Friedel vs. Labusch: the strong/weak pinning transition in solute strengthened metals

Abstract

Solute strengthening in substitutional alloys can be classified into two categories, strong-pinning (Friedel) and weak-pinning (Labusch), each with its own characteristic scaling with concentration and temperature. The transition between the two strengthening mechanisms as a function of solute concentration has previously been estimated at zero temperature. Here, the transition is investigated more completely, using a new model for the Labusch-type weak pinning model and considering finite temperature and strain rate. A parametric study of the transition as a function of solute concentration and dislocation core structure shows that the temperature dependence of the transition concentration greatly depends on the dislocation core structure and, in general, can differ significantly from the zero-temperature value. The zero-temperature transition concentration itself also differs from the standard estimate. Except for the most highly localized cores, the Labusch model controls the strengthening for concentrations greater than and temperatures greater than  K. Using dislocation core structures and solute/dislocation interaction energies derived from first-principles, the transition concentration at finite temperature for Al–X (X = Mg, Si, Cu, Cr, Mn and Fe) and Mg–Al (basal) alloys is also predicted to be in the range of . Overall, at temperatures and concentrations relevant to engineering applications, the Labusch model is therefore expected to control the strengthening mechanisms for these alloys and for most dislocation core structures in metals.

Keywords:

• strong-/weak-pinning transition
• Labusch model
• Friedel model
• finite temperature
• solute strengthening

Acknowledgments

The authors thank L.G. Hector Jr. and J.A. Yasi for helpful discussions. Support for this work was provided through the GM/Brown Collaborative Research Lab on Computational Materials Research, with additional support through the NSF Materials Research Science and Engineering Center at Brown on Micro- and Nano- Mechanics of Materials (Grant DMR-0520651).