Modeling bulk fracture with cohesive zones

Modeling bulk fracture with cohesive zones, an initially rigid traction-separation law and a dynamic insertion algorithm is possible for a three point bending specimen and can be implemented in Marc/Mentat. This report presented an initially rigid exponential mode I traction-separation law, which incorporated unloading behavior and is compatible with a local arc length solver. This initially rigid exponential mode I traction-separation law was, together with a dynamic insertion criterium, applied on a double cantilever beam specimen and on a simple tensile test using two elements. These tests proved that an initially rigid exponential mode I traction-separation law is able to describe unloading behavior and was suitable to be applied with a local arc length solver. The combination of the local arc length solver, the dynamic insertion algorithm and the initially rigid exponential mode I traction-separation law was also tested on a three point bending specimen to investigate the capability of the model to describe snap-back behavior. The three point bending simulations showed that it is not possible to accurately describe snap back behavior with above mentioned combination. Since there is no restriction on the energy which is dissipated per increment, the local arc length solver determines physically unrealistic stress equilibria around the crack due to the fact that only one cohesive zone element is allowed to be introduced per increment. A dissipative arc length solver was used which limited the energy being released in one increment. The combination of the initially rigid exponential mode I traction-separation law, the dynamic insertion criterium and the dissipative arc length solver was able to describe crack propagation in bulk materials. It is recommended to continue with the implementation of the dynamic insertion criterium in combination with a dissipative solver. Special attention should be payed to the energies which are released and which can be dissipated in one increment. A link should be made between the number of active cohesive zones in the model and the maximum of energy allowed to be dissipated in one increment in order to decrease simulation times. Additional research should be done to expand the initially rigid exponential mode I traction separation law to a mixed-mode law in order to incorporate crack propagation induced by shear deformations. Additional research is also required on the dynamic insertion algorithm in combination with triangular element classes in order to describe arbitrary non-straight cracks. Finally, the method can be expanded to three dimensions.