Plastic deformation phenomenology

From the standpoint of a stress-strain curve, the constitutive behavior discussed in the previous section corresponds to a limited range of loads and strains. In particular, as seen in fig. 2.10, for stresses beyond a certain level, the solid suffers permanent deformation and if the load is increased too far, the solid eventually fails via fracture. From a constitutive viewpoint, more challenges are posed by the existence of permanent deformation in the form of plasticity and fracture. Phenomenologically, the onset of plastic deformation is often treated in terms of a yield surface. The yield surface is the locus of all points in stress space at which the material begins to undergo plastic deformation. The fundamental idea is that until a certain critical load is reached, the deformation is entirely elastic. Upon reaching a critical state of stress (the yield stress), the material then undergoes plastic deformation. Because the state of stress at a point can be parameterized in terms of six numbers, the tensorial character of the stress state must be reflected in the determination of the yield surface. 

For the type of polycrystal yield surfaces described above, the elementary treatments of hardening are highly intuitive. The fundamental physical idea behind such laws is the recognition that as plastic deformation proceeds, it becomes increasingly difficult to inspire subsequent yield. In chap. II, we will attempt to describe the origins of this phenomenon in the evolution of the distribution of dislocations, while here our aim will be to advance phenomenological approaches to this effect. 

Our treatment thus far has centered on idealized geometries in which the dislocation is presumed to adopt highly symmetric configurations which allow for immediate insights from the linear elastic perspective. From the phenomenological standpoint, it is clear that we must go beyond such idealized geometries and our first such example will be the consideration of kinks. The formation of kink-antikink pairs plays a role in the interpretation of phenomena ranging from plastic deformation itself, to the analysis of internal friction. 

From the standpoint of the phenomenology of plastic deformation, one of the most important classes of three-dimensional configuration is that associated with dislocation intersections and junctions. As will become more evident in our... 

Hart and coworkers developed a phenomenological theory of plastic deformation by using the concept of equation of state [6, 7]. The proposed deformation model consists essentially of two parallel branches (Fig. 6.10). Branch 1 represents... 

Hart, E. W., A Phenomenological Theory for Plastic Deformation of Polycrys-talhne Metals, Acta Metall., 18 (1970), 599-610. 

In comparison the plastic deformation and fracture processes, both in the laboratory and in industrial practice, have largely been dealt with at a phenomenological level, and often separately for different polymers and blends, rather than from a unified and comprehensive mechanistic perspective. This has left the mechanisms governing the deformation and fracture resistance of polymers far less well understood. 

Fig. 4.14. A hierarchical point of view of interface fracture advance, whereby the complexities of material separation are lumped into a representative phenomenological cohesive rule that is representative of the system its essential features are the work per unit area Fo required for separation of the surfaces and the maximum cohesive traction <7 that arises in the process. The cohesive traction must be imposed by the surrounding film and substrate materials, viewed as elastic-plastic continua. The tendency for significant plastic deformation in either material is determined by the ratio of a to the yield stress of that material. The driving force necessary to effect separation is characterized by an energy release rate Q. To sustain crack growth, its value must be large enough to overcome Fq plus plastic dissipation per unit area Fp. Adapted from Hutchinson and Evans (2000).

The degree of anisotropy of a property may be negligible, but this is not usually the case in indentation hardness measurements on ceramic crystals. Later we will consider the phenomenological aspect of hardness anisotropy to demonstrate that, whatever the ramifications of the theoretical models, the nature of anisotropy is consistent and reproducible for a wide range of ceramics. Then we shall consider the models based on a resolved shear stress analysis and discuss their implications in terms of the role of plastic deformation and indentification of active dislocation slip systems. 

Kolmogorov V. L. Migachev B. A. Burdukovsky Century of To a question of creation of the generalized phenomenological model of destruction at plastic deformation [K... 

Unified Plasticity Model The time-independent plastic deformation and fee time-dependent creep deformation arise from fee same fundamental mechanism of dislocation motion. Hence, a constitutive model which captures both of these deformation mechanisms is desirable. Such a constitutive model is referred to as a unified plasticity model. A commonly-used unified plasticity model is the Anand s model. This is a rate-dependent phenomenological model (Ref 17 and 18). There are two basic characteristics of fee Anand s model. First, no explicit yield criterion is specified, and second, a single internal state variable (ISV) s, the deformation resistance, represents the isotropic resistance to inelastic strain hardening. Anand s model can represent fee strain rate and temperature sensitivity, strain rate history effects, strain hardening, and fee restoration process of dynamic recovery. Equation 9 shows the functional form of fee flow equation that accommodates fee strain rate dependence on the stress ... 

It is well-known that the antiphase boundaries (APBs) in intermetallic compounds affect many material properties, such as the dislocation structures, the associated plastic deformation, and microstructures of many intermetallic compounds. APBs are two-dimensional defects, i.e. intercrystalline interfaces similar to grain boundaries. Therefore, the phenomenology of APBs has many parallels with that of grain boundaries. The structure and chemistry of APBs are discussed in Chapter 21 by Sun in this volume. 

The densification of the parts by HIP implies primarily three phenomena i) fragmentation of the particles and rearrangement, ii) deformation of the interparticle areas of contact and iii) elimination of the pores. The first process is transitory and hardly contributes to the overall densification, at least if the initial forming (for example, by CIC) has been correcdy carried out. The second process brings into play effects of plastic deformation by movement of dislocations and diffusion phenomena that are similar to those indicated in the case of uniaxial pressure sintering. Lastly, by considering the final reduction of porosity, we can write phenomenologically ... 

The resulting, isolated, flow stress contribution is shown in Figure 31 (left). As was discussed in the first part of this chapter, dealing with the phenomenology of yielding, upon plastic deformation of the material all influence of its prior thermomechanical history is erased and the material shows a response independent of prior history. From the resulting minimum in stress 0, 0, we can, therefore, calculate with the help of eqn [5] a first estimate of the rejuvenated reference viscosity 7r,o, since fi and tq are known, Sa= 0, and, finally, the strain rate fi is prescribed. Note that we obtain an estimate of this parameter since its calculation is based on a number of assumptions as listed earlier. At the same time we can also obtain an estimate of the value of the state parameter Sa since the softening drop A[Pg.739]

The deformation of solid macromolecular systems and gels is, however, of paramount practical importance and, in the last decades, considerable progress has been made in the phenomenological study of the elasto-plastic behaviour of these objects, and also some more light has been thrown on the underlying mechanism of deformation in a few cases which may serve as a starting point for further reseach. 

Both the elastic and the plastic behaviour of polymers are time-dependent even at room temperature polymers are thus viscoelastic and viscoplastic. In this section, we discuss the time-dependent deformation behaviour phenomenologically and explain how thermal activation of relaxation processes causes the time-dependence of deformation. 

In a lumped plasticity model, locations within the structure that might undergo inelastic deformations in a severe seismic event are identified up front. Inelastic nonlinear zero-length springs are assigned to these locations, while the rest of the model components remain elastic. These simple phenomenological component models are calibrated with experimental outcomes to represent appropriate cyclic response behavior. 

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