Plastic deformation, 2.20

Continuing the discussion on the deformation of a solid bar loaded axially in tension, it is interesting to consider the phenomena after the limit of elastic deformation is reached. As the tension on the bar increases progressively, the atoms are pulled farther and farther apart 

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. 

The plastic deformation of a member terminates with its rupture which normally occurs at the smallest section of the neck formed due to plastic instability. After being loaded into the plastic range, if the member is unloaded before plastic instability occurs then the elastic component of the strain can be recovered. This is a consequence of the atoms returning to 

It may be pointed out that the term yield point is sometimes erroneously used as a synonym for elastic limit and proportional limit As it has been described in the paragraphs above it is actually a phenomenon that occurs in only a very small number of cases in tensile testing. As it has also been observed in the description that graphically and experimentally, it is an anomalous behaviour in which there is a strain occurring with no increase in stress. 

True stress, o, is defined as o = F/A where A is the actual area of cross section of the member corresponding to the load F. 

From an atomic perspective, plastic deformation corresponds to the breaking of bonds with original atom neighbors and then the re-forming of bonds with new neighbors as large numbers of atoms or molecules move relative to one another upon removal of the stress, they do not return to their original positions. The mechanism of this deformation is different for crystalline and amorphous materials. For crystalline solids, deformation is accomplished by means of a process called slip, which involves the motion of dislocations as discussed in Section 7.2. Plastic deformation in noncrystalline solids (as well as liquids) occurs by a viscous flow mechanism, which is outlined in Section 12.10. 

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). 

When a fine-grained, poly crystalline wire of a ductile material is deformed under an axial load the stress-strain curve obtained has the form shown by the full line in Fig. 3.2(a), where the initial area of cross-section is used to calculate the stress from the applied forces. Permanent deformation occurs when the stress exceeds the yield stress Oy so that, on reducing the stress to zero, a permanent deformation results. For example, if the specimen is unloaded when the point B is reached, the unloading path is not BAO but BC, which has approximately the same slope as OA. Of the total strain corresponding to the point B, the elastic strain 

Along the region of the curve ABD the stress increases with the total strain, which indicates that the material becomes progressively harder (though not usually at a constant rate) as it is deformed plastically, a phenomenon known as w ork hardening. If the test specimen is a suitably squat cylinder the behaviour observed in a compression test is very similar to that obse/ved in tension over the range of strain represented by the curve ABD there is a range of purely elastic deformation and, at a stress closely equal to the yield stress in tension, plastic deformation occurs and the material work hardens. 

Plastic deformation takes place at effectively constant volume of the specimen and, therefore, a cylinder under an axial stress undergoes a considerable change in cross-sectional area when the strain exceeds a few per cent. This is a much greater change in area than that observed in elastic deformation and it necessitates a more careful definition of stress. Two definitions are in common use. 

When 0 is plotted instead of (the dotted curve in Fig. 3.2(a)) there is very little difference at small strains, though is always larger than in tension. When the point of instability D is reached, 

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 

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In addition, on the basis of analogous specimens, the accumulation of damage and plastic deformation of metal structure were simulated. These results provide the possibility to obtain the prediction charts of the metal work s residual resource. 

The application of load in materials produces internal modifications such as crack growth, local plastic deformation, corrosion and phase changes, which are accompanied by the emission of acoustic waves in materials. These waves therefore contain information on the internal behaviour of the material and can be analysed to obtain this information. The waves are detected by the use of suitable sensors, that converts the surface movements of the material into electric signal. These signals are processed, analysed and recorded by an appropriate instrumentation. 

According to data /3/, the AE sources in the fibrous composites are plastic deformation and cracking of the die material, shift stratification on the fibre-die interphase border, fibre destmction and stretching fibres out of the die. 

Whereas in the scope of plastic deformations differences are observed Arc welding of pipes <6 32 mm, wall thickness 6,5 mm has caused own tensile stress of 260 MPa in the jont, relief at 720°C during 4 hours, has caused a lowering of stress to 60 MPa. 

The calibration graph for the probe using a strength machine, has been shown in Fig. 7 It can be observed that the dependence of indications of the device of Wirotest type on the loading is linear within the proportionality limit scope. After unloading the indications do not return to zero, but show own stress caused in effect of plastic deformation of the tested sample... 

The plastic deformation, the creep deformation, and the bonding process on the bonding interface can be presumed from the height of the echo. 

On the other hand, the reliability of the product improves, too, if each state of the plasticity deformation, the creep deformation, and the diffusion joint in the solid phase diffusion bonding as the bonding process, is accurately understood, and the bonding process is controlled properly. 

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. 

A number of friction studies have been carried out on organic polymers in recent years. Coefficients of friction are for the most part in the normal range, with values about as expected from Eq. XII-5. The detailed results show some serious complications, however. First, n is very dependent on load, as illustrated in Fig. XlI-5, for a copolymer of hexafluoroethylene and hexafluoropropylene [31], and evidently the area of contact is determined more by elastic than by plastic deformation. The difference between static and kinetic coefficients of friction was attributed to transfer of an oriented film of polymer to the steel rider during sliding and to low adhesion between this film and the polymer surface. Tetrafluoroethylene (Telfon) has a low coefficient of friction, around 0.1, and in a detailed study, this lower coefficient and other differences were attributed to the rather smooth molecular profile of the Teflon molecule [32]. 

In elastoplastic models, it is assumed that there exist plastic deformations denoted by ij. The Hencky law implies that the following relations hold (Annin, Cherepanov, 1983 Duvaut, Lions, 1972) ... 

Here ij denotes a plastic deformation velocity. Adding the relations (1.10), (1.11), we obtain the quasi-static elastoplastic model... 

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. 

Partially Plastic Thick-Walled Cylinders. As the internal pressure is increased above the yield pressure, P, plastic deformation penetrates the wad of the cylinder so that the inner layers are stressed plasticady while the outer ones remain elastic. A rigorous analysis of the stresses and strains in a partiady plastic thick-waded cylinder made of a material which work hardens is very compHcated. However, if it is assumed that the material yields at a constant value of the yield shear stress (Fig. 4a), that the elastic—plastic boundary is cylindrical and concentric with the bore of the cylinder (Fig. 4b), and that the axial stress is the mean of the tangential and radial stresses, then it may be shown (10) that the internal pressure, needed to take the boundary to any radius r such that is given by... 

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. 

Some materials that are atomically ordered also develop a sHp-iaduced anisotropy as a result of plastic deformation. The origin is thought to be identical to that of thermomagnetic anisotropy, ie, short-range directional order, except that the order is brought on by deformation rather than by heat treatment ia a field (3,4). 

It also is possible to develop square hysteresis loops via the sHp-iaduced anisotropy through plastic deformation. This technique had been employed ia the commercial processiag of Twistor memories (25) no longer used ia telephone electronic systems. 

Hot pressing to produce substantial texture and magnetic anisotropy via plastic deformation is accompHshed by a process referred to as... 

Working Treatments. Restricted plastic deformation takes place entirely within the confines of a closed die cavity. A sintered part may be placed in the die cavity and pressure appHed to the part. This pressure generally is of the same magnitude as the original compaction pressure. This second apphcation of pressure can be categorized as follows. 

A series of events can take place in response to the thermal stresses (/) plastic deformation of the ductile metal matrix (sHp, twinning, cavitation, grain boundary sliding, and/or migration) (2) cracking and failure of the brittle fiber (5) an adverse reaction at the interface and (4) failure of the fiber—matrix interface (17—20). 

Machine components ate commonly subjected to loads, and hence stresses, which vary over time. The response of materials to such loading is usually examined by a fatigue test. The cylinder, loaded elastically to a level below that for plastic deformation, is rotated. Thus the axial stress at all locations on the surface alternates between a maximum tensile value and a maximum compressive value. The cylinder is rotated until fracture occurs, or until a large number of cycles is attained, eg, lO. The test is then repeated at a different maximum stress level. The results ate presented as a plot of maximum stress, C, versus number of cycles to fracture. For many steels, there is a maximum stress level below which fracture does not occur called the... 

Case Hardening by Surface Deformation. When a metaUic material is plastically deformed at sufficiently low temperature, eg, room temperature for most metals and alloys, it becomes harder. Thus one method to produce a hard case on a metallic component is to plastically deform the surface region. This can be accomplished by a number of methods, such as by forcing a hardened rounded point onto the surface as it is moved. A common method is to impinge upon the surface fine hard particles such as hardened steel spheres (shot) at high velocity. This process is called shot... 

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