Orowan looping

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. 

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. 

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. 

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