The critical shear stress τc to move a dislocation through a random array of obstacles in the glide plane is calculated using a statistical theory. The result is an expression for τc in terms of the obstacle concentration, the line tension of the dislocation, and of the interaction force between the dislocation and a single obstacle. Fleischer's solution of the same problem is not reproduced by the statistical theory. Quantitatively the two results are not very different, but our new result is supported by some recent experimental evidence. Furthermore the theory provides a definite prescription how to combine the concentrations and interaction forces of obstacles of different kinds in the expression for τc.

A Statistical Theory of Solid Solution Hardening

Effect of interstitial solutes on the strength and ductility of titanium

Modelling solid solution hardening in high entropy alloys

The role of stacking fault energy (SFE) in deformation twinning and work hardening was systematically studied in Cu (SFE ∼78 ergs/cm2) and a series of Cu-Al solid-solution alloys (0.2, 2, 4, and 6 wt pct Al with SFE ∼75, 25, 13, and 6 ergs/cm2, respectively). The materials were deformed under quasi-static compression and at strain rates of ∼1000/s in a Split-Hopkinson pressure bar (SHPB). The quasi-static flow curves of annealed 0.2 and 2 wt pct Al alloys were found to be representative of solid-solution strengthening and well described by the Hall-Petch relation. The quasi-static flow curves of annealed 4 and 6 wt pct Al alloys showed additional strengthening at strains greater than 0.10. This additional strengthening was attributed to deformation twins and the presence of twins was confirmed by optical microscopy. The strengthening contribution of deformation twins was incorporated in a modified Hall-Petch equation (using intertwin spacing as the “effective” grain size), and the calculated strength was in agreement with the observed quasi-static flow stresses. While the work-hardening rate of the low SFE Cu-Al alloys was found to be independent of the strain rate, the work-hardening rate of Cu and the high SFE Cu-Al alloys (low Al content) increased with increasing strain rate. The different trends in the dependence of work-hardening rate on strain rate was attributed to the difference in the ease of cross-slip (and, hence, the ease of dynamic recovery) in Cu and Cu-Al alloys.

The influence of stacking fault energy on the mechanical behavior of Cu and Cu-Al alloys : Deformation twinning, work hardening, and dynamic recovery

https://hal.archives-ouvertes.fr/hal-01779154/document

P. Jax

Papers

Solid solution hardening of gold and other f.c.c. single crystals