An analytical scaling approach for low-velocity impact on composite structures

For the analysis of low-velocity impact, we provide an analytical scaling approach that permits to analyze structural impact scenarios on a small reference coupon. Thus, the numerical prediction of impact damage on large structures through high-fidelity methods is made possible. This local analysis approach provides an entirely new possibility for assessing impact damage in the design of composite structures. For that purpose, we developed an analytical spring-mass model to describe the damage state of a laminate. This model uses an additional spring to capture the additional indentation compliance by the arising damage. The resulting stiffness value of this spring as a function of the impact energy describes the damage state as a scalar parameter. To set up the spring-mass model, the determination of the elastic response and the real impact response are required. This process is commonly performed on a simple reference coupon. An elastic model with finite shell elements is the basis for the determination of the elastic parameters. A high-fidelity simulation or an experiment provides the respective impact response. This reference coupon functions as the origin of the impact scaling. The target can now be an arbitrary structure with the same material and laminate. On this target structure, the elastic properties have to be determined analogously to the origin. The spring-mass model recombines these elastic properties with the damage behavior of the reference coupon. The reverse evaluation of this spring-mass model enables the scaling of an impact scenario towards the target. Firstly, the impact energy for similar damage can be calculated. The continuous evaluation of this damage similarity provides a curve of equivalent impact energies between the reference coupon and the target structure. Secondly, it is possible to determine the damage state for given impact energy on the structure. In both cases, a single reference coupon can be valid for large areas of a structure. This validity permits an areal prediction of impact damage. This transfer from the origin to the target structure requires not only similar laminates and materials on both scales but also a sufficient similarity of the deformation behavior. For the assessment of this similarity, we developed check values of the deformation symmetry. These shall ensure that the damage behavior of the target and the origin is sufficiently similar. Other restrictions concern the scalable damage modes, the energy range and the geometric configuration concerning stiffening elements or fasteners which are part of the damage-prone zone. The validation of the developed methodology was conducted through experiments in two steps: The spring-mass model is tested for its capability to describe the damage state of a composite laminate. A series of coupon tests confirmed that it suits this need comparable to the projected delamination area. Secondly, the impact scaling itself was validated with experiments on the coupon and the sub-structural level. The respective results confirm that the damage prediction is of high quality. Beyond the validation, the application to a generic aircraft door structure demonstrates the capabilities of the scaling method in a design process. The analysis effort of impact damage on such a structure gets reduced significantly. Additionally, the areal impact analysis enables to work with the real worst instead of the maximum-sized barely visible impact damage. Accordingly, the damage tolerance assessment can be conducted in a less conservative manner which helps to make composite structures lighter