Plastic shear flow

Maloney, C. and Lemaitre, A. (2004a) Sub-extensive scaling in the athermal, quasistatic limit of amorphous matter in plastic shear flow, Phys. Rev. Lett., 93, 0160001 (1 ). 

We develop first the considerations related to shear response in a ID context of plastic-shear flow to state the basic kinetic response of the solid, where s stands for an applied shear stress, t stands for a threshold plastic-shear resistance, and y is taken to be the plastic-shear strain yP. As a useful simplification, we first consider the material to be rigid on the basis that the plastic-shear increments are large, in comparison with the elastic-strain increments. At temperatures T > OK, for which the elastic moduli of the solid are significantly lower than at 0 K, we expect that the rate-independent plastic-shear resistance z temperature dependence as the elastic-shear modulus (Chapter 4). Then, where the plastic response in a rate-independent manner is initiated when s = z(T), under conditions of s < z T), a plastic response is still possible by thermal assistanee and occurs at a (plastic) shear rate of (Argon 1973)... 

G. Mandl and R. F. Luque. "Fully developed plastic shear flow of granular materials," /. Geotechnique, 20(3), 277-307, 1970. 

Plastic Forming. A plastic ceramic body deforms iaelastically without mpture under a compressive load that produces a shear stress ia excess of the shear strength of the body. Plastic forming processes (38,40—42,54—57) iavolve elastic—plastic behavior, whereby measurable elastic respoase occurs before and after plastic yielding. At pressures above the shear strength, the body deforms plastically by shear flow. 

Bai [48] presents a linear stability analysis of plastic shear deformation. This involves the relationship between competing effects of work hardening, thermal softening, and thermal conduction. If the flow stress is given by Tq, and work hardening and thermal softening in the initial state are represented... 

For Newtonian fluids the dynamic viscosity is constant (Equation 2-57), for power-law fluids the dynamic viscosity varies with shear rate (Equation 2-58), and for Bingham plastic fluids flow occurs only after some minimum shear stress, called the yield stress, is imposed (Equation 2-59). 

Similar folds—fo ds that have the same geometric form, but where shear flow in the plastic beds has occurred (sec Figure 2-4.5). 

From the results obtained in [344] it follows that the composites with PMF are more likely to develop a secondary network and a considerable deformation is needed to break it. As the authors of [344] note, at low frequencies the Gr(to) relationship for Specimens Nos. 4 and 5 (Table 16) has the form typical of a viscoelastic body. This kind of behavior has been attributed to the formation of the spatial skeleton of filler owing to the overlap of the thin boundary layers of polymer. The authors also note that only plastic deformations occurred in shear flow. 

When reviewing the subject of plastic melt flow, the subject of viscosity is involved. Basically viscosity is the property of the resistance of flow exhibited within a body of material. Ordinary viscosity is the internal friction or resistance of a plastic to flow. It is the constant ratio of shearing stress to the rate of shear. Shearing is the motion of a fluid, layer by layer, like a deck of cards. When plastics flow through straight tubes or channels they are sheared and the viscosity expresses their resistance. 

The plastic deformation patterns can be revealed by etch-pit and/or X-ray scattering studies of indentations in crystals. These show that the deformation around indentations (in crystals) consists of heterogeneous rosettes which are qualitatively different from the homogeneous deformation fields expected from the deformation of a continuum (Chaudhri, 2004). This is, of course, because plastic deformation itself is (a) an atomically heterogeneous process mediated by the motion of dislocations and (b) mesoscopically heterogeneous because dislocation motion occurs in bands of plastic shear (Figure 2.2). In other words, plastic deformation is discontinuous at not one, but two, levels of the states of aggregation in solids. It is by no means continuous. And, it is by no means time independent it is a flow process. 

The descriptions presented in the foregoing sections are concerned mainly with composites containing brittle fibers and brittle matrices. If the composite contains ductile fibers or matrix material, the work of plastic deformation of the composite constituents must also be taken into account in the total fracture toughness equation. If a composite contains a brittle matrix reinforced with ductile libers, such as steel wire-cement matrix systems, the fracture toughness of the composite is derived significantly from the work done in plastically shearing the fiber as it is extracted from the cracked matrix. The work done due to the plastic flow of fiber over a distance on either side of the matrix fracture plane, which is of the order of the fiber diameter d, is given by (Tetelman, 1969)... 

Plastic processing is primarily the flow and shaping of viscous liquids. The scientific study of this flow is called rheology. Assuming laminar shear flow, viscosity is defined as the ratio of shear stress to shear rate. 

The analysis of mould filling requires rheological and thermal data for the plastic, and the mould dimensions. Polymer manufacturers usually provide shear flow curves at a range of temperatures these can be approximated by a power law relationship over a limited range of shear strain rates. In the days before computer analysis, flow lengths of short shots were determined in spiral test cavities, as a function of the injection pressure. However, the geometry of this constant cross section mould differs so much from most other moulds that the flow lengths in the two types of mould do not correlate well. 

Rheology is the science that deals with the deformation and flow of matter under various conditions an example is plastic melt flow. The rheology of plastics, particularly TPs, is complex but manageable. These materials combine the properties of an ideal viscous liquid (pure shear deformations) with those of an ideal elastic solid (pure elastic deformation). Plastics are therefore said to be viscoelastic (Figure 17). The mechanical behavior of plastics is dominated by the viscoelastic phenomena such as tensile... 

In contrast to the extrusion of plastics, we do not postulate wall adhesion and pure shear flow. As known from practice [1], the extrusion of ceramic bodies involves pronounced wall slippage, even in sharply conical dies. That being so, oixr main problem is friction. 

The extrusion body used in the production of continuous-column ceramic products is, by nature, highly kneadable and workable. Permanent deformation takes place due to the effects of external forces that induce states of stress within the material as soon as a certain boundary stress is exceeded. This kind of behaviour is summarized under the heading plasticity . The body s intrinsic dimensional stability, i.e. its resistance to creep induced by its own weight, stems from the presence of the aforementioned boundary (or minimum) stress, which in the case of pure shear flow is termed yield point or flow limit . The flow limit indicates at which applied pressure the body begins to flow. 

Eberle APR, et al. Modeling the rheology and orientation distribution of short glass fibers suspended by polymeric fluids simple shear flow. ANTEC, conference proceedings. Society of Plastics Engineers 2007. 

Processing (Primary Forming) of Plastics into Structural Components a shear flow b elongation flow... 

Most liquids, including plastic melts, do not behave in accordance with Newtonian flow at medium and high shear rates. The simple viscosity datum will therefore not suffice as a characterization of such liquids, but rather the flow behavior is indicated by a curve. Fig. 6, plastic melts flow viscously. ... 

---