Mumbai University > Mechanical Engineering > Sem 4 > Material Technology

Marks: 6M

Year: Dec 2014

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, dislocations must be generated in the material. This implies that, during deformation, dislocations must be primarily generated in these planes. Cold working of metal increases the number of dislocations by the Frank-Read mechanism. Higher dislocation density increases yield strength and causes work hardening of metals

We have a segment of dislocation firmly anchored at two points (red circles). The force $F = b • _{res}$ is shown by a sequence of arrows

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 $_{max} = \frac{Gb}{R}$

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.

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.

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.

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.

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.