Viscoplastic flow

Fluoropolymers, as well as other thermoplastics, exhibit a complicated nonlinear response when subjected to loads. The behavior is characterized by initial linear viscoelasticity at small deformations, followed by distributed yielding, viscoplastic flow, and material stiffening at large deformations until ultimate failure occurs. The response is further complicated by a strong dependence on strain rate and temperature, as illustrated in Fig. 11.1. It is clear that higher deformation rates and lower temperatures increase the stiffness of the material. 

A number of more advanced and general models attempting to predict the yielding, viscoplastic flow, time-dependence, and large strain behavior of fluoropolymers and other thermoplastics have recently been developed.in this section, we discuss the Dual Network Fluoropolymer (DNF) model. 

This will, in general, result in elastic and inelastic deformation gradients which both contain rotations. The rate of viscoplastic flow of network B is constitu-tively prescribed by... 

The rate of viscoplastic flow is captured by a simple phenomenological representation ... 

This model allows for direct simulations of the viscoplastic flow and temperature behavior of the hose in the different loading scenarios. Material parameters for the DNF model were obtained from the literature and the tension tests described above. 

As the shear stress reaches some value, xSchW(, the region of slow viscoplastic flow, known as Schwedov s region (Fig. IX-24, region II ), is observed in the system with almost undestroyed structure. In this region the shear strain is caused by fluctuational process of fracture and subsequent restoration of coagulation contacts. Due to the action of external pressures this process becomes directed in a certain way. Such mechanism of creep may be described analogously to the mechanisms of fluid flow, the description of which was developed by Ya.B. Frenkel and G. Eiring. 

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. 

In addition, a time-dependent viscoelastic component described by the so-called Voigt-Kelvin configuration, i.e. the combination of spring E and damper Yf comes into action. Further, a viscoplastic flow component may exist, modelled by the damper of viscosity... 

Quasi-viscoplastic flows of cohesionless grains, dispersive pressure support mechanism, localized, small-scale events... 

Huang XY, Liu CY, Gong HQ (1997) A viscoplastic flow modeling of ceramic tape casting. Mater Manuf Process 12 935-943... 

One unique characteristic of the borazine oligomer is that it has a very high mass yield observed upon conversion to BN. Figure 2.11 shows a thermogravimetric analysis (TGA) plot of the borazine oligomer. This data reveals that the mass yield upon conversion to BN is approximately 85% which is very high for a ceramic precursor [27]. Additional examination has revealed evidence for viscoplastic flow in the crosslinked oligomer under the application of pressure. This may increase the effective BN mass yield even further for a bulk structure such that the volume yield is between 60 and 70%. 

A) Rheological representation of the augmented HM. (B) Deformation map showing the kinematics and stress tensors used in the augmented HM. These figures illustrate how the model represents the viscoplastic flow, and how the deformation state is generalized into three dimensions. 

The stress driving the viscoplastic flow of the backstress network is obtained from the same hyperelastic representation tiiat was used to calculate tire back-stress, and has a similar framework as used in the Bergstrom-Boyce representation of crosslinked polymers at high temperatures (Bergstrom and Boyce 1998,2000) ... 

In total, the HM contains 13 material parameters 2 small strain elastic constants (E v ), 4 hyperelastic constants for the backstress network /Ia/ a, A, a)/ 5 flow constants of the backstress network (Sb, Sb/, Pbi t b), and 2 yield and viscoplastic flow parameters t c)- These parameters can... 

Yoshioka, N., K. Adachi, A. Nakamura, and H. Ishimura, An experimental investigation of viscoplastic flow past a circular cylinder at high Reynolds numbers, Rheol. Acta 74 993-1000 (1975). 

Fordham, E. J., Bittleston, S. H., and Ahmadi Tehran , M., Viscoplastic flow in centered annuli, pipes and slots, Ind. Eng. Chem. Res. iO(3) 517- 524 (1991). Worth, R. A., Accuracy of the parallel-plate analogy for representation of viscous flow between coaxial cylinders, J. Appl. Polym. Sci. 24 319-328 (1979). McKelvey, J. M., Polymer Processing, Wiley, New York, 1962. 

When the shear stress reaches a particular value, T chw. the system reveals a viscoplastic flow with an essentially preserved structure and enters the so-called Schwedow creep region (region II in Figures 3.20 and 3.21). In this region, shear is caused by the fluctuation process of the destruction and subsequent restoration of the coagulation contacts. Due to external stresses, this process becomes directional. This mechanism of creep may be considered by the analogy with the mechanism of flow of liquids developed by Frenkel [19]. 

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... 

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. 

In order to illustrate the effect that the fittings loss has in laminar viscoplastic flow, a simple system consisting of 10 m of straight 50 mm ID pipe and 5 fittings - the loss coefficient of the above diaphragm valve in laminar flow is kv=946/Re3, and for turbulent flow is constant at kv= 2.5 - is set and analysed. The fluid used for the analysis is a viscoplastic paste (xy = 100 Pa, K = 1 Pas, relative density = 1.5 and n = 1). These values were chosen so as to present a relatively simple viscoplastic rheology which would yield laminar flow in a 50 mm pipe at 3 m/ s. 

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