Chapter 7. DISLOCATIONS AND STRENGTHENING MECHANISM

Introduction
The key idea of the chapter is that plastic deformation is due to the motion of a large number of dislocations. The motion is called slip. Thus, the strength (resistance to deformation) can be improved by putting obstacles to slip.

Basic Concepts
Dislocations can be edge dislocations, screw dislocations and exist in combination of the two (Ch. 4.4). Their motion (slip) occurs by sequential bond breaking and bond reforming (Fig. 7.1). The number of dislocations per unit volume is the dislocation density, in a plane they are measured per unit area.

Characteristics of Dislocations
There is strain around a dislocation which influences how they interact with other dislocations, impurities, etc. There is compression near the extra plane (higher atomic density) and tension following the dislocation line (Fig. 7.4)
Dislocations interact among themselves (Fig. 7.5). When they are in the same plane, they repel if they have the same sign and annihilate if they have opposite signs (leaving behind a perfect crystal). In general, when dislocations are close and their strain fields add to a larger value, they repel, because being close increases the potential energy (it takes energy to strain a region of the material).
The number of dislocations increases dramatically during plastic deformation. Dislocations spawn from existing dislocations, and from defects, grain boundaries and surface irregularities.

Slip Systems
In single crystals there are preferred planes where dislocations move (slip planes). There they do not move in any direction, but in preferred crystallographic directions (slip direction). The set of slip planes and directions constitute slip systems.
The slip planes are those of highest packing density. How do we explain this? Since the distance between atoms is shorter than the average, the distance perpendicular to the plane has to be longer than average. Being relatively far apart, the atoms can move more easily with respect to the atoms of the adjacent plane. (We did not discuss direction and plane nomenclature for slip systems.)
BCC and FCC crystals have more slip systems, that is more ways for dislocation to propagate. Thus, those crystals are more ductile than HCP crystals (HCP crystals are more brittle).

Slip in Single Crystals
A tensile stress s will have components in any plane that is not perpendicular to the stress. These components are resolved shear stresses. Their magnitude depends on orientation (see Fig. 7.7).
tR = s cos f cos l
If the shear stress reaches the critical resolved shear stress tCRSS, slip (plastic deformation) can start. The stress needed is:
sy = tCRSS / (cos f cos l)max
at the angles at which tCRSS is a maximum. The minimum stress needed for yielding is when f = l = 45 degrees: sy = 2tCRSS. Thus, dislocations will occur first at slip planes oriented close to this angle with respect to the applied stress