Rate-dependent plasticity

An example of research in the micromechanics of shock compression of solids is the study of rate-dependent plasticity and its relationship to crystal structure, crystal orientation, and the fundamental unit of plasticity, the dislocation. The majority of data on high-rate plastic flow in shock-compressed solids is in the form of ... 

Wallace [15], [16] gives details on effects of nonlinear material behavior and compression-induced anisotropy in initially isotropic materials for weak shocks, and Johnson et ai. [17] give results for infinitesimal compression of initially anisotropic single crystals, but the forms of the equations are the same as for (7.10)-(7.11). From these results it is easy to see where the micromechanical effects of rate-dependent plastic flow are included in the analysis the micromechanics (through the mesoscale variables and n) is contained in the term y, as given by (7.1). 

Solids 12, 59 - 65 (1964) "A Generalized Theory of Strain- Rate- Dependent Plastic Wave Propagation in Bars 86) M. Lutzky, "The Flow Field Behind a Spherical Detonation in TNT, Using the Landau- Stanyukovich Equation, USNOL-White Oak, NOLTR 64-40 Dec 1964)... 

Here, following the development of Hutchinson and Obrecht (1977), we consider a perfect bar of a non-linear incompressible viscous solid as a reasonable approximation to a rate-dependent plastic material, in comparison with an imperfect bar of the same material with periodic undulations having a wave length 1, where the radius of the imperfect bar is given as... 

De Angehs F. (2013)—Computational issues and numerical apphcations in rate-dependent plasticity. Advanced Science Letters, Vol. 19, Number 8, pp. 2359-2362. 

It is well known that many materials have yield points that vary with strain rate. Notably mild steel has a significant variation in the yield stress with strain rate at high temperature, as do other metals. As a result, various rate dependent plasticity theories have been developed for metals and some of these have been extended to polymers. Early approaches used idealized stress-strain response such as that shown in Fig. 11.8 and Fig. 11.10. In Fig. 11.8 the material is assumed to be rigid but with a rate dependent... 

Models involving non-linear rate-dependent plastic elements such as the Eyring process -so-called viscoplastic models - have also been implemented in finite element schemes. Some of these will be discussed in Chapter 12. 

Metals Successful applications of metals in high-temperature process service depend on an appreciation of certain engineering factors. The important alloys for service up to I,I00°C (2,000°F) are shown in Table 28-35. Among the most important properties are creep, rupture, and short-time strengths (see Figs. 28-23 and 28-24). Creep relates initially applied stress to rate of plastic flow. Stress... 

Strength and Stiffness. Thermoplastic materials are viscoelastic which means that their mechanical properties reflect the characteristics of both viscous liquids and elastic solids. Thus when a thermoplastic is stressed it responds by exhibiting viscous flow (which dissipates energy) and by elastic displacement (which stores energy). The properties of viscoelastic materials are time, temperature and strain rate dependent. Nevertheless the conventional stress-strain test is frequently used to describe the (short-term) mechanical properties of plastics. It must be remembered, however, that as described in detail in Chapter 2 the information obtained from such tests may only be used for an initial sorting of materials. It is not suitable, or intended, to provide design data which must usually be obtained from long term tests. 

It is instructive to describe elastic-plastic responses in terms of idealized behaviors. Generally, elastic-deformation models describe the solid as either linearly or nonlinearly elastic. The plastic deformation material models describe rate-independent behaviors in terms of either ideal plasticity, strainhardening plasticity, strain-softening plasticity, or as stress-history dependent, e.g. the Bauschinger effect [64J01, 91S01]. Rate-dependent descriptions are more physically realistic and are the basis for viscoplastic models. The degree of flexibility afforded elastic-plastic model development has typically led to descriptions of materials response that contain more adjustable parameters than can be independently verified. 

Permeation Tubes A volatile liquid, when enclosed in an inert plastic tube, may escape by dissolving in and permeating through the walls of the tube at a constant and reproducible rate. The permeation rate depends on the properties of the tube material, its dimensions and on temperature. 

The rate of chemical attack will depend on the concentration according to the order of the reaction (i.e. in a zero-order reaction the rate is independent of concentration, in a first-order reaction the rate depends linearly on concentration, and in second-order reaction the rate depends on the square of concentration). Increasing the concentration, therefore, provides a means of acceleration. Remember, however, that chemical attack on plastics is a liquid-solid and not a liquid-liquid reaction, such that the reaction laws only hold if there is free movement of all chemical species with no limitations due to diffusion or transport and no barrier layers. Since this is rarely the case, temperature is preferred as a means of acceleration. 

Pore dimensions may have a more subtle effect on decay rate depending on component dimensions and production method of the manufactured material. Products made from pasted starch, LDPE, and EAA (2) typically appeared as laminates of starch and plastic when examined by scanning electron microscopy (Figure 1). The dimensions of inter-laminate channels (i.e., pores) were not uniform and ranged from about 50 to 325 m in cross-section (22). Since flux is dependent on diffusional path area, the smaller pores can be an impediment to movement of solutes from the interior to the surface of the films. Figure 5 illustrates two films in which the laminate units are the same thickness, but differ in length. When the starch is removed... 

Fluids that show viscosity variations with shear rates are called non-Newtonian fluids. Depending on how the shear stress varies with the shear rate, they are categorized into pseudoplastic, dilatant, and Bingham plastic fluids (Figure 2.2). The viscosity of pseudoplastic fluids decreases with increasing shear rate, whereas dilatant fluids show an increase in viscosity with shear rate. Bingham plastic fluids do not flow until a threshold stress called the yield stress is applied, after which the shear stress increases linearly with the shear rate. In general, the shear stress r can be represented by Equation 2.6 ... 

The strain rate dependence of the plastic flow, crpf, is shown at various temperatures in Fig. 20. It is clear that crpf is lightly dependent on the strain rate,... 

Fig. 20 Strain rate dependence of yield stress, ay, and plastic flow stress, apf, of PMMA at the indicated temperatures (From [33])...

Other excipients used in film-coating may influence the dissolution of the polymers [36], For instance, plasticizers may increase or decrease dissolution rate, depending on whether a lipophilic or a hydrophilic plasticizer was used. Using this effect, the time-to-action of a drug may be improved (e.g., by using a hydrophilic plasticizer like triethyl citrate). Usually these effects are not detectable, if... 

Odor loss by diffusion of perfume materials can also occur in products packaged in plastic containers Its rate depends on the following factors ... 

Fig. 23. Comparison of the predicted strain rate dependence of plastic yield of PS under uniaxial compression, tension, and shear...

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