Plastic Deformation

· The stress required to maintain an equilibrium radius, R; τ_R= (G b /R).
· The radius of curvature for a Frank-Reed source has its minimum value for a semi-circular loop (b).
· For (D, D') separated by L, R = L/2, and: τ_cr = (2Gb/L).
· Experimentally, L = 10⁴ b so that the critical shear stress on the dislocation model is: τ_cr = 2 x 10^-4 G.
· This dislocation model for the yield stress is in good agreement with the experimental measurements on bulk crystalline materials.