Polygonization: Theory and comparison with experiments

Within continuum dislocation theory (CDT) the energy functional of a bent beam, made of a single crystal having only one active slip system, is asymptotically analyzed. By relaxing the smooth minimizer of this energy functional, we construct a sequence of piecewise smooth displacements and piecewise constant plastic distortions reducing the energy and exhibiting polygonization. The number of polygons can be estimated from above by equating the surface energy of small angle tilt boundaries to the contribution of the gradient terms from the smooth minimizer in the bulk energy. The comparison with Gilman’s experimental results shows a good agreement.