Plasticity viscoplasticity

As discussed in Chapter 3, pseudo-plastic deformation is the key for cold-programmed thermosetting SMP to display shape memory functionality. Therefore, the deformation includes both plastic/viscoplastic and elastic/viscoelastic deformation. The thermomechanical cycle also includes thermal deformation. Based on Figure 4.5, the deformation gradient F can be multiplicatively decomposed into thermal Fj and mechanical Fm, which are further decomposed into plastic F and elastic F, as follows ... 

Carstensen C. (1994) Interface problems in viscoplasticity and plasticity. SIAM J. Math. Anal. 25 (6), 1468-1487. 

Fig. 2.6. Observed wave forms in the elastic-plastic regime are quite diverse representing nonideal elastic and viscoplastic behaviors (after Davison and Graham [79D01]).

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. 

Release waves for the elastic-plastic regime are dominated by the strength effect and the viscoplastic deformations. Here again, quantitative study of the release waves requires the best of measurement capability. The work of Asay et al. on release of aluminum as well as reloading, shown in Fig. 2.11, demonstrates the power of the technique. Early work by Curran [63D03] shows that limited time-resolution detectors can give a first-order description of the existence of elastic-plastic behavior on release. 

Fiber-reinforced composite materials such as boron-epoxy and graphite-epoxy are usually treated as linear elastic materials because the essentially linear elastic fibers provide the majority of the strength and stiffness. Refinement of that approximation requires consideration of some form of plasticity, viscoelasticity, or both (viscoplasticity). Very little work has been done to implement those models or idealizations of composite material behavior in structural applications. 

Viscoelasticity of metal This subject provides an introduction on the viscoelasticity of metals that has no bearing or relationship with viscoelastic properties of plastic materials. The aim is to have the reader recognize that the complex thermodynamic foundations of the theory of viscoplasticity exist with metals. There have been developments in the thermodynamic approach to combined treatment of rheologic and plastic phenomena and to construct a thermodynamic theory non-linear viscoplastic material that may be used to describe the behavior of metals under dynamic loads. 

As a result of simultaneous introduction of elastic, viscous and plastic properties of a material, a description of the actual state functions involves the history of the local configuration expressed as a function of the time and of the path. The restrictions, which impose the second law of thermodynamics and the principle of material objectivity, have been analyzed. Among others, a viscoplastic material of the rate type and a strain-rate sensitive material have been examined. 

Both polymeric and some biological reactors often contain non-Newtonian liquids in which viscosity is a function of shear rate. Basically, three types of non-Newtonian liquids are encountered power-law fluids, which consist of pseudoplastic and dilatant fluids viscoplastic (Bingham plastic) fluids and viscoelastic fluids with time-dependent viscosity. Viscoelastic fluids are encountered in bread dough and fluids containing long-chain polymers such as polyamide and polyacrylonitrite that exhibit coelastic flow behavior. These... 

Keywords Crack tip plasticity Elastic-viscoplastic material Crazing Cohesive surface Fracture... 

More work on a detailed description of the fibrillation process is needed to clarify the underlying mechanism and its relationship with molecular aspects, such as the entanglement density or the molecular mobility. Nevertheless, based on the observations reported by DOll [29,30] of time-dependent craze stress and Kramer s [31,32] description of fibrillation involving an active plastic zone, one can conclude that craze thickening is a viscoplastic process. 

As discussed in Sect. 3.2, once a mature fibril is created, further thickening occurs by a viscoplastic drawing mechanism which involves intense plastic deformation at the craze/bulk interface [32], Instead of using a non-Newtonian formulation as in [32] or a formulation based on Eyring s model [45], but on the basis of a preliminary study of the process [36], the craze thickening is described with a similar expression as the viscoplastic strain rate for the bulk in Eq. 3 as [20]... 

The toughening observed in Fig. 11 with increasing loading rate is quite surprising from a standard fracture mechanics point of view on the fracture of viscoplastic materials increasing the loading rate results in less energy dissipated by plasticity and a more brittle response is expected (if the failure process is assumed to be rate independent). One could also invoke a failure... 

For T < Tg, the viscoplastic model used here accounts for intrinsic softening upon yielding followed by progressive orientational hardening. Rate dependent flow is taken to be governed by Argon s formulation [5] of the equivalent plastic strain rate... 

FIGURE 8.7 Non-Newtonian flow behavior, a Structural viscosity (for high molecular solution). b Dilatant flow (suspension with high concentration), c Viscoplastic with flow limits 1, ideal plastic 2 or 3, nonlinear plastic flow, d 1, thixotropy flow 2, antithixotropy flow 3, viscoelastic flow e rheopexy flow. 

Besides of the media considered, there are media in which a finite yield stress to is required to initiate flow. For such media, the intercept of the flow curve with the stress axis 7 = 0 is (0, To), where to is nonzero (Figure 6.1). The value of t0 characterizes the plastic properties of a substance, and the slope of the flow curve to the 7-axis characterizes its fluidity. Such media are said to be viscoplastic. 

The motion of plastic fluids with finite yield stress to has some qualitative specific features not possessed by nonlinearly viscous fluids. Let us consider a layer of a viscoplastic fluid on an inclined plane whose slope is gradually varied. It follows from (6.2.5) that, irrespective of the rheological properties of the medium, the tangential stress decreases across the film from its maximum value Tjnax = pgh sin a on the solid wall to zero on the free surface. Therefore, a flow in a film of a viscoplastic fluid can be initiated only when the tangential stress on the wall becomes equal to or larger than the yield stress to ... 

A similar problem on a nonisothermal rectilinear flow of a viscoplastic Shvedov-Bingham fluid in a circular tube for the case in which the yield stress and the plastic viscosity are inversely proportional to temperature was studied in [298],... 

In the viscoplastic model of Carroll and Holt [49], later extended by Khasainov et al., [52] Butler et al., [158] and Frey [164] (Fig. 17b), pores in a viscous material collapse slowly behind the shock front via ID (radial) plastic deformation. Heating results from viscoplastic work. In the small Reynolds number limit (see below), the viscous time constant Xyis is independent of pore diameter [52] ... 

Thermoplastics are based on linear or branched polymers, copolymers or their blends that are reversibly transferred at heating into a plastic or viscoplastic state as a result of melting of the crystalline and/or softening of the amorphous (glassy) phase [29]. Inhibited CM based on thermoplastics are largely adopted in anticorrosion techniques. Most thermoplastics are produced at a large scale in petrochemical enterprises and are comparatively... 

The flow behavior of a vtscoplaslir fluid is identified by the. appearance of a yield Stress, i.e., the fluid flows in a viscous manner only after a threshold ha.s been exceeded. Below this threshold, or yield stress, the behavior of the fluid is similar to an elastic solid and should obey Eq. [4) when subjected to a strain or stress sweep. The simplest type of viscoplastic fluid is the so-called Bingham plastic, and its behavior can be expressed by means of the following mathematical model ... 

A comprehensive analytical model for predicting long term durability of resins and of fibre reinforced plastics (FRP) taking into account viscoelastic/viscoplastic creep, hygrothermal effects and the effects of physical and chemical aging on polymer response has been presented. An analytical tool consisting of a specialized test-bed finite element code, NOVA-3D, was used for the solution of complex stress analysis problems, including interactions between non-linear material constitutive behavior and environmental effects. 

Krieg, R.D. Key, S.W. (1976) Implementation of a time dependent plasticity into structural computer programs. Constitutive equations in Viscoplasticity Computational and... 

A fluid with a linear flow curve for Ty > ro is called a Bingham plastic fluid and is characterised by a constant plastic viscosity (the slope of the shear stress versus shear rate curve) and a yield stress. On the other hand, a substance possessing a yield stress as well as a non-linear flow curve on linear coordinates (for Xyx > ro ), is called a yield-pseudoplastic material. Figure 1.8 illustrates viscoplastic behaviour as observed in a meat extract and in a polymer solution. 

Figure 1.8 Representative shear stress-shear rate data showing viscoplastic behaviour in a meat extract (Bingham Plastic) and in an aqueous carbopol polymer solution (yield-pseudoplastic)...

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