Crack extension and energy release rates in finitely deformed sheets reinforced with inextensible fibres

Abstract

Plane stress of a torn sheet of finite extent is considered. The tear or crack, which is unstressed, runs from the boundary and is of fairly arbitrary shape. The sheet is reinforced by a continuous network of two families of inextensible fibres; this models a coated fabric or any other highly anisotropic material with two “strong” directions. The sheet is finitely deformed under in-plane dead loading of its boundary. For much of the paper the stiffness of the sheet, other than that contributed by the fibres, is assumed negligible compared with the applied loads, thus highlighting the effects of the strong anisotropy; otherwise, the material response is taken to be non-linearly elastic. Expressions for the stresses at the crack-tip are obtained in terms of the boundary loading. Equivalent expressions are also obtained for the energy release rate when the tear advances in an arbitrary direction (not necessarily parallel to the previous direction of the crack). Except in the limit of infinitesimal elastic deformation, there is no simple relation between the stress intensities (as measured by the fibre forces) at the crack tip and the energy release rate. Three possible fracture criteria—analogous to those based on maximum stress intensity or energy release rate in linear elasticity—are discussed, and their implications are illustrated by analysing the example of a torn rectangular sheet under uniform biaxial tensile loading.