Crack Propagation in the Third Fracture Mode in Fiber Reinforced Elastic Composites and in Piezoelectric Crystals

摘要

The paper considers the problem of incremental displacements ahead, behind and on the faces of the crack in antiplane incremental state contained in a fibre reinforced elastic composite and in a piezoelectric crystal. Our bodies are prestressed and respectively prestressed and prepolarized. The involved boundary value problems are reduced to the corresponding Riemann-Hilbert problems and are solved using Plemelj 's functions and Cauchy's integrals. It is shown that in the case of elastic composite, if it is monolithic, the displacements of the crack tips are non zero. These displacements vanish if the material is orthotropic. On the contrary, the above displacements vanish if the initial applied electric field is zero in our piezoelectric crystal. Analysing also the behaviour of the incremental displacement, we can not establish if the involved body is a fiber reinforced elastic composite or a piezoelectric crystal loaded by an initial applied electric field.