Theory of workhardening 1934-1984

The evolution of the theory of workhardening through the past fifty years has laid a secure basis, but much research still lies ahead. A guiding principle in the prevailing, so-called meshlength theory is that glide dislocations arrange into stress-screened, low-energy structures, the most common being the cell structure, and that the flow stress is the stress needed to generate new glide dislocations. Further, it makes extensive use of the “principle of similitude”. Remnant stresses due to dislocations with just one Burgers vector orientation are very often relieved by additional dislocations with other Burgers vectors which form not in response to the applied stress but to those remnant stresses. Such dislocations are commonly misnamed “forest” dislocations. The theory closely reproduces stages II and III of the typical workhardening curve. Stage I results in single glide from sources which initially are isolated from each other so that pile-ups form, which then may interact among neighboring pile-ups of opposite sign, so as to generate mats of dipoles parallel to the active glide plane. Stage II behavior is expected as long as similitude is obeyed so that the average free dislocation path shrinks inversely proportional with the root of the dislocation density. Stage III, finally, results when the free dislocation path is constant. At low temperatures, thermal activation can make the critical difference for the release of hair-trigger poised loops. This is the cause of creep effects whose magnitude is limited to less than the elastic strain. Computer calculations indicate the presence of longer-range (i.e., cell diameter scale) stresses whose sign changes with the cell’s sense of rotation. This suggests that rectangled dislocation cells with a common rotation axis, arranged into a three-dimensional checkerboard pattern in which the sense of rotation alternates from cell to cell, should minimize stored energy. Such cell patterns are increasingly reported in the literature. The fact that the average cell diameter tends to be inversely proportional to the applied stress is also readily explained through those stresses. In retrospect, Taylor’s theory of workhardening may be recognized as a variant of the meshlength theory of stage III, in that it is based on a stress-screened network obeying the principle of similitude while the free dislocation path, given by the spacing between the mosaic block walls, remains constant. This paper is based on a presentation made at the symposium “50th Anniversary of the Introduction of Dislocations” held at the fall meeting of the TMS-AIME in Detroit, Michigan in October 1984 under the TMS-AIME Mechanical Metallurgy and Physical Metallurgy Committees.