dislocation density
Dislocation density is a count of how many dislocations are packed into a metal, the total length of dislocation line threaded through each unit of volume. Because it is length divided by volume (meters of line per cubic meter), it comes out in units of one over area, or per square meter (m^-2). A handy way to picture it: imagine all the dislocation lines in a 1 cubic centimeter cube stitched end to end; the total could stretch from a few kilometers in soft metal to light-years in heavily worked metal.
The number swings over an enormous range. A carefully annealed (softened) metal holds around 10^10 dislocation lines per square meter; a severely cold-worked metal can reach 10^15 to 10^16, a hundred-thousand to a million times more. This is the hidden variable behind work hardening: deforming the metal multiplies its dislocations, and the denser they get, the more they tangle and block each other. Their strengthening effect follows Taylor's relation, tau = tau_0 + alpha times G times b times sqrt(rho), where G is the shear modulus, b the Burgers vector, rho the density, and alpha a constant near 0.5, so strength rises with the square root of dislocation density.
Dislocation density is the microscopic dial that connects processing to strength. Cold work turns it up; heating turns it back down, as recovery lets dislocations rearrange and annihilate, and recrystallization sweeps most of them away, resetting the metal to a low density and soft state. It is measured by counting dislocation lines in transmission-electron-microscope images or inferred from the broadening of X-ray diffraction peaks.
Annealed copper at about 10^10 m^-2 is soft; cold-drawing it to 10^14 m^-2 raises the tangle density ten-thousand-fold, and by Taylor's sqrt(rho) rule that is a hundred-fold increase in the dislocation contribution to shear strength.
Strength scales with the square root of dislocation density, so it takes a large jump in density to make a large jump in strength.
Do not read a low dislocation density as few defects and therefore weak in a bad way; a nearly dislocation-free whisker is extremely strong (near the theoretical limit). It is a moderate density of tangled dislocations, not their absence, that makes ordinary metals both weak and workable.