Numerical Constitutive Models of Woven and Braided Textile Structural Composites
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Equivalent, three-dimensional elastic moduli are determined from unit cell models of balanced plain weave, 2D braid, 2D triaxial braid and 4x4 twill textile composite materials consisting of interlaced or intertwined yarns. The yarn paths are modeled with undulation portions, in which one yarn passes over and under one or more yarns, and with straight portions. It is assumed that the centerline of a yarn in the undulation portions is described by the sine function, and that the cross-sectional area of a yarn and the thickness of a yarn, normal to the centerline, are uniform along the centerline. For the balanced plain weave architecture, equations for the fiber volume fraction and the cross-sectional shape of the yarn are derived for large crimp angles. It is shown that the maximum crimp angle is limited to forty-five degrees, and that limits on the ratio of the length of the undulation portion of the path to the width of the unit cell impose constraints on the fiber volume fraction and yarn packing density. For small crimp angles, approximations to the volume fraction and yarn shape equations are obtained. This assumption is used in the derivation of the geometry of the remaining architectures, and subsequent equations are obtained for the corresponding geometric parameters. For each architecture, the yarns are assumed to be transversely isotropic and a stress averaging technique based on an iso-strain assumption is used to determine the effective moduli of the unit cells. Comparisons of the effective moduli are made to other unit cell models in the literature. The micromechanical models are implemented in Fortran programs and user material subroutines for ABAQUS, called UMAT, are created out of these programs. For a balanced plain weave fabric under the small crimp angle approximation, a progressive failure model is developed to predict failure within each yarn and to degrade the material properties of the representative unit cell. Material failure is predicted by discretizing the yarns into slices and applying Tsai-Wu quadratic criterion to the on-axis strains in each slice. A stiffness and strength reduction scheme is then used to account for the change in yarn compliance. At the present time, the UMAT has only been tested as a stand-alone program with Visual Fortran 6.0, and would require further development to be used within ABAQUS on sample structural problems.
- Masters Theses