Transverse crack onset and growth in cross-ply [formula omitted] laminates under tension. Application of a coupled stress and energy criterion

Abstract

Crack initiation in the inner ply of symmetric [0/90]s laminates under tension is studied applying the coupled stress and energy criterion proposed by Leguillon (Eur. J. Mech. A/Solids 21, 2002) in the framework of the finite fracture mechanics. This criterion assumes that a crack of a finite extension appears abruptly when the stress criterion is fulfilled and this crack onset is energetically admissible.The stress state is calculated by applying the laminate theory to the undamaged laminate which provides explicit expressions to be used in the stress criterion. Assuming generalised plane strain, the magnitude involved in the (incremental) energy criterion is evaluated numerically by means of a boundary element code and a dimensional analysis. The two criteria lead to a theoretical model providing explicit expressions of the critical parameters for the crack onset, which depend only on the computational results through a scalar value.This model predicts that the crack grows unstably after the onset in the inner ply and is arrested close to the interface between the plies for a length larger than a certain threshold length independent of the fracture and strength properties. This threshold length depends only on the elastic and geometric properties of the laminate. The model also predicts the existence of a size effect which agrees with the experimental results found in the literature. In addition, the model provides a physical interpretation of this size effect.