Dislocation friction stress

D. Kuhlmann-Wilsdorf, Frictional Stress Acting on a Moving Dislocation in an Otherwise Perfect Crystal. Phys. Rev., 120,773 (1960). 

The values of obtained from Eq. (6.4) are usually found to be less than the experimental yield strength values in many materials and, thus, one concludes these materials must contain strengthening mechanisms. The frictional stress is clearly very sensitive to the dislocation width and, thus, it is important to identify the material properties that govern this parameter. Dislocation width is governed primarily by the nature of the atomic bonding and crystal structure. In covalent solids, the bonding is strong and directional and, hence, dislocations are very narrow (w b). In ionic solids and bcc metals, the dislocations are moderately narrow whereas in fee metals dislocations are wide (w>106). 

The stress, Tf, needed to move a dislocation along the slip plane is known as the Peirels-Nabarro (or frictional) stress and is given by... 

Other inner stresses, caused for example by other obstacles (see the next section), can counteract the external stress r in a similar way to the Peierls stress. They can thus also be considered as inner frictional forces or stresses. The stress t that is effectively available to move the dislocation is thus t = T — T[. If a certain kind of obstacle is investigated, it is often useful to combine the contributions of aU other obstacles to a single frictional stress Tj and to assume that the dislocation is driven by the effective stress t. ... 

Far away from the obstacle, a frictional stress t is required to move the dislocation (see section 6.2.9). In the region of the obstacle, the required stress increases and then decreases again behind it. If we assume that the effect of the obstacle is restricted to its vicinity, the required stress increases steeply. To simplify the calculations, we approximate the resulting stress curve by a rectangular one with the appropriate height and width. The width d of the rectangle is then a measure of the width of the obstacle. 

We subtracted the frictional stress n because it does not describe the effect of the obstacle, but of the material without it. Q is the obstacle energy, the energy barrier the dislocation has to overcome. 

The viscosity coefficients at dislocation cores can be measured either from direct observations of dislocation motion, or from ultrasonic measurements of internal friction. Some directly measured viscosities for pure metals are given in Table 4.1. Viscosities can also be measured indirectly from internal friction studies. There is consistency between the two types of measurement, and they are all quite small, being 1-10% of the viscosities of liquid metals at their melting points. It may be concluded that hardnesses (flow stresses) of pure... 

Under the influence of the applied stress, a dislocation loop can grow by glide only as sufficient HOH diffuses to the growing segment to saturate the newly created core and develop a cloud of hydrolyzed Si—O bonds in the neighborhood of the dislocation in order to reduce the Peierls stress (the fundamental friction to the glide of a dislocation in a perfect crystal) to a very low value. 

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. 

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