Dislocations and Strengthening Mechanisms

Dislocations and Strengthening Mechanisms

Plastic deformation –Dislocations

Permanent plastic deformation is due to shear process–atoms change their neighbors. Inter-atomic forces and crystal structure plays an important role during plastic deformation. Cumulative movement of dislocations leads to gross plastic deformation. Edge dislocation move by slip and climb, while screw dislocation move by slip and cross-slip.

During their movement, dislocations tend to interact. The interaction is very complex because of number of dislocations moving over many slip systems in different directions  Dislocations moving on parallel planes may annihilate each other, resulting in either vacancies or interstitials. Dislocations moving on non-parallel planes hinder each other’s movement by producing sharp breaks–jog (break out of slip plane), kink(break in slip plane) . Other hindrances to dislocation motion–interstitiall and substitutional atoms, foreign particles, grain  boundaries, external grain surface, and change in structure due to phase change.

Material strength can be increased by arresting dislocation motion

Plastic deformation mechanisms -Slip

Mainly two kinds :slip and twinning.

•       Slip is prominent among the two. It involves sliding of blocks of crystal over other along slip planes.

•       Slip occurs when shear stress applied exceeds a critical value.

•       Slip occurs most readily in specific directions(slip directions)on certain crystallographic planes.Feasible combination of a slip plane together with a slip direction is considered as a slip system.

•       During slip each atom usually moves same integral number of atomic distances along the slip plane

Extent of slip depends on many factors-external load and the corresponding value of shear stress produced by it, crystal structure, orientation of active slip planes with the direction of shearing stresses generated. Slip occurs when shear stress applied exceeds a critical value. For single crystal, Schmid defined critical shear stress,which can be expressed as:

Both factors τ and σ are measured in stress, which is calculated the same as pressure by dividing force by area. φ and λ are angles usually measured in degrees.

 In a poly-crystalline material, individual grains provide a mutual geometrical constraint on one other, and this precludes plastic deformation at low applied stresses.  Slip in polycrystalline material involves 

generation, movement and (re-) arrangement of dislocations. During deformation, mechanical integrity and coherency are maintained along the grain boundaries. A minimum of five independent slip systems must be operative for a polycrystalline solid to exhibit ductility and maintain grain boundary integrity–von Mises. On the other hand, crystal deform by twinning.

Strengthening mechanisms of material can be increased by hindering  dislocation, which is responsible for plastic deformation.Different ways to hinder dislocation motion/Strengthening mechanisms:

In single-phase materials

-Grain size reduction

-Solid solution strengthening

-Strain hardening

In multi-phase materials

-Precipitation strengthening

-Dispersion strengthening

-Fiber strengthening

-Martnsite strengthening

Strengthening by Grain size reduction

 It is based on the fact that dislocations will experience hindrances while trying to move from a grain in to the next because of abrupt change in orientation of planes. Hindrances can be two types: forcible change of slip direction, and discontinuous slip plane.  Smaller the grain size, often a dislocation encounters a hindrance. Yield strength of material will be increased.  Yield strength is related to grain size(diameter, d)as Hall-Petch relation:

Grain size can be tailored by controlled cooling or by plastic deformation followed by appropriate heat treatment

Solid solution strengthening

Impure foreign atoms in a single phase material produces lattice strains which can anchor the  dislocations. Effectiveness of this strengthening depends on two factors –size difference and volume fraction of solute. Solute atoms interact with dislocations in many ways:

-elastic interaction

-modulus interaction

-stacking-fault interaction

-electrical interaction

-short-range order interaction

-long-range order interaction

Elastic, modulus, and long-range order interactions are of long-range i.e. they are relatively insensitive to temperature and continue to act about 0.6Tm     

Yield point phenomenon

Localized, heterogeneous type of transition from elastic to plastic deformation marked by abrupt elastic-plastic transition–Yield point phenomenon. It characterizes that material needs higher stress to initiate plastic flow than to continue it.

The bands are called Lüders bands/Hartmann lines/stretcher stains, and generally are approximately 45 to the tensile axis.

Occurrence of yield point is associated with presence of small amounts of interstitial or substitutional impurities. It’s been found that either unlocking of dislocations by a high stress for the case of strong pinning or generation of new dislocations are the reasons for yield-point phenomenon. Magnitude of yield-point effect will depend on energy of interaction between solute atoms and dislocations and on the concentration of solute atoms at the dislocations.

Fracture is the separation of a single body into pieces by an imposed stress. Information about plastic deformation and fracture is given in this article. As polycrystalline material is made up of many grains which may have second phase particles and grain boundaries. It is therefore easier to study plastic deformation in a single crystal to eliminate the effects of grain boundaries and second phase particles

Plastic deformation mechanisms –Twinning

It results when a portion of crystal takes up an orientation that is related to the orientation of the rest of

The important role of twinning in plastic deformation is that it causes changes in plane orientation the untwined lattice in a definite, symmetrical way so that further slip can occur. Twinning also occurs in a definite direction on a specific plane for each crystal structure

Deformation by Slip. 

If a single crystal of a metal is stressed in tension beyond its elastic limit, it elongates slightly, a step appears on the surface indicating relative displacement of one part of the crystal with respect to the rest, and the elongation stops. Increasing the load will cause movement on another parallel plane, resulting in another step. It is as if neighboring thin sections of the crystal had slipped past one another like sliding cards on a deck. Each successive elongation requires a higher stress and results in the appearance of another step. With progressive increase of the load, a stage is reached which causes the material to fracture.

Sliding occurs in certain planes of atoms in the crystal and along certain directions in these planes. Thus the mechanism is a new type of flow that depends upon the perfectly repetitive structure of the crystal . It allows the atoms in one face of a slip plane to shear away from their original neighbors in the other face, to slide in an organized way along this face carrying their own half of the crystal with them, and finally to join up again with a new set of neighbors as nearly perfect as before. The movement in the crystal takes place along planes having highest atomic density with greatest distance between similar parallel planes and in the direction of close-packed atoms. This can be simply stated as: Slip occurs on planes that have h ighest planer density of atoms and in the direction with highest linear density of atoms.

Slip occurs in directions in which the atoms are most closely packed since this requires the least amount of energy. As shown in the figure, close-packed rows are vertically further apart from each other (d1) than rows that are not close-packed (d2), therefore they can slip past each other with less interference.

Black bars between atoms show the slope of the path of atoms. Since the slope is less steep in case of closed-packed rows, less force is required for a given horizontal displacement. In addition, less displacement (D1 < D2) is required by the atoms to move from one stable position (before slip) to other stable position (after slip).

To get a better grasp of this, think of gluing ping pong balls to two boards in a widely spaced pattern as shown in above figure. Put the boards together, ping pong balls to ping pong balls, and begin to tilt the bottom board. You will have to go to a very steep angle before the top board will slip from its position of the nestled ping pong balls. Now do the experiment again, but this time gluing the balls very close together. The top board will now slip at a much lesser angle.