Cohesive-Length Scales for Damage and Toughening Mechanisms

While toughening and damage might seem to be two contradictory concepts for the mechanics of crack growth, they are actually the same phenomena perceived from two different vantage points. Similarly, the concepts of extrinsic and intrinsic toughening, defined in terms of whether a toughening mechanism occurs behind or ahead of a crack, depend on the definition of a crack tip that, in the absence of a singularity, can be somewhat arbitrary. Cohesive-zone models provide useful numerical tools for rationalizing these different concepts and, here, we use them to show how different perspectives of toughening and damage can be understood. The concept of a cohesive length, defined in terms of an effective modulus and the magnitudes of the local tractions and displacements (or work done), can be generalized so that it can be used at any load before failure, and at any point along the interface. We show that this general concept allows multiple damage and toughening mechanisms, each with its own characteristic cohesive length, to be described and tracked in terms of a single traction-separation law. In general, the onset of damage corresponds to an increase in cohesive length. This tends to weaken a material unless compensated for by a sufficiently high increment of additional toughness. The ratio between the cohesive length of a particular damage / toughening mechanism and any relevant geometrical length determines whether the mechanism needs to be included in the cohesive-zone formulation. Furthermore, it appears that diffuse damage and crack jumping between interfaces may be induced when the cohesive length of a damage mechanism is large compared to a micro-structural length. It is speculated that this may be of some relevance to the design of hierarchical materials. (December 7, 2013) (Revised: May 27, 2014)