Material Homogenization of Local Fibre Particularities in Tailored Fibre Placement (TFP) Structures

Abstract

Tailored Fibre Placement (TFP) is a promising composite technology which exploits considerable reserves in fibre reinforced structures by means of adapted fibre alignments. At DLR, Institute of Composite Structures and Adaptive Systems, the TFP design tool TACO (Tailored Composite Design Code [1]) has been developed to optimize the fibre orientations in lightweight aerospace structures. TACO is embedded in an FE solver environment and works on macroscopic level applying homogeneous material properties. To close the gap in the design and production chain of TFP structures, a multi-scale approach is established which suitably considers local features like TFP roving turns, kinks or endings. Such interior singularities can be of global significance, but require refined discretisation to be properly assessed. For instance, a roving turn of just slight curvature results in a considerable drop of stiffness in tangential fibre direction, which cannot directly be reproduced by macroscopic finite element analysis. Therefore, such roving turns are modelled by refined, mesoscopic FE meshes representing the heterogeneous material by fibre rovings and matrix. The link between the specific local models and the global analysis is realised by a two-step solution: Firstly, local analyses are performed to determine homogenised properties of the local details. Secondly, a global analysis is performed to efficiently assess the material behaviour of the TFP structure by applying the homogenised properties. An appropriate homogenisation method computes homogeneous global parameters in such a way that the mechanical behaviour of the global and the local model are equivalent on macroscopic level. A common criterion for mechanical equivalence is the condition that the volume average of the strain energy density has to be equal. On the other hand, e.g. Lukkassen et al. [2] propose a homogenisation method which is based on the equilibrium equations of the internal forces in conjunction with asymptotic scale expansions for the displacement and force fields. To solve the arising cell problem, Lukkassen et al. derived the so-called displacement method, which prescribes unit average strain fields with only one nonzero component. Thus, only six deformation states are necessary to compute all 21 components of the homogenised anisotropic 3D elasticity tensor. Due to its efficiency and ease of automation, the displacement method is implemented to enhance the TFP design tool TACO in terms of a suitable global modelling of local material features.