Mode-mixity in Beam-like Geometries: Linear Elastic Cases and Local Partitioning

This work is conducted as a part of a wider international activity on mixed mode fractures in beam-like geometries under the coordination of European Structural Integrity Society, Technical Committee 4. In its initial phase, it considers asymmetric double cantilever beam geometry made of a linear elastic material with varying lower arm thickness and constant bending moment applied to the upper arm of the beam. A number of relevant analytical solutions are reviewed including classical Hutchinson and Suo local and Williams global partitioning solutions. Some more recent attempts by Williams, and Wang and Harvey to reproduce local partitioning results by averaging global solutions are also presented. Numerical simulations are conducted using Abaqus package. Mode-mixity is calculated by employing virtual crack closure technique and interaction domain integral. Both approaches gave similar results and close to the Hutchinson and Suo. This is expected as in this initial phase numerical results are based on local partitioning in an elastic material which does not allow for any damage development in front of the crack tip.