Dynamic effects in the mesh length theory of workhardening

According to the mesh length theory of workhardening, low-temperature strain rate effects in materials exhibiting a dislocation cell structure are due to the simultaneous operation of a number X of super-critically bowing links in the average, typically roughly equiaxed, cell of diameter L. The corresponding length of mobile dislocations per cell is then LX. Defining $\text{g =}\text{L}\text{l}\text{̄}$, with $\text{l}\text{̄}$ the average link length in the cell walls, dislocation cell breakdown is expected for X_max ≈ 0.3 g², on the criterion that at the most 50% of all cell wall dislocations may be simultaneously destabilized and therefore at most 10% of all possible dislocation sources may be activated simultaneously since each destabilizes four adjoining links besides itself. When X = X_max, the mobile dislocation density within the cells is about 30% of that in the walls, but significant interactions and thus extra hardening is expected only if the dislocation density in the cell interiors is about sixteen times the cell wall dislocation density. Therefore the mobile dislocations can add little, if anything, to the permanent strain hardening. However, on account of the decrease of average source length with increasing X a transient increase of flow stress and workhardening coefficient arises which typically amounts to a few percent per ten-fold increase of strain rate. Mobile dislocations remaining in the cell interiors decrease the elastic modulus and can give rise to anelastic creep as well as to recovery effects. Numerical estimates are in good agreement with observations.