Mode II fracture toughness of a brittle adhesive layer

This paper concerns the analytical estimation of the macroscopic mode II fracture toughness of a brittle adhesive layer sandwiched between and bonding together stiff substrates. The process of failure involves the propagation and coalescence of microscopic tensile cracks ahead of the macroscropic mode II crack tip. The basic problem at the heart of the analysis is the plane strain problem for a layer subject to shear and containing a periodic array of micro-cracks which grow and coalesce under the condition that their tips advance under pure mode I conditions. A numerical solution to this basic problem is obtained and is then used to make detailed predictions for conditions for tunneling of the micro-cracks and for the evolution of their shape and spacing. These predictions are used in turn to develop the shearing traction-displacement relation for the brittle adhesive layer. The work per unit length of layer needed to drive the microcracks to coalescence can be identified with the macroscopic work of fracture in mode II, ΓIIc, as is discussed via a cohesive zone model. The macroscopic model II toughness is predicted to be between three and four times the mode I fracture toughness, ΓIC, depending on constraints provided by substrates and very slightly on Poisson's ratio, ν. The theoretical predictions are compared with experimental data reported in the literature. Also discussed are the consequences of the assumption underlying the analysis that there exists an ample population of initial flaws whose largest dimension is roughly comparable to the thickness of the layer.