A hybrid dislocation deforming two welded anisotropic crystals

The elastic field of an angular dislocation line that has a branch placed in a crystal of a bi-material while the other branch is along a strongly bound or welded interface, is found when the two crystals have anisotropic properties. Since the field of this angular dislocation depends on the elastic constants of the two crystals, it can be called hybrid dislocation (HD). To face this problem already treated using isotropic elasticity, the analysis first formulates the elastic field of a closed dislocation loop whose surface S is that of a circular sector centred in a point O of the interface. By virtue of the Saint Venant principle, when the circular segment moves far away from O, the field induced by the loop near O tends towards that of a HD. The calculation is possible thanks to the knowledge of the Green's tensor of the bi-material which has already been the subject of several works. Thanks to the use of polar coordinates, the solution is reduced to convenient line-integral expressions which make the calculation faster. This work complements a previous approach to the HD problem based on the integral formalism. By combining two HD's, it also gives the solution to the problem of an interfacial angular dislocation. Some applications illustrate anisotropy effects and highlight an inability of integral formalism to deal with a interfacial branch strictly in the interface.

Automated summary

This paper investigates the elastic field in a bi-material crystal with an angular dislocation line with one branch placed in the crystal and the other along a strongly bound or welded interface. The analysis formulates the elastic field of a closed dislocation loop and solves it using the knowledge of the Green's tensor of the bi-material. The study provides a faster calculation method and has important implications for solving interfacial angular dislocation problems.