Mechanical plastic deformation

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

The resistance to plastic flow can be schematically illustrated by dashpots with characteristic viscosities. The resistance to deformations within the elastic regions can be characterized by elastic springs and spring force constants. In real fibers, in contrast to ideal fibers, the mechanical behavior is best characterized by simultaneous elastic and plastic deformations. Materials that undergo simultaneous elastic and plastic effects are said to be viscoelastic. Several models describing viscoelasticity in terms of springs and dashpots in various series and parallel combinations have been proposed. The concepts of elasticity, plasticity, and viscoelasticity have been the subjects of several excellent reviews (21,22). 

Traditionally, production of metallic glasses requites rapid heat removal from the material (Fig. 2) which normally involves a combination of a cooling process that has a high heat-transfer coefficient at the interface of the Hquid and quenching medium, and a thin cross section in at least one-dimension. Besides rapid cooling, a variety of techniques are available to produce metallic glasses. Processes not dependent on rapid solidification include plastic deformation (38), mechanical alloying (7,8), and diffusional transformations (10). 

A hardness indentation causes both elastic and plastic deformations which activate certain strengthening mechanisms in metals. Dislocations created by the deformation result in strain hardening of metals. Thus the indentation hardness test, which is a measure of resistance to deformation, is affected by the rate of strain hardening. 

Once the precipitates grow beyond a critical size they lose coherency and then, in order for deformation to continue, dislocations must avoid the particles by a process known as Orowan bowing(23). This mechanism appHes also to alloys strengthened by inert dispersoids. In this case a dislocation bends between adjacent particles until the loop becomes unstable, at which point it is released for further plastic deformation, leaving a portion behind, looped around the particles. The smaller the interparticle spacing, the greater the strengthening. 

Two approaches have been taken to produce metal-matrix composites (qv) incorporation of fibers into a matrix by mechanical means and in situ preparation of a two-phase fibrous or lamellar material by controlled solidification or heat treatment. The principles of strengthening for alloys prepared by the former technique are well estabUshed (24), primarily because yielding and even fracture of these materials occurs while the reinforcing phase is elastically deformed. Under these conditions both strength and modulus increase linearly with volume fraction of reinforcement. However, the deformation of in situ, ie, eutectic, eutectoid, peritectic, or peritectoid, composites usually involves some plastic deformation of the reinforcing phase, and this presents many complexities in analysis and prediction of properties. 

Table 13 is a representative Hst of nickel and cobalt-base eutectics for which mechanical properties data are available. In most eutectics the matrix phase is ductile and the reinforcement is britde or semibritde, but this is not invariably so. The strongest of the aHoys Hsted in Table 13 exhibit ultimate tensile strengths of 1300—1550 MPa. Appreciable ductiHty can be attained in many fibrous eutectics even when the fibers themselves are quite britde. However, some lamellar eutectics, notably y/y —5, reveal Htde plastic deformation prior to fracture. 

Mechanical properties of mbber-modifted epoxy resins depend on the extent of mbber-phase separation and on the morphological features of the mbber phase. Dissolved mbber causes plastic deformation and necking at low strains, but does not result in impact toughening. The presence of mbber particles is a necessary but not sufficient condition for achieving impact resistance. Optimum properties are obtained with materials comprising both dissolved and phase-separated mbber (305). 

Machining of metals involves extensive plastic deformation (shear strain of ca 2—8) of the work material in a narrow region ahead of the tool. High tool temperatures (ca 1000°C) and freshly generated, chemically active surfaces (underside of the chip and the machined surface) that interact extensively with the tool material, result in tool wear. There are also high mechanical and thermal stresses (often cycHc) on the tool (3). 

This mechanism of crack inhibition is almost unique among ceramic systems, which do not undergo the plastic deformation under stress which is found in metallic systems (Figure 7.3). 

The fact that shock waves continue to steepen until dissipative mechanisms take over means that entropy is generated by the conversion of mechanical energy to heat, so the process is irreversible. By contrast, in a fluid, rarefactions do not usually involve significant energy dissipation, so they can be regarded as reversible, or isentropic, processes. There are circumstances, however, such as in materials with elastic-plastic response, in which plastic deformation during the release process dissipates energy in an irreversible fashion, and the expansion wave is therefore not isentropic. 

A. H. Cottrell, The Mechanical Properties of Matter, Wiley, 1964, Chap. 9. R. W. K. Honeycombe, The Plastic Deformation of Metals, Arnold, 1968,... 

From strength of materials one can move two ways. On the one hand, mechanical and civil engineers and applied mathematicians shift towards more elaborate situations, such as plastic shakedown in elaborate roof trusses here some transient plastic deformation is planned for. Other problems involve very complex elastic situations. This kind of continuum mechanics is a huge field with a large literature of its own (an example is the celebrated book by Timoshenko 1934), and it has essentially nothing to do with materials science or engineering because it is not specific to any material or even family of materials. 

Later, after the War, Tammann moved further towards physics by becoming interested in the mechanism of plastic deformation and the repair of deformed metals by the process of recrystallisation (following in the footsteps of Ewing and Rosenhain in Cambridge at the turn of the century), paving the way for the very extensive studies of these topics that followed soon after. Tammann thus followed... 

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