Near-tip dual-length scale mechanics of mode I cracking in laminate brittle matrix composites

Abstract

This paper presents the results of a numerical study on the near-tip mechanics of mode I cracking in brittle matrix composite laminates. A finite element model is developed within the context of two competing characteristic lengths present in the composite, i.e., the microstructural length such as the layer thickness and the macro-length such as the crack length, uncracked ligament size, etc.. The crack surfaces are assumed to be traction free and perpendicular to the reinforcing layers. Conditions leading to macroscopic homogeneous orthotropic mechanical behavior are also assumed. Thus, the near-tip numerical studies are carried out within a small scale heterogeneous zone which surrounds the crack tip and is dominated at its outer boundary by the displacements associated with a mode I crack in a homogeneous orthotropic medium. The model is used to calculate the stresses and stress intensities in the vicinity of the crack tip which develop due to the alternating fiber/matrix heterogeneous composite microstructure. Parameter studies elucidating the effects of the two competing composite characteristic lengths on the evolution and structure of the near-tip heterogeneous stress fields are carried out. The results indicate that when the characteristic microstructural length is relatively large compared to the macroscopic length, the singular heterogeneous stress fields may deviate substantially from the assumed homogenized orthotropic fields. The study can be used to determine the necessary conditions under which homogenization applies in obtaining an accurate description of the stresses in the vicinity of the crack tip in a laminated composite.