Dislocation creep is a
deformation mechanism
A deformation mechanism, in geology, is a process occurring at a microscopic scale that is responsible for changes in a material's internal structure, shape and volume. The process involves planar discontinuity and/or displacement of atoms from th ...
in
crystalline materials. Dislocation creep involves the movement of
dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to ...
s through the
crystal lattice
In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by
: \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n_ ...
of the material, in contrast to
diffusion creep Diffusion creep refers to the deformation of crystalline solids by the diffusion of vacancies through their crystal lattice. Diffusion creep results in plastic deformation rather than brittle failure of the material.
Diffusion creep is more sen ...
, in which diffusion (of vacancies) is the dominant creep mechanism. It causes
plastic deformation
In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strai ...
of the individual
crystals, and thus the material itself.
Dislocation creep is highly sensitive to the
differential stress Differential stress is the difference between the greatest and the least compressive stress experienced by an object. For both the geological and civil engineering convention \sigma_1 is the greatest compressive stress and \sigma_3 is the weakest,
...
on the material. At low temperatures, it is the dominant deformation mechanism in most crystalline materials. Some of the mechanisms described below are speculative, and either cannot be or have not been verified by experimental microstructural observation.
Principles
Dislocations in crystals
Dislocation creep takes place due to the movement of
dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to ...
s through a crystal lattice. Each time a dislocation moves through a crystal, part of the crystal shifts by one
lattice point
In geometry and group theory, a lattice in the real coordinate space \mathbb^n is an infinite set of points in this space with the properties that coordinate wise addition or subtraction of two points in the lattice produces another lattice po ...
along a plane, relative to the rest of the crystal. The plane that separates the shifted and unshifted regions along which the movement takes place is the
slip
Slip or SLIP may refer to:
Science and technology Biology
* Slip (fish), also known as Black Sole
* Slip (horticulture), a small cutting of a plant as a specimen or for grafting
* Muscle slip, a branching of a muscle, in anatomy
Computing an ...
plane. To allow for this movement, all
ionic bond
Ionic bonding is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, or between two atoms with sharply different electronegativities, and is the primary interaction occurring in ionic compounds. ...
s along the plane must be broken. If all bonds were broken at once, this would require so much energy that dislocation creep would only be possible in theory. 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.
By moving a dislocation step by step through a crystal lattice, a linear
lattice defect is created between parts of the crystal lattice. Two types of dislocations exist: edge and screw dislocations.
Edge dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to s ...
s form the edge of an extra layer of atoms inside the crystal lattice.
Screw dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to s ...
s 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, but the crystal can still be perfect on all sides of the line.
The length of the displacement in the crystal caused by the movement of the dislocation is called the
Burgers vector
In materials science, the Burgers vector, named after Dutch physicist Jan Burgers, is a vector, often denoted as , that represents the magnitude and direction of the lattice distortion resulting from a dislocation in a crystal lattice.
The vecto ...
. 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.
Glide planes in crystals
Both edge and screw dislocations move (slip) in directions parallel to their
Burgers vector
In materials science, the Burgers vector, named after Dutch physicist Jan Burgers, is a vector, often denoted as , that represents the magnitude and direction of the lattice distortion resulting from a dislocation in a crystal lattice.
The vecto ...
. Edge dislocations move in directions perpendicular to their dislocation lines and screw dislocations move in directions parallel to their dislocation lines. This causes a part of the crystal to shift relative to its other parts. Meanwhile, the dislocation itself moves further on along a glide plane. The
crystal system of the material (
mineral
In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid chemical compound with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.John P. Rafferty, ed. ( ...
or
metal
A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typica ...
) 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. 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.
Origin of dislocations
When a crystalline material is put under differential stress, dislocations form at the grain boundaries and begin moving through the crystal.
New dislocations can also form from
Frank–Read source
In materials science, a Frank–Read source is a mechanism explaining the generation of multiple dislocations in specific well-spaced slip planes in crystals when they are deformed. When a crystal is deformed, in order for slip to occur, disloc ...
s. These form when a dislocation is stopped in two places. The part of the dislocation in between will move forward, causing the dislocation line to curve. This curving can continue until the dislocation curves over itself to form a circle. In the centre of the circle, the source will produce a new dislocation, and this process will produce a sequence of concentric 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
In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and therm ...
(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 (needs a reference). 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
Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physi ...
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
Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in fr ...
, it is
hardened, meaning deformation of the material will be more difficult (the material becomes stronger). The carbon atoms act as
interstitial
An interstitial space or interstice is a space between structures or objects.
In particular, interstitial may refer to:
Biology
* Interstitial cell tumor
* Interstitial cell, any cell that lies between other cells
* Interstitial collagenase, ...
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
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of ther ...
point of view increase the amount of
free energy in the
system
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...
. 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
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
. 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.
To reduce the free energy in the system, dislocations tend to concentrate themselves in low-energy regions, so other regions will be free of dislocations. This leads to the formation of 'dislocation walls', or planes in a crystal where dislocations localize. Edge dislocations form
tilt walls, 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.
Kinetics
In general, the power law for stage 2
creep is:
:
where
is the stress exponent and
is the creep activation energy,
is the ideal gas constant,
is temperature, and
is a mechanism-dependent constant.
The exponent
describes the degree of stress-dependence the creep mechanism exhibits. Diffusional creep exhibits an
of 1 to 2, climb-controlled creep an
of 3 to 5, and glide-controlled creep an
of 5 to 7.
Dislocation glide
The rate of dislocation glide creep can be determined using an
Arrhenius equation
In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 18 ...
for the rate of dislocation motion. The forward rate can be written as:
:
where
is the energy of the barrier and
is the work provided by the applied stress and from thermal energy which helps the dislocation cross the barrier.
is the Boltzmann constant and
is the temperature of the system.
Similarly, the backward rate is given by:
:
The total creep rate is as follows:
:
Thus, the rate of creep due to dislocation glide is:
:
At low temperatures, this expression becomes:
:
The energy supplied to the dislocation is:
:
where
is the applied stress,
is the Burgers vector, and
is the area of the slip plane. Thus, the overall expression for the rate of dislocation glide can be rewritten as:
: