Mathematical prediction of dislocation cell sizes with strain using the mesh-length theory of work hardening

An example of the evolution of cell structures which is directly predicted by the principle of similitude in the mesh-length theory of work hardening is the reduction of dislocation cell size with total strain. In tensile samples, total strain can be easily represented by the reduction of area of the gauge length. The relationship between dislocation cell size D and reduction of area RA has been measured for several different metals using transmission electron microscopy and this information is of great significance in the interpretation of microstructural development during straining.This paper develops a mathematical representation for the relationship between D and RA using the dislocation density and the approximate shear stress. Although the agreement between the mathematical calculations and the experimental data in the copper and steel samples tested is not precise, the general trends are relatively well represented. Further refinements in the necessary models of materials properties could well improve this relationship considerably and lead to a mathematical model which would be very useful in the prediction of microstructural development and materials properties.