JEC Group have brought together the international community of composites leaders and executives in our Composites Circle as an unique networking opportunity to meet with both peers and future partners.
Fibre-placed, variable-stiffness composites could be the next generation of composite aerospace structures. They offer designers more freedom to tailor load paths by continuously changing the laminate stiffness. This can result in more efficient and thus lighter structures.
AGNES BLOM, ADVANCED COMPOSITE RESEARCHER, FOKKER AEROSTRUCTURES, PHD STUDENT, DELFT UNIVERSITY OF TECHNOLOGY(published on June-July 2010 - JEC Magazine #58)
Composites containing plies with continuously varying fibre orientations are called variable-stiffness composites because the changing fibre angle causes the laminate stiffness to vary spatially. They allow the designer to tailor the internal load distribution and to increase the structural efficiency. Variable-stiffness composites have several advantages over traditionally tailored laminates: i) the stiffness change is gradual such that stress concentrations are avoided; ii) it is possible to change the laminate stiffness while maintaining a constant laminate thickness; and iii) the laminate thickness can be increased gradually by allowing individual fibre courses to overlap. A recent design study for a composite cylinder under bending will be used to illustrate the concept of designing variable-stiffness composites and to demonstrate the weight reduction potential in composite structures.
Design of a variable-stiffness cylinder subjected to bending
The design study included the optimization of a variablestiffness cylinder for maximum buckling load carrying capability at a given weight, while subjected to manufacturing, strength and stiffness constraints; the production of a variable-stiffness cylinder using fibre placement; a modal test and a structural bending test. A conventional 0°, 90° and ±45° laminate was optimized to serve as a baseline.
The cylinders were made of 24 plies of graphite-epoxy material, with a 30 cm radius and a test length of 81 cm. The layup of the baseline shell was: [±45, 02, 902, 0, ±45, ±45, 90]S, the variable-stiffness shell was a hybrid of variablestiffness plies and constant-angle plies. The variable-stiffness plies had an angle variation in the circumferential direction, see Figure 1(a). The variation of the fibre angle within a ply was determined by a small number of design variables Ti, which fixed the fibre angle at 45° increments around the circumference, as shown in Figure 1(b). The fibre orientations in between these locations are defined by a constant curvature path, such that the fibre angle varies as:
where θi is the circumferential coordinate at which the fibre angle is defined by Ti
The calculated buckling moment of the optimum variablestiffness cylinder was 805 kNm, an improvement of 18% compared with the buckling moment of the baseline cylinder, which was 678 kNm. The buckling load improvement was achieved by redistributing the load around the circumference due to the non-uniform stiffness. The layup of the variable-stiffness shell was [±45, ±ψ1, 0, 90, ±ψ3, 0, 90, ±ψ5]S, where ψ1, ψ3 and ψ5 represent three different steered ply definitions. The design variables, T0 to T4, for each of the three steered plies are given in Table 1.
The variation of the axial stiffness with the circumferential coordinate is given in Figure 2(a), where the stiffness of the variable-stiffness cylinder Exv is normalized with the axial stiffness of the baseline cylinder Exb. The axial stiffness on the tension side, between θ = 270° and θ = 180°, was more than 80% larger than the stiffness of the baseline cylinder, while the stiffness on the compression side, near θ = 180°, was slightly smaller than that of the baseline. The bending moment was applied to the ends of the cylinder through rigid end plates. Therefore, the distribution of the axial load depended on the distribution of the axial stiffness. The load distributions of the baseline and the variable-stiffness cylinder are shown in Figure 2(b).
The compressive side of the cylinder was critical for buckling, so redistributing the compressive loads over a larger portion of the cylinder and reducing the compressive peak load permitted a higher bending moment to be carried before buckling occurred.
The variable-stiffness and the baseline cylinder were manufactured using an Ingersoll fibre placement machine at the developmental centre of the Boeing Company in Seattle, Figure 3a. The 7 degrees of freedom of the machine allowed the placement of curved fibre courses, while the machine’s tow cutting and restarting capabilities were used to maintain a constant ply thickness. A variable-stiffness ply is shown in Figure 3b.
Two experiments were performed to validate the ABAQUS finiteelement model of the variable-stiffness cylinder. A modal test was first performed and then modal frequencies, mode shapes and physical responses were compared. The analytically-predicted and experimental modal frequencies matched within 5% up to a frequency of 1000 Hz. The modal response simulations also showed good agreement with the experimental results both for the location and the amplitude of the response.
The second experiment was a bending test. The set-up resembled a 4-point bending set-up: the cylinder was mounted in the area where there was no shear force, such that the cylinder was subjected to pure bending, Figure 4. A 3.5 MN MTS test bench was used to load the test fixture in tension, causing a bending moment such that the upper side of the cylinder was in tension and the lower side was in compression. Displacements and rotations were measured using LVDTs, while strains were measured using strain gauges and a digital image correlation system.
The experimental results of the baseline cylinder were used to calibrate the boundary conditions in the finite-element model, which was then used to predict the response of the variablestiffness cylinder. Geometric nonlinearities, the test mechanism and geometric imperfections were also included in the finiteelement model, which affected the value of the predicted buckling moments. The variable-stiffness cylinder showed an improvement of 20% compared with the baseline cylinder, i.e. 589 kNm versus 488 kNm.
The global response (Figure 5a) and the strain distribution, plotted as a function of the vertical coordinate in Figure 5b, showed good agreement between the finite-element analysis (FEA) and the experimental (Exp) results. The extreme tensile and compressive strain values of the variable-stiffness cylinder were lower than those of the baseline cylinder at any given load level. Strength constraints in the aerospace industry are often based on maximum strain values, which means that the variable-stiffness cylinder would have an advantage over the baseline cylinder.
Variable-stiffness laminates can be used to increase the structural efficiency of a composite structure by redistributing loads. A few variables are needed to design a variable-stiffness composite, which can be manufactured using fibre placement. Many challenges for the design, analysis and validation of variable-stiffness composites still exist, but the potential for weight reduction makes variablestiffness composites a candidate to become the composite aerospace structure of the future.