Orowan mechanism

Although the external shear stress on this so-called secondary slip plane or cross slip plane is smaller than on the primary one, moving along this path can be easier than trying to overcome the obstacle by cutting or the Orowan mechanism. This is the case if the effective shear stress t (see section 6.2.9) on the secondary slip plane is larger than on the primary one due to the absence of the obstacle force. Because screw dislocations can use this additional mechanism, they are frequently able to overcome obstacles more easily than edge dislocations. 

The influence of the dislocation density on the strength of a metal can be estimated Consider a dislocation line moving through an array of dislocations perpendicular to it as sketched in figure 6.34. Let the distance between the dislocation obstacles be 2A. If the dislocations were insurmountable, they would have to be by-passed with the Orowan mechanism. As they can be cut instead, the necessary stress is smaller than the Orowan stress. This results in Tout = kd Gbj2X, with fed 0.1... 0.2. 

Small particles of a second phase, evenly distributed in the grains of the first phase, form a strong barrier to dislocation motion. This was previously discussed in section 6.3, and we saw there that there are two possible ways to overcome such obstacles, the Orowan mechanism and cutting of the particles. The mechanism actually occurring depends on the strength of the obstacles and on their distance. This strengthening mechanism is frequently called precipitation hardening, because the particles are usually created by a precipitation process, described below. 

Consequently, large radii are disadvantageous because the particles are overcome by the Orowan mechanism as the particle distance increases. 

A further increase in dislocation density occurs during plastic deformation because plastic deformation is usually limited to the matrix, leading to a formation of dislocation loops around the fibres (see also section 6.4.4). The Orowan mechanism (see section 6.3.1 and figure 6.45), which would impede dislocation movement, is not relevant, though, because the fibre diameter and distance are too large. 

Research work conducted over many years [118-121] has demonstrate that through composite electrodeposition, significant improvements in the properties of the pure metal matrix can be achieved, including hardness, wear resistance, and corrosion behavior. In particular, the incorporation of ceramic or other hard particles is an effective way to improve coating hardness and wear resistance. Hardness increase can be explained according to the Orowan mechanism of dispersion hardening [122], as long as particle size is less than 1 pm [119]. This increase depends on the interparticle distance, i.e., on particle size and volume fraction of the hard phase. 

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. 

E. Orowan, Zur Kristallplastizitat. III. Uberden Mechanisms des Gleitvorganges, Z. Phys. 89, Nenntes und Zehntes Heft, 634-659 (1934). 

Orowan bowing mechanisms, 13 502 Orphan Drug Act, 18 686 Orpiment, 3 263t Orris, in perfumes, 18 369 Orr-Sherby-Dorn parameter, 13 478 Ortacrone, molecular formula and structure, 5 95t... 

Polanyi, My time with x-rays and crystals, in Fifty Years of X-Ray Diffraction, 636. G.I. Taylor, The mechanism of plastic deformation of crystals, Proceedings of the Royal Society A145 (1934) 362-415 E. Orowan, "Zur Kristallplastizitat, Zeitschriftfur Physik 89 (1934) 605-659. On recent studies of dislocation, see R. F. Service, Materials scientists view hot wires and bends by the bay, Science 272 (1996) 484-485. 

Fig. 11.31. Schematic of the Orowan looping and particle cutting mechanisms that arise from interaction of dislocations with foreign particles (adapted from Gerrold (1979)).

Note that we have followed Reppich (1993) in this equation by burying the dependence of the results on the particular mechanism of hardening in the parameter h. One of the key observations that we can make at this point is that with increasing particle radius it becomes increasingly difficult to cut the particles. Evidently, if there is some competing mechanism and a certain size is reached for which it is easier to institute that mechanism, we will see a transition in the dependence on particle size. The mechanism of Orowan looping alluded to earlier is just such a mechanism. 

Plausible back of the envelope models may be developed for the emergence of the Orowan looping mechanism. We have already seen that the stress at which such looping commences is given by xioop = 2T/bLgff. As we noted earlier, these results can be cast in a much more desirable form if their dependence on microstructural parameters is made manifest. Our earlier discussion culminating in eqn (11.85) showed that... 

A seeond venue within which it is possible to examine the validity of the various approximations considered above is through a direct appeal to the experiments themselves as shown in fig. 11.34. The experimental observations reported in the figure consider fhe relatively simpler case in which the critical stress for Orowan looping is evaluated for a variety of different interparticle spacings. As seen above, because of the wide variety of different mechanisms all giving rise to FmaxS to be used in conjunction with the expression for particle cutting, it is more difficult to make a defiiutive falsification of the theoretical models. 

Orowan, E. (1943). The calculation of roll pressure in hot and cold flat rolling. Proceedings of the Institution of Mechanical Engineers, 150, 140-167. 

Slip bands and kink bands were first studied in compression of oriented nylon 6,6 and 6,10 by Zaukelies, and subsequently in tensile specimens of oriented high density polyethylene (HOPE) by Kurakawa and Ban and Keller and Rider Zaukelies interpreted the angle between kink bands in oriented nylon and the compression axis in terms of Orowan s theory of crystal kinking, postulating dislocation mechanisms for the process. Keller and Rider ° and Kurakawa and Ban were impressed by the appearance of deformation bands in high density polyethylene in directions close to the IDD. In this polymer system the... 

Orowan, E. (1954) Dislocations and mechanical properties, in Dislocations in Metals, edited by M. Cohen, New York AIME-Institute of Metals. 

Because of the importance of failure phenomena in any consideration of multicomponent polymer systems, a brief review of the energetics and mechanics of fracture follows (Andrews, 1968, 1972 Berry, 1961 Broutman and Kobayashi, 1972 Eirich, 1965 Griffith, 1921 Halpin and Polley, 1967 Hertzberg et al, 1973 Johnson and Radon, 1972 Kambour and Robertson, 1972 Krauss, 1963 Lannon, 1967 Manson and Hertzberg, 1973u Mark, H., 1943,1971 Orowan, 1948 Prevorsek, 1971 Prevorsek and Lyons, 1964 Radon, 1972 Riddell et ai, 1966 Rivlin and Thomas, 1953 Rosen, 1964 Tobolsky and Mark, 1971 Williams, M. L., and DeVries, 1970 Zhurkhov and Tomashevskii, 1966). Specific cases are discussed in Sections 3.2 and 12.1.2. 

As noted above and discussed below, the key micro-mechanism in the deformation of the MAX phases is the kink band (KB). The KBs in crystalline solids were first observed in Cd single crystals loaded parallel to their basal planes by Orowan, who... 

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