Obstacles to dislocation motion

It is now worth summarizing some of the mechanisms that lead to the formation of such obstacles. 

As pointed out earlier, dislocations can interact strongly with each other and, thus, techniques to increase the dislocation density will also act to strengthen the material. As dislocations intersect, jogs are often formed and these act to pin dislocations. In addition, reactions can occur between dislocations to form sessile dislocations, which then act as barriers to the other glide dislocations. 

After the various dislocation interactions, the stress needed for further plastic deformation will depend on the mean free dislocation length L. The dislocation density should be proportional to ML and thus Eq. (6.22) can be used to estimate the shear stress needed to overcome the obstacles, i.e.. 

Dislocation structures at high strains can become rather complex, often forming cellular structures. In these cases, the process is closer to a boundary interaction, which will be described next. 

The introduction of small particles into a ductile material can substantially increase the yield strength, even if the volume fraction is low ( 10 vol.%). The particles can be introduced by precipitation (precipitation hardening) or by physical addition (dispersion strengthening). For example. Fig. 6.28 shows the effect of precipitation of Mg0.Fe203 on the stress-strain behavior of MgO. The extent of the strengthening is determined by several factors, including volume fraction. 

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Two types of basic creep mechanisms have been identified in models for dislocation creep. (1) In glide-controlled creep, the obstacles to dislocation motion are on the scale of the dislocation core the obstacles are overcome by... 

From a mechanistic perspective, what transpires in the context of all of these strengthening mechanisms when viewed from the microstructural level is the creation of obstacles to dislocation motion. These obstacles provide an additional resisting force above and beyond the intrinsic lattice friction (i.e. Peierls stress) and are revealed macroscopically through a larger flow stress than would be observed in the absence of such mechanisms. Our aim in this section is to examine how such disorder offers obstacles to the motion of dislocations, to review the phenomenology of particular mechanisms, and then to uncover the ways in which they can be understood on the basis of dislocation theory. 

Figure 6.26 Obstacles to dislocation motion leads to bowing of dislocations as they glide through the material.

Although Y ions present only weak obstacles to dislocation motion [58], they are present in high concentrations and could, in theory, yield a large contribution to the flow stress. However, the crystals presently available apparently contain very small precipitates of ZrN [71] which provide stronger obstacles to slip than do unassociated Y ions [58, 72, 73]. Nonetheless, these unassociated Y ions do cause plastic instabilities, such as dynamic strain aging or the Portevin-Le Chatelier effect in... 

The yield and ultimate tensile strengths of annealed oxygen-free copper are shown in Fig. 3.7. This figure shows that the yield strength of a material can be insensitive to temperature while its tensile strength is increasing by more than a factor of 2. The material has work-hardened. That is, the material has hardened itself by generating obstacles to dislocation motion. 

The host of interesting kinetic processes associated with the movement of dislocations through materials containing various obstacles to their motion is far too large to be described in this book. The reader is therefore referred to specialized texts [2, 7-9]. 

As noted above, our working hypothesis concerning the various hardening mechanisms is that chemical impurities, second-phase particles and even other dislocations serve as obstacles to the motion of a given dislocation. As a result of the presence of these obstacles, the intrinsic lattice resistance tp is supplemented by additional terms related to the various strengthening mechanisms. We further assume that the flow stress can be written as... 

A dislocation line can encounter various obstacles to its motion. In such a case, the dislocation becomes pinned by the obstacle and curves, due to the forces exerted by the obstacle resisting its motion. Small forces cannot make such a dislocation move. Figure 3.45 shows the bowing of a dislocation line after it has been pinned at both ends, at points A and B, by obstacles, perhaps foreign particles in the material or some other precipitates. In order to better understand this phenomenon, consider Eq. (3.35), which allows (3.45) to be rewritten as ... 

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. 

Our current ambition is to elucidate one of the microscopic mechanisms that has been charged with giving rise to solution and precipitate hardening. The argument is that by virtue of the elastic fields induced by an obstacle there will be a force on a dislocation which the dislocation must overcome in its motion through the crystal. As a first step towards modeling this phenomenon, we imagine the obstacle to be a spherical disturbance within the material. As was already demonstrated in chap. 7, such an obstacle produces spherically symmetric displacement fields of the form Ur = Ar + bjr. ... 

A more sophisticated consideration of the forces that are exerted upon a dislocation as it glides through a medium populated by a distribution of obstacles is depicted in fig. 11.26. In this case, the fundamental idea that is being conveyed is to divide the character of various obstacles along the lines of whether or not they are localized or diffuse and whether or not they are strong or weak . These different scenarios result in different scaling laws for the critical stress to induce dislocation motion. 

As noted above, one interesting application of these ideas is to the motion of a dislocation through an array of obstacles. An alternative treatment of the field due to the disorder is to construct a particular realization of the random field by writing random forces at a series of nodes and using the finite element method to interpolate between these nodes. An example of this strategy is illustrated in fig. 12.27. With this random field in place we can then proceed to exploit the type of line tension dislocation dynamics described above in order to examine the response of a dislocation in this random field in the presence of an increasing stress. A series of snapshots in the presence of such a loading history is assembled in fig. 12.28. 

As will be seen later, the use of obstacles such as particles is often used to strengthen ductile materials by impeding dislocation motion. 

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