Plastic deformation slip

Grady and Asay [49] estimate the actual local heating that may occur in shocked 6061-T6 Al. In the work of Hayes and Grady [50], slip planes are assumed to be separated by the characteristic distance d. Plastic deformation in the shock front is assumed to dissipate heat (per unit area) at a constant rate S.QdJt, where AQ is the dissipative component of internal energy change and is the shock risetime. The local slip-band temperature behind the shock front, 7), is obtained as a solution to the heat conduction equation with y as the thermal diffusivity... 

The papers which introduced the concept of a dislocation all appeared in 1934 (Polanyi 1934, Taylor 1934, Orowan 1934). Figure 3.20 shows Orowan s original sketch of an edge dislocation and Taylor s schematic picture of a dislocation moving. It was known to all three of the co-inventors that plastic deformation took place by slip on lattice planes subjected to a higher shear stress than any of the other symmetrically equivalent planes (see Chapter 4, Section 4.2.1). Taylor and his collaborator Quinney had also undertaken some quite remarkably precise calorimetric research to determine how much of the work done to deform a piece of metal... 

The (110) dislocations are from our calculations not expected to contribute significantly to the plastic deformation in hard oriented NiAl because of the very high Peierls stresses. Experimentally, these dislocations do not appear unless the temperature is raised to about 600 K [18]. At this temperature the experimental data strongly suggest a transition from (111) to (110) slip. 

Fig. 4. Model of local plastic deformation of lamellae beneath the stress field of the indenter. The mosaic block structure introduces a weakness element allowing faster slip at block boundaries leading to fracture (right)...

In static friction, the change of state from rest to motion is caused by the same mechanism as the stick-slip transition. The creation of static friction is in fact a matter of choice of system state for a more stable and favorable energy condition, and thus does not have to be interpreted in terms of plastic deformation and shear of materials at adhesive junctions. 

Yielding is a manifestation of the possibility that some of the atoms (or molecules) in the stressed material may slip to new equilibrium positions due to the distortion produced by the applied tensile force. The displaced atoms can form new bonds in their newly acquired equilibrium positions. This permits an elongation over and above that produced by a simple elastic separation of atoms. The material does not get weakened due to the displacement of the atoms since they form new bonds. However, these atoms do not have any tendency to return to their original positions. The elongation, therefore, is inelastic, or irrecoverable or irreversible. This type of deformation is known as plastic deformation and materials that can undergo significant plastic deformation are termed ductile. 

If slip-line fields do not control plastic indentation, what does The answer is not the beginning of the plastic deformation, but the end of it. The end means after deformation hardening has occurred. That is, it is not the initial yield stress, Y0, that controls indentation, but the limiting yield stress, Y. This is... 

In textbooks, plastic deformation is often described as a two-dimensional process. However, it is intrinsically three-dimensional, and cannot be adequately described in terms of two-dimensions. Hardness indentation is a case in point. For many years this process was described in terms of two-dimensional slip-line fields (Tabor, 1951). This approach, developed by Hill (1950) and others, indicated that the hardness number should be about three times the yield stress. Various shortcomings of this theory were discussed by Shaw (1973). He showed that the experimental flow pattern under a spherical indenter bears little resemblance to the prediction of slip-line theory. He attributes this discrepancy to the neglect of elastic strains in slip-line theory. However, the cause of the discrepancy has a different source as will be discussed here. Slip-lines arise from deformation-softening which is related to the principal mechanism of dislocation multiplication a three-dimensional process. The plastic zone determined by Shaw, and his colleagues is determined by strain-hardening. This is a good example of the confusion that results from inadequate understanding of the physics of a process such as plasticity. 

The continuous chain model includes a description of the yielding phenomenon that occurs in the tensile curve of polymer fibres between a strain of 0.005 and 0.025 [ 1 ]. Up to the yield point the fibre extension is practically elastic. For larger strains, the extension is composed of an elastic, viscoelastic and plastic contribution. The yield of the tensile curve is explained by a simple yield mechanism based on Schmid s law for shear deformation of the domains. This law states that, for an anisotropic material, plastic deformation starts at a critical value of the resolved shear stress, ry =/g, along a slip plane. It has been... 

A second line of evidence Is provided by an experiment In which the degree of crosslinking of photopolymerlzed specimens was progressively Increased by exposure to Y-rays. The expectation was that crosslinking should reduce plastic deformation by preventing macromolecules from slipping past one another. 

Figure 5.9 Schematic illustration of plastic deformation in single crystals by (a) slip and (b) twinning. From Z. Jastrzebski, The Nature and Properties of Engineering Materials, 2nd ed. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

Beside dislocation density, dislocation orientation is the primary factor in determining the critical shear stress required for plastic deformation. Dislocations do not move with the same degree of ease in all crystallographic directions or in all crystallographic planes. There is usually a preferred direction for slip dislocation movement. The combination of slip direction and slip plane is called the slip system, and it depends on the crystal structure of the metal. The slip plane is usually that plane having the most dense atomic packing (cf. Section 1.1.1.2). In face-centered cubic structures, this plane is the (111) plane, and the slip direction is the [110] direction. Each slip plane may contain more than one possible slip direction, so several slip systems may exist for a particular crystal structure. Eor FCC, there are a total of 12 possible slip systems four different (111) planes and three independent [110] directions for each plane. The... 

As the applied stress, ct, increases, the maximum resolved shear stress increases according to Eq. (5.19), finally reaching a critical value, called the critical resolved shear stress, Xcr, at which slip along the preferred plane begins and plastic deformation commences. We refer to the applied stress at which plastic deformation commences as... 

The presence of grain boundaries also affect slip in the material even after plastic deformation has commenced. A phenomenon known as strain hardening, or work hardening or cold working, is the result of constrained dislocation mobility and increased... 

Despite the similarities in brittle and ductile behavior to ceramics and metals, respectively, the elastic and permanent deformation mechanisms in polymers are quite different, owing to the difference in structure and size scale of the entities undergoing movement. Whereas plastic deformation (or lack thereof) could be described in terms of dislocations and slip planes in metals and ceramics, the polymer chains that must be deformed are of a much larger size scale. Before discussing polymer mechanical properties in this context, however, we must first describe a phenomenon that is somewhat unique to polymers—one that imparts some astounding properties to these materials. That property is viscoelasticity, and it can be described in terms of fundamental processes that we have already introduced. 

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. 

This is the process by which a crystal undergoes plastic deformation, as a result of which one atomic plane moves over another. Slip is believed to occur through the movement of dislocations. The total deformation of a given crystal is the sum of many small lateral displacements in parallel crystallographic planes of a given family. Moreover, each slip plane becomes more resistanl to further deformation than the remaining potential slip planes. 

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