Adriana W. Blom

A Theoretical Model to Study the Influence of Tow-drop Areas on the Stiffness and Strength of Variable-stiffness Laminates:

Variable-stiffness laminates that have fiber orientation variation across its planform can be manufactured using advanced fiber placement technology. For such laminates, successive passes of the fiber placement head often overlap resulting in thickness build-up. If a constant thickness is desired, tows will be cut at the course boundary, which can result in small triangular resin-rich areas without any fibers. In this article a theoretical, numerical investigation of the influence of these tow-drop areas on the strength and stiffness of variable-stiffness laminates is performed. The effects of tow width, laminate thickness and staggering in combination with tow-drop areas are studied by making use of finite element simulations. A method for the localization of tow-drop areas is presented, and the expressions for implementing the tow-drop areas in a finite element model are given. Subsequently, progressive failure analyses using the LaRC failure criteria are performed. Failure occurs at tow-drop locations in both the surface plies and underlying plies. Wider tows result in lower strength. No correlation seems to exist between thickness and laminate strength, while staggering has a positive influence on strength.

Generating Curvilinear Fiber Paths from Lamination Parameters Distribution

Contrary to the classical stacking sequence design of composite laminates with straight fibers, each ply can be designed with curvilinear fiber paths resulting in variation of the stiffness properties over the structure. Such laminates are often denoted as “variablestiffness panels” in the literature. Instead of treating fiber orientation angles as spatial design variables, lamination parameters can be used. However, retrieving the actual stacking sequence requires additional efforts at a post processing level. In this paper, we presume that the optimal distribution of lamination parameters is already obtained for a particular design problem. Then we use curve fitting techniques to obtain continuous fiber paths that result in a distribution of the lamination parameters close to the optimal distribution in a least square sense while satisfying the manufacturing curvature constraint. The fiber orientation angle is expanded using a set of basis functions and unknown coefficients. The unknown coefficients are then computed such t hat the assumed form represents the optimal distribution of the lamination parameters in a least square sense. The key feature of such approach is that at this post-processing step, no more expensive finite element analyses are needed and the curve fitting is performed using simple polynomial and trigonometric function evaluations. The curve fitting problem is then solved using a constrained nonlinear least square solver where maximum curvature is controlled using a side constraint. Numerical results demonstrate the efficiency of the proposed formulation for minimum compliance design problems. For the cantilever plate problem investigated, the compliance of the approximate design is only than 2.5% larger than than the compliance of optimal lamination parameters design. A methodology is also proposed to estimate the thickness buildup due to the curved fiber paths.

Bending Test of a Variable-Stiffness Fiber-Reinforced Composite Cylinder

Two carbon-fiber-reinforced composite cylinders were tested in bending. One cylinder, the baseline cylinder, consisted of 0o, 90o and ±45o plies, whereas the other cylinder, called the variable-stiffness cylinder, contained plies with fiber orientations that varied in the circumferential direction, which caused a variation in laminate stiffness. The cylinders were optimized for maximum buckling load carrying capability under bending. Simulations showed that the variable-stiffness cylinder was able to redistribute the applied loads around the circumference, resulting in lower strain values at both the tension and the compression side of the cylinder and an improvement of the buckling load by 18 percent compared to the baseline cylinder. The purpose of the bending test was to show that the improvements obtained in the analytical results could also be achieved experimentally. The baseline cylinder was tested first to serve as a benchmark for the variable-stiffness cylinder. The finite element model was adjusted based on the baseline cylinder tests to represent the experimental conditions correctly. The model took into account the flexible connection between the cylinder and the test fixture, the test mechanism and geometric imperfections present in the cylinder and showed good agreement with the experimental results. The variable-stiffness cylinder was tested twice: first oriented in the direction it was designed for and later rotated 180 degrees about the cylinder axis, such that the loading direction on the cylinder was reversed. The predicted global response and strain distributions for both configurations corresponded well with the experimental data. The flexible boundary conditions and the geometric imperfections affected the load and strain distributions of the baseline and the variable-stiffness cylinders, but the relative improvements of the variablestiffness cylinder in the preferred orientation with respect to the baseline cylinder were not affected. Follow-up tests of the cylinders including cutouts or induced damage are planned in the future.