Frank-Read source is a type of dislocation multiplication mechanism. Consider a segment whose ends are pinned(corresponding to nodes in a network, precipitates, or sites where the dislocation leaves the glide plane). Under a certain applied stress the segment bows out by glide. As bow-out proceeds, the radius of curvature of the line decreases and the line-tension forces tending to restore the line to a straight configuration increase. For stress less than a critical value, a metastable equilibrium configuration is attained, in which the line-tension force balances that caused by the applied stress. For the large bow-out case, following equilibrium condition holds:
where r is the radius of the loop. The radius of the curvature is a minimum when r=L/2. Hence the maximum stress for which local equilibrium is possible is given b the equation above with r=L/2. For the typical case that L = 103ρ