Plastic deformation slip plane

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... 

Mark, Polanyi and Schmid, of the constant resolved shear-stress law, which specifies that a crystal begins to deform plastically when the shear stress on the most favoured potential slip plane reaches a critical value. 

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... 

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... 

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. 

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. 

This is slip that occurs simultaneously on several slip planes having Ihe same slip direction. See Fig. 14. This type of plastic deformation is normally associated with the movement of screw dislocations. Screw dislocations can move on any slip plane that passes through the dislocation. This is a result of the fact that the slip plane of a dislocation is that plane which contains both the dislocation and its Burgers veclor, and the fact that the Burgers vector of a screw dislocation lies parallel io the dislocation itself,... 

Microcrystalline cellulose is one of the most commonly used filler-binders in direct compression formulations because it provides good binding properties as a dry binder, excellent compactibility, and a high dilution potential. It also contributes good disintegration and lubrication characteristics to direct compression formulas. When compressed, microcrystalline cellulose undergoes plastic deformation. The acid hydrolysis portion of the production process introduces slip planes and dislocations into the material. Slip planes, dislocations, and the small size of the individual crystals aid in the plastic flow that takes place. The spray-dried particle itself, which has a higher porosity compared with the absolute porosity of cellulose, also deforms... 

Once the crack is initiated, the metal surface inside the crack may be quite different from the normal surface of the metal. Thus, in the course of plastic deformation, the metal could have developed slip steps [see Fig. 12.77(c)] which contain crystallographic planes of high Miller index at which the specific dissolution rate (or exchange current density) may be larger than that at the normal metal surface. Anodic current densities of some 104 times those at a passive surface have been shown to appear at a metal surface that is yielding under stress (Despic and Raicheff, 1978). 

Slip planes Plastic deformation (or yielding) of a solid metal occurs when parallel lattice planes slip past each other. Those planes are called slip planes. 

The absence of a lattice-based mechanism, such as slip planes, does not necessarily preclude aU deformation in brittle materials. Plastic flow can proceed in other modes. For example, at temperatures of about 40 percent to 50 percent of their melting points, grain-boundary shding can become important. Grain-boundary sliding is beheved to be the major contributor to the superplasticity observed in some polycrystal-hne ceramics. 

Slip relies on chemical bond breaking and bond reformation as two planes of atoms pull apart. It is observed that the critical resolved shear stress required to cause plastic deformation in real materials is much lower (by several orders of magnitude) than the shear stress required in deforming perfect defect-free crystals, the so-called ideal shear stress. The latter is equivalent to the stress required for the simultaneous ghding motion (bond breaking and reformation) of aU the atoms in one plane, over another plane. 

Single-crystal and poly crystalline transition metal carbides have been investigated with respect to creep, microhardness, plasticity, and shp systems. The fee carbides show slip upon mechanical load within the (111)plane in the 110 direction. The ductile-to-brittle transformation temperature of TiC is about 800 °C and is dependent on the grain size. The yield stress of TiC obeys a Hall Petch type relation, that is, the yield stress is inversely proportional to the square root of the grain size. TiC and ZrC show plastic deformation at surprisingly low temperatures around 1000 °C. 

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