No abstract

It is seen that 2.5D interlocks are particular reinforcements for high advanced applications (i.e., spatial and aeronautics fields) that are believed to have a high structural potential. This kind of reinforcement entails to consider the composite as a structure because interlocks are built by crossing the warp yarns with the weft (or fill) yarns in the three directions. In this article, a new numerical and analytical model is proposed. To evaluate the mechanical behavior, one may obtain numerically, the anisotropic elastic engineering constants from a finite element model (FEM). This technique of virtual testing consists of modeling the composite at the meso-scale to obtain a macro-scale response with a stress—strain analysis. At the moment, numerical simulations of such materials mainly involve geometrical models and automated tetrahedral meshes that make it difficult to cope with the orthotropic behavior of yarns materials. We thus propose a new meshing methodology to build an elementary volume made of tetrahedra for the isotropic matrix and of mapped hexaedra for the transversely isotropic yarns in order to achieve the FE discretization. A new analytical model is also been proposed, based on a geometrical modeling of the yarns using sinusoidal function and on homogenization at the macrolevel based on both iso-strain and iso-stress assumptions. This model allows the estimation of stiffness matrix of the composite in terms of the properties of its constituents and the geometry of the fabric. Two 2.5D interlock composites from the ‘layer—layer’ family are studied where the nine engineering constants are evaluated. The FEM and the analytical model show a good agreement with each other and with available in-plane Young’s modulus and Poisson’s ratio experimental results.

In this article, the problem that is faced when the developed analytical model is applied to 2.5D interlocks of the ‘yarn—yarn’ type is discussed. The difficulty encountered is taking into account the influence of the number of weft yarns covered by the warp yarn. Different architectures of these interlocks will have the same stiffness matrix when modeled with the developed analytical model that uses the volume proportion of the three phases: warp, weft, and matrix. The influence of the number of weft yarns on the longitudinal Young’s modulus is studied. A corrective function has been evaluated using a finite element numerical modeling of four fictive woven composites created with ‘ANSYS’ software. These woven composite have the same undulated warp and linear weft yarns, while they differ in the number of weft yarns covered by a warp yarn. The longitudinal Young’s modulus is evaluated for each composite using a numerical model which is also presented in this study. Moreover, a cross-ply laminate (0,90) is modeled by the classical laminate theory in the estimation procedure of the corrective function. The corrected longitudinal Young’s moduli show better agreement with numerical results compared to noncorrected ones.