The stress field of a dislocation array in an ultra thin anisotropic heterogeneous bicrystal

Abstract

The problem of a dislocation parallel and close to two free surfaces of a thin foil made up of two plates of different nature, using anisotropic elasticity, is treated numerically. Different applications are presented for the thin homogeneous crystals Al/Al and Cu/Cu and also for the thin bicrystal Al/Cu.

Anisotropic elasticity of multilayered crystals deformed by a biperiodic network of misfit dislocations

“…[12][13][14] Even for the simpler twodimensional ͑2D͒ problem of periodic misfit dislocations, only the elastic field for layered structures containing a few layers has been calculated. 9,10 Based on published reports, we concluded that the elasticity associated with a multilayered crystal system containing a biperiodic array of interfacial misfit dislocations is still far from complete.…”

“…The elastic fields for a multilayered composite containing one periodic ͑or biperiodic͒ array of interfacial misfit dislocations have been investigated by using Fourier or double Fourier series expansion methods. [9][10][11][12][13][14] However, this method is limited and time consuming as it requires the inversion of a 6N ϫ 6N matrix for a laminated medium containing N interfaces. This is especially problematic when N is very large ͑say, N = 100, 1000, or 10 000͒, not to mention that the inversion of the 6N ϫ 6N matrix is only for one term in the Fourier or double Fourier series.…”