Yield phenomena

Fig. 2.10. Certain high strength solids with low thermal conductivity show a loss or reduction of shear strength when loaded above the Hugoniot elastic limit. The idealized behavior of such solids upon loading is shown here. The complex, heterogeneous nature of such yield phenomena probably results in processes that are far from thermodynamic equilibrium.

The non-linear response of plastic materials is more challenging in many respects than pseudoplastic materials. While some yield phenomena, such as that seen in clay dispersions of montmorillonite, can be catastrophic in nature and recover very rapidly, others such as polymer particle blends can yield slowly. Not all clay structures catastrophically thin. Clay platelets forming an elastic structure can be deformed by a finite strain such that they align with the deforming field. When the strain... 

An overview of the origins of yield stress and parameters which can lead to variations in behaviour with highly filled polymer dispersions is given by Malkin [1]. Much of the following literature, describing experimental work undertaken, demonstrates that yield phenomena can be correlated with the extent of interaction between the filler particles and the formation of a network structure. However, the actual behaviour observed during experimentation may also depend on the deformation history of the material, or the time and temperature of imposed deformation, especially if the material exhibits thixotropic properties. 

It has been suggested that the three-dimensional network structures discussed above, which are believed to occur from particle interactions at high filler loadings, may, in the case of plate-like particles, lead to anisotropic shear yield values [35]. Although this effect has not been substantiated experimentally, further theoretical interpretation of shear yield phenomena in talc- and mica-filled thermoplastics has been attempted [31,35]. 

Although appealing from an engineering perspective, the analyses based on linear thermoelasticity do not address the action of defects and dislocations created by microscopic yield phenomena below the CRSS and of those that are incorporated in the crystal at the solidification front. In the previous works cited (104-108), the authors assume that no defects exist at the melt-crystal interface and that the stresses on this surface are zero. Constitutive equations incorporating models for plastic deformation in the crystal due to dislocation motion have been proposed by several authors (109-111) and have been used to describe dislocation motion in the initial stages of... 

Above about 45°C, however, considerable yielding can be observed. Note that the transition between brittle and ductile behavior occurs at a temperature that is significantly below the T. Various theories have been advanced to explain yielding phenomena in polymers, some involving free volume arguments while others involve various types of molecular motion. As far as we can make out, none of these are entirely satisfactory and we won t discuss them here. Instead, we will finish off our discussion of stress/strain behavior by considering rubber elasticity. 

Doraiswamy et al. (1991) developed a non-linear rheological model combining elastic, viscous and yielding phenomena for filled polymers. The model predicts a modified Cox Merz relationship for filled melts ... 

Finally, the rheological behavior of block copolymers serves as a model for well compatibilized blends, with perfect adhesion between the phases. The copolymers provide important insight into the effects of the chemical nature of the two components, and the origin of the yield phenomena. 

Polyethylenes undergo interlaminar deformation during tensile elongation. This can give rise to a double yield phenomenon. At the onset of the hrst tensile yield, chain slip and lamella rotation occur and this process is reversible. The second tensile yield is irreversible and coinsides with lamella fragmentation (36). These mechanically induced morphological changes and the observation of any double yield phenomena are dependent on several structural factors that can be controlled by... 

Even the first observations of damage of this kind in the development of ammonia synthesis showed that the effects of pressurized hydrogen on steel are both chemical and physical (Bosch 1933). The physical effect presumably takes place in different stages. Since molecular hydrogen does not diffuse in the steel, the first step must be surface adsorption with dissociation at elevated temperature. In this process, the metallic wall acts as a catalyst. With pure, dry pressurized hydrogen, for example, dissociation produced by yielding phenomena on the steel surface can supply critical quantities of diffusible hydrogen even at room temperature. 

Fig. 1.16 Prominent yield phenomena and strong strain softening accompan5nng inception of plastic flow in a Zr65Al2oCui5 BMG, strained at a strain rate of e = 5 x 10 s at eight different temperatures (from Kawamura et al. (1996) courtesy of the AIP).

Fig. 7.18 Computer-simulation results on the stress-strain behavior of amorphous silicon showing yield phenomena, strain softening, steady-state flow, annealing and re-straining (from Argon and Demkowicz (2008) courtesy of TMS).

Figure 8.2 shows a series of stress-strain curves at different temperatures for bisphenol-A polyearbonate (PQ recorded at an effective uniaxial strain rate of 10 " s obtained from extensional deformation in pre-contoured tensile bars using the special instrumentation mentioned above that resulted in deviatoric, effective true-stress-true-strain curves (G Sell et al. 1992). In these experiments the initial state of the material was fully annealed, exhibiting strong yield phenomena and strain softening. Figure 8.3 shows the temperature dependence of the yield stress of PC in tension and compression at a strain rate of = 4.16 x 10 s . 

Fig. 8.18 Compression stress-strain curves of nearly glassy PET (crystalline content 9%) for seven temperatures reaching Tg, showing strong yield phenomena and strain-softening effects that decrease with increasing temperature, having a relatively temperature-independent entropic strain-hardening contribution (from Zaroulis and Boyce (1997) courtesy of Elsevier).

All stress-strain curves show prominent yield phenomena and strong strain softening that decrease with increasing temperature and disappear at Tg. The six curves within 15 K of Tg show no important dependence of the strainhardening behavior on temperature once a flow state has been reached. This conforms with expectations that the strain hardening by molecular alignment... 

A number of factors affect the rheology of emulsions composition, the viscosity ratio of the dispersed-to-matrix phase (1 s 7/2/771), the droplet size and its distribution, rheology of the interphase, and so on. Often, well-stabilized emulsions follow the viscosity-concentration relationships developed for hard sphere suspensions, including the yield phenomena. In contrast, emulsions with deformable dispersed... 

In metals, several topics are often considered when discussing yield phenomena ... 

Figure 4.51 indicates that the yielding in sapphire undergoing basal slip is a consequence of dislocation multiplication and is not due to the unpinning of a Cottrell-type atmosphere, where dislocation pinning results from impurities. The study of two types of sapphires, with different initial dislocation densities, was meant to point out the difference in their surface dislocation densities and the consequent differences in their yield phenomena. 

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