Nonlinear crack opening integral: Mode mixity for finite cracks

In this work the incremental energy release rate is analyzed for single-lap adhesive joints by means of the crack closure/opening integral. To this aim, geometrically nonlinear numerical analyses are performed. For nonlinear elastic analyses the relationship between nodal forces and displacements during nodal load reduction generally cannot be approximated linearly. In the case of a nonlinear relation the forces must be integrated over the displacements in order to calculate the incremental energy release rates. Additionally for a nonlinear analysis the nodal forces and displacements must be transformed into a local nodal coordinate system to separate individual modes and calculate mode mixity. As an alternative, the mode mixity for a finite crack is estimated on basis of the stress state just before or after crack initiation. The mixity values and the resulting critical energy release rates needed for an energy criterion are finally compared to the direct evaluation of the mode separated energy release rates.