Abstract Scope |
Can curvilinear anisotropy be used to remove the stress singularity in cracks and sharp V-notches while also enhancing the damage tolerance of the structure? This work aims at answering this question through a simple analytical and numerical investigation. Towards this goal, V-notched circular power transmission shafts under torsion reinforced with curvilinear fibers are investigated.
Assuming linear elasticity, the equations for the fiber paths maximizing the torsional stiffness are found showing that they follow specific helicoidal trajectories. At the same time, taking advantage of a new conformal map, the closed-form solution for the entire stress field is found. It is shown that, similar to a screw, helicoidal fibers introduce a coupling between torque and axial displacement. Furthermore, different from standard torsion problems, not only the shear stresses but also the hoop stress is singular at the notch tip. In other words, the notch is subject to Mode III and Mode O simultaneously.
Finally, thanks to the closed-form solution of the stress field, it is shown that it is possible to identify a distribution of fiber orientations that eliminates the stress singularity virtually eliminating the driving force for crack propagation. To verify this and explore the nonlinear damage progression in the structure, simulations via the Discrete Model for Composites (DM4C) are presented. Thanks to the capability of the model to explicitly simulate fibers and matrix, damage mechanisms are explored. It is shown that not only the proposed fiber distribution eliminates the stress singularity but it also promotes a very damage tolerant behavior. |