a Frank-Read source
/ frank-reed /
Bend a paperclip hard and it stays bent, and to do that the crystal shears by a huge amount — far more slip than the dislocations that were there at the start could ever produce, even if every one of them ran clear out of the metal. So where do all the extra dislocations come from? The metal MAKES more of them as it deforms, and the classic factory is the Frank-Read source: a dislocation segment pinned at both ends that, under stress, repeatedly spits out complete dislocation loops, one after another, like a bubble-blower churning out bubbles.
Watch it work. Take a dislocation segment lying in its slip plane, anchored at two points a distance L apart (pinned, say, by precipitates, other dislocations, or nodes). Apply a shear stress. The segment cannot move at its pinned ends, so it bows out into an arc between them, like a rope pushed sideways between two nails. The more it bows, the tighter it curves; the tightest it can curve is a semicircle of radius L/2, and that happens at a definite critical stress tau = G b / L (G shear modulus, b Burgers vector, L the pin spacing). Push past that and the loop is unstable: it balloons outward, wraps around behind the two pins, the two arms meet and annihilate where they touch (opposite line sense), pinching off a complete closed loop that glides away — and leaving the original pinned segment behind to do it all over again.
The consequences are enormous. One Frank-Read source can emit hundreds or thousands of loops, so the dislocation density climbs from about 10^10 per square metre in an annealed metal to 10^15 or 10^16 in a heavily worked one. That multiplication is the engine of plastic strain (it supplies the mobile dislocations needed to keep deforming) AND, paradoxically, of work hardening: the flood of new dislocations tangle with and block each other, so the metal gets stronger the more you deform it. The critical-stress formula tau = Gb/L also carries a design message: the shorter the pin spacing L, the higher the stress needed to fire the source — the seed of precipitation and dislocation strengthening.
A source with pins L = 1 micrometre apart in copper (G = 48 GPa, b = 0.256 nm) fires at tau = G b / L = (48e9 x 0.256e-9) / 1e-6 = 12 MPa. Shrink the pin spacing to L = 100 nm (say by fine precipitates) and the stress needed jumps ten-fold to 120 MPa — shorter segments are stiffer sources, the essence of dislocation strengthening.
A pinned segment bows out, wraps around, and pinches off a loop, regenerating itself: a factory for dislocations.
A Frank-Read source multiplies dislocations but does NOT create Burgers vector from nothing — every loop it emits carries the same b as the parent segment, and the net Burgers vector stays conserved. It is regeneration, not violation of the conservation rule.