Please explain Frank read source with close reference to the formula τ =Gb/l.Somewhere I have heard that l is the length of the Frank Read source please explain me this vividly.
This is expression for shear stress arising on a dislocation locked by a pair of precipitates throughout external loading of a material with a modulus G. Burgers vector is designed as b, the distance between the precipitates is designed as l. Throughout the loading, the locked dislocation obtains higher and higher curvature, and then is finally broken with a formation of two loops and one partial dislocation able to move further.
When two barrier points are intersections with transversal (forest) disslocations rather than precipitates , L means a square root of dislocation density. In this case the formula you mention becomes nothing else but the classical expression by Taylor for the yield stress.
In this formula l is the distance between 2 pined points, that dislocation segment responds to the force by bowing out. lf the force is large enough, the critical configuration of a semicircle may be reached . This require a max shear sress of T=Gb/R. After this critical shear stress the radius of curvature is too small to stop bowing out.
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