Dislocation creep

Dislocation creep is highly sensitive to the differential stress on the material.

If all bonds were broken at once, this would require so much energy that dislocation creep would only be possible in theory.

The length of the displacement in the crystal caused by the movement of the dislocation is called the Burgers vector.

Both edge and screw dislocations move (slip) in directions parallel to their Burgers vector.

The crystal system of the material (mineral or metal) determines how many glide planes are possible, and in which orientations.

The orientation of the differential stress determines which glide planes are active and which are not.

The Von Mises criterion states that to deform a material, movement along at least five different glide planes is required.

When a crystalline material is put under differential stress, dislocations form at the grain boundaries and begin moving through the crystal.

In such cases a part of the dislocation could slow down or even stop moving altogether.

The carbon atoms act as interstitial particles (point defects) in the crystal lattice of the iron, and dislocations will not be able to move as easily as before.

Dislocations are imperfections in a crystal lattice, that from a thermodynamic point of view increase the amount of free energy in the system.

Recovery of the crystal structure can also take place when two dislocations with opposite displacement meet each other.

This leads to the formation of 'dislocation walls', or planes in a crystal where dislocations localize.

is the work provided by the applied stress and from thermal energy which helps the dislocation cross the barrier.

[2] This expression is derived from a model from which plastic strain does not devolve from atomic diffusion.

All creep rate expressions have similar terms, but the strength of the dependency (i.e. the

However, at higher temperatures, the solute atoms become mobile and contribute to creep.

After some initial energy input, the dislocation breaks away and begins to move with velocity

A high diffusivity decreases the drag, and greater misfit parameters lead to greater binding energies between the solute atom and the dislocation, resulting in an increase in drag.

This permits solute atoms to catch up to the dislocation, thereby increasing the stress once more.

The stress then increases, and the cycle begins again, resulting in the serrations observed in the stress–strain diagram.

If the strain rate is high enough, the flow stress is greater than the breakaway stress, and the dislocation continues to move and the solute atom cannot "catch up"; thus, serrated flow is not observed.

Thus, the solute drag creep rate can be rewritten as: where it is noted that the diffusion coefficient is a function of temperature.

This is conceptually similar to a high-temperature cross-slip, where dislocations circumvent obstacles via climb at low temperatures.

The dislocation motion involves climb and glide, thus the name climb-glide creep.

Considering a model in which dislocations are emitted by a source, to maintain the constant microstructure evolution from Stage I to Stage II creep, each source is associated with a constant number of dislocation loops that it has emitted.

, the climb-glide creep rate is: As the microstructure must remain fixed for the transition between these stages,

The expression for the climb-glide creep rate reduces to: As dislocation climb is driven by stress but accomplished by diffusion, we can say

[2] At higher stress levels, a finer microstructure is observed, which correlates to the inverse relationship between

Harper-Dorn creep is characterized by a linear steady-state strain rate relationship with stress at constant temperature and as independent of grain size, and activation energies that are typically close to those expected for lattice diffusion.

Schematic representation of an edge dislocation in a crystal lattice. The yellow plane is the glide plane , the vector u represents the dislocation, b is the Burgers vector . When the dislocation moves from left to right through the crystal, the lower half of the crystal has moved one Burgers vector length to the left, relative to the upper half.
Schematic representation of a screw dislocation in a crystal lattice. The yellow plane (Σ) is again the glide plane, u the dislocation and b the Burgers vector. When the dislocation moves from the back to the front of the crystal, the lower half moves one Burgers vector length to the front, relative to the upper half.
Schematic of internal energy of a dislocation passing through an obstacle when (a) no additional work is provided and when (b) work is provided from the applied stress and thermal energy
Schematic stress–strain curve of a material exhibiting serrated flow. The local stress maxima are from the stress required for dislocation to breakaway from the solute atoms pinning them. The local stress minima are from the stress required to move the dislocation with no drag. They are linked by the solute atoms catching up to the moving dislocations by the process described above, resulting in a repetitive motion from local stress maxima to local stress minima. [ 2 ]
Different types of serrations, dependent on the magnitude of the breakaway stress and flow stress