Linear Defects - Edge Dislocations
• A dislocation is a linear or one-dimensional defect around which some of the atoms are
misaligned. charaterized by a vector in the lattice called the Burger’s vector b, a crystal
vector, [uvw], which is a measure of the distortion of the lattice around the defect.
• An extra portion of a plane of atoms, or half-
plane, the edge of which terminates within
the crystal. This is termed an edge
dislocation.
• the line that is defined along the end of the
extra half-plane of atoms is sometimes
termed the dislocation line, which, for the
edge dislocation in Figure, is perpendicular
to the plane of the slide.
b ┴ to dislocation line
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Linear Defects - Screw Dislocations
Screw Dislocation: The trace of the atomic planes around the screw dislocation makes a
spiral or helical path (shade) like a screw.
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Linear Defects - Mixed Dislocations
Burger vector and dislocation line neither parallel, antiparallel, or perpendicular
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Linear Defects - Dislocations
one-dimensional defects
• Edge dislocation
b ┴ to dislocation line
• Screw dislocation
b II to dislocation line
• Mixed dislocation
b ┴ to dislocation line
b II to dislocation line
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Motion of an edge dislocation - shear stress
Atomic rearrangements that accompany the motion of an edge dislocation as it moves in
response to an applied shear stress.
a) The extra half-plane of atoms is labeled A.
b) The dislocation moves one atomic distance to the right as A links up to the lower portion of
plane B; in the process, the upper portion of B becomes the extra half-plane.
c) A step forms on the surface of the crystal as the extra half-plane exits.
d) The process by which plastic deformation is produced by dislocation motion is termed slip;
the crystallographic plane along which the dislocation line traverses is the slip plane
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Plastic shear deformation by sliding of an edge dislocation. The blue
arrows show the dislocation direction, the grey area shows the sliding
zone and the green dashed line shows the dislocation line.
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Macroscopic deformation
• The formation of a step on the surface of
a crystal by the motion of
(a) an edge dislocation and
(b) a screw dislocation.
for an edge, the dislocation line moves in the
direction of the applied shear stress;
for a screw, the dislocation line motion is
perpendicular to the stress direction.
However, the net plastic deformation for the
motion of both dislocation types is the same
The number of dislocations, or dislocation density in a material, is expressed as the total
dislocation length per unit volume or, equivalently, the number of dislocations that intersect a unit
area of a random section
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Dislocation motion
Dislocation motion is analogous to the mode of locomotion employed by a caterpillar
• Incrementally breaking bonds
• If dislocations don't move, deformation doesn't happen! (But fracture will, like in ceramic)
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Characteristics of Dislocations
• Some atomic lattice distortion exists around
the dislocation line because of the presence
of the extra half-plane of atoms.
• As a consequence, there are regions in
which compressive, tensile, and shear
lattice strains are imposed on the
neighboring atoms
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Slip Systems
• Dislocations do not move with the same degree of ease on all crystallographic planes of
atoms and in all crystallographic directions.
• Ordinarily there is a preferred plane, and in that plane there are specific directions along
which dislocation motion occurs. This plane is called the slip plane; it follows that the
direction of movement is called the slip direction.
• This combination of the slip plane and the slip direction is termed the slip system.
Slip occurs along <110> type directions within the
{111} planes, as indicated by arrows in Figure.
{111} and <110> represents the slip system for
FCC.
A given slip plane may contain more than a single
slip direction.
Thus, several slip systems may exist for a
For face-centered cubic, there are 12 slip particular crystal structure; the number of
systems: four unique {111} planes and, within independent slip systems represents the different
each plane, three independent directions. possible combinations of slip planes and directions.
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Slip in Single Crystals
Crystals: When a single crystal is deformed under a tensile stress,
it is observed that plastic deformation occurs by slip on well‐defined
parallel crystal planes
Slip always occurs on a
particular set of crystallographic
planes, known as slip planes
Slip always takes place along a
consistent set of directions
within these planes –these are
called slip directions
The combination of slip plane
and slip direction together
makes up a slip system
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However, one slip system is generally oriented most favorably—that is, has the largest resolved shear stress,
τR(max):
In response to an applied tensile or compressive stress, slip in a single crystal commences on the most
favorably oriented slip system when the resolved shear stress reaches some critical value, termed the critical
resolved shear stress τcrss; it represents the minimum shear stress required to initiate slip and is a property of
the material that determines when yielding occurs. The single crystal plastically deforms or yields when τR (max)
= τcrss, and the magnitude of the applied stress required to initiate yielding (i.e., the yield strength σy) is
In a cubic unit cell the angle between the direction vector [u1v1w1] and [u2v2w2] is given by
• A single crystal of aluminum is oriented for a tensile test such that its slip plane
normal makes an angle of 28.1° with the tensile axis. Three possible slip
directions make angles of 62.4°, 72.0°, and 81.1° with the same tensile axis.
(i) Which of these three slip directions is most favoured? (ii) If plastic deformation
begins at a tensile stress of 1.95 MPa, determine the critical resolved shear stress
for aluminum.
(i) 62.4° is most favourable
(ii)
= 0.8 MPa
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School of Mechanical Engineering, VIT University, Vellore
School of Mechanical Engineering, VIT University, Vellore
