A single crystal beam bent in double slip

TL;DR

This paper develops a theoretical model for plastic bending of single crystal beams with two slip systems, deriving analytical solutions for key mechanical properties and analyzing energy dissipation effects.

Contribution

It introduces a variational-asymptotic approach to reduce the complex 3D problem to a solvable 1D model with analytical solutions for symmetric slip systems.

Findings

Threshold value for plastic yielding determined

Dislocation density calculated

Moment-curvature relationship derived

Abstract

The theory of plastic bending of single crystal beam having two active slip systems is proposed. Applying the variational-asymptotic method we reduce the energy functional of the beam to the one-dimensional energy functional which admits analytical solutions for the symmetric slip systems. The threshold value at the onset of plastic yielding, the dislocation density, as well as the moment-curvature curve are found. We solve also a similar problem that takes the energy dissipation into account.