Anisotropic size effect law for notched strength of unidirectional carbon/epoxy laminates – Part 1: Formulation

Abstract

A multiaxial quasi-brittle failure criterion for notched orthotropic composites is developed with an emphasis on establishment of an analytical formula to predict their anisotropic notched strength for any notch size under any multiaxial proportional loading. It is formulated by replacing the principal unnotched strengths with the principal notched strengths in the framework of the Tsai–Hill static failure criterion for orthotropic composites. The effects of notch size and specimen width on the principal notched strengths are described by means of the Suo-Ho-Gong model that can consider notch ductile-to-brittle transition. From the proposed multiaxial quasi-brittle failure criterion, an analytical formula is derived to predict the notched strength of finite orthotropic composite plates under multiaxial proportional loading at any angle with the principal directions of material anisotropy. The notched strength prediction formula involves a generalized notch sensitivity parameter that can be defined for any multiaxial state of stress. The multiaxial notch sensitivity parameter allows uniquely defining an intrinsic equivalent mode-I fracture toughness that is independent of notch size as well as of specimen width for any multiaxial proportional loading. Furthermore, an anisotropic size effect law for apparent equivalent mode-I fracture toughness that considers not only the effect of notch size but also the effect of specimen width is derived from the failure criterion. Finally, a quasi-brittle failure criterion for notched interface is briefly discussed as a particular case of the proposed quasi-brittle failure criterion for notched orthotropic composites.