Geometric mapping of yarn structures due to shape change in 3-D braided composites

The internal yarn structure in 3-D braided preforms possesses a certain topological character which is unique to the braiding method used. Hence, preforms of different shapes but braided by the same method have topologically similar yarn structures. This unique property offers the possibility that the yarn structure in preform of one shape may be geometrically mapped to that in another shape, and vice versa.

This study discusses a geometric mapping methodology, the objective of which is to obtain the appropriate mapping which analytically links the yarn structures in two preforms of different shapes; if the yarn structure in one preform is known, the yarn structure in the other can be determined by the derived geometric mapping.

Two broad classes of mapping are discussed. The first concerns mapping between two preforms that are braided directly in two different shapes; the second concerns mapping between the initial and final shapes of one single preform which is deformed after braiding. In each case, the mathematical forms of the desired mapping functions are obtained, satisfying the geometric constraints imposed by the internal yarns in the respective preforms. The determined mapping functions are then used to investigate the braidability and/or deformability of the considered preforms. Specifically, limiting windows for the braiding parameters that insure the braidability and/or deformability of the preforms are obtained using the appropriately derived mapping functions.

The 4-step 1 × 1 braiding method is used throughout this paper to illustrate the general mapping procedure; rigorous and explicit geometric relationships are derived leading to mapping functions between preforms of rectangular and curvilinear cross-sections. Numerical examples involving mapping between preforms of rectangular and tubular cross-sections are investigated in detail, along with examination of the preform braidability and/or formability.