Crack path selection in a brittle adhesive layer

Cracks in a brittle adhesive layer joining two substrates have been observed to propagate in a variety of ways, including straight or wavy paths within the adhesive layer, paths along one of the interfaces, and paths alternating from interface to interface through the layer. The effective toughness of the joint depends on the nature of the path. An asymptotic elasticity problem is analyzed in this paper which allows one to predict whether a straight crack path can occur within a brittle adhesive layer. In the asymptotic problem, an adhesive layer between two semi-infinite blocks contains a semi-infinite straight crack. The joint is loaded remotely by the first three terms of the stress field expansion for a cracked homogeneous solid, parameterzed by stress intensity factors K_i and K_u and the non-singular stress acting parallel to the crack. T'. These are the apparent, or applied, load factors determined from the analysis of an actual specimen by neglecting the presence of the layer. Also present is a residual stress in the adhesive layer. We calculate the local stress intensity factors, K_i and K_u and the non-singular stress, T, associated with the field at the tip of the crack in the layer in terms of the corresponding applied quantities and the residual stress. A necessary condition for the existence of a straight path within the layer is the location of a path with K_u = 0, Such a path will only be stable (i.e. grow in a straight, non-wavy manner) if T < 0. Our analysis provides the location of the crack in terms of the combination of applied intensity factors and the mismatch in elastic moduli between the layer and the adjoining material. Stability depends on the residual stress and T', as well as on the moduli mismatch. For a compliant adhesive with predominant applied mode 1 loading, the crack will lend to run slahlv within the layer unless T' and the residual stress are positive and relatively large.