscoplastic flow, whose molecular mechanisms are so different, can be described by substantially different parameters within otherwise the same model. Such subdivision of complex behavior into a finite number of simpler constituents with particular quantitative characteristics illustrates the universal role of macrorheology. At the same time, detailed description of a mechanism involved in each of these elementary stages requires the use of molecular-kinetic concepts and may be characterized as a microrheological approach. 

Here we introduced a designation Go = -po> which corresponds to agreement about the sign of tension in the continuous mechanics. The last law is a law of flow with a limit tension of the shift (Bingham s body). This law as a limit case describes the rheology of clays, which are examined in experiments, Mitchell (1976). So, following this model we can receive the theory of the rheological properties of clays and this theory is in conformity with experimental results. 

It is found that the shear stress and yield stress of the PAG suspension are higher than those of the pure PANI suspension at the equal electric field strength. Furthermore, under electric fields, the shear stress of the PAG suspension shows a decline as a function of shear rate to a minimum value after the appearance of yield stress. The widely accepted flow model for ER suspensions, i.e., the Bingham fluid model cannot fit well the flow curves of the PAG suspension, especially in the low shear rate region (see Figure 14.8a). However, the flow curves of the pure PANI suspension maintain a relatively stable level, which can be fitted by the Bingham fluid model (see Figure 14.8b). This different flow behavior reflects that the PAG sheets possess a different ER response from the pure PANI particles under the simultaneous effect of both electrical and mechanical fields. In addition. 

Bingham RC, Dewar MJS, Lo DH. Ground states of molecules. 25. MINDO-3 Improved version of MINDO semiempirical SCF-MO method. J Am Chem Soc. 1975 97 1285-93. Dewar MJS, Zoebisch EG, Healy EF. Development and use of quantum mechanical molecular models. 76. AMI a new general purpose quantum mechanical molecular model. J Am Chem Soc. 1985 107 3902 9. 

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