Structural Performance of Fiber-Placed, Variable-Stiffness Composite Conical and Cylindrical Shells

Abstract

The use of fiber-reinforced composites in aerospace structures has increased dramatically over the past decades. The high specific strength and stiffness, the tailorability, and the possibilities to integrate parts and reduce the number of fasteners give composites an advantage over metals. Automation of the production process enables large-scale production of composites in a repeatable, reliable fashion. Fiber-reinforced composite laminates are traditionally made of 0?, 90? and ±45? plies. Automated manufacturing techniques, such as advanced fiber placement, allow for fiber orientations other than 0?, 90? and ±45?, and for the placement of curved fibers such that the fiber orientation within a ply is continuously varied. Laminates that contain plies with spatially varying fiber orientations have a spatially varying stiffness and are called variable-stiffness composites. Tailoring the stiffness variation can be used to improve the structural efficiency of a composite. Analytical and experimental work on flat variable-stiffness composite panels with and without central holes has shown that large improvements in structural efficiency are feasible, such as increasing the panel strength or buckling load while maintaining the same overall weight. The research presented in this dissertation expands the work on variable-stiffness composite laminates from flat panels to conical and cylindrical shells. Variable-stiffness plies with either an axial or a circumferential stiffness variation are defined based on the shifted course principle, where a full ply is formed by shifting identical courses in the direction perpendicular to the direction in which the fiber angle is varied. Four different types of fiber paths are discussed: i) geodesic paths, ii) constant angle paths, iii) paths with a linearly varying fiber angle, and iv) paths with a constant curvature. General mathematical descriptions to define the coordinates of these paths on a conical or cylindrical shell and expressions for the in-plane curvature are derived. The in-plane curvature is limited to a maximum value to ensure a good laminate quality, assuming the variable-stiffness laminate is manufactured using advanced fiber placement. A procedure to determine the exact stacking sequence for a given location within a laminate is given. Structural analyses were carried out using the finite element rogram ABAQUS. The stiffness variation was implemented in the finite element shell model as a user-written FORTRAN subroutine, such that each element was uniquely defined. Two design studies were carried out, using the ABAQUS models to evaluate the structural performance of variable-stiffness composite laminates. The first design study was the optimization of conical and cylindrical shells with different dimensions for maximum fundamental frequency. The 8-ply laminates had a [±45±?(x)]s layup, where ?(x) denotes a ply with an axially varying fiber angle, and the laminate thickness was assumed to be constant. Manufacturability of the variable-stiffness plies was judged based on the maximum in-plane path steering allowed by the fiber placement process. Numerical examples showed that manufacturability can have a large influence on the value of the maximum fundamental frequency of conical and cylindrical composite shells with an axial stiffness variation, and that it is necessary to take the manufacturing constraints into account in the design phase of a variable-stiffness laminate. It was shown that the fundamental frequency of conical and cylindrical shells can be improved up to 30 percent by using variable-stiffness laminates, especially for larger cones. The second design study covered the maximization of the buckling load of a variable-stiffness composite cylinder loaded in bending. It was shown that the use of variable-stiffness constant-thickness laminates may improve the buckling load of a cylinder under pure bending because it allows the redistribution of in-plane loads between the compression and tension parts around the circumference by tailoring the circumferential in-plane stiffness distribution in the cylinder skin. The compressive loads were reduced and spread out over a larger part of the cylinder circumference thus increasing the buckling load and changing the buckling mode shape. Loading was also shifted from buckling-critical compression loads into buckling-noncritical tension loads. The redistributed loads caused the first buckling mode to change such that a larger part of the cylinder participated in the buckling deformations. Introduction of curvature, strength and stiffness constraints caused a small reduction in buckling load carrying capability of the variable-stiffness designs. These manufacturable and more practical laminates showed improvements of up to 18 percent compared to the optimized baseline consisting of 0?, 90? and ±45? plies. The buckling load carrying capability of variable-stiffness designs that included overlapping fiber courses was optimized by increasing the laminate thickness on the compression side of the cylinder. The larger laminate thickness, which is coupled to the fiber angle variation, was achieved by having a small fiber orientation on the compression side of the cylinder and a large fiber orientation near the neutral axis. The increased laminate thickness and the small fiber orientation caused high axial stiffness, resulting in high axial loads on the compression side of the cylinder. The laminate bending stiffness on the compression side increased more than the in-plane laminate stiffness, however, such that it compensated for the higher axial loads and dominated the response. Including the curvature and strength constraints had a higher impact on the variable-stiffness designs with overlap than on the ones with a constant thickness. The amount of thickness buildup on the compression side was limited, because the shift of the neutral axis associated with the high axial laminate stiffness on the compression side caused failure on the tension side of the cylinder. The laminate stiffness and thickness on the tension side became similar to those on the compression side. One constant-thickness, variable-stiffness specimen and two baseline specimens were manufactured using advanced fiber placement technology. Both designs were optimized for maximum buckling load carrying capability under bending. The small dimensions of the cylinder required a small turning radius, causing puckers to form during lay-down which were not visible in the end product. The amount of small triangular gaps and overlaps within the constant-thickness laminate was minimized by using a 50 percent coverage parameter, while long gaps between parallel courses were avoided by adjusting the shift between courses. The minimum cut length requirement was taken into account during the design, preventing any deficiencies in placing tows on the surface. Cutting tows on the outside of a steered course caused the tows to straighten, because the outer tows were not restrained and thus followed a geodesic path. Adjustments are needed in future variable-stiffness designs to avoid fiber straightening. A modal test was carried out on the variable-stiffness and on one of the baseline fiber-reinforced composite cylinders that were optimized for bending. An ABAQUS finite element model was used to predict the modal behavior of the cylinders. The analytically predicted mode shapes and modal frequencies showed a good agreement with the experimental results, both for the baseline and for the variable-stiffness cylinder. The modal frequencies of the variable-stiffness cylinder were lower than those of the baseline cylinder due to the lower laminate bending stiffness in the circumferential direction, which plays an important role in the formation of waves in the circumferential direction. The larger axial stiffness of the variable-stiffness cylinder became apparent for modes with an increasing number of axial half waves and the modal frequency of the variable-stiffness cylinder approached or even exceeded the modal frequency of the baseline cylinder. The modal response simulations executed in ABAQUS matched the experimental results both for location and amplitude of the response. Although only 2 cylinders were tested, the presented results indicated that the finite element model for the variable-stiffness cylinder provides a good representation of the cylinder in terms of mass and stiffness distributions. A fixture was designed to test the baseline and the variable-stiffness cylinders in pure bending. Strains and displacements were measured using strain gauges, digital image correlation, LVDT’s and lasers. Three carbon fiber-reinforced cylinders were tested: two with a baseline laminate and one with circumferentially varying laminate stiffness. The variable-stiffness cylinder was tested in two configurations: i) it was tested in the orientation for which it was optimized, called the preferred configuration, and ii) it was tested while rotated 180? about the longitudinal axis, such that the loading on the cylinder was reversed, this was called the reversed configuration. This resulted in three test configurations: the baseline, the variable-stiffness in the preferred orientation and the variable-stiffness in the reversed orientation. A comparison of the experimental response of the two baseline cylinders with the finite element predictions revealed that the experimental boundary conditions were more flexible than originally modeled in the finite element model. The introduction of flexible boundary conditions in the finite element model resulted in good agreement between the experimental and the analytical results. A final improvement of the finite element predictions was achieved by including geometric imperfections in the model and by performing a Riks analysis. The latter model was used to make a prediction for the variable-stiffness test results. A comparison of the experimental results with the finite element predictions of the Riks analysis in general showed a good agreement for all three configurations. The match of the end rotations and strains was equally good for the variable-stiffness cylinder and the baseline cylinder. The variable-stiffness cylinder was stiffer than the baseline cylinder when comparing the global behavior in terms of end rotations, which was to be expected because of the larger laminate stiffness of the variable-stiffness cylinder. The variable-stiffness cylinder response was stiffer in the reversed orientation than in the preferred orientation due to the boundary condition effects. The most important observation resulted from the strain distribution with the vertical coordinate of the cylinder: at equal load level the maximum compressive strains of the variable-stiffness cylinder in the preferred orientation were about 10 percent lower than those of the baseline cylinder; the tensile strains were 35 percent smaller. This difference in extreme strain values is a large improvement in performance when strain-based strength criteria are applied. In addition, the circumferential stiffness variation resulted in a redistribution of the loads, such that the tension side was more effective in carrying loads, the compressive loads were carried by a larger part of the cylinder and the compressive load peak at ? = 180? was reduced by 25 percent compared to the baseline cylinder. The adjusted finite element model predicted an increase in buckling load of 18 percent compared to the baseline cylinder as a result of this load redistribution.