Plastic deformation constant strain-rate

Fig. 6.17. Map of polycluster mechanical states. Region I elastic and anelastic (shaded area) deformations Region II inhomogeneous plastic deformation Region III homogeneous diffusional-viscous flow. Curves 1-3 show the temperature dependence of the stress at different constant strain rates...

On the map of mechanical states in region I, elastic and anelastic (shaded areas) deformations take place. In the region II, the inhomogeneous plastic deformation with the formation of shear bands takes place. The horizontal broken line corresponds to the theoretical yield stress of LRC. In the region III, the homogeneous diffusional-viscous flow takes place and, in the region IV, the mixed viscous flow is realized. Curves 1,2, 3 show the temperature dependence of the stress at different constant strain rates. The continuations of these curves in regions IV and II correspond to the mixed nonuniform plastic deformation. 

We have now discussed in turn, the stresses required to produce yield, the relationship between stress and plastic strain increment, the structural reorientation occurring as a result of yield, and the relationship between constant strain-rate yield and features of non-linear recoverable creep deformation. Theoretical models to describe the behaviour have ranged from single crystal plasticity through to the oriented continuum ideas of plasticity and viscoelasticity. On many points both the experimental data and the interpretations appear almost contradictory and it is therefore helpful to see if any common ground can be established. 

According to the change of strain rate versus stress the response of the material can be categorized as linear, non-linear, or plastic. When linear response take place the material is categorized as a Newtonian. When the material is considered as Newtonian, the stress is linearly proportional to the strain rate. Then the material exhibits a non-linear response to the strain rate, it is categorized as Non Newtonian material. There is also an interesting case where the viscosity decreases as the shear/strain rate remains constant. This kind of materials are known as thixotropic deformation is observed when the stress is independent of the strain rate [2,3], In some cases viscoelastic materials behave as rubbers. In fact, in the case of many polymers specially those with crosslinking, rubber elasticity is observed. In these systems hysteresis, stress relaxation and creep take place. 

The change in the physical mechanism of deformation from elasticity, viscoelasticity to plasticity depends on the time scales in which the amorphous solid is measured and relaxed. The dependene of stress-strain relationship on relaxation time is conceptualized in Fig. 18, where the yield stress is defined. The yield occurs when the product of the relaxation time and the applied strain rate reaches a constant value [28, 38, 39]. Using Eq. (50) and replacing yield stress components ... 

B Zero stress limit of activation energy for plastic deformation C SAXS constant product of flow stress and craze fibril diameter C Pre-exponential factor for craze strain rate, (=Qb )... 

For perfectly plastic materials, post>yieldtng the strain rate is a constant function of the stress and the stress is constant and never exceeds ay (Fig. ISA). The extent of pla.stic deformation p depends upon the proportionality between plastic strain rate and the stress and the how long the. stress is applied as shown in Figure 17A. The elastic perfectly plastic material is highly idealized and not many materials exhibit this type of behavior. 

The measurement of rheological properties for non-Newtonian, lipid-based food systems, such as dilatant, pseudoplastic, and plastic, as depicted in Figure 4.1, are much more difficult. There are several measurement methods that may involve the ratio of shear stress and rate of shear, and also the relationship of stress to time under constant strain (i.e., relaxation) and the relationship of strain to time under constant stress (i.e., creep). In relaxation measurements, a material, by principle, is subjected to a sudden deformation, which is held constant and in many food systems structure, the stress will decay with time. The point at which the stress has decayed to some percentage of the original value is called the relaxation time. When the strain is removed at time tg, the stress returns to zero (Figure 4.8). In creep experi-... 

Due to the viscoelastic nature of plastics, deformations depend on such factors as the time under load and the temperature. Therefore the classical equations available for the design of structural components, such as springs, beams, plates, and cylinders, and derived under the assumptions that (1) the modulus is constant and (2) the strains are small and independent of loading rate or history and are immediately reversible, cannot be used indiscriminately. For example, classical equations are derived using the relation... 

The mechanics of stability and localization of deforma tion for plastic rigid materials has been considered by Hill (1957), who stated that, in general, the conditions for loss of load-carrying capacity under controlled boundary displacements or large distortions under constant boundary loads are different from the conditions for localization by inhomogeneous deformation. The conditions for the latter are more akin to those of uniqueness. For the plastic rigid bar the two conditions coincide. As Hart (1967) has shown, and as was developed in more detail by Hutchinson and Neale (1977), the two conditions are always separate for strain-rate-sensitive materials, where much stable extension can follow a load maximum. 

The idealized laws just reviewed can, however, not describe the behavior of matter if the ratios of stress to strain or of stress to rate of strain is not constant, known as stress anomalies. Plastic deformation is a common example of such non-ideal behavior. It occurs for solids if the elastic limit is exceeded and irreversible deformation takes place. Another deviation from ideal behavior occurs if the stress depends simultaneously on both, strain and rate of strain, a property called a time anomaly. In case of time anomaly the substance shows both solid and liquid behavior at the same time. If only time anomalies are present, the behavior is called linear... 

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