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 a nd bonding together stiff substrates. The process of failure involves the propagation and coalescence of n-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 she ar and containing a periodic array of micro-cracks which grow and coal esce under the condition that their tips advance under pure mode I con ditions. A numerical solution to this basic problem is obtained and is then used to make detailed predictions for conditions for tunneling o f the micro-cracks and for the evolution of their shape and spacing. T hese predictions are used in tum to develop the shearing traction-disp lacement relation for the brittle adhesive layer. The work per unit le ngth of layer needed to drive the microcracks to coalescence can be id entified with the macroscopic work of fracture in mode II, GAMMA(IIc), as is discussed via a cohesive zone model. The macroscopic model II t oughness is predicted to be between three and four times the mode I fr acture toughness, GAMMA(Ic) depending on constraints provided by subst rates and very slightly on Poisson's ratio, nu. The theoretical predic tions are compared with experimental data reported in the literature. Also discussed are the consequences of the assumption underlying the a nalysis that there exists an ample population of initial flaws whose l argest dimension is roughly comparable to the thickness of the layer.