A combined analytical and numerical analysis method for low-velocity impact on composite structures

Understanding impact damage is essential to building lightweight composite structures. The present doctoral thesis proposes a comprehensive impact analysis approach that combines analytical and numerical methods. This approach assists in understanding the details of laminate damage modes and in analyzing the impact scenarios of a typical aircraft structure. This thesis approaches numerical impact analysis through an examination of various existing methods. An explicit finite element model that captures the laminate on the meso-scale can be used to plausibly predict impact-induced delamination, inter-fiber failure, and fiber failure. This model involves two fracture-mechanical methods: first, cohesive surfaces catch the delamination damage while, second, continuum damage mechanics addresses the intra-ply failure modes. Building on this model, the present work describes the development of an appropriate degradation method for inter-fiber cracks in oblique fracture planes. Using a rank-eight damage tensor, this method enables the calculation of the resulting stiffness tensor including the coupling effects of shear and normal deformation. A simplified approach in fracture plane coordinates is derived on the basis of this tensorial degradation. Compression experiments with oblique fracture planes and coupon impacts serve as validation of this new progressive damage model. The computational cost of this high-fidelity approach impedes a direct application on the structural level. However, a typical property of damage resulting from impact with low velocity and large mass helps to reduce the scope of the structural model: as the impact damage is small in comparison to the full structure, the relevant zone for damage analysis is limited to a small cross-section around the impact location. This model reduction permits a very efficient analysis of structural impact. An analytical transfer approach allows the reduced model to comply with the original structural impact. A newly developed spring-mass model captures the damage that occurs. In this model, a damage element objectively describes the damage for a laminate configuration. Thus, the spring-mass model offers a method for transferring the damage behavior to any sufficiently similar impact configuration. Wherever qualitatively similar damage occurs, this model scales the impact energy for damage similarity. In this manner, a structural impact scenario can be analyzed on a numerical or experimental reference coupon of minimal size. Impact experiments validate the method and show its range of applicability. Finally, the transfer method enables impact analysis on sizeable structural areas through the areal evaluation of the damage description in the spring-mass model. This development allows for the establishment of a damage-tolerant design based on the actual impact threat to structures