An attempt to extend the 2D coupled criterion for crack nucleation in brittle materials to the 3D case

• Original 3D extension.
• Identical fomulations in 2D and 3D.
• Indirect validation with experiments.

The extension of the 2D coupled criterion is based on the joint used of the 3D singularity theory and matched asymptotic expansions. Formally, the formulation of the 3D criterion is similar to that of the 2D case, although some differences appear to establish it. Moreover an additional hypothesis on the geometry of the crack extensions is needed, only plane crack extensions are considered. Again, its fulfillment requires two conditions: a stress and an energy one. If the assumption of a small crack extension, which is necessary within the framework of asymptotic expansions, does not hold true, it is still possible to use the coupled criterion in a more general form based on FE computations of the stress field and of the change in potential energy. There are few sufficiently complete data in the literature to enable validation. Present results are compared to a single family of fracture tests carried out on bimaterial samples. Confirmation is indirect, the criterion allows returning the interface properties (tensile strength and toughness) of the assembly. The obtained values are consistent with existing results on the behavior of joints made with a polymer adhesive.