Macroscopic plastic deformation

In the unstrained material far from the center of an indentation, dislocations can move freely at much lower stresses than in the material near the center where the stress (and the deformation) is much larger. Thus, local plastic shear bands can form at the edges of the indenter, and do (Chaudhri, 2004). The lengths of these shear bands are often several times the size of an indentation. The leading dislocations in these bands move in virgin (undeformed) material, so they can move at lower stresses than the dislocations in the strain-hardened material near the center of an indentation.. The patterns they form are called rosettes.  

Microscopic mechanisms of plastic deformation are far too complex to be described in detail. Many attempts have been made, but they have all had a variety of shortcomings. Part of the problem is that several important deformation mechanisms involve atomic interactions which interact with one another, so not only must the interactions be described by means of quantum mechanics, but also ordinary statistical mechanics cannot be applied. Therefore, a very rough statistical approach must suffice. 

In general terms, as has already been mentioned, plastic deformation is a transport process analogous with electrical and thermal conductivity. These involve an entity to be transported, a carrier that does the transporting, and a rate of transport. In the case of electrical conductivity, charge is the transport entity, electrons (or holes) are the carriers, and the electron net velocities determine the rate. In the case of plastic deformation, displacement, b (cm) is the transport entity, dislocations are the carriers, N ( /cm2), and their velocities, v (cm/sec) determine the shear deformation rate, d8/dt. In two dimensions, the latter is given by the Orowan Equation  

In three dimensions, there may be more than one glide system, and the dislocation line need not be straight, and there may be more than one velocity, so this becomes  

Using average values, the density of mobile dislocations, N which increases with the deformation, may be written  

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The deformation is essentially a thermally activated process and the strain at the molecular level determines the overall macroscopic plastic deformation. 

Under the action of a local shear stress, a, a straight dislocation line that is fixed at two points will bend out. The bending radius is inversely proportional to a. The dislocation becomes unstable if the bending radius is <1/2, where / is the distance between the anchor points (Fig. 3-3). Dislocation loops can be formed and macroscopic plastic deformation can continuously occur under stress if... 

This suggests that and a, are similar, and confirms the invariance of the craze length versus crack-craze velocity in air. The value of approximately 2000 A is almost identical to the activation volume measured in a usual macroscopic plastic deformation test in PMMA. 

Brittleness is the opposite of toughness. A brittle crack propagates with little or no macroscopic plastic deformation. Crack propagation requires very little energy and is rapid, usually resulting in rupture. Engineering codes contain rules to avoid brittle fractures. 

These ductile features of these glasses may be observed microscopically in Fig. 3.18a and b, respectively. However, the stress—strain curves of these Zr-based amorphous glasses did not display appreciable macroscopic plastic deformation prior to catastrophic fracture, rather they mainly deformed elastically, followed by catastrophic failure along their shear bands. Examination of the fracture regions... 

Yield strength is a measnre of the force that a material can withstand before it suffers macroscopic plastic deformation. For most materials, e.g., metal, it is taken as the point on the stress-strain cnrve when the line becomes non-linear (the elastic limit). However, for plastics, it is taken as the peak of the stress-strain curve, as that is simpler to measure. In practice, most parts are designed so that they never experience a force approaching the yield stress because yielding represents failure of the material. 

Dislocations occur in lattices other than those of atomic-scale crystals. The best known examples, no doubt, are those in the experiments of Bragg and Nye with rafts of soap bubbles [1]. Their work illustrated the geometry and kinematics of the edge dislocations in these two-dimensional hexagonal lattices, and vividly revealed how macroscopic plastic deformation of crystals is effected by the motion of large numbers of such dislocations. Ahead of the definitive identification of moving dislocations in atomic crystals by electron microscopy [2], Bragg and Nye s experiments had convinced many of the reality and the potential of what had initially been a purely theoretical concept [3-5]. 

Although the results described above have been observed for thin films under tension and large-strain plastic deformation is usually observed only for localized regions - crazes or shear deformation zones - Meijer has demonstrated that macroscopic plastic deformation can be indeed observed for these amorphous polymers under tension, as far as the thickness of the deformed polymer is less than a critical value [3-8]. Thin... 

Separation of a solid accompanied by little or no macroscopic plastic deformation. Typically, brittle fracture occurs by rapid crack propagation with less expenditure of energy than for ductile fracture. 

Some materials, notably annealed mild steel, show a rather different yielding behaviour, indicated schematically in Fig. 3.2(b). Starting at 0, a long elastic range is sharply terminated at A, when the stress reaches a value known as the upper yield stress. There is an abrupt partial unloading and macroscopic plastic deformation... 

This change in behaviour under a confining pressure accounts for the macroscopic plastic deformation of many materials normally considered brittle. Many rocks, for example, deform plastically under a sufficiently high confining pressure. 

The process by which plastic deformation is produced by dislocation motion is termed slip the crystallographic plane along which the dislocation line traverses is the slip plane, as indicated in Figure 7.1. Macroscopic plastic deformation simply corresponds to permanent deformation that results from the movement of dislocations, or slip, in response to an applied shear stress, as represented in Figure 7.2a. 

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