Plastic deformation by slip

One fundamental experimental observation on simple crystals is that, except at very high pressures, the application of a uniform hydrostatic pressure to a crystal does not lead to plastic deformation. Application of the methods of section 2.9 shows that, when an isotropic solid is subjected to a uniform hydrostatic pressure, the shear stress on any plane in the solid is zero. From this it may be surmised that plastic deformation of a crystalline solid occurs as the result of shearing processes. 

Microscopic and X-ray studies on deformed crystals bear this out. When a crystalline specimen with polished surfaces is deformed plastically and then examined under a low-power light microscope, the surfaces are, in general, found to be crossed by a large number of fine dark lines, known as slip lines. They result from a process in which adjacent blocks of molecules slip past each other. Because of the periodic nature of the molecular structure of crystals, it is expected that the blocks will slip over each other by one or more complete inter molecular distances. This would leave the crystal structure essentially unchanged by the slipping process, a result confirmed by X-ray diffraction. 

When the relative displacement of two adjacent blocks is large enough, a small slip step is produced on the polished surface of the crystal, and this appears in the light microscope as a fine dark line. A surface on which slip has taken place is known as a slip surface in many situations this surface is planar, when it is referred to as a slip plane. 

Plastic deformation is produced by the shear stresses set up in the material and another basic law of plastic deformation, applicable most simply to single crystals, is that the plastic strain depends only on the shear stress in the slip plane, resolved parallel to the slip direction. Further, appreciable plastic deformation by slip starts when this resolved shear stress reaches a fairly well-defined value called the critical resolved shear stress (c.r.s.s.). This is Schmidt s law and it embodies the result that the yield stress is a characteristic of a given material, other conditions being the same. 

A single crystal under tension will slip as shown in Fig. 3.3 and in this case it is a straightforward matter to calculate the resolved 

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A dislocation is defined as being perfect when b is a lattice translation vector and imperfect when it is not a lattice translation vector. A lattice translation vector is any vector which joins two points of the crystal lattice and when the line is extended these points are repeated at regular intervals along the line. Since plastic deformation by slip does not change the crystal structure, the Burgers vectors, that is, the slip vectors for the dislocations which accomplish slip, must be lattice translation vectors and the dislocations must be perfect dislocations. Furthermore, dislocations with the smallest possible lattice translation vectors, the primitive lattice translation vectors, are expected because these have the least energy. The Burgers vector for face-centered cubic metals and NaCl structured ionic crystals is thus a<110> and it is fl for body-centered cubic metals, where a is the lattice parameter of the unit cell. 

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. 

The block-like slip produced by the shear or offset of a crystal between layers of atoms that maintains that the same crystal structure and cohesion before and after slip occurs. Metals commonly plastically deform by intra-crystalline slip. 

Inelastic deformation can occur in crystalline materials by plastic flow . This behavior can lead to large permanent strains, in some cases, at rapid strain rates. In spite of the large strains, the materials retain crystallinity during the deformation process. Surface observations on single crystals often show the presence of lines and steps, such that it appears one portion of the crystal has slipped over another, as shown schematically in Fig. 6.1(a). The slip occurs on specific crystallographic planes in well-defined directions. Clearly, it is important to understand the mechanisms involved in such deformations and identify structural means to control this process. Permanent deformation can also be accomplished by twinning (Fig. 6.1(b)) but the emphasis in this book will be on plastic deformation by glide (slip). 

Slip. (1) The mechanism by which shear stress causes plastic deformation, by driving lines of dislocation across certain crystal planes, the slip or glide planes. 

It is reasonable to assume that a solid will deform in an affine manner this is the elastic assumption. Note that in metal crystals plastic deformation by dislocation glide on slip planes is not affine. The crystal between the slip planes is not plastically distorted all the deformation occurs at the slip plane. 

Shear fracture (microscopically ductile fracture) occurs by plastic deformation with slip in the direction of planes of maximum shear stress (see sections 3.3.2 and 6.2.5). Therefore, it occurs only in ductile materials. In most cases, shear fracture is associated with large macroscopic deformations, as, for example, in a tensile test. However, if this is prevented by the component geometry, the component may fail macroscopically brittle, but still with a shear fracture. This may happen if there are notches or cracks in the material (see chapters 4 and 5). 

Slip Plastic deformation by irreversible shear displacement of one part of crystal with respect to another in a definite crystallographic direction and on a specific crystallographic plane. 

These spinel materials are densified at stresses and temperatures at which plastic deformation by multiple slip processes is readily induced in densified poly crystalline spinel (/ 24 there is no reason to think that the material... 

As early as the 1930s Scheil (1932) predicted the formation of martensite above M, by the application of a stress. According to him, the shear stress required to activate the transformation decreases with decreasing temperature (being zero at M,) whereas the shear stress required for austenite slip increases with decreasing temperature. Thus, at temperatures near applied stresses should induce plastic deformation by the martensitic mode rather than by 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... 

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. 

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... 

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.

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. 

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