Chapter 7. Dislocations and Strengthening Mechanisms


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Chapter 7. Dislocations and Strengthening Mechanisms

    1. Introduction
    2. 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.

    3. Basic Concepts
    4. 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.

    5. Characteristics of Dislocations
    6. 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.

    7. Slip Systems
    8. 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).

    9. 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 (Figs. 7.8 and 7.9).

    1. Plastic Deformation of Polycrystalline Materials
    2. Slip directions vary from crystal to crystal. When plastic deformation occurs in a grain, it will be constrained by its neighbors which may be less favorably oriented. As a result, polycrystalline metals are stronger than single crystals (the exception is the perfect single crystal, as in whiskers.)

    3. Deformation by Twinning
    4. This topic is not included.

      Mechanisms of Strengthening in Metals

      General principles. Ability to deform plastically depends on ability of dislocations to move. Strengthening consists in hindering dislocation motion. We discuss the methods of grain-size reduction, solid-solution alloying and strain hardening. These are for single-phase metals. We discuss others when treating alloys. Ordinarily, strengthening reduces ductility.

    5. Strengthening by Grain Size Reduction
    6. This is based on the fact that it is difficult for a dislocation to pass into another grain, especially if it is very misaligned. Atomic disorder at the boundary causes discontinuity in slip planes. For high-angle grain boundaries, stress at end of slip plane may trigger new dislocations in adjacent grains. Small angle grain boundaries are not effective in blocking dislocations.

      The finer the grains, the larger the area of grain boundaries that impedes dislocation motion. Grain-size reduction usually improves toughness as well. Usually, the yield strength varies with grain size d according to:

      sy = s0 + ky / d1/2

      Grain size can be controlled by the rate of solidification and by plastic deformation.

    7. Solid-Solution Strengthening
    8. Adding another element that goes into interstitial or substitutional positions in a solution increases strength. The impurity atoms cause lattice strain (Figs. 7.17 and 7.18) which can "anchor" dislocations. This occurs when the strain caused by the alloying element compensates that of the dislocation, thus achieving a state of low potential energy. It costs strain energy for the dislocation to move away from this state (which is like a potential well). The scarcity of energy at low temperatures is why slip is hindered.

      Pure metals are almost always softer than their alloys.

    9. Strain Hardening
    10. Ductile metals become stronger when they are deformed plastically at temperatures well below the melting point (cold working). (This is different from hot working is the shaping of materials at high temperatures where large deformation is possible.) Strain hardening (work hardening) is the reason for the elastic recovery discussed in Ch. 6.8.

      The reason for strain hardening is that the dislocation density increases with plastic deformation (cold work) due to multiplication. The average distance between dislocations then decreases and dislocations start blocking the motion of each one.

      The measure of strain hardening is the percent cold work (%CW), given by the relative reduction of the original area, A0 to the final value Ad :

      %CW = 100 (A0Ad)/A0

      Recovery, recrystallization and Grain Growth

      Plastic deformation causes 1) change in grain size, 2) strain hardening, 3) increase in the dislocation density. Restoration to the state before cold-work is done by heating through two processes: recovery and recrystallization. These may be followed by grain growth.

    11. Recovery
    12. Heating increased diffusion enhanced dislocation motion relieves internal strain energy and reduces the number of dislocation. The electrical and thermal conductivity are restored to the values existing before cold working.

    13. Recrystallization
    14. Strained grains of cold-worked metal are replaced, upon heating, by more regularly-spaced grains. This occurs through short-range diffusion enabled by the high temperature. Since recrystallization occurs by diffusion, the important parameters are both temperature and time.

      The material becomes softer, weaker, but more ductile (Fig. 7.22).

      Recrystallization temperature: is that at which the process is complete in one hour. It is typically 1/3 to 1/2 of the melting temperature. It falls as the %CW is increased. Below a "critical deformation", recrystallization does not occur.

    15. Grain Growth

The growth of grain size with temperature can occur in all polycrystalline materials. It occurs by migration of atoms at grain boundaries by diffusion, thus grain growth is faster at higher temperatures. The "driving force" is the reduction of energy, which is proportional to the total area. Big grains grow at the expense of the small ones.

Important Terms:

Cold working
Critical resolved shear stress
Dislocation density
Grain growth
Lattice strain
Recovery
Recrystallization
Recrystallization temperature
Resolved shear stress
Slip
Slip system
Strain hardening
Solid-solution strengthening