Dislocation creep

Dislocation creep is a deformation mechanism in crystalline materials. Dislocation creep involves the movement of dislocations through the crystal lattice of the material. It causes plastic deformation of the individual crystals and in the end the material itself.

Dislocation creep is highly sensitive to the differential stress on the material. At relatively low temperatures it is the dominant deformation mechanism in most crystalline materials.^[1]

Principles

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.

Dislocations and glide planes in crystals

Dislocation creep takes place due to the movement of dislocations through a crystal lattice. Each time a dislocation moves through a crystal, part of the crystal moves one lattice point along a plane, relative to the rest of the crystal. The plane that separates both parts and along which the movement takes place is called a slip plane. To allow the movement, all ionic bonds along the plane have to be broken. If all bonds were broken at once, this would require so much energy that dislocation creep would only in theory be possible. When it is assumed that the movement takes place step by step, the breaking of bonds is immediately followed by the creation of new ones and the energy required is much lower. Calculations of molecular dynamics and analysis of deformed materials have shown that deformation creep can be an important factor in deformation processes, under certain circumstances.

By moving a dislocation step by step through a crystal lattice a linear lattice defect is created between parts of the crystal lattice, which is called a dislocation.^[2] Two types of dislocations exist. Edge dislocations form the edge of an extra layer of atoms inside the crystal lattice. Screw dislocations form a line along which the crystal lattice jumps one lattice point. In both cases the dislocation line forms a linear defect through the crystal lattice, the crystal can be perfect on all sides of the line.

Both edge and screw dislocations move (slip) in directions parallel to their burgers vector. This means edge dislocations move in directions parallel to their dislocation lines and screw dislocations move in directions perpendicular to their dislocation lines. In both cases this causes a part of the crystal to move relative to other parts. Meanwhile the dislocation itself moves further on along a glide plane. 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 then 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. A dislocation will not always be a straight line and can thus move along more than one glide plane. Where the orientation of the dislocation line changes, a screw dislocation can continue as an edge dislocation and vice versa.

The length of the displacement in the crystal caused by the movement of the dislocation is called the Burgers vector. It equals the distance between two atoms or ions in the crystal lattice. Therefore each material has its own characteristic Burgers vectors for each glide plane.

Origin of dislocations

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

Another way in which new dislocations can form are so called Frank-Read sources. These form when a dislocation is stopped at two places. The part of the dislocation in between will move along, causing the dislocation line to curve. This curving can continue until the dislocation curves over itself to form a circle. In the centre of such a circle the source will produce a new dislocation, and this process will produce a sequence of dislocations on top of each other. Frank-Read sources are also created when screw dislocations double cross-slip (change slip planes twice), as the jogs in the dislocation line pin the dislocation in the 3rd plane.

Dislocation movement

Dislocation glide

A dislocation can ideally move through a crystal until it reaches a grain boundary (the boundary between two crystals). When it reaches a grain boundary, the dislocation will disappear. In that case the whole crystal is sheared a little. There are however different ways in which the movement of a dislocation can be slowed or stopped. When a dislocation moves along several different glide planes, it can have different velocities in these different planes, due to the anisotropy of some materials. Dislocations can also encounter other defects in the crystal on their ways, such as other dislocations or point defects. In such cases a part of the dislocation could slow down or even stop moving altogether.

In alloy design, this effect is used to a great extent. On adding a dissimilar atom or phase, such as a small amount of carbon to iron, it is hardened, meaning deformation of the material will be more difficult (the material becomes stronger). 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.

Dislocation climb and recovery

Dislocations are imperfections in a crystal lattice, that from a thermodynamic point of view increase the amount of free energy in the system. Therefore, parts of a crystal that have more dislocations will be relatively unstable. By recrystallisation the crystal can heal itself. Recovery of the crystal structure can also take place when two dislocations with opposite displacement meet each other.

A dislocation that has been brought to a halt by an obstacle (a point defect) can overcome the obstacle and start moving again by a process called dislocation climb. For dislocation climb to occur, vacancies have to be able to move through the crystal. When a vacancy arrives at the place where the dislocation is stuck it can cause the dislocation to climb out of its glide plane, after which the point defect is no longer in its way. Dislocation climb is therefore dependent from the velocity of vacancy diffusion. As with all diffusion processes, this is highly dependent on the temperature. At higher temperatures dislocations will more easily be able to move around obstacles. For this reason, many hardened materials become exponentially weaker at higher temperatures.

At low stresses, materials with a low initial dislocation density may creep by dislocation climb alone, known as Harper-Dorn creep. This creep behavior is characterized by a linear dependence on stress, an independence of grain size, and activation energies that are typically close to those expected for lattice diffusion.^[3]

To reduce the free energy in the system, dislocations can tend to concentrate themselves in certain zones, so that other regions will stay free of dislocations. This leads to the formation of 'dislocation walls', planes in a crystal where dislocations localise. Edge dislocations form so called tilt walls,^[4] while screw dislocations form twist walls. In both cases the increasing localisation of dislocations in the wall will increase the angle between the orientation of the crystal lattice on both sides of the wall. This leads to the formation of subgrains. The process is called subgrain rotation (SGR) and can eventually lead to the formation of new grains when the dislocation wall becomes a new grain boundary.