Design, analysis and verification of conventional and non-conventional cylindrical cfrp composite shell with optimized cutout under the effect of combined loading

The rate of the usage of fiber reinforced composite structures both in aerospace and automotive industries has been increasing very rapidly over the past few decades. In addition to conventional fiber orientation laminate composites, the steered fiber layup composites have also become in the center of interests. Having higher specific strength and stiffness and being light-weight compare to metallic structures give polymer composites an important advantage over metals. Traditional fiber-reinforced composite laminates are composed of 0, 90 and 45 degree plies and are called as constant stiffness (CS) composites. Those specific fiber orientation selections are due to the ease of manufacturing, since at the initial times of composite manufacturing the only way was to manufacture manually. On the other hand, with the development of automated fiber placement machines, recently designed steered fiber composites have been able to put into service. This manufacturing technique allows fibers to be oriented other than 0, 90 and 45 degrees such that the curved fiber orientation within a ply changes continuously. Due to spatially oriented fibers within a ply, the laminate has spatially varying stiffness and therefore, those fiber composites are called as variable-stiffness (VS) composites. The purpose of having VS is to improve the mechanical properties of the composite. There have been various researches on the VS composites including flat panels, conical and cylindrical shells with some of the works including cutouts as well. The work presented in this dissertation includes the effect of cutouts varying circumferentially and geometrically on both CS and VS cylindrical shells under pure bending and combined loading. The geometry and cutout configurations of the CFRP cylindrical composite shell was selected to simulate the fuselage of the airframe. The structure under consideration is a circular cylinder with a radius R of 304.5 mm (12 in), length L of 813 mm (32 in), and an overall shell thickness H of 4.392 mm (0.173 in). Loading is introduced at each end of the cylinder and for this study is confined to a pure bending, applied in a direction so that the bottom of the cylinder is under compression and the top in tension. In the combined loading study, in addition to bending moment, vertical shear force applied from one end of the cylinder while applying encastre boundary condition to the other end. The results of a parametric study, concerning on the effects of a pair of cutouts symmetrically located with respect to the vertical axis perpendicular to the bending axis, varying both the location and size of the cutouts and evaluating their effects on the maximum load levels and predominant failure modes of a circular cylindrical shell were presented. Several baseline cases were presented to illustrate the type of results that were encountered. Overall failure trends from the study were introduced, and a supplemental study to highlight an interesting aspect of the results was demonstrated. The analysis methods that were used for the evaluation of the buckling and failure characteristics of shells include linear buckling analysis, nonlinear analysis using Riks method and nonlinear progressive failure analysis using Riks method. During the nonlinear analysis, the imperfections coming from the buckling analysis were also included at a rate of 10% of the shell thickness. Analyses were performed using the commercial FEM solution ABAQUS using S4R element. In that model, the stacking sequence was defined using the COMPOSITE option of the SHELL SECTION designator to define the fiber orientation angle of each layer. For the VS case, additional computations were required due to the spatial variation of the fiber orientation angle within the plies. Subroutines were generated with FORTRAN coding to produce fiber orientation angles for each ply. The fiber angle values were introduced into the model through the DISTRIBUTION TABLE designator within ABAQUS. This feature allows the user to construct tables to list specified values for each element or node. In this case, one table was used for each distinct ply and default values were used for the CS plies. During finite element analysis S4R shell element which possesses one integration point at the centroid of the element was used. The centroid was calculated from the four connected nodes of each element and the fiber orientation angle values were calculated there based on the parametric formulation of the circumferential variation. A Python script was used to construct both the input file and the tables based on the model parameters (geometry, mesh size, material properties, stacking sequence, and cutout configuration), where the tables used the FORTRAN subroutines interactively to calculate the fiber orientation angles. The tables were written to external files so they could be easily changed without having to alter the original input file. During nonlinear progressive failure analysis, Helius PFA commercial tool was used. It is composed of a set of software modules and a composite material library that integrates with the ABAQUS finite element analysis system. Helius PFA utilizes a form of material modeling that is based on Multi-continuum Theory in addition to other common composite failure criteria like Tsi-wu, Hashin, Larc etc. In the analysis of cylindrical shell model with cutouts, failure modes were defined and tables of failure modes were generated for the prescribed cutout size and locations. It was discovered that, there are generally three types of failure modes, which appears under pure bending for cylindrical shells with cutouts. To classify them; Failure Mode I may be defined as strength failure driven by global buckling of the cylinder. Failure Mode II can be defined as; strength failure around the cutout driven by local cutout edge buckling. As third mode, in Failure Mode III, before global buckling, material strength failure starts due to high stress concentration and therefore, it was defined as the strength failure initiated around the cutout without buckling. Finally, comparison of the finite element predictions with the experimental results were realized by matching the end rotations and strains. Although, the VS cylinder was designed to be stiffer than the CS cylinder and expected to have higher failure load in bending, after placing cutouts with certain size and locations on the cylinder, the effect of steered fiber laminae reduced dramatically. The effect of steered fiber is reduced due to the change in the failure mode as a result of applied cutouts. When the cutouts are below the neutral axis, that is the compression side of the cylinder, failures are usually driven by local buckling around the holes in contrast to global buckling from the bottom of the cylinder. The steered fiber laminate were designed to increase the failure load under pure bending and it can be effective in global buckling since the VS shell was optimized without cutouts. Therefore under local buckling conditions failure load were dropped for both CS and VS laminates. After completing the nonlinear analyses and finalizing the cutout size and locations, the cylinders without cutouts were machined with the 0.3R/120 cutout configurations. Following the machining, real imperfections were measured with Digital Image Correlation method. A final improvement of the finite element predictions was achieved by including real geometric imperfections in the model and by performing nonlinear progressive failure analysis using Riks method. Testing of cylindrical shells with cutouts was performed in TU Delft using a fixture that was designed to test the constant-stiffness and the variable-stiffness cylinders in pure bending. Strains and displacements were measured using strain gauges, digital image correlation, LVDT's and lasers. Two cylinders were tested: one with conventional layup laminate baseline cylinder (CS) and one with circumferentially varying laminate stiffness (VS). A comparison of the experimental response of the two cylindrical shells with the finite element predictions showed that the experimental boundary conditions has almost the same flexibility as modeled in the finite element model and resulted in good agreement between the experimental and the numerical results. The ultimate failure loads of testing also showed very good correlations with the finite element predictions. The results of this study show that, during the numerical analyses of composite structures it is important to apply nonlinear progressive failure analyses in order to obtain realistic results close to the test results. It was also proved that there are basically three failure modes of the cylindrical shells with cutouts. Although, the failure resulting from the global buckling of the cylinder has the highest failure load, generally the cylinders with moderate cutout size will tend to either buckle or tear up from the cutout edge. Therefore, in the design of cylindrical aerospace structures the window or door cutouts, the sizes and locations of the cutouts should be adjusted so that the buckling will tend to start from cutout edge to increase the post buckling strength of the cylindrical shells .