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Whereas we now learned a little bit
about the complications that may occur when dislocations move, we first must
have some dislocations before plastic
deformation can happen. In other words: We need mechanisms that
generate
dislocations in the first
place! |
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Of course, dislocations can just be generated at the surface
of the crystal; the simple pictures
showing plastic deformation by an (edge) dislocation mechanism give an idea how
this may happen. But more important are mechanisms that generate dislocations
in the bulk of a crystal. The most important mechanism is the Frank-Read
mechanism shown below. |
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We have a segment of dislocation firmly anchored
at two points (red circles). The force F = b ·
τres is shown by a sequence of
arrows |
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The dislocation segment responds to the force by
bowing out. If the force is large
enough, the critical configuration of a semicircle may be reached. This
requires a maximum shear stress of
τmax = Gb/R |
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If the shear stress is higher than
Gb/R, the radius of curvature is too small to stop
further bowing out. The dislocation is unstable and the following process now
proceeds automatically and quickly. |
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The two segments shortly before they touch. Since
the two line vectors at the point of contact have opposite signs (or, if you
only look at the two parts almost touching: the Burgers vectors have different
signs for the same line vectors), the segments in contact will annihilate each
other. |
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The configuration shown is what you have
immediately after contact; it is totally unstable (think of the rubber band
model!). It will immediately form a straight segment and a "nice"
dislocation loop which will expand under the influence of the resolved shear
stress. |
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The regained old segment will immediately start
to go through the whole process again, and again, and again, ... - as long as
the force exists. A whole sequence of nested dislocation loops will be
produced. |
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Stable configuration after the process. The loop
is free to move, i.e. grow much larger under the applied stress. It will
encounter other dislocations, form knots and become part of a network. The next
loop will follow and so on - as long as there is enough shear stress. |
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The Frank-Read process, although
looking a bit odd, will occur many times under sufficient load. It can produce
any density of dislocations in short times, because the newly formed
dislocations will move, become anchored at some points, and start to generate
Frank-Read loops, too. |
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Of course, Frank-Read dislocation sources can also be stopped
- e.g. by cutting through the generating dislocation by another dislocation. We
thus will have a certain finite dislocation density under certain external
conditions. It may, however, depend on many parameters, including the history
of the material. |
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Some kind of Frank-Read mechanism may also
operate from irregularities on the surface (external or internal), an example
of such a source is shown in the
X-ray topography
below. |
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This picture comes from the work of K.B. Kostin (a former
student in Kiel) together with many
others in St. Petersburg. It is a result of investigations into "wafer
bonding", where to Si wafers are placed on top of each other and
"bonded", so that a single piece of Si results - with a grain
boundary in between. The mottled area in the upper left hand corner shows such
a bonded structure, whereas the dark area containing the dislocations as white
lines, remained unbonded. |
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Dislocations were introduced into one of the wafers and one
point on the edge of the bonded area acted as a Frank-Read source. The nested
series of dislocation loops is splendidly visible. There are also lots of
straight dislocations which have moved considerable distances from their point
of origin. |
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How else can we make dislocations?
Suffice it to mention that there are variants of the basic Frank-Read
mechanism, too and some more exotic mechanisms. We will not go into details;
the important part is that it is generally an easy process to generate many
dislocations provided you already have a few to start with. |
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Last but not least: "Frank" is not the first name of Mr. Read - as ever so often, two independent persons
figured out this mechanism at practically the same time (in 1950) -
look up the link
for details. |
© H. Föll