Plastic deformation, defined

Elastic Behavior. Elastic deformation is defined as the reversible deformation that occurs when a load is appHed. Most ceramics deform in a linear elastic fashion, ie, the amount of reversible deformation is a linear function of the appHed stress up to a certain stress level. If the appHed stress is increased any further the ceramic fractures catastrophically. This is in contrast to most metals which initially deform elastically and then begin to deform plastically. Plastic deformation allows stresses to be dissipated rather than building to the point where bonds break irreversibly. 

Viscosity has been replaced by a generahzed form of plastic deformation controlled by a yield stress which may be determined by compression e)meriments. Compare with Eq. (20-48). The critical shear rate describing complete granule rupture defines St , whereas the onset of deformation and the beginning of granule breakdown defines an additional critical value SVh... 

A metal bar of width w is compressed between two hard anvils as shown in Fig. Al.l. The third dimension of the bar, L, is much greater than zu. Plastic deformation takes place as a result of shearing along planes, defined by the dashed lines in the figure, at a shear stress k. Find an upper bound for the load F when (a) there is no friction between anvils and bar, and (b) there is sufficient friction to effectively weld the anvils to the bar. Show that the solution to case (b) satisfies the general formula... 

That fraction of the applied work which is not consumed in the elastic-plastic deformation remains to create the new crack surface, i.e., the crack driving force. Therefore, a nonlinear fracture toughness, G, may be defined as follows ... 

Typical stress-time profiles for the various materials (28.5-at. % Ni, fee and bcc) and various stress regions are shown in Fig. 5.12. The leading part of the profile results from the transition from elastic to plastic deformation. The extraordinarily sharp rise in stress for the second wave in Fig. 5.12(a) and the faster arrival time compared with that in Fig. 5.12(b) is that expected if the input stress is above the transition, whereas the slower rise in Fig. 5.12(b) is that expected if the stress input to the sample is below the transition. The profile in Fig. 5.12(c) for the bcc alloy was obtained for an input particle velocity approximately equal to that in Fig. 5.12(a) for the fee alloy. The bcc alloy shows a poorly defined precursor region, but, in any event, much faster arrival times are observed for all stress amplitudes, as is indicative of lower compressibility. 

Plasticity is defined as the ability of such particle groups to deform rapidly without cracking or crumbling. It also refers to the ability of such groups to change volume with relatively small rebound when the deforming force is removed. 

The present review shows how the microhardness technique can be used to elucidate the dependence of a variety of local deformational processes upon polymer texture and morphology. Microhardness is a rather elusive quantity, that is really a combination of other mechanical properties. It is most suitably defined in terms of the pyramid indentation test. Hardness is primarily taken as a measure of the irreversible deformation mechanisms which characterize a polymeric material, though it also involves elastic and time dependent effects which depend on microstructural details. In isotropic lamellar polymers a hardness depression from ideal values, due to the finite crystal thickness, occurs. The interlamellar non-crystalline layer introduces an additional weak component which contributes further to a lowering of the hardness value. Annealing effects and chemical etching are shown to produce, on the contrary, a significant hardening of the material. The prevalent mechanisms for plastic deformation are proposed. Anisotropy behaviour for several oriented materials is critically discussed. 

Microindentation hardness normally is measured by static penetration of the specimen with a standard indenter at a known force. After loading with a sharp indenter a residual surface impression is left on the flat test specimen. An adequate measure of the material hardness may be computed by dividing the peak contact load, P, by the projected area of impression1. The hardness, so defined, may be considered as an indicator of the irreversible deformation processes which characterize the material. The strain boundaries for plastic deformation, below the indenter are sensibly dependent, as we shall show below, on microstructural factors (crystal size and perfection, degree of crystallinity, etc). Indentation during a hardness test deforms only a small volumen element of the specimen (V 1011 nm3) (non destructive test). The rest acts as a constraint. Thus the contact stress between the indenter and the specimen is much greater than the compressive yield stress of the specimen (a factor of 3 higher). 

The hardness, defined as the resistance to plastic deformation, of microporous silicon decreases with porosity p from the bulk silicon value of about 11.5 GaP to values around 4 GaP for porosities in the order of 75% following a (1-p)2/3 dependence. For porosities above 75% a further decrease in hardness is observed. The hardness of PS formed on highly doped p-type substrates is found to be somewhat less than that observed for low doped substrates, which may be caused by the more columnar structure of meso PS [Du5]. 

The application of force to a stationary or moving system can be described in static, kinematic, or dynamic terms that define the mechanical similarity of processing equipment and the solids or liquids within their confines. Static similarity relates the deformation under constant stress of one body or structure to that of another it exists when geometric similarity is maintained even as elastic or plastic deformation of stressed structural components occurs [53], In contrast, kinematic similarity encompasses the additional dimension of time, while dynamic similarity involves the forces (e.g., pressure, gravitational, centrifugal) that accelerate or retard moving masses in dynamic systems. The inclusion of tune as another dimension necessitates the consideration of corresponding times, t and t, for which the time scale ratio t, defined as t = t It, is a constant. 

Various models 1-2,42 43) have been proposed to describe the extent and shape of the localised plastic deformation zone at the crack tip. From these models one may define a parameter known as the crack opening displacement, 5, (see Fig. 16) and the value of 5,c for the onset of crack growth is given by... 

Dislocations are line defects. They bound slipped areas in a crystal and their motion produces plastic deformation. They are characterized by two geometrical parameters 1) the elementary slip displacement vector b (Burgers vector) and 2) the unit vector that defines the direction of the dislocation line at some point in the crystal, s. Figures 3-1 and 3-2 show the two limiting cases of a dislocation. If b is perpendicular to s, the dislocation is named an edge dislocation. The screw dislocation has b parallel to v. Often one Finds mixed dislocations. Dislocation lines close upon themselves or they end at inner or outer surfaces of a solid. 

It is understood that the (local) Gibbs energy depends on the local stress, and thus aH(NH) and (A/h) reflect the self- and coherency stresses in the Me-H system. In addition, if coherency is lost due to plastic deformation or cracking, the Me atoms in the deformation zone may well become mobile and Me then is well defined near the interface. This could explain the fact that aK(N (P)) (= aH(Ajj(a))) corresponds, in essence, to the value of the a/p equilibrium calculated using independent thermodynamic data. 

Plasticity can be defined as ease of deformation so that a highly plastic rubber is one that deforms or flows easily. Viscosity is the resistance to plastic deformation or flow and, hence, the inverse of plasticity. It is defined as shear stress/shear rate. Unfortunately, the terms are often used... 

Shape-Memory Alloys. Stoeckel defines a shape-memory alloy as the ability of some plastically deformed metals (and plastics) to resume their original shape upon heating. This effect has been observed in numerous metal alloys, notably the Ni—Ti and copper-based alloys, where commercial utilization of this effect lias been exploited. (An example is valve springs that respond automatically to change in transmission-fluid temperature.) Copper-based alloy systems also exhibit this effect. These have been Cu-Zn-Al and Cu-Al-Ni systems. In fact, the first thermal actuator to utilize this effect /a greenhouse window opener) uses a Cu—Zn-Al spring. 

Creep, yielding, and post-yielding plastic deformation (drawing) as well as flow are brought about by the stress-biased deformation and displacement (jumps) of molecular groups and chain segments. Creep is defined as the time-... 

Besides deformation, fracture is the other response of materials to a stress. Fracture is the stress-induced breakup of a material. Two types of fracture are commonly defined. A brittle fracture is breakup which occurs abruptly without localized reduction in area. A ductile fracture is the failure of the material which is preceded by appreciable plastic deformation and localized reduction in area (necked region). The brittle fracture and ductile fracture are schematically illustrated in Fig. 1.10. 

Most of the technical raw materials used in solid reactions are polycrystalhne, and these - when in solid form - undergo a range of modifications during milling. The first observation is the fracture of the solid into smaller pieces. The fracture mechanics are a topic of discussion, and fracture can be divided into two steps, namely crack formation and crack propagation . Depending on the ability of the material to undergo plastic deformation before fracture, either brittle or ductile fracture can be defined ... 

Figure 7.2. Definitions of stress, strain, and modulus. Stress is defined as force per unit area, and strain is the change in length divided by the original length. When stress is plotted versus strain, then the slope is the modulus (A). When the load is removed, any strain remaining is called permanent or plastic deformation (B). When elastic materials are loaded, they are characterized by a constant strain as a function of time, whereas viscoelastic materials have strains that increase with time (C).

Plastics are defined as those materials that suffer irreversible deformation when subjected to a shear stress that is, when subjected to pressure they will flow and take up a new shape. However, the term plastic is used in general to define those organic polymeric materials derived from synthetic monomers. 

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